Stack operation of tensor networks by Zhang, Tianning, Chen, Tianqi, Li, Erping, Yang, Bo, Ang, L. K.

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Berry connection polarizability tensor and third-order Hall effect by Liu, Huiying, Zhao, Jianzhou, Huang, Yue-Xin, Feng, Xiaolong, Xiao, Cong, Wu, Weikang, Lai, Shen, Gao, Weibo, Yang, Shengyuan A.

“…Here, we show that the Berry connection polarizability (BCP) tensor, as another intrinsic band geometric quantity, plays a key role in the third-order Hall effect. …”
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One-loop corrections to the primordial tensor spectrum from massless isocurvature fields by Tan, Hai Siong

“…We study one-loop corrections to the two-point correlation function of tensor perturbations in primordial cosmology induced by massless spectator matter fields. …”
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Third-order nonlinear Hall effect induced by the Berry-connection polarizability tensor by Lai, Shen, Liu, Huiying, Zhang, Zhaowei, Zhao, Jianzhou, Feng, Xiaolong, Wang, Naizhou, Tang, Chaolong, Liu, Yuanda, Novoselov, K. S., Yang, Shengyuan A., Gao, Weibo

“…Theory predicts that another intrinsic band geometric property, the Berry-connection polarizability tensor10, gives rise to higher-order signals, but it has not been probed experimentally. …”
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Sparse tensor product high dimensional finite elements for two-scale mixed problems by Chu, Van Tiep, Hoang, Viet Ha, Lim, Roktaek

“…We develop the essentially optimal sparse tensor product finite element method for solving two-scale mixed problems in both the primal and dual forms. …”
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Sparse tensor Galerkin discretization of parametric and random parabolic PDEs - analytic regularity and generalized polynomial chaos approximation by Hoang, Viet Ha., Schwab, Christoph.

“…The present results imply convergence rates and stability of sparse, adaptive space-time tensor product Galerkin discretizations of these infinite dimensional, parametric problems in the parameter space recently proposed in [C. …”
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High dimensional finite elements for multiscale wave equations by Xia, Bingxing, Hoang, Viet Ha

“…With sufficient regularity, the sparse tensor product approximation achieves a convergence rate essentially equal to that for the full tensor product approximation, but requires only an essentially equal number of degrees of freedom as for solving an equation in $\mathbb{R}^d$ for the same level of accuracy. …”
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General relativistic Lagrangian continuum theories part I: reduced variational principles and junction conditions for hydrodynamics and elasticity by Gay-Balmaz, François

“…For the latter case, our setting also allows to clarify the relation between formulations of relativistic elasticity based on the relativistic right Cauchy-Green tensor or on the relativistic Cauchy deformation tensor. …”
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High dimensional finite elements for two-scale Maxwell wave equations by Chu, Van Tiep, Hoang, Viet Ha

“…This problem depends on two variables in Rd, one for each scale that the original two-scale equation depends on, and is thus posed in a high dimensional tensorized domain. The straightforward full tensor product finite element (FE) method is exceedingly expensive. …”
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The QCD mass gap and quark deconfinement scales as mass bounds in strong gravity by Burikham, Piyabut, Harko, Tiberiu, Lake, Matthew James

“…It may therefore be used to explore the stability and confinement of gauge singlet hadrons, though not to describe scattering processes that require color interactions. It is a two-tensor theory of both strong interactions and gravity, in which the strong tensor field is governed by equations formally identical to the Einstein equations, apart from the coupling parameter, which is of order 1 GeV−1 . …”
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Anisotropic centroidal voronoi tessellations and their applications by Wang, Desheng, Du, Qiang

“…In this paper, we introduce a novel definition of the anisotropic centroidal Voronoi tessellation (ACVT) corresponding to a given Riemann metric tensor. A directional distance function is used in the definition to simplify the computation. …”
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Dynamics of binary mixtures in inhomogeneous temperature by Giuseppe, Gonnella, Antonio, Lamura, Antonio, Piscitelli

“…Then an expression for the pressure tensor is derived. As examples of applications, interface behavior and phase separation have been numerically studied in two dimensions neglecting the contributions of the velocity field. …”
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Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains by Shen, Jie, Wang, Li-Lian, Yu, Haijun

“…The approximation results for both the usual tensor product space and hyperbolic cross space are established, with the latter particularly suitable for higher-dimensional problems.…”
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Regularity and generalized polynomial chaos approximation of parametric and random second-order hyperbolic partial differential equations by Hoang, Viet Ha., Schwab, Christoph.

“…The results allow obtaining convergence rates and stability of sparse space-time tensor product Galerkin discretizations in the parameter space.…”
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Noncommutative spacetime geometry and one-loop effects in primordial cosmology by Tan, Hai Siong

“…After deforming the algebra of functions on the inflationary background to a spatially noncommutative one, we find that this induces momentum-dependent corrections to one-loop terms which imply that the vacuum fluctuations of the energy-momentum tensor source that of the curvature fluctuation even for distances beyond horizon scales. …”
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High dimensional finite element method for multiscale nonlinear monotone parabolic equations by Tan, Wee Chin, Hoang, Viet Ha

“…However, it is posed in a high dimensional tensorized domain. We develop the sparse tensor product FE method for this equation that uses an essentially optimal number of degrees of freedom to obtain an approximation for the solution within a prescribed accuracy. …”
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Hybrid surface waves in two-dimensional Rashba-Dresselhaus materials by Yudin, Dmitry, Gulevich, Dmitry R., Shelykh, Ivan A.

“…It is demonstrated that off-diagonal components of the conductivity tensor resulting from a delicate interplay between Rashba and Dresselhaus couplings lead to the hybridization of transverse electric and transverse magnetic surface electromagnetic modes localized at the interface. …”
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Entanglement of random hypergraph states by Zhou, You, Hamma, Alioscia

“…In particular, we study the two ensembles generated by random Controlled-Z(CZ) and Controlled-Controlled-Z(CCZ) gates, respectively. By applying tensor network representation and combinational counting, we analytically show that the average subsystem purity and entanglement entropy for the two ensembles feature the same volume law, but greatly differ in typicality, namely the purity fluctuation is small and universal for the CCZ ensemble while it is large for the CZ ensemble. …”
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High-dimensional finite elements for multiscale Maxwell-type equations by Chu, Van Tiep, Hoang, Viet Ha

“…Solving it, we get all the necessary macroscopic and microscopic information. Sparse tensor product finite elements (FEs) are employed, using edge FEs. …”
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Bayesian inverse problems for recovering coefficients of two scale elliptic equations by Hoang, Viet Ha, Quek, Jia Hao

“…Although this equation is posed in a high dimensional tensorized domain, it can be solved with essentially optimal complexity by the sparse tensor product finite element method, which reduces the computational complexity of the MCMC sampling method substantially. …”
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