Tensor Form Research Articles

Spherical doubly warped spacetimes for radiating stars and cosmology

Spherically symmetric spacetimes are ambient spaces for models of stellar collapse and inhomogeneous cosmology. We obtain results for the Weyl tensor and the covariant form of the Ricci tensor on general doubly warped (DW) spacetimes. In a spherically symmetric metric, the Ricci and electric tensors become rank-2, built with the metric tensor, a velocity vector field and its acceleration. Their structure dictates the general form of the energy-momentum tensor in the Einstein equations in DW spherical metrics. The anisotropic pressure and the heat current of an imperfect fluid descend from the gradient of the acceleration and the electric part of the Weyl tensor. For radiating stellar collapse with heat flow, the junction conditions of the doubly warped metric with the Vaidya metric are reviewed, with the boundary condition for the radial pressure. The conditions for isotropy simply accomodate various models in the literature. The anisotropy of the Ricci tensor in the special case of spherical GRW space-times (geodesic velocity), gives Friedmann equations deviating from standard FRW cosmology by terms due to the electric tensor. We introduce “perfect 2-scalars” to discuss f(R) gravity with anisotropic fluid source in a doubly warped spacetime, and show that the new geometric terms in the field equations do not change the tensor structure of the fluid energy-momentum tensor.

Quantum Markov monogamy inequalities

Markovianity lies at the heart of communication problems. This in turn makes the information-theoretic characterization of Markov processes worthwhile. Data processing inequalities are ubiquitous in this sense, assigning necessary conditions for all Markov processes. We address here the problem of the information-theoretic analysis of constraints on Markov processes in the quantum regime. We show the existence of a novel class of quantum data processing inequalities called here quantum Markov monogamy inequalities. This new class of necessary conditions on quantum Markov processes is inspired by its counterpart for classical Markov processes, and thus providing a strong link between classical and quantum constraints on Markovianity. We go on to construct a family of multitime quantum Markov monogamy inequalities, based on the process tensor formalism and that exploits multitime correlations. We then show, by means of an explicit example, that the Markov monogamy inequalities can be stronger than the usual quantum data processing inequalities.

Analytical Solutions for Simple Turbulent Shear Flows on a Basis of a Generalized Newton's Law.

In the presented article a generalization of Newton’s formula for the shear stress in a fluid is carried out by giving it a power-law form. After the introduction of the corresponding strain rate tensor, a generalization is made to the spatial case of flow and the rheological relation is presented in tensor form. Depending on the power value in this rheological ratio, one can come either to a description of a laminar flow regime (in the form of Navier–Stokes equations), or to a description of the flow in turbulent regime. In the latter case, a set of differential equations with the no-slip boundary condition is specified, which is significantly different from that for the laminar flow regime, but which also allows one to obtain analytical solutions for simple shear flows and obtain the Blasius resistance law for the flow in a pipe. Therefore, the considered approach to solving problems of turbulent flows compares favorably with modern differential turbulence models. Solutions are given for simple shear flows of a fluid, when there is only one longitudinal component of the velocity, which depends on the transversal coordinate only. These solutions in terms of velocity profiles and resistance coefficients are in satisfactory agreement with the experimental data.

Quasi-local stress-tensor formalism and the Casimir effect

We apply the quasi-local stress–energy tensor formalism to the Casimir effect of a scalar field confined between conducting planes located in a static spacetime. We show that the surface energy vanishes for both Neumann and Dirichlet boundary conditions and consequently the volume Casimir energy reduces to the famous zero point energy of the quantum field, i.e. [Formula: see text]. This enables us to reinforce previous results in the literature and extend the calculations to the case of massive and arbitrarily coupled scalar field. We found that there exists a first-order perturbation correction to the Casimir energy contrary to previous claims which state that it vanishes. This shows many orders of magnitude greater than previous estimations for the energy corrections and makes it detectable by near future experiments.

A fast and storage-saving method for direct volumetric integration of FWH acoustic analogy

This paper proposes a new method that makes the direct volume integration of the Lighthill stress term in FWH acoustic analogy affordable in terms of both computational time and disk storage requirement. The method is based on a dual mesh concept, i.e. while a fine mesh is used in CFD, a relatively coarse mesh is used for the acoustic calculation. The terms being independent of the observer positions in the integral formula of FWH acoustic analogy are calculated on the CFD mesh and mapped onto the acoustic mesh during the simulation. These sound source terms are used for the on-the-fly acoustic computation or saved for later use in the post-processing. A formulation of the Lighthill stress tensor in cavitating flow is also derived. The method is verified with the acoustic assessment of an inclined marine propeller case. A reduction of the calculation time by 98% and disk storage by 99% is achieved while maintaining small acoustic error.

