相关论文: Geodesics around line defects in elastic solids
In this work, we investigate the topological properties of knotted defects in smectic liquid crystals. Our story begins with screw dislocations, whose radial surface structure can be smoothly accommodated on $S^3$ for fibred knots by using…
Topological defects are distinctive signatures of liquid crystals. They profoundly affect the viscoelastic behavior of the fluid by constraining the orientational structure in a way that inevitably requires global changes not achievable…
The modeling of the elastic properties of disordered or nanoscale solids requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which…
We investigate equatorial geodesics in the gravitational field of a rotating and deformed source described by the approximate Hartle-Thorne metric. In the case of massive particles, we derive within the same approximation analytic…
We consider the tidal forces between test particles falling along geodesics in the exterior spacetime generated by a static and axially symmetric compact matter source with non-vanishing mass quadrupole. Specifically, we analyze the radial…
We study geodetic lines on a surface generated by a small deformation of the standard 2D-sphere. We construct an auxiliary hamiltonian system with the view of describing geodetic coils and almost closed geodesics, by using the fact that…
The problem of heterogeneous nucleation of second-phase in alloys in the vicinity of elastic defects is considered. The defect can be a dislocation line or a crack tip residing in a crystalline solid. We use the Ginzburg-Landau equation to…
Understanding the fundamental mechanisms behind plastic instabilities and shear band formation in amorphous media under applied deformation remains a long-standing challenge. Leveraging on the mathematical concept of topology, we revisit…
The continuum mechanics of line defects representing singularities due to terminating discontinuities of the elastic displacement and its gradient field is developed. The development is intended for application to coupled phase…
Topological defects in graphene, dislocations and grain boundaries, are still not well understood despites the considerable number of experimental observations. We introduce a general approach for constructing dislocations in graphene…
We analyze a mathematical model of elastic dislocations with applications to geophysics, where by an elastic dislocation we mean an open, oriented Lipschitz surface in the interior of an elastic solid, across which there is a discontinuity…
Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in finite samples. These general expressions are valid for anisotropic media as well. Specifically for the…
The energy density of asymptotically flat gravitational fields can be calculated from a simple expression involving the trace of the torsion tensor. Integration of this energy density over the whole space yields the ADM energy. Such…
In this article, the ray tracing method is studied beyond the classical geometrical theory. The trajectories are here regarded as geodesics in a Riemannian manifold, whose metric and topological properties are those induced by the…
We investigate the problem of estimating geodesic tortuosity and constrictivity as two structural characteristics of stationary random closed sets. They are of central importance for the analysis of effective transport properties in porous…
Geodesics deviation equation (GDE) is itroduced. In "adiabatic" approximation exact solution of the GDE if found. Perturbation theory in general case is formulated. Geometrical criterion of local instability which may lead to chaos is…
The complex arrangements of atoms near grain boundaries are difficult to understand theoretically. We propose a phenomenological (Ginzburg-Landau-like) description of crystalline phases based on symmetries and fairly general stability…
A rigorous methodology is developed for computing elastic fields generated by experimentally observed defect structures within grains in a polycrystal that has undergone tensile extension. An example application is made using a near-field…
We present a differential geometric framework for the motion of a non-Brownian particle in the presence of fixed obstacles in a quiescent fluid, in the deterministic Stokesian regime. While the Helmholtz Minimum Dissipation Theorem suggests…
We propose an approach to measure surface elastic constants of soft solids. Generally, this requires one to probe interfacial mechanics at around the elastocapillary length scale, which is typically microscopic. Deformations of microscopic…