A <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e328" altimg="si3.gif"><mml:mi>C</mml:mi></mml:math>-eigenvalue problem for tensors with applications to higher-order multivariate Markov chains

This paper mainly considers the C-eigenvalues of a piezoelectric-type tensor. For this, we first discuss its relationship with <inline-formula><tex-math id="M1">\begin{document}$ l^{k, s} $\end{document}</tex-math></inline-formula>-singular values of a partially symmetric rectangular tensor, and then present three types of C-eigenvalue inclusion intervals which can be used to locate all C-eigenvalues of a piezoelectric-type tensor and can provide an upper and a lower bound for the largest C-eigenvalue of a piezoelectric-type tensor. Finally, we present an alternative method to compute all C-eigenpairs of a piezoelectric-type tensor.

show abstract

“…Consequently, λ * (A) ≤ min{ρ G , ρ B , ρ S }, which shows that the second inequality in (18) follows.…”

mentioning

confidence: 82%

Properties and calculation for C-eigenvalues of a piezoelectric-type tensor

Zhao

Luo

2022

JIMO

View full text Add to dashboard Cite

show abstract

“…In particular, the definition of generalized eigenvalues and eigenvectors of A given in section 2.3 would be missed. A strategy has recently been developed in [24,63,64,122] to overcome this difficulty and to attempt at providing a similar treatment for both piezoelectric and fully symmetric octupolar tensors. Here, we briefly present this strategy, following mainly [24].…”

Section: Curie Potentialmentioning

confidence: 99%

A review on octupolar tensors

Gaeta

Virga

2023

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

In its most restrictive definition, an octupolar tensor is a fully symmetric traceless third-rank tensor in three space dimensions. So great a body of works have been devoted to this specific class of tensors and their physical applications that a review would perhaps be welcome by a number of students. Here, we endeavour to place octupolar tensors into a broader perspective, considering non-vanishing traces and non-fully symmetric tensors as well. A number of general concepts are recalled and applied to either octupolar and higher-rank tensors. As a tool to navigate the diversity of scenarios we envision, we introduce the octupolar potential, a scalar-valued function which can easily be given an instructive geometrical representation. Physical applications are plenty; those to liquid crystal science play a major role here, as they were the original motivation for our interest in the topic of this review.

show abstract

“…In our paper, we explore it using gas-kinetic scheme coupled with Menter's Shear Stress Transport (SST) turbulence model [25], and a gas-kinetic scheme coupled with SST turbulence model has been introduced in the Ref. [28].…”

Section: Case 2: Incompressible Turbulent Flow Around a Square Cylindermentioning

confidence: 99%

Implementation of dual time-stepping strategy of the gas-kinetic scheme for unsteady flow simulations

Zhong

Wang

et al. 2017

Phys. Rev. E

View full text Add to dashboard Cite

In our study, the dual time-stepping strategy of the gas-kinetic scheme is constructed and used for the simulation of unsteady flows. In comparison to the previous implicit gas-kinetic scheme, both the inviscid and viscous flux Jacobian are considered in our work, and the linear system of the pseudo-steady-state is solved by applying generalized minimal residual algorithm. The accuracy is validated by several numerical cases, the incompressible flow around blunt bodies (stationary circular cylinder and square cylinder), and the transonic buffet on the NACA0012 airfoil under hybrid mesh. The numerical cases also demonstrate that the present method is applicable to approach the fluid flows from laminar to turbulent and from incompressible to compressible. Finally, the case of acoustic pressure pulse is carried out to evaluate the effects of enlarged time step, and the side effect of enlarged time step is explained. Compared with the explicit gas-kinetic scheme, the proposed scheme can greatly accelerate the computation and reduce the computational costs for unsteady flow simulations.

show abstract

A C-eigenvalue problem for tensors with applications to higher-order multivariate Markov chains

Cited by 8 publications

References 34 publications

Properties and calculation for <i>C</i>-eigenvalues of a piezoelectric-type tensor

Properties and calculation for <i>C</i>-eigenvalues of a piezoelectric-type tensor

A review on octupolar tensors

Implementation of dual time-stepping strategy of the gas-kinetic scheme for unsteady flow simulations

Contact Info

Product

Resources

About