arXiv subjects

Hong Zhang

Publications and source records attributed to Hong Zhang.

358 records · Page 20Linked to original sources

arXiv2013

Partitioned and implicit-explicit general linear methods for ordinary differential equations

Implicit-explicit (IMEX) time stepping methods can efficiently solve differential equa- tions with both stiff and nonstiff components. IMEX Runge-Kutta methods and IMEX linear multistep methods have been studied in the literature. In this pa- per we study new implicit-explicit methods of general linear type (IMEX-GLMs). We develop an order conditions theory for high stage order partitioned GLMs that share the same abscissae, and show that no additional coupling order conditions are needed. Consequently, GLMs offer an excellent framework for the construction of multi-method integration algorithms. Next, we propose a family of IMEX schemes based on diagonally-implicit multi-stage integration methods and construct practical schemes of order three. Numerical results confirm the theoretical findings.

math.NA↗

arXiv2012

Virasoro constraint for Nekrasov instanton partition function

We show that Nekrasov instanton partition function for SU(N) gauge theories satisfies recursion relations in the form of U(1)+Virasoro constraints when β = 1. The constraints give a direct support for AGT conjecture for general quiver gauge theories.

hep-th↗

arXiv2011

Selberg Integral and SU(N) AGT Conjecture

An intriguing coincidence between the partition function of super Yang-Mills theory and correlation functions of 2d Toda system has been heavily studied recently. While the partition function of gauge theory was explored by Nekrasov, the correlation functions of Toda equation have not been completely understood. In this paper, we study the latter in the form of Dotsenko-Fateev integral and reduce it in the form of Selberg integral of several Jack polynomials. We conjecture a formula for such Selberg average which satisfies some consistency conditions and show that it reproduces the SU(N) version of AGT conjecture.

hep-th↗

arXiv2010

Reconsidering the galactic coordinate system

Initially defined by the IAU in 1958, the galactic coordinate system was thereafter in 1984 transformed from the B1950.0 FK4-based system to the J2000.0 FK5-based system. In 1994, the IAU recommended that the dynamical reference system FK5 be replaced by the ICRS, which is a kinematical non-rotating system defined by a set of remote radio sources. However the definition of the galactic coordinate system was not updated. We consider that the present galactic coordinates may be problematic due to the unrigorous transformation method from the FK4 to the FK5, and due to the non-inertiality of the FK5 system with respect to the ICRS. This has led to some confusions in applications of the galactic coordinates. We tried to find the transformation matrix in the framework of the ICRS after carefully investigating the definition of the galactic coordinate system and transformation procedures, however we could not find a satisfactory galactic coordinate system that is connected steadily to the ICRS. To avoid unnecessary misunderstandings, we suggest to re-consider the definition of the galactic coordinate system which should be directly connected with the ICRS for high precise observation at micro-arcsecond level.

astro-ph.GA↗

arXiv2010

Lyapunov indices with two nearby trajectories in a curved spacetime

We compare three methods for computing invariant Lyapunov exponents (LEs) in general relativity. They involve the geodesic deviation vector technique (M1), the two-nearby-orbits method with projection operations and with coordinate time as an independent variable (M2), and the two-nearby-orbits method without projection operations and with proper time as an independent variable (M3). An analysis indicates that M1 and M3 do not need any projection operation. In general, the values of LEs from the three methods are almost the same. As an advantage, M3 is simpler to use than M2. In addition, we propose to construct the invariant fast Lyapunov indictor (FLI) with two-nearby-trajectories and give its algorithm in order to quickly distinguish chaos from order. Taking a static axisymmetric spacetime as a physical model, we apply the invariant FLIs to explore the global dynamics of phase space of the system where regions of chaos and order are clearlyidentified.

gr-qc↗

arXiv2010

Quark-gluon correlation functions relevant to single transverse spin asymmetries

We investigate the relative size of various twist-3 quark-gluon correlation functions relevant to single transverse spin asymmetries (SSAs) in a quark-diquark model of the nucleon. We calculate the quark-gluon correlation function $T_{q,F}(x, x)$ that is responsible for the gluonic pole contribution to the SSAs, as well as $T_{q,F}(0, x)$ and $T_{Δ{q}, F}(0, x)$ responsible for the fermionic pole contributions. We find in both cases of a scalar diquark and an axial-vector diquark that at the first nontrivial order only the $\tq(x, x)$ is finite while all other quark-gluon correlation functions vanish. Using the same model, we evaluate quark Sivers function and discuss its relation to the $\tq(x, x)$. We also discuss the implication of our finding to the phenomenological studies of the SSAs.

hep-ph↗

arXiv2010

FACETS - a Framework for Parallel Coupling of Fusion Components

Coupling separately developed codes offers an attractive method for increasing the accuracy and fidelity of the computational models. Examples include the earth sciences and fusion integrated modeling. This paper describes the Framework Application for Core-Edge Transport Simulations (FACETS).

