arXiv subjects

Hong Qin

Publications and source records attributed to Hong Qin.

At least 109 records · Page 6Linked to original sources

arXiv2020

Energy Transformations in a Relativistic Engine

In a previous paper we have shown that Newton's third law cannot strictly hold in a distributed system of which the different parts are at a finite distance from each other. This is due to the finite speed of signal propagation which cannot exceed the speed of light at vacuum, which in turn means that when summing the total force in the system the force does not add up to zero. This was demonstrated in a specific example of two current loops with time dependent currents, the above analysis led to suggestion of a relativistic engine. Since the system is effected by a total force for a finite period of time this means that the system acquires mechanical momentum and energy, the question then arises how can we accommodate the law of momentum and energy conservation. The subject of momentum conversation was discussed in a previous paper, while preliminary results regarding energy conservation were discussed in previous papers. Here we give a complete analysis of the exchange of energy between the mechanical part of the relativistic engine and the field part, the energy radiated from the relativistic engine is also discussed. We show that the relativistic engine effect on the energy is 4th-order in 1/c and no lower order relativistic engine effect on the energy exist.

physics.gen-ph↗

arXiv2020

The Physics of Spontaneous Parity-Time Symmetry Breaking in the Kelvin-Helmholtz Instability

We show that the dynamics, in particular the Kelvin-Helmholtz (KH) instability, of an inviscid fluid with velocity shear admits Parity-Time (PT) symmetry, which provides a physical explanation to the well-known observation that the spectrum of the perturbation eigenmodes of the system is symmetric with respect to the real axis. It is found that the KH instability is triggered when and only when the PT symmetry is spontaneously broken. The analysis of PT symmetry also reveals that the relative phase between parallel velocity and pressure perturbations needs to be locked at $π/2$ when the instability is suppressed.

physics.plasm-ph↗

arXiv2019

Machine learning and serving of discrete field theories -- when artificial intelligence meets the discrete universe

A method for machine learning and serving of discrete field theories in physics is developed. The learning algorithm trains a discrete field theory from a set of observational data on a spacetime lattice, and the serving algorithm uses the learned discrete field theory to predict new observations of the field for new boundary and initial conditions. The approach to learn discrete field theories overcomes the difficulties associated with learning continuous theories by artificial intelligence. The serving algorithm of discrete field theories belongs to the family of structure-preserving geometric algorithms, which have been proven to be superior to the conventional algorithms based on discretization of differential equations. The effectiveness of the method and algorithms developed is demonstrated using the examples of nonlinear oscillations and the Kepler problem. In particular, the learning algorithm learns a discrete field theory from a set of data of planetary orbits similar to what Kepler inherited from Tycho Brahe in 1601, and the serving algorithm correctly predicts other planetary orbits, including parabolic and hyperbolic escaping orbits, of the solar system without learning or knowing Newton's laws of motion and universal gravitation. The proposed algorithms are also applicable when effects of special relativity and general relativity are important. The illustrated advantages of discrete field theories relative to continuous theories in terms of machine learning compatibility are consistent with Bostrom's simulation hypothesis.

physics.comp-ph↗

arXiv2019

Linear Beam Stability in Periodic Focusing Systems:Krein Signature and Band Structure

The general question of how a beam becomes unstable has been one of the fundamental research topics among beam and accelerator physicists for several decades. In this study, we revisited the general problem of linear beam stability in periodic focusing systems by applying the concepts of Krein signature and band structure. We numerically calculated the eigenvalues and other associated characteristics of one-period maps, and discussed the stability properties of single-particle motions with skew quadrupoles and envelope perturbations in high-intensity beams on an equal footing. In particular, an application of the Krein theory to envelope instability analysis was newly attempted in this study. The appearance of instabilities is interpreted as the result of the collision between eigenmodes of opposite Krein signatures and the formation of a band gap.

physics.acc-ph↗

arXiv2019

Corrected Bayesian information criterion for stochastic block models

Estimating the number of communities is one of the fundamental problems in community detection. We re-examine the Bayesian paradigm for stochastic block models and propose a "corrected Bayesian information criterion",to determine the number of communities and show that the proposed estimator is consistent under mild conditions. The proposed criterion improves those used in Wang and Bickel (2016) and Saldana et al. (2017) which tend to underestimate and overestimate the number of communities, respectively. Along the way, we establish the Wilks theorem for stochastic block models. Moreover, we show that, to obtain the consistency of model selection for stochastic block models, we need a so-called "consistency condition". We also provide sufficient conditions for both homogenous networks and non-homogenous networks. The results are further extended to degree corrected stochastic block models. Numerical studies demonstrate our theoretical results.

