arXiv subjects

Xiang Zhou

Publications and source records attributed to Xiang Zhou.

At least 163 records · Page 9Linked to original sources

arXiv2018

Estimation on the neutrino masses by using neutrino oscillation parameters

It has been shown that neutrino masses can be determined under the particle ansatz. In this paper, we give the general formulas of neutrino masses related to the neutrino oscillation parameters which show that there is a mass hierarchy transition. Using the best fit values measured by electron and muon neutrino oscillation experiments, the total neutrino mass is about 0.25 eV. According to the standard neutrino cosmology, the neutrino energy density is about 55 eV/cm$^3$ and $Ω_m h^2>Ω_νh^2\sim 0.0055$.

hep-ph↗

arXiv2018

Mass measurable phase differences in neutrino oscillations

We propose an ansatz, named the "particle ansatz", that in the rest frame of a flavor neutrino all its mass eigenstate momentums should simultaneously be zero. Under the particle ansatz, the mass measurable phase differences (mmPhDs) can be derived as $Δϕ_{ji}\simeq [2m_{ν_α}(m_j-m_i)/4 E_{ν_α}]L$. We show that using mmPhDs all three neutrino masses can be determined. In the foreseeable future all neutrino masses are expected to be determined by the spectral analysis of neutrino experiments.

hep-ph↗

arXiv2018

Quenching of fluorescence for linear alkylbenzene

Linear alkylbenzene (LAB) based liquid scintillator is adopted as the central detector for the Jiangmen Underground Neutrino Observatory (JUNO) liquid scintillator detectors. A quenching factor measurement instrument is designed based on the Compton scattering process. Two different quenchers for the liquid scintillator have been investigated and the result shows that the scintillation light of the JUNO liquid scintillator can be quenched to a level. The emission spectrum with the absence of the quencher is also showing a desired behavior.

physics.ins-det↗

arXiv2017

Estimation of exciton diffusion lengths of organic semiconductors in random domains

Exciton diffusion length plays a vital role in the function of opto-electronic devices. Oftentimes, the domain occupied by an organic semiconductor is subject to surface measurement error. In many experiments, photoluminescence over the domain is measured and used as the observation data to estimate this length parameter in an inverse manner based on the least square method. However, the result is sometimes found to be sensitive to the surface geometry of the domain. In this paper, we employ a random function representation for the uncertain surface of the domain. After non-dimensionalization, the forward model becomes a diffusion-type equation over the domain whose geometric boundary is subject to small random perturbations. We propose an asymptotic-based method as an approximate forward solver whose accuracy is justified both theoretically and numerically. It only requires solving several deterministic problems over a fixed domain. Therefore, for the same accuracy requirements we tested here, the running time of our approach is more than one order of magnitude smaller than that of directly solving the original stochastic boundary-value problem by the stochastic collocation method. In addition, from numerical results, we find that the correlation length of randomness is important to determine whether a 1D reduced model is a good surrogate for the 2D model.

math.NA↗

arXiv2017

Event generators for $η/η^{\prime}$ decays at BESIII

The light unflavoured meson $η/η^{\prime}$ decays are valuable for testing non-perturbative quantum chromodynamics and exploring new physics beyond the Standard Model. This paper describes a series of event generators, including $η/η^{\prime}\toγl^{+}l^{-}$, $η/η^{\prime}\toγπ^{+}π^{-}$, $η^{\prime}\toωe^{+}e^{-}$, $η\toπ^{+}π^{-}π^{0}$, $η/η^{\prime}\toπ^{0}π^{0}π^{0}$, $η^{\prime}\toηππ$ and $η^{\prime}\toπ^{+}π^{-}π^{+}π^{-}/π^{+}π^{-}π^{0}π^{0}$, which have been developed for investigating $η/η^\prime$ decay dynamics. For most of these generators, their usability has been validated in BESIII analyses for determining the detection efficiency, and background studies. The consistency between data and Monte Carlo shows that these generators work well in the BESIII simulation, and will also be useful for ongoing BESIII analyses and other experiments for studying $η/η^\prime$ physics.