Sparse Bayesian Learning Based Channel Extrapolation for RIS Assisted MIMO-OFDM

Reconfigurable intelligent surface (RIS) is a revolutionary technology and can be used to assist communication systems by adaptively manipulating the wireless environment. In this paper, we propose a novel cascaded channel estimation algorithm for the RIS-assisted multiple-input multiple-output orthogonal frequency division multiplexing systems. Inspired by the channel compression idea, we can obtain a sub-sampled channel by turning off a fraction of RIS elements and then extrapolate it to the complete one, by which the pilot overhead is greatly reduced. The problem of channel extrapolation is transformed into recovering the physical parameters of the cascaded channel from the partial channel observations and is then formulated by the sparse Bayesian learning (SBL) framework. In order to circumvent the curse of high dimensional matrices inversion in the vector-matrix system, we further introduce the tensor structure into the SBL framework. Specially, by leveraging of the channel sparsity over the angle domain and delay domain, we derive the virtual channel expression in tensor form and model a Kronecker-structured prior distribution for the virtual channels. The multi-domain sparse properties of the virtual channel tensor can be effectively captured by a group of low-dimensional hyper-parameters, and thus reduce the computational complexity. In addition, the Cramer-Rao lower bound is derived for the proposed channel extrapolation. Simulation results show the superior performance of the proposed scheme.

ModMax model of nonlinear electrodynamics without the linear term

The ModMax model of nonlinear electrodynamics (NED) is investigated in the absence of the linear term. The linear term is itself a ModMax model, however, the nonlinear term is not. First, in (3+1)-dimensional Minkowski spacetime, we introduce the electromagnetic theory in this NED model. We find the vacuum electric permittivity and magnetic permeability which both are in tensor form. This shows that the propagation of the speed of the electromagnetic wave depends on the direction. Finally, we couple our NED Lagrangian density minimally with the standard gravity and find a dyonic black hole solution.

Nonintrusive model order reduction for cross-diffusion systems

In this paper, we investigate tensor based nonintrusive reduced-order models (ROMs) for parametric cross-diffusion equations. The full-order model (FOM) consists of ordinary differential equations (ODEs) in matrix or tensor form resulting from finite difference discretization of the differential operators by taking the advantage of Kronecker structure. The matrix/tensor differential equations are integrated in time with the implicit–explicit (IMEX) Euler method. The reduced bases, relying on a finite sample set of parameter values, are constructed in form of a two-level approach by applying higher-order singular value decomposition (HOSVD) to the space–time snapshots in tensor form, which leads to a large amount of computational and memory savings. The nonintrusive reduced approximation for an arbitrary parameter value is obtained through tensor product of the reduced basis by the parameter dependent core tensor that contains the reduced coefficients. The reduced coefficients for new parameter values are computed with the radial basis functions. The efficiency of the proposed method is illustrated through numerical experiments for two-dimensional Schnakenberg and three-dimensional Brusselator cross-diffusion equations. The spatiotemporal patterns are accurately predicted by the reduced-order models with speedup factors of orders two and three over the full-order models.

Energy-Momentum Tensor Form Factors in QED

We present the results for the Energy-Momentum Tensor (EMT) form factor D(t) at one-loop accuracy in quantum electrodynamics for an electron state. We report the the results in the case of both zero and nonzero photon mass. Moreover, individual electron and photon contributions to the EMT are investigated.

Connected and Disconnected Sea Partons from CT18 Parametrization of PDFs

The separation of the connected and disconnected sea partons, which were uncovered in the Euclidean path-integral formulation of the hadronic tensor, is accommodated with the CT18 parametrization of the global analysis of the parton distribution functions (PDFs). This is achieved with the help of the distinct small xx behaviors of these two sea parton components and the constraint from the lattice calculation of the ratio of the strange momentum fraction to that of the {\bar u}u‾ or {\bar d}d‾ in the disconnected insertion. This allows lattice calculations of separate flavors in both the connected and disconnected insertions to be directly compared with the global analysis results term by term.

Detection of blood flow through artery in the presence of steno-occlusive disease post liver transplantation by modeling for theatrical and detrimental environmental changes

This research intends to expand a mathematical model for studying the non-Newtonian surge of blood through a hepatic artery in the presence of steno occlusive disease post-liver transplantation. Power law liquid demonstrates the non- Newtonian character of blood. The hemodynamic conduit of the fluid is altered by the occurrence of arterial stenosis. In our study, the difficulty is resolved by applying diagnostic methods with the assistance of marginal circumstances and consequences. The outcomes are explained graphically for unusual cases for such stenosis. The study design is based on a tensorial form and converts its solution using numerical and analytical techniques. Our study outcome suitably demonstrates that the mathematical model used corroborates with the clinical scenario of the patient with hepatic disease.