stat.ME↗

arXiv2019

Using Maximum Entry-Wise Deviation to Test the Goodness-of-Fit for Stochastic Block Models

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 article, we propose a novel goodness-of-fit test based on the maximum entry of the centered and re-scaled adjacency matrix for the stochastic block model. One noticeable advantage of the proposed test is that the number of communities can be allowed to grow linearly with the number of nodes ignoring a logarithmic factor. We prove that the null distribution of the test statistic converges in distribution to a Gumbel distribution, and we show that both the number of communities and the membership vector can be tested via the proposed method. Further, we show that the proposed test has asymptotic power guarantee against a class of alternatives. We also demonstrate that the proposed method can be extended to the degree-corrected stochastic block model. Both simulation studies and real-world data examples indicate that the proposed method works well.

stat.ME↗

arXiv2019

General field theory and weak Euler-Lagrange equation for classical particle-field systems in plasma physics

A general field theory for classical particle-field systems is developed. Compared with the standard classical field theory, the distinguish feature of a classical particle-field system is that the particles and fields reside on different manifolds. The fields are defined on the 4D space-time, whereas each particle's trajectory is defined on the 1D time-axis. As a consequence, the standard Noether's procedure for deriving local conservation laws in space-time from symmetries is not applicable without modification. To overcome this difficulty, a weak Euler-Lagrange equation for particles is developed on the 4D space-time, which plays a pivotal role in establishing the connections between symmetries and local conservation laws in space-time. Especially, the non-vanishing Euler derivative in the weak Euler-Lagrangian equation generates a new current in the conservation laws. Several examples from plasma physics are studied as special cases of the general field theory. In particular, the relations between the rotational symmetry and angular momentum conservation for the Klimontovich-Poisson system and the Klimontovich-Darwin system are established.

physics.plasm-ph↗

arXiv2019

Structure-preserving geometric particle-in-cell algorithm suppresses finite-grid instability -- Comment on "Finite grid instability and spectral fidelity of the electrostatic Particle-In-Cell algorithm'' by Huang et al

A recent paper by Huang et al. [Computer Physics Communications 207, 123 (2016)] thoroughly analyzed the Finite Grid Instability(FGI) and spectral fidelity of standard Particle-In-Cell (PIC) methods. Numerical experiments were carried out to demonstrate the FGIs for two PIC methods, the energy-conserving algorithm and the momentum-conserving algorithm. The paper also suggested that similar numerical experiments should be performed to test the newly developed Structure-Preserving Geometric (SPG)-PIC algorithm. In this comment, we supply the results of the suggested numerical experiments, which show that the SPG-PIC algorithm is able to suppress the FGI.

physics.plasm-ph↗

arXiv2019

PT-symmetry entails pseudo-Hermiticity regardless of diagonalizability

We prove that in finite dimensions, a Parity-Time (PT)-symmetric Hamiltonian is necessarily pseudo-Hermitian regardless of whether it is diagonalizable or not. This result is different from Mostafazadeh's, which requires the Hamiltonian to be diagonalizable. PT-symmetry breaking often occurs at exceptional points where the Hamiltonian is not diagonalizable. Our result implies that PT-symmetry breaking is equivalent to the onset of instabilities of pseudo-Hermitian systems, which was systematically studied by Krein et al. in 1950s. In particular, we show that the mechanism of PT-symmetry breaking is the resonance between eigenmodes with different Krein signatures.

quant-ph↗

arXiv2019

Field theory and structure-preserving geometric particle-in-cell algorithm for drift wave instability and turbulence

A field theory and the associated structure-preserving geometric Particle-In-Cell (PIC) algorithm are developed to study low frequency electrostatic perturbations with fully kinetic ions and adiabatic electrons in magnetized plasmas. The algorithm is constructed by geometrically discretizing the field theory using discrete exterior calculus, high-order Whitney interpolation forms, and non-canonical Hamiltonian splitting method. The discretization preserves the non-canonical symplectic structure of the particle-field system, as well as the electromagnetic gauge symmetry. As a result, the algorithm is charge-conserving and possesses long-term conservation properties. Because drift wave turbulence and anomalous transport intrinsically involve multi time-scales, simulation studies using fully kinetic particle demand algorithms with long-term accuracy and fidelity. The structure-preserving geometric PIC algorithm developed adequately servers this purpose. The algorithm has been implemented in the \textsl{SymPIC} code, tested and benchmarked using the examples of ion Bernstein waves and drift waves. We apply the algorithm to study the Ion Temperature Gradient (ITG) instability and turbulence in a 2D slab geometry. Simulation results show that at the early stage of the turbulence, the energy diffusion is between the Bohm scaling and gyro-Bohm scaling. At later time, the observed diffusion is closer to the gyro-Bohm scaling, and density blobs generated by the rupture of unstable modes are the prominent structures of the fully developed ITG turbulence.

