Topic
Two-dimensional space
About: Two-dimensional space is a research topic. Over the lifetime, 104 publications have been published within this topic receiving 2309 citations. The topic is also known as: 2D & bi-dimensional space.
Papers published on a yearly basis
Papers
TL;DR: A design criteria for a volume-of-fluid interface reconstruction algorithm to be second-order accurate is proposed, which is that it reproduce lines in two space dimensions or planes in three space dimensions exactly.
766 citations
TL;DR: In this article, the authors compared the accuracy of four modeling techniques for solid state and vidicon cameras, including linear spline, quadratic, and two-plane models.
218 citations
TL;DR: For arbitrary single-input real analytic systems in the plane, in which the control enters linearly, the authors proved the existence of a regular synthesis for the optimal control problem in which it is desired to minimize the integral of a strictly positive real analytic Lagrangian that does not depend on the control variable.
Abstract: For arbitrary single-input real analytic systems in the plane, in which the control enters linearly, we prove the existence of a regular synthesis for the optimal control problem in which it is desired to minimize the integral of a strictly positive real analytic Lagrangian that does not depend on the control variable. The analysis proceeds by applying our previous results on nondegenerate $\mathcal{C}^\infty $ systems, as well as those on arbitrary real analytic ones, to study the local structure of the time optimal trajectories. The structure of the optimal trajectories for our problem is derived by reparametrization of time. The existence of a synthesis is then proved by using subanalytic set theory.
114 citations
TL;DR: Based on the weighted and shifted Gr{u}nwald difference (WSGD) operators, the authors constructed the compact finite difference discretizations for the fractional operators and theoretically proved and numerically verified that the provided numerical schemes have the convergent orders 3 in space and 2 in time.
Abstract: Based on the weighted and shifted Gr\"{u}nwald difference (WSGD) operators [24], we further construct the compact finite difference discretizations for the fractional operators. Then the discretization schemes are used to approximate the one and two dimensional space fractional diffusion equations. The detailed numerical stability and error analysis are theoretically performed. We theoretically prove and numerically verify that the provided numerical schemes have the convergent orders 3 in space and 2 in time.
97 citations
TL;DR: In this paper, the authors provide a framework for building periodic boundary conditions on the pseudosphere (or hyperbolic plane), the infinite two-dimensional Riemannian space of constant negative curvature.
Abstract: We provide a framework for building periodic boundary conditions on the pseudosphere (or hyperbolic plane), the infinite two-dimensional Riemannian space of constant negative curvature. Starting from the common case of periodic boundary conditions in the Euclidean plane, we introduce all the required mathematical notions and sketch a classification of periodic boundary conditions on the hyperbolic plane. We stress the possible applications in statistical mechanics for studying the bulk behavior of physical systems, and illustrate how to implement such periodic boundary conditions in two examples, the dynamics of particles on the pseudosphere and the study of classical spins on hyperbolic lattices.
69 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 6 |
| 2020 | 4 |
| 2019 | 3 |
| 2018 | 2 |
| 2017 | 2 |
| 2016 | 1 |