# Hong Qin

## Contact Details

NameHong Qin |
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## Pubs By Year |
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## Pub CategoriesPhysics - Plasma Physics (33) Physics - Computational Physics (11) Physics - Accelerator Physics (9) Statistics - Theory (4) Mathematics - Statistics (4) Mathematical Physics (3) Statistics - Methodology (3) Quantum Physics (3) Mathematics - Mathematical Physics (3) Computer Science - Graphics (2) Nuclear Theory (2) Nonlinear Sciences - Pattern Formation and Solitons (1) Physics - Fluid Dynamics (1) Quantitative Biology - Molecular Networks (1) Quantitative Biology - Populations and Evolution (1) Physics - Atomic Physics (1) Mathematics - Numerical Analysis (1) Mathematics - Symplectic Geometry (1) Nuclear Experiment (1) Solar and Stellar Astrophysics (1) |

## Publications Authored By Hong Qin

The stochastic block model is widely used for detecting community structures in network data. How to test the goodness-of-fit of the model is one of the fundamental problems and has gained growing interests in recent years. In this paper, we propose a new goodness-of-fit test based on the maximum entry of the centered and re-scaled observed adjacency matrix for the stochastic block model in which the number of communities can be allowed to grow linearly with the number of nodes ignoring a logarithm factor. Read More

Affiliation network is one kind of two-mode social network with two different sets of nodes (namely, a set of actors and a set of social events) and edges representing the affiliation of the actors with the social events. Although a number of statistical models are proposed to analyze affiliation networks, the asymptotic behaviors of the estimator are still unknown or have not been properly explored. In this paper, we study an affiliation model with the degree sequence as the exclusively natural sufficient statistic in the exponential family distributions. Read More

In many biological, agricultural, military activity problems and in some quality control problems, it is almost impossible to have a fixed sample size, because some observations are always lost for various reasons. Therefore, the sample size itself is considered frequently to be a random variable (rv). The class of limit distribution functions (df's) of the random bivariate extreme generalized order statistics (GOS) from independent and identically distributed RV's are fully characterized. Read More

This paper presents Poisson vector graphics, an extension of the popular first-order diffusion curves, for generating smooth-shaded images. Armed with two new types of primitives, namely Poisson curves and Poisson regions, PVG can easily produce photorealistic effects such as specular highlights, core shadows, translucency and halos. Within the PVG framework, users specify color as the Dirichlet boundary condition of diffusion curves and control tone by offsetting the Laplacian, where both controls are simply done by mouse click and slider dragging. Read More

Proposals to reach the next generation of laser intensities through Raman or Brillouin backscattering have centered on optical frequencies. Higher frequencies are beyond the range of such methods mainly due to the wave damping that accompanies the higher density plasmas necessary for compressing higher frequency lasers. However, we find that an external magnetic field transverse to the direction of laser propagation can reduce the required plasma density. Read More

Structure-preserving geometric algorithm for the Vlasov-Maxwell (VM) equations is currently an active research topic. We show that spatially-discretized Hamiltonian systems for the VM equations admit a local energy conservation law in space-time. This is accomplished by proving that for a general spatially-discretized system, a global conservation law always implies a discrete local conservation law in space-time when the algorithm is local. Read More

An infinite dimensional canonical symplectic structure and structure-preserving geometric algorithms are developed for the photon-matter interactions described by the Schr\"odinger-Maxwell equations. The algorithms preserve the symplectic structure of the system and the unitary nature of the wavefunctions, and bound the energy error of the simulation for all time-steps. This new numerical capability enables us to carry out first-principle based simulation study of important photon-matter interactions, such as the high harmonic generation and stabilization of ionization, with long-term accuracy and fidelity. Read More

The number of constituent quark (NCQ) scaling behavior of elliptic flow has been systematically studied at the LHC energy within the framework of a multiphase transport model (AMPT) in this work. We find that the parameters used to generate the initial states and the collision centrality are important for the existence of NCQ scaling even when hadronic rescattering contribution is off in Pb-Pb collisions of $\sqrt{s_{NN}}=2.76$ TeV. Read More

