arXiv subjects
Publications and source records attributed to Donghyun Kim.
We study the Cauchy problem for a system of cubic nonlinear Klein-Gordon equations in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the solution exists globally and decays of the order $O(t^{-1/2})$ in $L^\infty$ as $t$ tends to infinity without the condition of a compact support on the Cauchy data which was assumed in the previous works.
In this paper we present advancements in control and trajectory generation for agile behavior in bipedal robots. We demonstrate that Whole-Body Operational Space Control (WBOSC), developed a few years ago, is well suited for achieving two types of agile behaviors, namely, balancing on a high pitch split terrain and achieving undirected walking on flat terrain. The work presented here is the first implementation of WBOSC on a biped robot, and more specifically a biped robot with series elastic actuators. We present and analyze a new algorithm that dynamically balances point foot robots by choosing footstep placements. Dealing with the naturally unstable dynamics of these type of systems is a difficult problem that requires both the controller and the trajectory generation algorithm to operate quickly and efficiently. We put forth a comprehensive development and integration effort: the design and construction of the biped system and experimental infrastructure, a customization of WBOSC for the agile behaviors, and new trajectory generation algorithms. Using this custom built controller, we conduct, for first time, an experiment in which a biped robot balances in a high pitch split terrain, demonstrating our ability to precisely regulate internal forces using force sensing feedback techniques. Finally, we demonstrate the stabilizing capabilities of our online trajectory generation algorithm in the physics-based simulator and through physical experiments with a planarized locomotion setup.
In 2010 Spergel introduced an alternative to the traditional Sersic form for galactic luminosity profiles based on modified Bessel functions of the second kind. His motivation was the desire for an accurate one-parameter profile form with a simple Fourier transform (in contrast to the Fourier transform of the Sersic profile which can't be written in closed form), but we have found that the Spergel profile almost universally makes integrals easier when it replaces the Sersic profile in the integrand. In the original paper on the subject Spergel noted that his profile seems to fit galaxies on average just as well as Sersic's. Here we make this observation quantitative by comparing the residuals from fitting Sersic and Spergel forms to data. We find that the Spergel profile actually fits better than the Sersic for a random sample of 16 galaxies.
We consider the initial value problem for a system of cubic nonlinear Schrödinger equations with different masses in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the small amplitude solution exists globally and decays of the rate $O(t^{-1/2}(\log t)^{-1/2})$ in $L^\infty$ as $t$ tends to infinity, if the system satisfies certain mass relations.
We study the Cauchy problem for systems of cubic nonlinear Klein-Gordon equations with different masses in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the solution exists globally and decays of the rate $O(t^{-(1/2-1/p)})$ in $L^p$, $p\in[2,\infty]$ as $t$ tends to infinity even in the case of mass resonance, if the Cauchy data are sufficiently small, smooth and compactly supported.
We consider the Cauchy problem for systems of cubic nonlinear Klein-Gordon equations in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the small amplitude solution gains an additional logarithmic decay in comparison with the free evolution in the sense of $L^p$, $2\le p \le \infty$.
We study O($N+1$) nonlinear $σ$-model in $(p+1+N)$-dimensional curved spacetime with negative cosmological constant, and find a new $σ$-lump solution with half-integer winding and divergent energy. When the spatial structure of $N$ extra-dimensions is determined by this global defect, a black $σp$-brane surrounded by the degenerated horizon is formed and its near-horizon geometry is identified as a warp geometry of cigar type.