physics.plasm-ph↗

arXiv2019

Magnetohydrodynamical equilibria with current singularities and continuous rotational transform

We revisit the Hahm-Kulsrud-Taylor (HKT) problem, a classic prototype problem for studying resonant magnetic perturbations and 3D magnetohydrodynamical equilibria. We employ the boundary-layer techniques developed by Rosenbluth, Dagazian, and Rutherford (RDR) for the internal $m=1$ kink instability, while addressing the subtle difference in the matching procedure for the HKT problem. Pedagogically, the essence of RDR's approach becomes more transparent in the simplified slab geometry of the HKT problem. We then compare the boundary-layer solution, which yields a "DC" current singularity at the resonant surface, to the numerical solution obtained using a flux-preserving Grad-Shafranov solver. The remarkable agreement between the solutions demonstrates the validity and universality of RDR's approach. In addition, we show that RDR's approach consistently preserves the rotational transform, which hence stays continuous, contrary to a recent claim that RDR's solution contains a discontinuity in the rotational transform.

physics.plasm-ph↗

arXiv2019

Lifting Spacetime's Poincaré Symmetries

In the following work, we pedagogically develop 5-vector theory, an evolution of scalar field theory that provides a stepping stone toward a Poincaré-invariant lattice gauge theory. Defining a continuous flat background via the four-dimensional Cartesian coordinates $\{x^a\}$, we `lift' the generators of the Poincaré group so that they transform only the fields existing upon $\{x^a\}$, and do not transform the background $\{x^a\}$ itself. To facilitate this effort, we develop a non-unitary particle representation of the Poincaré group, replacing the classical scalar field with a 5-vector matter field. We further augment the vierbein into a new $5\times5$ fünfbein, which `solders' the 5-vector field to $\{x^a\}$. In so doing, we form a new intuition for the Poincaré symmetries of scalar field theory. This effort recasts `spacetime data', stored in the derivatives of the scalar field, as `matter field data', stored in the 5-vector field itself. We discuss the physical implications of this `Poincaré lift', including the readmittance of an absolute reference frame into relativistic field theory. In a companion paper, we demonstrate that this theoretical development, here construed in a continuous universe, enables the description of a discrete universe that preserves the 10 infinitesimal Poincaré symmetries and their conservation laws.

physics.gen-ph↗

arXiv2019

Restoring Poincaré Symmetry to the Lattice

The following work demonstrates the viability of Poincaré symmetry in a discrete universe. We develop the technology of the discrete principal Poincaré bundle to describe the pairing of (1) a hypercubic lattice `base manifold' labeled by integer vertices-denoted $\{\mathbf{n}\}=\{(n_t,n_x,n_y,n_z)\}$-with (2) a Poincaré structure group. We develop lattice 5-vector theory, which describes a non-unitary representation of the Poincaré group whose dynamics and gauge transformations on the lattice closely resemble those of a scalar field in spacetime. We demonstrate that such a theory generates discrete dynamics with the complete infinitesimal symmetry-and associated invariants-of the Poincaré group. Following our companion paper, we `lift' the Poincaré gauge symmetries to act only on vertical matter and solder fields, and recast `spacetime data'--stored in the $\partial_μϕ(x)$ kinetic terms of a free scalar field theory--as `matter field data'-stored in the $ϕ^μ[\mathbf{n}]$ components of the 5-vector field itself. We gauge 5-vector theory to describe a lattice gauge theory of gravity, and discuss the physical implications of a discrete, Poincaré-invariant theory.