Fusion energy will be the ultimate clean energy source for mankind. One of the most visible concerns of the future fusion device is the threat of deleterious runaway electrons (REs) produced during unexpected disruptions of the fusion plasma. Both efficient long-term algorithms and super-large scale computing power are necessary to reveal the complex dynamics of REs in a realistic fusion reactor. Read More

Estimating the number of communities is one of the fundamental problems in the stochastic block model. We re-examine the Bayesian paradigm for stochastic block models and propose a "corrected Bayesian information criterion", to decide the block number and show that the produced estimator is consistent. The novel penalty function improves those used in Wang and Bickel (2016) and Saldana, Yu and Feng (2016) which tend to underestimate and overestimate the block number, respectively. Read More

A manifestly covariant, or geometric, field theory for relativistic classical particle-field system is developed. The connection between space-time symmetry and energy-momentum conservation laws for the system is established geometrically without splitting the space and time coordinates, i.e. Read More

Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. It is often multi-scale and requires accurate long-term numerical simulations using symplectic integrators. For modern large-scale particle simulations in complex, time-dependent electromagnetic field, explicit symplectic algorithms are much more preferable. Read More

In an uncoupled linear lattice system, the Kapchinskij-Vladimirskij (KV) distribution, formulated on the basis of the single-particle Courant-Snyder (CS) invariants, has served as a fundamental theoretical basis for the analyses of the equilibrium, stability, and transport properties of high-intensity beams for the past several decades. Recent applications of high-intensity beams, however, require beam phase-space manipulations by intentionally introducing strong coupling. In this Letter, we report the full generalization of the KV model by including all of the linear (both external and space-charge) coupling forces, beam energy variations, and arbitrary emittance partition, which all form essential elements for phase-space manipulations. Read More

**Category:**Physics - Plasma Physics

The Accurate Particle Tracer (APT) code is designed for large-scale particle simulations on dynamical systems. Based on a large variety of advanced geometric algorithms, APT possesses long-term numerical accuracy and stability, which are critical for solving multi-scale and non-linear problems. Under the well-designed integrated and modularized framework, APT serves as a universal platform for researchers from different fields, such as plasma physics, accelerator physics, space science, fusion energy research, computational mathematics, software engineering, and high-performance computation. Read More

In this paper, the Lorentz covariance of algorithms is introduced. Under Lorentz transformation, both the form and performance of a Lorentz covariant algorithm are invariant. To acquire the advantages of symplectic algorithms and Lorentz covariance, a general procedure for constructing Lorentz covariant canonical symplectic algorithms (LCCSA) is provided, based on which an explicit LCCSA for dynamics of relativistic charged particles is built. Read More

We show that the geometric phase of the gyro-motion of a classical charged particle in a uniform time-dependent magnetic field described by Newton's equation can be derived from a coherent Berry phase for the coherent states of the Schroedinger equation or the Dirac equation. This correspondence is established by constructing coherent states for a particle using the energy eigenstates on the Landau levels and proving that the coherent states can maintain their status of coherent states during the slow varying of the magnetic field. It is discovered that orbital Berry phases of the eigenstates interfere coherently to produce an observable effect (which we termed "coherent Berry phase"), which is exactly the geometric phase of the classical gyro-motion. Read More

Exact eigen modes with orbital angular momentum (OAM) in the complex media of unmagnetized homogeneous plasma are studied. Three exact eigen modes with OAM are discovered, i.e. Read More

We study the time evolution of the magnetic field in a plasma with a chiral magnetic current. The Vector Spherical Harmonic functions (VSH) are used to expand all fields. We define a measure for the Chandrasekhar-Kendall-Woltjer (CKW) state, which has a simple form in VSH expansion. Read More

We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general construction of volume-preserving methods that can be applied to systems with time-dependent electromagnetic fields. The newly derived methods provide numerical solutions with good accuracy and conservative properties over long time of simulation. Read More