Thomson Scattering above Solar Active Regions and an Ad Hoc Polarization Correction Method for the Emissive Corona

Thomson-scattered photospheric light is the dominant constituent of the lower solar corona’s spectral continuum viewed off-limb at optical wavelengths. Known as the K-corona, it is also linearly polarized. We investigate the possibility of using the a priori polarized characteristics of the K-corona, together with polarized emission lines, to measure and correct instrument-induced polarized crosstalk. First we derive the Stokes parameters of the Thomson scattering of unpolarized light in an irreducible spherical tensor formalism. This allows forward synthesis of the Thomson-scattered signal for the more complex scenario that includes symmetry-breaking features in the incident radiation field, which could limit the accuracy of our proposed technique. For this, we make use of an advanced 3D radiative magnetohydrodynamic coronal model. Together with synthesized polarized signals in the Fe xiii 10746 Å emission line, we find that an ad hoc correction of telescope- and instrument-induced polarization crosstalk is possible under the assumption of a nondepolarizing optical system.

Numerical Modeling on Blasting Stress Wave in Interbedding Rheological Rockmass for the Stability of the Main Shaft of Mine

High rheological property and strong mining disturbance are prominent conditions in deep rock projects, and often present a coupled process to induce rockbursts, collapse and land subsidence. This paper aims to investigate the effect of surrounding rheological rockmass on the main shaft of mine with interbedding structure under coupled blasting stress wave condition. Based on elastic damage theory and the constitutive equation of rheological rockmass, considering the total strain rate in tensor form, a double-rock model was established. The model was then validated by comparing the numerical simulations with the test results. Matlab was used to develop the COMSOL software, allowing numerical simulation of the failure of shaft rock sequentially subjected to this complex loading path. The results from the rheology-impact numerical simulations show that the double-rock rheology was greatly affected by the dynamic disturbance. Under high creep stress and constant impact stress wave, the last failure of the double-rock with higher creep stress is more severe than that of double-rock with lower creep stress. The numerical simulation of the shaft in situ stress was used to predict the collapse of the rheological rockmass with interbedding structure. The preliminary results suggest that one contribution to this phenomenon is likely related to irreversible damage in the rock during the creep-disturbance process. Dynamic disturbance also promoted the failure of the rock near the interbedding structure, but also increased the strain and stress. This may reflect the initial compaction and elastic phase the rock near the interbedding structure related to the large compressive strength of the hard rock during the dynamic disturbance. The numerical results indicate that a circle-shaped spalling damage zone is prone to develop around the shaft with increased time. We discuss the reason for the decreased stress on point A2 near the interbedding structure of the shaft by visco-elastic theory. The results clearly showed insufficient stability of surrounding rockmass, thus the initial design of shaft is not reasonable. This study has important referential significance for main shaft design for similar mines.

Next-to-leading order QCD calculation of Bc to charmonium tensor form factors

We present a next-to-leading order (NLO) QCD corrections to $B_c\to \eta_c$ and $B_c\to J/\psi$ tensor form factors within nonrelativistic QCD (NRQCD) framework. The full analytical results for $B_c$ to S-wave charmonium tensor form factors are obtained. We also studied the asymptotic behaviours of tensor form factors in hierarchy heavy quark limit, i.e. $m_b\to\infty,~ m_c\to\infty, ~\mathrm{and }~m_c/m_b\to0$. A compact expression for tensor form factors are given analytically in the hierarchy heavy quark limit. The relation among different form factors is also analyzed especially at large momentum recoil point. The numerical results for the $B_c$ to charmonium tensor form factors in all the physical region are given in the end.

New method of atomistic modeling of [formula omitted] phase transition in Fe–Cr alloy with effective accounting for vibrational entropy

In this work, a novel approach was developed for studying the early stages of the formation of Cr-rich precipitates (α′ phase) in Fe–Cr system. The approach accounts for vibrational entropy of the system. The research was conducted using machine-learning potentials. The potentials have a form of low-rank tensors. Two such potentials were optimized in order to reproduce the results of DFT computations and experimental data on vibrational entropy, respectively. Combination of the potentials was used for on-lattice kinetic Monte-Carlo simulations. The formulated approach was tested to evaluate enthalpy of mixing, diffusion coefficients, and α−α′ phase transition boundary data for a Fe–Cr system. Importance of accounting the vibrational entropy for accurate modeling of Cr-rich clusters was demonstrated. Obtained characteristics of the α′ precipitates were in a good agreement with the experimental results. Particularly, concentration and the average radius of Cr-rich precipitates in LRP-based computations were close to APT data within the error of experimental studies.

