arXiv subjects

Hong Zhang

Publications and source records attributed to Hong Zhang.

At least 343 records · Page 19Linked to original sources

arXiv2015

Fractionally diffusing passing through the saddle point of metastable potential

The diffusion of a fractional Brownian particle passing over the saddle point is studied in the field of the metastable potential. The barrier escaping probability is found to be greatly related to the fractional exponent $α$. Properties are revealed to move reversely in the opposite direction of diffusion when $α$ is relatively large despite of the zero-approximating effective friction of the system. This is very anomalous to the standard Brownian motion.

cond-mat.stat-mech↗

arXiv2015

Neumann problem for non-divergence elliptic and parabolic equations with BMO$_x$ coefficients in weighted Sobolev spaces

We prove the unique solvability in weighted Sobolev spaces of non-divergence form elliptic and parabolic equations on a half space with the homogeneous Neumann boundary condition. All the leading coefficients are assumed to be only measurable in the time variable and have small mean oscillations in the spatial variables. Our results can be applied to Neumann boundary value problems for {\em stochastic} partial differential equations with BMO$_x$ coefficients.

math.AP↗

arXiv2014

Modeling Epidermis Homeostasis and Psoriasis Pathogenesis

We present a computational model to study the spatiotemporal dynamics of the epidermis homeostasis under normal and pathological conditions. The model consists of a population kinetics model of the central transition pathway of keratinocyte proliferation, differentiation and loss and an agent-based model that propagates cell movements and generates the stratified epidermis. The model recapitulates observed homeostatic cell density distribution, the epidermal turnover time and the multilayered tissue structure. We extend the model to study the onset, recurrence and phototherapy-induced remission of psoriasis. The model considers the psoriasis as a parallel homeostasis of normal and psoriatic keratinocytes originated from a shared stem-cell niche environment and predicts two homeostatic modes of the psoriasis: a disease mode and a quiescent mode. Interconversion between the two modes can be controlled by interactions between psoriatic stem cells and the immune system and by the normal and psoriatic stem cells competing for growth niches. The prediction of a quiescent state potentially explains the efficacy of the multi-episode UVB irradiation therapy and recurrence of psoriasis plaques, which can further guide designs of therapeutics that specifically target the immune system and/or the keratinocytes.

q-bio.MN↗

arXiv2014

Virasoro irregular conformal block and beta deformed random matrix model

Virasoro irregular conformal block is presented as the expectation value of Jack-polynomials of the beta-deformed Penner-type matrix model and is compared with the inner product of Gaiotto states with arbitrary rank. It is confirmed that there are non-trivial modifications of the Gaiotto states due to the normalization of the states. The relation between the two is explicitly checked for rank 2 irregular conformal block.

hep-th↗

arXiv2014

Factorized power expansion for high-$p_T$ heavy quarkonium production

We show that when the factorized cross section for heavy quarkonium production includes next-to-leading power (NLP) contributions associated with the production of the heavy quark pair at short distances, it naturally reproduces all high $p_T$ results calculated in non-relativistic QCD (NRQCD) factorization. This extended formalism requires fragmentation functions for heavy quark pairs, as well as for light partons. When these fragmentation functions are themselves calculated using NRQCD, we find that two of the four leading NRQCD production channels, ${^3\hspace{-0.6mm}S_{1}^{[1]}}$ and ${^1\hspace{-0.6mm}S_{0}^{[8]}}$, are dominated by the NLP contributions for a very wide $p_T$ range. The large next-to-leading order corrections of NRQCD are absorbed into the leading order of the first power correction. The impact of this finding on the heavy quarkonium production and its polarization is discussed.

hep-ph↗

arXiv2014

Application of approximate matrix factorization to high order linearly implicit Runge-Kutta methods

Linearly implicit Runge-Kutta methods with approximate matrix factorization can solve efficiently large systems of differential equations that have a stiff linear part, e.g. reaction-diffusion systems. However, the use of approximate factorization usually leads to loss of accuracy, which makes it attractive only for low order time integration schemes. This paper discusses the application of approximate matrix factorization with high order methods; an inexpensive correction procedure applied to each stage allows to retain the high order of the underlying linearly implicit Runge-Kutta scheme. The accuracy and stability of the methods are studied. Numerical experiments on reaction-diffusion type problems of different sizes and with different degrees of stiffness illustrate the efficiency of the proposed approach.

math.NA↗

arXiv2014

High Order Implicit-Explicit General Linear Methods with Optimized Stability Regions