hep-ex↗

arXiv2017

Convex Splitting Method for the Calculation of Transition States of Energy Functional

Among numerical methods for partial differential equations arising from steepest descent dynamics of energy functionals (e.g., Allen-Cahn and Cahn-Hilliard equations), the convex splitting method is well-known to maintain unconditional energy stability for a large time step size. In this work, we show how to use the convex splitting idea to find transition states, i.e., index-1 saddle points of the same energy functionals. Based on the iterative minimization formulation (IMF) for saddle points (SIAM J. Numer. Anal., vol. 53, p1786, 2015), we introduce the convex splitting method to minimize the auxiliary functional at each cycle of the IMF. We present a general principle of constructing convex splitting forms for these auxiliary functionals and show how to avoid solving nonlinear equations. The new numerical scheme based on the convex splitting method allows for large time step sizes. The new methods are tested for the one dimensional Ginzburg-Landau energy functional in the search of the Allen-Cahn or Cahn-Hilliard types of transition states. We provide the numerical results of transition states for the two dimensional Landau-Brazovskii energy functional for diblock copolymers.

math.NA↗

arXiv2017

Transform Analysis for Hawkes Processes with Applications in Dark Pool Trading

Hawkes processes are a class of simple point processes that are self-exciting and have clustering effect, with wide applications in finance, social networks and many other fields. This paper considers a self-exciting Hawkes process where the baseline intensity is time-dependent, the exciting function is a general function and the jump sizes of the intensity process are independent and identically distributed non-negative random variables. This Hawkes model is non-Markovian in general. We obtain closed-form formulas for the Laplace transform, moments and the distribution of the Hawkes process. To illustrate the applications of our results, we use the Hawkes process to model the clustered arrival of trades in a dark pool and analyze various performance metrics including time-to-first-fill, time-to-complete-fill and the expected fill rate of a resting dark order.

q-fin.TR↗

arXiv2017

varbvs: Fast Variable Selection for Large-scale Regression

We introduce varbvs, a suite of functions written in R and MATLAB for regression analysis of large-scale data sets using Bayesian variable selection methods. We have developed numerical optimization algorithms based on variational approximation methods that make it feasible to apply Bayesian variable selection to very large data sets. With a focus on examples from genome-wide association studies, we demonstrate that varbvs scales well to data sets with hundreds of thousands of variables and thousands of samples, and has features that facilitate rapid data analyses. Moreover, varbvs allows for extensive model customization, which can be used to incorporate external information into the analysis. We expect that the combination of an easy-to-use interface and robust, scalable algorithms for posterior computation will encourage broader use of Bayesian variable selection in areas of applied statistics and computational biology. The most recent R and MATLAB source code is available for download at Github (https://github.com/pcarbo/varbvs), and the R package can be installed from CRAN (https://cran.r-project.org/package=varbvs).

stat.CO↗

arXiv2017

Multiscale Gentlest Ascent Dynamics for Saddle Point in Effective Dynamics of Slow-Fast System

Here we present a multiscale method to calculate the saddle point associated with the effective dynamics arising from a stochastic system which couples slow deterministic drift and fast stochastic dynamics. This problem is motivated by the transition states on free energy surfaces in chemical physics. Our method is based on the gentlest ascent dynamics which couples the position variable and the direction variable and has the local convergence to saddle points. The dynamics of the direction vector is derived in terms of the covariance function with respective to the equilibrium distribution of the fast stochastic process. We apply the multiscale numerical methods to efficiently solve the obtained multiscale gentlest ascent dynamics, {and discuss the acceleration techniques based on the adaptive idea.} The examples of stochastic ordinary and partial differential equations are presented.

