arXiv subjects

Hong Qin

Publications and source records attributed to Hong Qin.

168 records · Page 10Linked to original sources

arXiv2014

Gauge properties of the guiding center variational symplectic integrator

Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields. As a direct consequence of their derivation from a discrete variational principle, these algorithms have very good long-time energy conservation, as well as exactly preserving discrete momenta. We present stability results for these algorithms, focusing on understanding how explicit variational integrators can be designed for this type of system. It is found that for explicit algorithms an instability arises because the discrete symplectic structure does not become the continuous structure in the $t \rightarrow 0$ limit. We examine how a generalized gauge transformation can be used to put the Lagrangian in the "antisymmetric discretization gauge," in which the discrete symplectic structure has the correct form, thus eliminating the numerical instability. Finally, it is noted that the variational guiding center algorithms are not electromagnetically gauge invariant. By designing a model discrete Lagrangian, we show that the algorithms are approximately gauge invariant as long as $\boldsymbol{A}$ and $ϕ$ are relatively smooth. A gauge invariant discrete Lagrangian is very important in a variational particle-in-cell algorithm where it ensures current continuity and preservation of Gauss's law

physics.plasm-ph↗

arXiv2014

Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme

A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of Discrete Exterior Calculus, the field solver, interpolation scheme and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law.

physics.plasm-ph↗

arXiv2014

VEST: abstract vector calculus simplification in Mathematica

We present a new package, VEST (Vector Einstein Summation Tools), that performs abstract vector calculus computations in Mathematica. Through the use of index notation, VEST is able to reduce three-dimensional scalar and vector expressions of a very general type to a well defined standard form. In addition, utilizing properties of the Levi-Civita symbol, the program can derive types of multi-term vector identities that are not recognized by reduction, subsequently applying these to simplify large expressions. In a companion paper (Burby et al., 2013), we employ VEST in the automation of the calculation of high-order Lagrangians for the single particle guiding center system in plasma physics, a computation which illustrates its ability to handle very large expressions. VEST has been designed to be simple and intuitive to use, both for basic checking of work and more involved computations.

physics.comp-ph↗

arXiv2013

A network model for cellular aging

What is aging? Mechanistic answers to this question remain elusive despite decades of research. Here, we propose a mathematical model of cellular aging based on a model gene interaction network. Our network model is made of only non-aging components - the biological functions of gene interactions decrease with a constant mortality rate. Death of a cell occurs in the model when an essential gene loses all of its interactions to other genes, equivalent to the deletion of an essential gene. Gene interactions are stochastic based on a binomial distribution. We show that the defining characteristic of biological aging, the exponential increase of mortality rate over time, can arise from this gene network model during the early stage of aging. Hence, we demonstrate that cellular aging is an emergent property of this model network. Our model predicts that the rate of aging, defined by the Gompertz coefficient, is approximately proportional to the average number of active interactions per gene and that the stochastic heterogeneity of gene interactions is an important factor in the dynamics of the aging process. This theoretic framework offers a mechanistic foundation for the pleiotropic nature of aging and can provide insights on cellular aging.

q-bio.MN↗

arXiv2013

4-Dimensional Geometry Lens: A Novel Volumetric Magnification Approach

We present a novel methodology that utilizes 4-Dimensional (4D) space deformation to simulate a magnification lens on versatile volume datasets and textured solid models. Compared with other magnification methods (e.g., geometric optics, mesh editing), 4D differential geometry theory and its practices are much more flexible and powerful for preserving shape features (i.e., minimizing angle distortion), and easier to adapt to versatile solid models. The primary advantage of 4D space lies at the following fact: we can now easily magnify the volume of regions of interest (ROIs) from the additional dimension, while keeping the rest region unchanged. To achieve this primary goal, we first embed a 3D volumetric input into 4D space and magnify ROIs in the 4th dimension. Then we flatten the 4D shape back into 3D space to accommodate other typical applications in the real 3D world. In order to enforce distortion minimization, in both steps we devise the high dimensional geometry techniques based on rigorous 4D geometry theory for 3D/4D mapping back and forth to amend the distortion. Our system can preserve not only focus region, but also context region and global shape. We demonstrate the effectiveness, robustness, and efficacy of our framework with a variety of models ranging from tetrahedral meshes to volume datasets.

cs.GR↗

arXiv2013

A Lagrangian perspective on the stability of ideal MHD equilibria with flow

We take a careful look at two approaches to deriving stability criteria for ideal MHD equilibria. One is based on a tedious analysis of the linearized equations of motion, while the other examines the second variation of the MHD Hamiltonian computed with proper variational constraints. For equilibria without flow, the two approaches are known to be fully consistent. However, for equilibria with flow, the stability criterion obtained from the constrained variation approach was claimed to be stronger than that derived using the linearized equations of motion. We show this claim is incorrect by deriving and comparing both criteria within the same framework. It turns out that the criterion obtained from the constrained variation approach has stricter requirements on the initial perturbations than the other. Such requirements naturally emerge in our new treatment of the constrained variation approach using the Euler-Poincaré structure of ideal MHD, which is more direct and simple than the previous derivation from the Poisson perspective.

physics.plasm-ph↗