Generalized nonconservative gravitational field equations from Herglotz action principle

We formulate a nonconservative gravitational theory based on the Herglotz variational principle in a tensorial covariant form. The model presented here may be seen as an improvement of the theory proposed in [ et al., Phys. Rev. D 95, 101501 (2017)], whose resulting field equations are meaningful just in particular coordinate systems. The new theory we report in this work is free from such a restriction. In comparison to the standard general relativity, both theories based on the Herglotz principle contain an extra vector field, the Herglotz field, but the new theory is formulated by taking advantage of the restricted equivalence between Lagrangian functions in the scope of the Herglotz action principle. The more restricted class of equivalent Lagrangian functions, in comparison with the Hamilton variational principle, is the key point to finding a Lagrangian that generates a new alternative gravitational theory in a covariant form. Once the equations that govern the dynamics of the gravitational field are obtained, a few simple cosmological models are investigated. It is found that the Herglotz vector field reduces to a single function that, under certain conditions, plays the role of the cosmological constant in general relativity, turning unnecessary the introduction of dark energy to explain the accelerated expansion of the Universe. The linearized version of the theory is also investigated and it is verified that the theory shows a dissipative character regarding the propagation of gravitational perturbations. From observational data, in both scenarios, the magnitude of the Herglotz field is estimated.

Complete analysis of beam analyzing powers in at near threshold energies

Focusing attention on the photon spin in at near threshold energies of interest to Big Bang Nucleosynthesis, a complete analysis of beam analyzing powers in reaction is carried out. A complete analysis of the reaction needs not only measurements using one state of linear polarization of photon but also measurements using another state of linear polarization inclined to the first at π/4 and the two states of circular polarization of the photon. A discussion on the complete characterization of the states of photon polarization is presented. The beam analyzing powers with respect to photon polarization are discussed theoretically, using model independent irreducible tensor formalism.

Double copy of spontaneously broken Abelian gauge theory

Similarity in the structure of scattering amplitudes in Yang-Mills theories and General Relativity led to the idea that graviton could be described as the double copy of a vector gauge field. In this letter we discuss a realization of this idea emerging directly from solutions of equations of General Relativity. A general form of the energy momentum tensor for the electric field is derived that leads to the metric tensor in terms of the double copy of a corresponding gauge potential. We then use this general property to find the double copy of spontaneously broken scalar electrodynamics. The result is a screened Reissner-Nordström-like metric. When the horizon radius and the Compton wavelength of the massive photon become comparable the black hole becomes a quantum object. An exact solution of the horizon wave equation is found and the corresponding energy spectrum is described. It turns out that highly excited states show a characteristic string-like behavior.

Two Invariants for Geometric Mappings

Two invariants for mappings of affine connection spaces with a special form of deformation tensors are obtained in this paper. We used the methodology of Vesić to obtain the form of these invariants. At the end of this paper, we used these forms to obtain two invariants for third-type almost-geodesic mappings of symmetric affine connection.

Mathematical model of convective heat transfer for peristaltic flow of Rabinowitsch fluid in a wavy rectangular duct with entropy generation

This research article unfolds a novel mathematical model that interprets the ‘peristaltic flow of Heated Rabinowitsch fluid’ inside a wavy rectangular duct. The fluid flow characteristics are thoroughly examined for Pseudo-plastic in addition to Dilatant nature, (i.e. α > 0 for pseudo-plastic nature and α < 0 for dilatant nature respectively). Peristaltic flow inside a wavy rectangular duct is widely being studied due to immense number of biomedical and engineering applications. We have derived the dimensionless nonlinear partial differential equations in coupled form after applying certain relevant dimensionless quantities, the lubrication technique of low Reynolds number and long wavelength estimations (i.e., ). The dimensionless energy equation is solved by dividing it into two additional equations and after employing suitable procedures, an exact temperature profile solution is computed. The present study has been developed by using hit and trial method to solve the single partial differential equation having two dependent variables in form of extra stress tensors. The solution of temperature profile provides a detailed solution method to exactly solve such complex partial differential equations. For both dilatant and Pseudo-plastic fluids, effective physical parameters are used to depict velocity distribution, pressure gradient and pressure rise, convection and entropy phenomena. When compared with Pseudo-plastic fluid, the Dilatant nature of fluid has a high convection rate. Finally, the phenomenon of entrapment is examined through streamlines that provide a flow visualization inside the wavy sinusoidal duct. Peristaltic pumps are being used for transportation of many fluids like toxic chemicals in nuclear industry, food processing, heart-lung machines, roller and finger pumps and transportation of slurries etc. These usage of these pumps leads to an upgraded mechanical efficiency and lower cost for transportation purposes.