Related papers: The atomic structure of ancient grain boundaries
Singular solutions of the harmonic Einstein evolution equation are constructed which are related to spatially global and time-local solutions for a certain class of quasilinear hyperbolic systems of second order. The constructed…
We provide several characterisations of collapsing and noncollapsing in convex ancient mean curvature flow, establishing in particular that collapsing occurs if and only if the flow is asymptotic to at least one Grim hyperplane. As a…
Grain boundaries, the two-dimensional (2D) defects between differently oriented crystals, control mechanical and transport properties of materials. Our fundamental understanding of grain boundaries is still incomplete even after nearly a…
With few exceptions, known explicit solutions of the curve shortening flow (CSE) of a plane curve, can be constructed by classical Lie point symmetry reductions or by functional separation of variables. One of the functionally separated…
Orbit-finite models of computation generalise the standard models of computation, to allow computation over infinite objects that are finite up to symmetries on atoms, denoted by $\mathbb{A}$. Set theory with atoms is used to reason about…
We show that, for the scalar field cosmology with exponential potential, the set of values of the coupling parameter for which the solutions undergo a transient period of acceleration is much larger than the set discussed in the literature.…
In contrast to Einstein's theory, the first order formulation of gravity turns out to be a natural habitat for double-sheeted spacetime solutions which satisfy the vacuum field equations everywhere. These bridge-like geometries exhibit…
One of the prime motivation for topology was Homotopy theory, which captures the general idea of a continuous transformation between two entities, which may be spaces or maps. In later decades, an algebraic formulation of topology was…
The response of low-dimensional solid objects combines geometry and physics in unusual ways, exemplified in structures of great utility such as a thin-walled tube that is ubiquitous in nature and technology. Here we provide a particularly…
There is an extensive and growing body of work analyzing convex ancient solutions to Mean Curvature Flow (MCF), or equivalently of Rescaled Mean Curvature Flow (RMCF). The goal of this paper is to complement the existing literature, which…
The dynamics of an M-dimensional extended object whose M+1 dimensional world volume in M+2 dimensional space-time has vanishing mean curvature is formulated in term of geometrical variables (the first and second fundamental form of the…
We study translators of the mean curvature flow in the product space $\h^2\times\r$. In $\h^2\times\r$ there are three types of translations: vertical translations due to the factor $\r$ and parabolic and hyperbolic translations from…
A class of energy-transport equations without electric field under mixed Dirichlet-Neumann boundary conditions is analyzed. The system of degenerate and strongly coupled parabolic equations for the particle density and temperature arises in…
Our representation of the Universe is built with sequences of symbols, numbers, operators, rules and undecidable propositions defining our mathematical truths, represented either by classical, quantum and probabilistic Turing Machines…
We are concerned with the formation of singularities and the existence of global continuous solutions of the Cauchy problem for the one-dimensional non-isentropic Euler equations for compressible fluids. For the isentropic Euler equations,…
The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…
Motivated by the power of subregion/subregion duality for constraining the bulk geometry in gauge/gravity duality, we pursue a comprehensive and systematic approach to the behavior of extremal surfaces under perturbations. Specifically, we…
Classical atomistic simulations based on interatomic potentials resolve lattice instabilities, defect nucleation, and microstructure evolution with high fidelity, but their accessible system sizes remain far below those required for…
We prove that if an orientable 3-manifold $M$ admits a complete Riemannian metric whose scalar curvature is positive and has a subquadratic decay at infinity, then it decomposes as a (possibly infinite) connected sum of spherical manifolds…
We present a unified causal general relativistic formulation of dissipative and non-dissipative continuum mechanics. The presented theory is the first general relativistic theory that can deal simultaneously with viscous fluids as well as…