math.NA↗

arXiv2017

Two-parameter asymptotic expansions for elliptic equations with small geometric perturbation and high contrast ratio

We consider the asymptotic solutions of an interface problem corresponding to an elliptic partial differential equation with Dirich- let boundary condition and transmission condition, subject to the small geometric perturbation and the high contrast ratio of the conductivity. We consider two types of perturbations: the first corresponds to a thin layer coating a fixed bounded domain and the second is the per perturbation of the interface. As the perturbation size tends to zero and the ratio of the conductivities in two subdomains tends to zero, the two-parameter asymptotic expansions on the fixed reference domain are derived to any order after the single parameter expansions are solved be- forehand. Our main tool is the asymptotic analysis based on the Taylor expansions for the properly extended solutions on fixed domains. The Neumann boundary condition and Robin boundary condition arise in two-parameter expansions, depending on the relation of the geometric perturbation size and the contrast ratio.

math.AP↗

arXiv2017

Bayesian Approximate Kernel Regression with Variable Selection

Nonlinear kernel regression models are often used in statistics and machine learning because they are more accurate than linear models. Variable selection for kernel regression models is a challenge partly because, unlike the linear regression setting, there is no clear concept of an effect size for regression coefficients. In this paper, we propose a novel framework that provides an effect size analog of each explanatory variable for Bayesian kernel regression models when the kernel is shift-invariant --- for example, the Gaussian kernel. We use function analytic properties of shift-invariant reproducing kernel Hilbert spaces (RKHS) to define a linear vector space that: (i) captures nonlinear structure, and (ii) can be projected onto the original explanatory variables. The projection onto the original explanatory variables serves as an analog of effect sizes. The specific function analytic property we use is that shift-invariant kernel functions can be approximated via random Fourier bases. Based on the random Fourier expansion we propose a computationally efficient class of Bayesian approximate kernel regression (BAKR) models for both nonlinear regression and binary classification for which one can compute an analog of effect sizes. We illustrate the utility of BAKR by examining two important problems in statistical genetics: genomic selection (i.e. phenotypic prediction) and association mapping (i.e. inference of significant variants or loci). State-of-the-art methods for genomic selection and association mapping are based on kernel regression and linear models, respectively. BAKR is the first method that is competitive in both settings.

stat.ME↗

arXiv2017

Moderate Deviation for Random Elliptic PDEs with Small Noise

Partial differential equations with random inputs have become popular models to characterize physical systems with uncertainty coming from, e.g., imprecise measurement and intrinsic randomness. In this paper, we perform asymptotic rare event analysis for such elliptic PDEs with random inputs. In particular, we consider the asymptotic regime that the noise level converges to zero suggesting that the system uncertainty is low, but does exists. We develop sharp approximations of the probability of a large class of rare events.

math.PR↗

arXiv2017

Asymptotic Expansion with Boundary Layer Analysis for Strongly Anisotropic Elliptic Equations

In this article, we derive the asymptotic expansion, up to an arbitrary order in theory, for the solution of a two-dimensional elliptic equation with strongly anisotropic diffusion coefficients along different directions, subject to the Neumann boundary condition and the Dirichlet boundary condition on specific parts of the domain boundary, respectively. The ill-posedness arising from the Neumann boundary condition in the strongly anisotropic diffusion limit is handled by the decomposition of the solution into a mean part and a fluctuation part. The boundary layer analysis due to the Dirichlet boundary condition is conducted for each order in the expansion for the fluctuation part. Our results suggest that the leading order is the combination of the mean part and the composite approximation of the fluctuation part for the general Dirichlet boundary condition.