In the numerical solution of partial differential equations using a method-of-lines approach, the availability of high order spatial discretization schemes motivates the development of sophisticated high order time integration methods. For multiphysics problems with both stiff and non-stiff terms implicit-explicit (IMEX) time stepping methods attempt to combine the lower cost advantage of explicit schemes with the favorable stability properties of implicit schemes. Existing high order IMEX Runge Kutta or linear multistep methods, however, suffer from accuracy or stability reduction. This work shows that IMEX general linear methods (GLMs) are competitive alternatives to classic IMEX schemes for large problems arising in practice. High order IMEX-GLMs are constructed in the framework developed by the authors [34]. The stability regions of the new schemes are optimized numerically. The resulting IMEX-GLMs have similar stability properties as IMEX Runge-Kutta methods, but they do not suffer from order reduction, and are superior in terms of accuracy and efficiency. Numerical experiments with two and three dimensional test problems illustrate the potential of the new schemes to speed up complex applications.

math.NA↗

arXiv2014

Construction of Gaiotto states with fundamental multiplets through Degenerate DAHA

We construct Gaiotto states with fundamental multiplets in $SU(N)$ gauge theories, in terms of the orthonormal basis of spherical degenerate double affine Hecke algebra (SH in short), the representations of which are equivalent to those of $W_n$ algebra with additional $U(1)$ current. The generalized Whittaker conditions are demonstrated under the action of SH, and further rewritten in terms of $W_n$ algebra. Our approach not only consists with the existing literature but also holds for general $SU(N)$ case.

hep-th↗

arXiv2014

Heavy quarkonium fragmentation functions from a heavy quark pair. I. $S$ wave

A QCD factorization formalism was recently proposed for evaluating heavy quarkonium production at large $p_T$ at collider energies. With systematically calculated short-distance partonic hard parts and evolution kernels of fragmentation functions (FFs), the predictive power of this factorization approach relies on our knowledge of a large number of universal FFs at an input factorization scale $μ_0\gtrsim 2m_Q$ with heavy quark mass $m_Q$. With the large heavy quark mass, the relative motion of the heavy quark pair inside a heavy quarkonium is effectively non-relativistic. We evaluate these universal input FFs using non-relativistic QCD (NRQCD) factorization, and express the large number of FFs in terms of a few universal NRQCD long-distance matrix elements (LDMEs) with perturbatively calculated coefficients. We derive complete contributions to the single-parton FFs at both ${\cal O}(α_s)$ and ${\cal O}(α_s^2)$, and the heavy quark pair FFs at ${\cal O}(α_s)$. We present detailed derivation for all contributions involving LDMEs of $S$-wave NRQCD $Q\bar{Q}$-states ($P$-wave contributions in a companion paper). Our results bridge the gap between the QCD factorization formalism and its phenomenological applications.

hep-ph↗

arXiv2014

Heavy quarkonium fragmentation functions from a heavy quark pair. II. $P$ wave

Recently, a new perturbative QCD factorization formalism for heavy quarkonium production at a large transverse momentum was proposed. Phenomenological application of this new approach relies on our knowledge of a large number of universal fragmentation functions (FFs) at an input factorization scale $μ_0\gtrsim 2m_Q$ with heavy quark mass $m_Q$, which are nonperturbative, and in principle, should be extracted from data. With heavy quark mass $m_Q\gg Λ_{\rm QCD}$, we calculate these input FFs in terms of non-relativistic QCD (NRQCD) factorization. In a companion paper, we calculated these input FFs in NRQCD factorization approach including all contributions from $S$-wave NRQCD $Q\bar{Q}$-states. In this paper, we calculate contributions to the heavy quark-pair FFs from all $P$-wave NRQCD $Q\bar{Q}$-states.

hep-ph↗

arXiv2014

Chiral selection and frequency response of spiral waves in reaction-diffusion systems under a chiral electric field

Chirality is one of the most fundamental properties of many physical, chemical and biological systems. However, the mechanisms underlying the onset and control of chiral symmetry are largely understudied. We investigate possibility of chirality control in a chemical excitable system (the BZ reaction) by application of a chiral (rotating) electric field using the Oregonator model. We find that unlike previous findings, we can achieve the chirality control not only in the field rotation direction, but also opposite to it, depending on the field rotation frequency. To unravel the mechanism, we further develop a comprehensive theory of frequency synchronization based on the response function approach. We find that this problem can be described by the Adler equation and show phase-locking phenomena, known as the Arnold tongue. Our theoretical predictions are in good quantitative agreement with the numerical simulations and provide a solid basis for chirality control in excitable media.