An explicit high-order noncanonical symplectic algorithm for ideal two-fluid systems is developed. The fluid is discretized as particles in the Lagrangian description, while the electromagnetic fields and internal energy are treated as discrete differential form fields on a fixed mesh. With the assistance of Whitney interpolating forms, this scheme preserves the gauge symmetry of the electromagnetic field, and the pressure field is naturally derived from the discrete internal energy. Read More

In this paper, we develop Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations by applying conforming finite element methods in space and splitting methods in time. For the spatial discretisation, the criteria for choosing finite element spaces are presented such that the semi-discrete system possesses a discrete non-canonical Poisson structure. We apply a Hamiltonian splitting method to the semi-discrete system in time, then the resulting algorithm is Poisson preserving and explicit. Read More

In this paper, the secular full-orbit simulations of runaway electrons with synchrotron radiation in tokamak fields are carried out using a relativistic volume-preserving algorithm. Detailed phase-space behaviors of runaway electrons are investigated in different dynamical timescales spanning 11 orders. When looking into the small timescale, i. Read More

Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term accuracy and fidelity. For long-term simulations with high efficiency, explicit symplectic algorithms are desirable. However, it is widely accepted that explicit symplectic algorithms are only available for sum-separable Hamiltonians, and that this restriction severely limits the application of explicit symplectic algorithms to charged particle dynamics. Read More

We report the discovery of an envelope Hamiltonian describing the charged-particle dynamics in general linear coupled lattices. Read More

The two-stream instability is probably the most important elementary example of collective instabilities in plasma physics and beam-plasma systems. For a warm plasma with two charged particle species based on a 1D warm-fluid model, the instability diagram of the two-stream instability exhibits an interesting band structure that has not been explained. We show that the band structure for this instability is the consequence of the Hamiltonian nature of the warm two-fluid system. Read More

A relativistic quantum field theory with nontrivial background fields is developed and applied to study waves in plasmas. The effective action of the electromagnetic 4-potential is calculated ab initio from the standard action of scalar QED using path integrals. The resultant effective action is gauge invariant and contains nonlocal interactions, from which gauge bosons acquire masses without breaking the local gauge symmetry. Read More

The well observed inward drift of current carrying runaway electrons during runaway plateau regime after disruption is studied by considering the phase space dynamic of runaways in a large aspect ratio toroidal system. We consider the case where the toroidal field is unperturbed and the toroidal symmetry of the system is preserved. The balance between the change in canonical angular momentum and the input of mechanical angular momentum in such system requires runaways to drift horizontally in configuration space for any given change in momentum space. Read More

Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithm conserves a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially-discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. Read More

It is discovered that the tokamak field geometry generates a pitch-angle scattering effect for runaway electrons. This neoclassical pitch-angle scattering is much stronger than the collisional scattering and invalidates the gyro-center model for runaway electrons. As a result, the energy limit of runaway electrons is found to be larger than the prediction of the gyro-center model and to depend heavily on the background magnetic field. Read More

Recently a variational integrator for ideal magnetohydrodynamics in Lagrangian labeling has been developed. Its built-in frozen-in equation makes it optimal for studying current sheet formation. We use this scheme to study the Hahm-Kulsrud-Taylor problem, which considers the response of a 2D plasma magnetized by a sheared field under sinusoidal boundary forcing. Read More

We study the non-canonical symplectic structure, or K-symplectic structure inherited by the charged particle dynamics. Based on the splitting technique, we construct non-canonical symplectic methods which is explicit and stable for the long-term simulation. The key point of splitting is to decompose the Hamiltonian as four parts, so that the resulting four subsystems have the same structure and can be solved exactly. Read More

In this paper, the nonlinear mode conversion of extraordinary waves in nonuniform magnetized plasmas is studied using the variational symplectic particle-in-cell simulation. The accuracy of the nonlinear simulation is guaranteed by the long-term accuracy and conservativeness of the symplectic algorithm. The spectra of the electromagnetic wave, the evolution of the wave reflectivity, the energy deposition profile, and the parameter-dependent properties of radio-frequency waves during the nonlinear mode conversion are investigated. Read More

Hamiltonian integration methods for the Vlasov-Maxwell equations are developed by a Hamiltonian splitting technique. The Hamiltonian functional is split into five parts, i.e. Read More