physics.plasm-ph↗

arXiv2008

Novel interface-selected waves and their influences on wave competitions

The topic of interface effects in wave propagation has attracted great attention due to their theoretical significance and practical importance. In this paper we study nonlinear oscillatory systems consisting of two media separated by an interface, and find a novel phenomenon: interface can select a type of waves (ISWs). Under certain well defined parameter condition, these waves propagate in two different media with same frequency and same wave number; the interface of two media is transparent to these waves. The frequency and wave number of these interface-selected waves (ISWs) are predicted explicitly. Varying parameters from this parameter set, the wave numbers of two domains become different, and the difference increases from zero continuously as the distance between the given parameters and this parameter set increases from zero. It is found that ISWs can play crucial roles in practical problems of wave competitions, e.g., ISWs can suppress spirals and antispirals.

nlin.CD↗

arXiv2008

Lattice complexity and fine graining of symbolic sequence

A new complexity measure named as Lattice Complexity is presented for finite symbolic sequences. This measure is based on the symbolic dynamics of one-dimensional iterative maps and Lempel-Ziv Complexity. To make Lattice Complexity distinguishable from Lempel-Ziv Complexity, an approach called fine-graining process is also proposed. When the control parameter fine-graining order is small enough, the two measures are almost equal. While the order increases, the difference between the two measures becomes more and more significant. Applying Lattice Complexity to logistic map with a proper order, we find that the sequences that are regarded as complex are roughly at the edges of chaotic regions. Further derived properties of the two measures concerning the fine-graining process are also discussed.

nlin.CD↗

arXiv2007

Negative phase velocity in nonlinear oscillatory systems --mechanism and parameter distributions

Waves propagating inwardly to the wave source are called antiwaves which have negative phase velocity. In this paper the phenomenon of negative phase velocity in oscillatory systems is studied on the basis of periodically paced complex Ginzbug-Laundau equation (CGLE). We figure out a clear physical picture on the negative phase velocity of these pacing induced waves. This picture tells us that the competition between the frequency $ω_{out}$ of the pacing induced waves with the natural frequency $ω_{0}$ of the oscillatory medium is the key point responsible for the emergence of negative phase velocity and the corresponding antiwaves. $ω_{out}ω_{0}>0$ and $|ω_{out}|<|ω_{0}|$ are the criterions for the waves with negative phase velocity. This criterion is general for one and high dimensional CGLE and for general oscillatory models. Our understanding of antiwaves predicts that no antispirals and waves with negative phase velocity can be observed in excitable media.

cond-mat.mtrl-sci↗

arXiv2007

Negative refraction in nonlinear wave systems

People have been familiar with the phenomenon of wave refraction for several centuries. Recently, a novel type of refraction, i.e., negative refraction, where both incident and refractory lines locate on the same side of the normal line, has been predicted and realized in the context of linear optics in the presence of both right- and left-handed materials. In this work, we reveal, by theoretical prediction and numerical verification, negative refraction in nonlinear oscillatory systems. We demonstrate that unlike what happens in linear optics, negative refraction of nonlinear waves does not depend on the presence of the special left-handed material, but depends on suitable physical condition. Namely, this phenomenon can be observed in wide range of oscillatory media under the Hopf bifurcation condition. The complex Ginzburg-Landau equation and a chemical reaction-diffusion model are used to demonstrate the feasibility of this nonlinear negative refraction behavior in practice.

cond-mat.other↗

arXiv2003

Turbulence control by developing a spiral wave with a periodic signal injection in the complex Ginzburg-Landau equation

Turbulence control in the two-dimensional complex Ginzburg-Landau equation is investigated. A new approach is proposed for the control purpose. In the presence of a small spiral wave seed initiation, a fully developed turbulence can be completely annihilated by injecting a single periodic signal to a small fixed space area around the spiral wave tip. The control is achieved in a parameter region where the spiral wave of the uncontrolled system is absolutely unstable. The robustness, convenience and high control efficiency of this method is emphasized, and the mechanism underlying these practical advantages are intuitively understood.

cond-mat.soft↗

arXiv2001

Evolution of the Chern-Simons Vortices

Based on the gauge potential decomposition theory and the $ϕ$-mapping theory, the topological inner structure of the Chern-Simons-Higgs vortex has been showed in detail. The evolution of CSH vortices is studied from the topological properties of the Higgs scalar field. The vortices are found generating or annihilating at the limit points and encountering, splitting or merging at the bifurcation points of the scalar field $ϕ.$

hep-th↗

arXiv2001

Topological excitation in the Fractional Quantum Hall system

Two kinds of topological excitations, vortices and skyrmions, are studied in the frame of Ginzburg-Landau theory. We obtain the rigorous relation between the topological excitation and the order parameters in the fractional quantum Hall systems. We also discuss the evolution of the vortices in fractional quantum Hall systems.

cond-mat.mes-hall↗

arXiv1999

Topological current of point defects and its bifurcation

From the topological properties of a three dimensional vector order parameter, the topological current of point defects is obtained. One shows that the charge of point defects is determined by Hopf indices and Brouwer degrees. The evolution of point defects is also studied. One concludes that there exist crucial cases of branch processes in the evolution of point defects when the Jacobian $D(\frac ϕx)=0$.

hep-th↗

arXiv1999

Topological quantum mechanics and the first Chern class

Topological properties of quantum system is directly associated with the wave function. Based on the decomposition theory of gauge potential, a new comprehension of topological quantum mechanics is discussed. One shows that a topological invariant, the first Chern class, is inherent in the Schrödinger system, which is only associated with the Hopf index and Brouwer degree of the wave function. This relationship between the first Chern class and the wave function is the topological source of many topological effects in quantum system.

hep-th↗