nlin.PS↗

arXiv2014

Conormal problem of higher-order parabolic systems

The paper is a comprehensive study of the $L_p$ and the Schauder estimates for higher-order divergence type parabolic systems with discontinuous coefficients in the half space and cylindrical domains with conormal derivative boundary condition. For the $L_p$ estimates, we assume that the leading coefficients are only bounded measurable in the $t$ variable and $VMO$ with respect to $x$. We also prove the Schauder estimates in two situations: the coefficients are Hölder continuous only in the $x$ variable; the coefficients are Hölder continuous in both variables.

math.AP↗

arXiv2013

Stopping Rules for Bag-of-Words Image Search and Its Application in Appearance-Based Localization

We propose a technique to improve the search efficiency of the bag-of-words (BoW) method for image retrieval. We introduce a notion of difficulty for the image matching problems and propose methods that reduce the amount of computations required for the feature vector-quantization task in BoW by exploiting the fact that easier queries need less computational resources. Measuring the difficulty of a query and stopping the search accordingly is formulated as a stopping problem. We introduce stopping rules that terminate the image search depending on the difficulty of each query, thereby significantly reducing the computational cost. Our experimental results show the effectiveness of our approach when it is applied to appearance-based localization problem.

cs.CV↗

arXiv2013

Fractional Entropy Decaying and the Third Law of Thermodynamics

The quantum thermodynamic property of the fractional damping system is investigated extensively. A fractional power-law decaying entropy function is revealed which presents another evidence for the validity of the third law of thermodynamics in the quantum dissipative region. Several non-trivial characters are excavated such as that the entropy varies from a non-linear diverging function to a semi-linear decaying function of the fractional exponent as the temperature tends to absolute zero.

cond-mat.stat-mech↗

arXiv2013

An Efficient Index for Visual Search in Appearance-based SLAM

Vector-quantization can be a computationally expensive step in visual bag-of-words (BoW) search when the vocabulary is large. A BoW-based appearance SLAM needs to tackle this problem for an efficient real-time operation. We propose an effective method to speed up the vector-quantization process in BoW-based visual SLAM. We employ a graph-based nearest neighbor search (GNNS) algorithm to this aim, and experimentally show that it can outperform the state-of-the-art. The graph-based search structure used in GNNS can efficiently be integrated into the BoW model and the SLAM framework. The graph-based index, which is a k-NN graph, is built over the vocabulary words and can be extracted from the BoW's vocabulary construction procedure, by adding one iteration to the k-means clustering, which adds small extra cost. Moreover, exploiting the fact that images acquired for appearance-based SLAM are sequential, GNNS search can be initiated judiciously which helps increase the speedup of the quantization process considerably.

cs.CV↗

arXiv2013

The Schauder estimates for higher-order parabolic systems with time irregular coefficients

We prove Schauder estimates for solutions to both divergence and non-divergence type higher-order parabolic systems in the whole space and the half space. We also provide an existence result for divergence type systems in a cylindrical domain. All coefficients are assumed to be only measurable in the time variable and Hölder continuous in the spatial variables.

math.AP↗

arXiv2013

Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function

We derive an infinite set of recursion formulae for Nekrasov instanton partition function for linear quiver U(N) supersymmetric gauge theories in 4D. They have a structure of a deformed version of W_{1+\infty} algebra which is called SH^c algebra (or degenerate double affine Hecke algebra) in the literature. The algebra contains W_N algebra with general central charge defined by a parameter β, which gives the $Ω$ background in Nekrasov's analysis. Some parts of the formulae are identified with the conformal Ward identity for the conformal block function of Toda field theory.

hep-th↗

arXiv2013

Extrapolation-based implicit-explicit general linear methods

For many systems of differential equations modeling problems in science and engineering, there are natural splittings of the right hand side into two parts, one non-stiff or mildly stiff, and the other one stiff. For such systems implicit-explicit (IMEX) integration combines an explicit scheme for the non-stiff part with an implicit scheme for the stiff part. In a recent series of papers two of the authors (Sandu and Zhang) have developed IMEX GLMs, a family of implicit-explicit schemes based on general linear methods. It has been shown that, due to their high stage order, IMEX GLMs require no additional coupling order conditions, and are not marred by order reduction. This work develops a new extrapolation-based approach to construct practical IMEX GLM pairs of high order. We look for methods with large absolute stability region, assuming that the implicit part of the method is A- or L-stable. We provide examples of IMEX GLMs with optimal stability properties. Their application to a two dimensional test problem confirms the theoretical findings.

math.NA↗