English
Related papers

Related papers: Generic uniqueness and stability for the mixed ray…

200 papers

In this paper, we introduce tensor involved peridynamics, a unified framework for simulating both isotropic and anisotropic materials. While traditional peridynamics models effectively simulate isotropic materials, they face challenges with…

Materials Science · Physics 2024-12-23 Hao Tian , Jinlong Shao , Chenguang Liu , Shuo Liu , Xu Guo

We consider three extensions of the standard 2D Ising model with Glauber dynamics on a finite torus at low temperature. The first model is an anisotropic version, where the interaction energy takes different values on vertical and on…

Probability · Mathematics 2019-07-02 Kaveh Bashiri

We write a space-time Feynman path integral representation for scattered elastic wave fields from a weakly compact supported anisotropic non-homogeneity.Replacement by a new version where We (I!) propose a new tomographic inversion…

Mathematical Physics · Physics 2019-08-22 Luiz C. L. Botelho

We consider the nonlinear problem of determining a connection and a Higgs field from the corresponding parallel transport along geodesics on a Riemannian manifold with boundary, in any dimension. The problem can be reduced to an integral…

Analysis of PDEs · Mathematics 2016-10-18 Hanming Zhou

We prove a sharp $L^2\to H^{1/2}$ stability estimate for the geodesic X-ray transform of tensor fields of order $0$, $1$ and $2$ on a simple Riemannian manifold with a suitable chosen $H^{1/2}$ norm. We show that such an estimate holds for…

Metric Geometry · Mathematics 2019-03-12 Yernat Assylbekov , Plamen Stefanov

The spatial diffusion of cosmic rays in turbulent magnetic fields can, in the most general case, be fully anisotropic, i.e. one has to distinguish three diffusion axes in a local, field-aligned frame. We reexamine the transformation for the…

We consider the equilibrium equations for a conducting elastic rod placed in a uniform magnetic field, motivated by the problem of electrodynamic space tethers. When expressed in body coordinates the equations are found to sit in a…

Mathematical Physics · Physics 2010-07-06 D. Sinden , G. H. M. van der Heijden

In this paper we consider the geodesic X-ray transform with attenuation coefficient as a combination of smooth complex function and 1-form. We show that attenuated X-ray transform applied to the pair of tensors is injective modulo the…

Differential Geometry · Mathematics 2017-03-07 Yernat M. Assylbekov

Wavefield travel time tomography is used for a variety of purposes in acoustics, geophysics and non-destructive testing. Since the problem is non-linear, assessing uncertainty in the results requires many forward evaluations. It is…

Geophysics · Physics 2023-08-21 James Ludlam , Katherine Tant , Victorita Dolean , Andrew Curtis

Consider a compact Riemannian manifold of dimension $\geq 3$ with strictly convex boundary, such that the manifold admits a strictly convex function. We show that the attenuated ray transform in the presence of an arbitrary connection and…

Differential Geometry · Mathematics 2018-06-05 Gabriel P. Paternain , Mikko Salo , Gunther Uhlmann , Hanming Zhou

We consider the anisotropic Calderon problem of recovering a conductivity matrix or a Riemannian metric from electrical boundary measurements in three and higher dimensions. In the earlier work \cite{DKSaU}, it was shown that a metric in a…

Analysis of PDEs · Mathematics 2014-05-13 David Dos Santos Ferreira , Yaroslav Kurylev , Matti Lassas , Mikko Salo

In this paper we show the invertibility of the geodesic X-ray transform on one forms and 2-tensors on asymptotically conic manifolds, up to the natural obstruction, allowing existence of certain kinds of conjugate points. We use the 1-cusp…

Differential Geometry · Mathematics 2022-12-06 Qiuye Jia , András Vasy

In this article we study the linearized anisotropic Calder\'on problem on a compact Riemannian manifold with boundary. This problem amounts to showing that products of pairs of harmonic functions of the manifold form a complete set. We…

Analysis of PDEs · Mathematics 2020-09-15 Katya Krupchyk , Tony Liimatainen , Mikko Salo

We introduce a variational manifold of simple tensor network states for the study of a family of constrained models that describe spin-1/2 systems as realized by Rydberg atom arrays. Our manifold permits analytical calculation via…

Quantum Physics · Physics 2024-05-13 Joey Li , Giuliano Giudici , Hannes Pichler

We consider compact smooth Riemmanian manifolds with boundary of dimension greater than or equal to two. For the initial-boundary value problem for the wave equation with a lower order term $q(t,x)$, we can recover the X-ray transform of…

Analysis of PDEs · Mathematics 2014-08-01 Alden Waters

We study an inverse problem of determining a time-dependent potential appearing in the wave equation in conformally transversally anisotropic manifolds of dimension three or higher. These are compact Riemannian manifolds with boundary that…

Analysis of PDEs · Mathematics 2024-10-22 Boya Liu , Teemu Saksala , Lili Yan

We study inverse boundary problems for magnetic Schr\"odinger operators on a compact Riemannian manifold with boundary of dimension $\ge 3$. In the first part of the paper we are concerned with the case of admissible geometries, i.e.…

Analysis of PDEs · Mathematics 2018-08-01 Katya Krupchyk , Gunther Uhlmann

This paper concerns the imaging of a complex-valued anisotropic tensor {\gamma} = {\sigma}+{\iota}{\omega}{\epsilon} from knowledge of several inter magnetic fields H where H satisfies the anisotropic Maxwell system on a bounded domain with…

Analysis of PDEs · Mathematics 2015-01-27 Chenxi Guo , Guillaume Bal

In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…

Analysis of PDEs · Mathematics 2025-07-17 Lindsey van der Aalst , Jan Bouwe van den Berg , Jean-Philippe Lessard

We apply the Minkowski tensor statistics to three dimensional Gaussian random fields. Minkowski tensors contain information regarding the orientation and shape of excursion sets, that is not present in the scalar Minkowski functionals. They…

Cosmology and Nongalactic Astrophysics · Physics 2018-08-29 Stephen Appleby , Pravabati Chingangbam , Changbom Park , K. P. Yogendran , P. K. Joby