相关论文: Recovering the normal form of an elasticity tensor

We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based…

We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic decomposition of higher-order tensors subject to a rank and genericity constraint. Reformulating this computational problem as a system…

In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…

We present an algorithm for low rank decomposition of tensors of any symmetry type, from fully asymmetric to fully symmetric. It recovers the decomposition one summand at a time via the higher-order power method. This approach is known to…

Detecting symmetry is crucial for effective object grasping for several reasons. Recognizing symmetrical features or axes within an object helps in developing efficient grasp strategies, as grasping along these axes typically results in a…

A challenge in soft robotics and soft actuation is the determination of an elastic system which spontaneously recovers its trivial path during postcritical deformation after a bifurcation. The interest in this behaviour is that a…

Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks…

An algorithmic method to exploit a general class of infinitesimal symmetries for reducing stochastic differential equations is presented and a natural definition of reconstruction, inspired by the classical reconstruction by quadratures, is…

We present a new algorithm for recovering paths from their third-order signature tensors, an inverse problem in rough analysis. Our algorithm provides the exact solution to this learning problem and improves upon current approaches by an…

Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study…

We decompose the velocity gradient tensor for turbulence into normal and non-normal parts, and condition our analysis on the strain eigenvector alignments between these tensors. We identify states that always enhance, and always counteract…

It is shown that classical spaces with geometries emerge on boundaries of randomly connected tensor networks with appropriately chosen tensors in the thermodynamic limit. With variation of the tensors, the dimensions of the spaces can be…

We present a general deconstruction procedure aimed at recognizing whether a given conformal model may be obtained as an orbifold of another one, and to identify the twist group and the original model in terms of some readily available…

Using electromagnetism to study analogue space-times is tantamount to considering consistency conditions for when a given (meta-)material would provide an analogue space-time model or --- vice versa --- characterizing which given metric…

We present a general, constructive procedure to find the basis for tensors of arbitrary order subject to linear constraints by transforming the problem to that of finding the nullspace of a linear operator. The proposed method utilizes…

Matrix congruence extends naturally to the setting of tensors. We apply methods from tensor decomposition, algebraic geometry and numerical optimization to this group action. Given a tensor in the orbit of another tensor, we compute a…

In this paper, we present an analytic non-iterative approach for recovering a planar isotropic elastic inclusion embedded in an unbounded medium from the elastic moment tensors (EMTs), which are coefficients for the multipole expansion of…

A method to retrieve the elastic constants of rectangular wooden plates is presented, relying on the measurement of a set of eigenfrequencies and the identification of the corresponding mode shapes, and belonging to the more general…

We prove that the symmetry group of an elasticity tensor is equal to the symmetry group of the corresponding Christoffel matrix.

Minimizing the bending energy within knot classes leads to the concept of elastic knots which has been initiated in [von der Mosel, Asymptot. Anal. 1998]. Motivated by numerical experiments in arxiv:1804.02206 (doi:10.1090/mcom/3633) we…