The paper [1] by Crouseilles, Einkemmer, and Faou used an incorrect Poisson bracket for the Vlasov-Maxwell equations. If the correct Poisson bracket is used, the solution of one of the subsystems cannot be computed exactly in general. As a result, one cannot construct a symplectic scheme for the Vlasov-Maxwell equations using the splitting Hamiltonian method proposed in Ref [1]. Read More

The dynamics of charged particles in general linear focusing lattices with quadrupole, skew-quadrupole, dipole, and solenoidal components, as well as torsion of the fiducial orbit and variation of beam energy is parameterized using a generalized Courant-Snyder (CS) theory, which extends the original CS theory for one degree of freedom to higher dimensions. The envelope function is generalized into an envelope matrix, and the phase advance is generalized into a 4D symplectic rotation, or an U(2) element. The 1D envelope equation, also known as the Ermakov-Milne-Pinney equation in quantum mechanics, is generalized to an envelope matrix equation in higher dimensions. Read More

It has been realized in recent years that coupled focusing lattices in accelerators and storage rings have significant advantages over conventional uncoupled focusing lattices, especially for high-intensity charged particle beams. A theoretical framework and associated tools for analyzing the spectral and structural stability properties of coupled lattices are formulated in this paper, based on the recently developed generalized Courant-Snyder theory for coupled lattices. It is shown that for periodic coupled lattices that are spectrally and structurally stable, the matrix envelope equation must admit matched solutions. Read More

This paper makes use of a one-dimensional kinetic model to investigate the nonlinear longitudinal dynamics of a long coasting beam propagating through a perfectly conducting circular pipe with radius $r_{w}$. The average axial electric field is expressed as $\langle E_{z}\rangle=-(\partial/\partial z)\langle\phi\rangle=-e_{b}g_{0}\partial\lambda_{b}/\partial z-e_{b}g_{2}r_{w}^{2}\partial^{3}\lambda_{b}/\partial z^{3}$, where $g_{0}$ and $g_{2}$ are constant geometric factors, $\lambda_{b}(z,t)=\int dp_{z}F_{b}(z,p_{z},t)$ is the line density of beam particles, and $F_{b}(z,p_{z},t)$ satisfies the 1D Vlasov equation. Detailed nonlinear properties of traveling-wave and traveling-pulse (solitons) solutions with time-stationary waveform are examined for a wide range of system parameters extending from moderate-amplitudes to large-amplitude modulations of the beam charge density. Read More

It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g. Read More

Massive runaway positrons are generated by runaway electrons in tokamaks. The fate of these positrons encodes valuable information about the runaway dynamics. The phase space dynamics of a runaway position is investigated using a Lagrangian that incorporates the tokamak geometry, loop voltage, radiation and collisional effects. Read More

**Authors:**Hong Qin, Jian Liu, Jianyuan Xiao, Ruili Zhang, Yang He, Yulei Wang, Yajuan Sun, Joshua W. Burby, Leland Ellison, Yao Zhou

Particle-in-Cell (PIC) simulation is the most important numerical tool in plasma physics. However, its long-term accuracy has not been established. To overcome this difficulty, we developed a canonical symplectic PIC method for the Vlasov-Maxwell system by discretizing its canonical Poisson bracket. Read More

Newcomb's Lagrangian for ideal magnetohydrodynamics (MHD) in Lagrangian labeling is discretized using discrete exterior calculus. Variational integrators for ideal MHD are derived thereafter. Besides being symplectic and momentum-preserving, the schemes inherit built-in advection equations from Newcomb's formulation, and therefore avoid solving them and the accompanying error and dissipation. Read More

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. Read More

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. Read More

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. Read More

Maximum entropy models, motivated by applications in neuron science, are natural generalizations of the $\beta$-model to weighted graphs. Similar to the $\beta$-model, each vertex in maximum entropy models is assigned a potential parameter, and the degree sequence is the natural sufficient statistic. Hillar and Wibisono (2013) has proved the consistency of the maximum likelihood estimators. Read More

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. Read More

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. Read More

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. Read More