math.AP↗

arXiv2016

Letter of Intent: Jinping Neutrino Experiment

Jinping Neutrino Experiment (Jinping) is proposed to significantly improve measurements on solar neutrinos and geoneutrinos in China Jinping Laboratory - a lab with a number of unparalleled features, thickest overburden, lowest reactor neutrino background, etc., which identify it as the world-best low-energy neutrino laboratory. The proposed experiment will have target mass of 4 kilotons of liquid scintillator or water-based liquid scintillator, with a fiducial mass of 2 kilotons for neutrino-electron scattering events and 3 kilotons for inverse-beta interaction events. A number of initial sensitivities studies have been carried out, including on the transition phase for the solar neutrinos oscillation from the vacuum to the matter effect, the discovery of solar neutrinos from the carbon-nitrogen-oxygen (CNO) cycle, the resolution of the high and low metallicity hypotheses, and the unambiguous separation on U and Th cascade decays from the dominant crustal anti-electron neutrinos in China.

physics.ins-det↗

arXiv2016

Explore Stochastic Instabilities of Periodic Points by Transition Path Theory

We consider the noise-induced transitions in the randomly perturbed discrete logistic map from a linearly stable periodic orbit consisting of T periodic points. The traditional large deviation theory and asymptotic analysis for small noise limit as well as the derived quasi-potential can not distinguish the quantitative difference in noise-induced stochastic instabilities of these T periodic points. We generalize the transition path theory to the discrete-time continuous-space stochastic process to attack this problem. As a first criterion of quantifying the relative instability among T periodic points, we compare the distribution of the last passage locations in the transitions from the whole periodic orbit to a prescribed set far away. This distribution is related to the contributions to the transition rate from each periodic points. The second criterion is based on the competency of the transition paths associated with each periodic point. Both criteria utilise the reactive probability current in the transition path theory. Our numerical results for the logistic map reveal the transition mechanism of escaping from the stable periodic orbit and identify which peri- odic point is more prone to lose stability so as to make successful transitions under random perturbations.

nlin.CD↗

arXiv2015

Escaping from an attractor: Importance sampling and rest points I

We discuss importance sampling schemes for the estimation of finite time exit probabilities of small noise diffusions that involve escape from an equilibrium. A factor that complicates the analysis is that rest points are included in the domain of interest. We build importance sampling schemes with provably good performance both pre-asymptotically, that is, for fixed size of the noise, and asymptotically, that is, as the size of the noise goes to zero, and that do not degrade as the time horizon gets large. Simulation studies demonstrate the theoretical results.

math.PR↗

arXiv2015

Rayleigh scattering of linear alkylbenzene in large liquid scintillator detectors

Rayleigh scattering poses an intrinsic limit for the transparency of organic liquid scintillators. This work focuses on the Rayleigh scattering length of linear alkylbenzene (LAB), which will be used as the solvent of the liquid scintillator in the central detector of the Jiangmen Underground Neutrino Observatory. We investigate the anisotropy of the Rayleigh scattering in LAB, showing that the resulting Rayleigh scattering length will be significantly shorter than reported before. Given the same overall light attenuation, this will result in a more efficient transmission of photons through the scintillator, increasing the amount of light collected by the photosensors and thereby the energy resolution of the detector.

physics.ins-det↗

arXiv2015

Preliminary study of light yield dependence on LAB liquid scintillator composition

Liquid scintillator (LS) will be adopted as the detector material in JUNO (Jiangmen Underground Neutrino Observatory). The energy resolution requirement of JUNO is 3%, which has never previously been reached. To achieve this energy resolution, the light yield of liquid scintillator is an important factor. PPO (the fluor) and bis-MSB (the wavelength shifter) are the two main materials dissolved in LAB. To study the influence of these two materials on the transmission of scintillation photons in LS, 25 and 12 cm-long quartz vessels were used in a light yield experiment. LS samples with different concentration of PPO and bis-MSB were tested. At these lengths, the light yield growth is not obvious when the concentration of PPO is higher than 4 g/L. The influence from bis-MSB becomes insignificant when its concentration is higher than 8 mg/L. This result could provide some useful suggestions for the JUNO LS.

physics.ins-det↗