Related papers: On the range of 3D dislocation pair correlations
The behavior of dislocations is essential to understand material properties, but their subsurface dynamics that are representative of bulk phenomena cannot be resolved by conventional transmission electron microscopy (TEM). Dark field X-ray…
Theoretical results on the dynamics of dislocations in Rayleigh-B\'enard convection are reported both for Swift-Hohenberg models and the Boussinesq equations. For intermediate Prandtl numbers the motion of dislocations is found to be driven…
The thermodynamic dislocation theory developed for non-uniform plastic deformations is used here to simulate the stress-strain curves for crystals subjected to anti-plane shear-controlled load reversal. We show that the presence of the…
The three-body general problem is formulated as a problem of geodesic trajectories flows on the Riemannian manifold. It is proved that a curved space with local coordinate system allows to detect new hidden symmetries of the internal motion…
Point configurations have been widely used as model systems in condensed matter physics, materials science and biology. Statistical descriptors such as the $n$-body distribution function $g_n$ is usually employed to characterize the point…
Dispersion relations are nonperturbative formulas that relate the ultraviolet and infrared behavior of an observable with wide-ranging applications applications in linear response theory, quantum field theory scattering amplitudes, and…
We present measurements of the spatial clustering statistics in redshift space of various scalar field modified gravity simulations. We utilise the two-point and the three-point correlation functions to quantify the spatial distribution of…
It is known that discrete scale invariance leads to log-periodic corrections to scaling. We investigate the correlations of a system with discrete scale symmetry, discuss in detail possible extension of this symmetry such as translation and…
Several applications such as autonomous driving, augmented reality and virtual reality require a precise prediction of the 3D human pose. Recently, a new problem was introduced in the field to predict the 3D human poses from observed 2D…
We present a method for learning 3D spatial relationships between object pairs, referred to as object-object spatial relationships (OOR), by leveraging synthetically generated 3D samples from pre-trained 2D diffusion models. We hypothesize…
In this study, we investigate the problem of tracking objects with unknown shapes using three-dimensional (3D) point cloud data. We propose a Gaussian process-based model to jointly estimate object kinematics, including position,…
We consider Gaussian graphical models associated with an equicorrelational and one-dimensional conditional independence graph. We show that pairwise correlation decays exponentially as a function of distance. We also provide a limit when…
We introduce one dimensional sets to help describe and constrain the integral curves of an $n$ dimensional dynamical system. These curves provide more information about the system than the zero-dimensional sets (fixed points) do. In fact,…
Thermodynamic dislocation theory incorporating dislocation impediment by the grain boundaries is developed to analyze the shear test of polycrystals. With a small set of physics based material parameters, we are able to simulate the…
This paper develops the small strain continuum dislocation theory accounting for statistically stored dislocations and Taylor hardening for single crystals. As illustration, the problem of anti-plane constrained shear of single crystal…
We show how wall-crossing formulas in coupled 2d-4d systems, introduced by Gaiotto, Moore and Neitzke, can be interpreted geometrically in terms of the deformation theory of holomorphic pairs, given by a complex manifold together with a…
Correlations between two variables of a high-dimensional system can be indicative of an underlying interaction, but can also result from indirect effects. Inverse Ising inference is a method to distinguish one from the other. Essentially,…
This is a significantly expanded version of the survey paper "Mixing and decay of correlations in non-uniformly expanding maps: a survey of recent results" math/0301319. We discuss recent results on decay of correlations for non-uniformly…
We present a new method for visualizing implicit real algebraic curves inside a bounding box in the $2$-D or $3$-D ambient space based on numerical continuation and critical point methods. The underlying techniques work also for tracing…
Traction-separation relationship is an important material characteristic describing the fracture behaviour of quasi-brittle solids. A new numerical scheme for identification of the traction-separation relation by inverse analysis of data…