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Li Chen

Publications and source records attributed to Li Chen.

At least 739 records · Page 41Linked to original sources
arXiv2012

A Test for Radial Mixing Using Local Star Samples

We use samples of local main-sequence stars to show that the radial gradient of [Fe/H] in the thin disk of the Milky Way decreases with mean effective stellar temperature. Many of these stars are visiting the solar neighborhood from the inner and outer Galaxy. We use the angular momentum of each star about the Galactic center to determine the guiding center radius and to eliminate the effects of epicyclic motion, which would otherwise blur the estimated gradients. We interpret the effective temperature as a proxy for mean age, and conclude that the decreasing gradient is consistent with the predictions of radial mixing due to transient spiral patterns. We find some evidence that the trend of decreasing gradient with increasing mean age breaks to a constant gradient for samples of stars whose main-sequence life-times exceed the likely age of the thin disk.

astro-ph.GA↗
arXiv2012

Spectral Lags Obtained by CCF of Smoothed Lightcurves

We present a new technique to calculate the spectral lags of gamma-ray bursts (GRBs). Unlike previous processing methods, we first smooth the light curves of gamma-ray bursts in high and low energy bands using the "Loess" filter, then, we directly define the spectral lags as such to maximize the cross-correlation function (CCF) between two smoothed light curves. This method is suitable for various shapes of CCF; it effectively avoids the errors caused by manual selections for the fitting function and fitting interval. Using the method, we have carefully measured the spectral lags of individual pulses contained in BAT/Swift gamma-ray bursts with known redshifts, and confirmed the anti-correlation between the spectral lag and the isotropy luminosity. The distribution of spectral lags can be well fitted by four Gaussian components, with the centroids at 0.03 s, 0.09 s, 0.15 s, and 0.21 s, respectively. We find that some spectral lags of the multi-peak GRBs seem to evolve with time.

astro-ph.HE↗
arXiv2011

A stochastic maximum principle for backward delayed system via advanced stochastic differential equation (ASDE)

The main contributions of this paper are three fold. First, our primary concern is to investigate a class of stochastic recursive delayed control problems which arise naturally with sound backgrounds but have not been well-studied yet. For illustration purpose, some concrete examples are also provided here. We derive the stochastic maximum principle of sufficient condition to the optimal control in both cases with and without control delay. Second, it is interesting that a new class of time-advanced stochastic differential equations (ASDEs) is introduced as the adjoint process via duality relation. To our best knowledge, such equations have never been discussed in literature although they possess more academic values besides the control study here. Some existence and uniqueness result to ASDEs is presented. Third, to illustrate our theoretical results, some dynamic optimization problems are discussed based on our stochastic maximum principles. In particular, the optimal controls are derived explicitly by solving the associated time-advanced ordinary differential equation (AODE), the counterpart of the ASDE in its deterministic setup.

math.OC↗
arXiv2011

Harmonic Functions for Data Reconstruction on 3D Manifolds

In computer graphics, smooth data reconstruction on 2D or 3D manifolds usually refers to subdivision problems. Such a method is only valid based on dense sample points. The manifold usually needs to be triangulated into meshes (or patches) and each node on the mesh will have an initial value. While the mesh is refined the algorithm will provide a smooth function on the redefined manifolds. However, when data points are not dense and the original mesh is not allowed to be changed, how is the "continuous and/or smooth" reconstruction possible? This paper will present a new method using harmonic functions to solve the problem. Our method contains the following steps: (1) Partition the boundary surfaces of the 3D manifold based on sample points so that each sample point is on the edge of the partition. (2) Use gradually varied interpolation on the edges so that each point on edge will be assigned a value. In addition, all values on the edge are gradually varied. (3) Use discrete harmonic function to fit the unknown points, i.e. the points inside each partition patch. The fitted function will be a harmonic or a local harmonic function in each partitioned area. The function on edge will be "near" continuous (or "near" gradually varied). If we need a smoothed surface on the manifold, we can apply subdivision algorithms. This paper has also a philosophical advantage over triangulation meshes. People usually use triangulation for data reconstruction. This paper employs harmonic functions, a generalization of triangulation because linearity is a form of harmonic. Therefore, local harmonic initialization is more sophisticated then triangulation. This paper is a conceptual and methodological paper. This paper does not focus on detailed mathematical analysis nor fine algorithm design.

math.NA↗
arXiv2011

Rate of Convergence in Nonlinear Hartree Dynamics with Factorized Initial Data

The mean field dynamics of an $N$-particle weekly interacting Boson system can be described by the nonlinear Hartree equation. In this paper, we present estimates on the 1/N rate of convergence of many-body Schrödinger dynamics to the one-body nonlinear Hartree dynamics with factorized initial data with two-body interaction potential $V$ in $L^3 (\mathbb{R}^3)+ L^{\infty} (\mathbb{R}^3)$.