physics.gen-ph↗

arXiv2018

Stochastic simulation of collisions using high-order weak convergence algorithms

Electron collisions, described by stochastic differential equations (SDEs), were simulated using a second-order weak convergence algorithm. Using stochastic analysis, we constructed an SDE for energetic electrons in Lorentz plasma to incorporate the collisions with heavy static ions as well as background thermal electrons. Instead of focusing on the errors of each trajectory, we initiated from the weak convergence condition to directly improve the numerical accuracy of the distribution and its moments. A second-order weak convergence algorithm was developed, estimated the order of the algorithm in a collision simulation case, and compared it with the results obtained using the Euler-Maruyama method and the Cadjan-Ivanov method. For a fixed error level, the second order method largely reduce the computation time compared to the Euler-Maruyama method and the Cadjan-Ivnaov method. Finally, the backward runaway phenomenon was numerically studied and the probability of this runaway was calculated using the new method.

physics.plasm-ph↗

arXiv2018

Reducing Noise for PIC Simulations Using Kernel Density Estimation Algorithm

Noise is a major concern for Particle-In-Cell (PIC) simulations. We propose a new theoretical and algorithmic framework to evaluate and reduce the noise level for PIC simulations based on the Kernel Density Estimation (KDE) theory, which has been widely adopted in machine learning and big data science. According to this framework, the error on particle density estimation for PIC simulations can be characterized by the Mean Integrated Square Error (MISE), which consists of two parts, systematic error and noise. A careful analysis shows that in the standard PIC methods noise is the dominate error, and the noise level can be reduced if we select different shape functions that are capable of balancing the systematic error and the noise. To improve performance, we use the von Mises distribution as the shape function and seek an optimal particle width that minimizes the MISE, represented by a Cross-Validation (CV) function. This procedure significantly reduces both the noise and the MISE for PIC simulations. A particle-wise width adjustment algorithm and a width update algorithm are further developed to reduce the MISE. Simulations using the examples of Langmuir wave and Landau Damping demonstrate that the KDE algorithm developed in the present study reduces the noise level on density estimation by 98%, and gives a much more accurate result on the linear damping rate compared to the standard PIC methods. Meanwhile, it is computational efficient that can save 40% time to achieve the same accuracy.

physics.comp-ph↗

arXiv2018

Kelvin-Helmholtz instability is the result of parity-time symmetry breaking

Parity-Time (PT)-symmetry is being actively investigated as a fundamental property of observables in quantum physics. We show that the governing equations of the classical two-fluid interaction and the incompressible fluid system are PT-symmetric, and the well-known Kelvin-Helmholtz instability is the result of spontaneous PT-symmetry breaking. It is expected that all classical conservative systems governed by Newton's law admit PT-symmetry, and the spontaneous breaking thereof is a generic mechanism for classical instabilities. Discovering the PT-symmetry of systems in fluid dynamics and plasma physics and identifying the PT-symmetry breaking responsible for instabilities enable new techniques to classical physics and enrich the physics of PT-symmetry.

physics.flu-dyn↗

arXiv2018

A necessary and sufficient condition for the stability of linear Hamiltonian systems with periodic coefficients

Linear Hamiltonian systems with time-dependent coefficients are of importance to nonlinear Hamiltonian systems, accelerator physics, plasma physics, and quantum physics. It is shown that the solution map of a linear Hamiltonian system with time-dependent coefficients can be parameterized by an envelope matrix $w(t)$, which has a clear physical meaning and satisfies a nonlinear envelope matrix equation. It is proved that a linear Hamiltonian system with periodic coefficients is stable iff the envelope matrix equation admits a solution with periodic $\sqrt{w^{\dagger}w}$ and a suitable initial condition. The mathematical devices utilized in this theoretical development with significant physical implications are time-dependent canonical transformations, normal forms for stable symplectic matrices, and horizontal polar decomposition of symplectic matrices. These tools systematically decompose the dynamics of linear Hamiltonian systems with time-dependent coefficients, and are expected to be effective in other studies as well, such as those on quantum algorithms for classical Hamiltonian systems.

math-ph↗

arXiv2018

Explicit High-Order Gauge-Independent Symplectic Algorithms for Relativistic Charged Particle Dynamics

Symplectic schemes are powerful methods for numerically integrating Hamiltonian systems, and their long-term accuracy and fidelity have been proved both theoretically and numerically. However direct applications of standard symplectic schemes to relativistic charged particle dynamics result in implicit and electromagnetic gauge-dependent algorithms. In the present study, we develop explicit high-order gauge-independent noncanonical symplectic algorithms for relativistic charged particle dynamics using a Hamiltonian splitting method in the 8D phase space. It also shown that the developed algorithms can be derived as variational integrators by appropriately discretizing the action of the dynamics. Numerical examples are presented to verify the excellent long-term behavior of the algorithms.

physics.plasm-ph↗