math-ph↗
arXiv2011

Rate of Convergence Towards Hartree Dynamics

We consider a system of N bosons interacting through a two-body potential with, possibly, Coulomb-type singularities. We show that the difference between the many-body Schrödinger evolution in the mean-field regime and the effective nonlinear Hartree dynamics is at most of the order 1/N, for any fixed time. The N-dependence of the bound is optimal.

math-ph↗
arXiv2011

Rapid dynamical mass segregation and properties of fractal star clusters

We investigate the evolution of young star clusters using N-body simulations. We confirm that subvirial and fractal-structured clusters will dynamically mass segregate on a short timescale (within 0.5 Myr). We adopt a modified minimum-spanning-tree (MST) method to measure the degree of mass segregation, demonstrating that the stars escaping from a cluster's potential are important for the temporal dependence of mass segregation in the cluster. The form of the initial velocity distribution will also affect the degree of mass segregation. If it depends on radius, the outer parts of the cluster would expand without undergoing collapse. In velocity space, we find 'inverse mass segregation,' which indicates that massive stars have higher velocity dispersions than their lower-mass counterparts.

astro-ph.GA↗
arXiv2010

XMM-Newton observation of the eclipsing binary Algol

We present an {\sl XMM-Newton} observation of the eclipsing binary Algol which contains an X-ray dark B8V primary and an X-ray bright K2IV secondary. The observation covered the optical secondary eclipse and captured an X-ray flare that was eclipsed by the B star. The EPIC and RGS spectra of Algol in its quiescent state are described by a two-temperature plasma model. The cool component has a temperature around 6.4$\times 10^{6}$ K while that of the hot component ranges from 2 to 4.0$\times 10^{7}$ K. Coronal abundances of C, N, O, Ne, Mg, Si and Fe were obtained for each component for both the quiescent and the flare phases, with generally upper limits for S and Ar, and C, N, and O for the hot component. F-tests show that the abundances need not to be different between the cool and the hot component and between the quiescent and the flare phase with the exception of Fe. Whereas the Fe abundance of the cool component remains constant at $\sim$0.14, the hot component shows an Fe abundance of $\sim$0.28, which increases to $\sim$0.44 during the flare. This increase is expected from the chromospheric evaporation model. The absorbing column density $N_H$ of the quiescent emission is 2.5$\times10^{20}$ cm$^{-2}$, while that of the flare-only emission is significantly lower and consistent with the column density of the interstellar medium. This observation substantiates earlier suggestions of the presence of X-ray absorbing material in the Algol system.

astro-ph↗
arXiv2010

A Digital-Discrete Method For Smooth-Continuous Data Reconstruction

A systematic digital-discrete method for obtaining continuous functions with smoothness to a certain order (C^(n)) from sample data is designed. This method is based on gradually varied functions and the classical finite difference method. This new method has been applied to real groundwater data and the results have validated the method. This method is independent from existing popular methods such as the cubic spline method and the finite element method. The new digital-discrete method has considerable advantages for a large number of real data applications. This digital method also differs from other classical discrete methods that usually use triangulations. This method can potentially be used to obtain smooth functions such as polynomials through its derivatives f^(k) and the solution for partial differential equations such as harmonic and other important equations.

math.NA↗
arXiv2010

Smoothness and Smooth Extensions (I): Generalization of MWK Functions and Gradually Varied Functions

A mathematical smooth function means that the function has continuous derivatives to a certain degree C(k). We call it a k-smooth function or a smooth function if k can grow infinitively. Based on quantum physics, there is no such smooth surface in the real world on a very small scale. However, we do have a concept of smooth surfaces in practice since we always compare whether one surface is smoother than another one. This paper deals with the possible definitions of "natural" smoothness and their relationship to the original mathematical definition of smooth functions. The motivation of giving the definition of a smooth function is to study smooth extensions for practical applications. We observe this problem from two directions: From discrete to continuous, we suggest considering both micro smooth, the refinement of a smoothed function, and macro smooth, the best approximation using existing discrete space. (For two-dimensional or higher dimensional cases, we can use Hessian matrices.) From continuous to discrete, we suggest a new definition of natural smooth, it uses a scan from down scaling to up scaling to obtain the a ratio for sign changes by ignoring zero to represent the smoothness. For differentiable functions, mathematical smoothness does not mean a "good looking" smooth for a sampled set in discrete space. Finally, we discuss the Lipschitz continuity for defining the smoothness, which will be called discrete smoothness. This paper gives philosophical consideration of smoothness for practical problems, rather than a mathematical deduction or reduction, even though our inferences are based on solid mathematics.

math.NA↗
arXiv2010

Applications of the Digital-Discrete Method in Smooth-Continuous Data Reconstruction

This paper presents some applications using recently developed algorithms for smooth-continuous data reconstruction based on the digital-discrete method. The classical discrete method for data reconstruction is based on domain decomposition according to guiding (or sample) points. Then the Spline method (for polynomial) or finite elements method (for PDE) is used to fit the data. Our method is based on the gradually varied function that does not assume the property of being linearly separable among guiding points, i.e. no domain decomposition methods are needed. We also demonstrate the flexibility of the new method and its potential to solve a variety of problems. The examples include some real data from water well logs and harmonic functions on closed 2D manifolds. This paper presents the results from six different algorithms. This method can be easily extended to higher multi-dimensions. We also include an advanced consideration related to the use of gradually varied mapping.

math.NA↗
arXiv2010

Applications of the Digital-Discrete Method in Smooth-Continuous Data Reconstruction

This paper presents some applications of using recently developed algorithms for smooth-continuous data reconstruction based on the digital-discrete method. The classical discrete method for data reconstruction is based on domain decomposition according to guiding (or sample) points. Then uses Splines (for polynomial) or finite elements method (for PDE) to fit the data. Our method is based on the gradually varied function that does not assume the property of the linearly separable among guiding points, i.e. no domain decomposition methods are needed. We also demonstrate the flexibility of the new method and the potential to solve variety of problems. The examples include some real data from water well logs and harmonic functions on closed 2D manifolds. This paper presented the results from six different algorithms. This method can be easily extended to higher multi-dimensions.

math.NA↗
arXiv2010

Digital-Discrete Surface Reconstruction: A true universal and nonlinear method

The most common problem in data reconstruction is to fit a function based on the observations of some sample (guiding) points. This paper provides a methodological point of view of digital-discrete surface reconstruction. We explain our method along with why it is a truly universal and nonlinear method unlike most popular methods, which are linear and restricted. This paper focuses on what the surface reconstruction problem is and why the digital-discrete method is important, necessary, and how it can be accomplished.

math.NA↗
arXiv2010

Gradual Variation Analysis for Groundwater Flow

Groundwater flow in Washington DC greatly influences the surface water quality in urban areas. The current methods of flow estimation, based on Darcy's Law and the groundwater flow equation, can be described by the diffusion equation (the transient flow) and the Laplace equation (the steady-state flow). The Laplace equation is a simplification of the diffusion equation under the condition that the aquifer has a recharging boundary. The practical way of calculation is to use numerical methods to solve these equations. The most popular system is called MODFLOW, which was developed by USGS. MODFLOW is based on the finite-difference method in rectangular Cartesian coordinates. MODFLOW can be viewed as a "quasi 3D" simulation since it only deals with the vertical average (no z-direction derivative). Flow calculations between the 2D horizontal layers use the concept of leakage. In this project, we have established a mathematical model based on gradually varied functions for groundwater data volume reconstruction. These functions do not rely on the rectangular Cartesian coordinate system. A gradually varied function can be defined in a general graph or network. Gradually varied functions are suitable for arbitrarily shaped aquifers. Two types of models are designed and implemented for real data processing: (1) the gradually varied model for individual (time) groundwater flow data, (2) the gradually varied model for sequential (time) groundwater flow data. In application, we also established a MySQL database to support the related research. The advantage of the gradually varied fitting and its related method does not need the strictly defined boundary condition as it is required in MODFLOW.

math.NA↗
arXiv2009

Genus Computing for 3D digital objects: algorithm and implementation

This paper deals with computing topological invariants such as connected components, boundary surface genus, and homology groups. For each input data set, we have designed or implemented algorithms to calculate connected components, boundary surfaces and their genus, and homology groups. Due to the fact that genus calculation dominates the entire task for 3D object in 3D space, in this paper, we mainly discuss the calculation of the genus. The new algorithms designed in this paper will perform: (1) pathological cases detection and deletion, (2) raster space to point space (dual space) transformation, (3) the linear time algorithm for boundary point classification, and (4) genus calculation.

cs.CV↗
arXiv2009

A Note on Gradually Varied Functions and Harmonic Functions

Any constructive continuous function must have a gradually varied approximation in compact space. However, the refinement of domain for $σ-$-net might be very small. Keeping the original discretization (square or triangulation), can we get some interesting properties related to gradual variation? In this note, we try to prove that many harmonic functions are gradually varied or near gradually varied; this means that the value of the center point differs from that of its neighbor at most by 2. It is obvious that most of the gradually varied functions are not harmonic.This note discusses some of the basic harmonic functions in relation to gradually varied functions.

cs.DM↗
arXiv2009

Digital Curvatures Applied to 3D Object Analysis and Recognition: A Case Study

In this paper, we propose using curvatures in digital space for 3D object analysis and recognition. Since direct adjacency has only six types of digital surface points in local configurations, it is easy to determine and classify the discrete curvatures for every point on the boundary of a 3D object. Unlike the boundary simplicial decomposition (triangulation), the curvature can take any real value. It sometimes makes difficulties to find a right value for threshold. This paper focuses on the global properties of categorizing curvatures for small regions. We use both digital Gaussian curvatures and digital mean curvatures to 3D shapes. This paper proposes a multi-scale method for 3D object analysis and a vector method for 3D similarity classification. We use these methods for face recognition and shape classification. We have found that the Gaussian curvatures mainly describe the global features and average characteristics such as the five regions of a human face. However, mean curvatures can be used to find local features and extreme points such as nose in 3D facial data.

cs.CG↗