arXiv subjects

Zhongming Wang

Publications and source records attributed to Zhongming Wang.

18 recordsLinked to original sources

arXiv2026

A Spatial-Resolved Proton Energy Spectrometer Based on a Scintillation-Fiber Cube

Advanced particle acceleration methods have produced high-peak-current ion beams with broad energy spread and complex spatial distribution. There is an urgent need to develop online spatial-resolved energy spectrometers for high-energy pulsed ions. This paper introduces a novel spectrometer based on a scintillation-fiber cube for online diagnosis of proton beams with broadband energy spread and complex spatial distribution. We present its working principles, experimental setup, and comprehensive calibration using monoenergetic and spatially uniform proton beams generated by a synchrotron accelerator. Calibration results confirm an energy measurement range of 6-93 MeV, a relative energy uncertainty of 0.6% at 80 MeV, and a pixel size of 0.5 mm for beam profile reconstruction. By exploiting a custom-designed energy degrader, we generated a complex proton beam and measured it with the scintillation-fiber cube spectrometer (SFICS). The results demonstrate the spectrometer's potential for online measurement of the energy spectrum and spatial distribution of complex proton beams.

physics.acc-ph↗

arXiv2025

Soliton profiles: Classical Numerical Schemes vs. Neural Network - Based Solvers

We present a comparative study of classical numerical solvers, such as Petviashvili's method or finite difference with Newton iterations, and neural network-based methods for computing ground states or profiles of solitary-wave solutions to the one-dimensional dispersive PDEs that include the nonlinear Schrödinger, the nonlinear Klein-Gordon and the generalized KdV equations. We confirm that classical approaches retain high-order accuracy and strong computational efficiency for single-instance problems in the one-dimensional setting. Physics-informed neural networks (PINNs) are also able to reproduce qualitative solutions but are generally less accurate and less efficient in low dimensions than classical solvers due to expensive training and slow convergence. We also investigate the operator-learning methods, which, although computationally intensive during training, can be reused across many parameter instances, providing rapid inference after pretraining, making them attractive for applications involving repeated simulations or real-time predictions. For single-instance computations, however, the accuracy of operator-learning methods remains lower than that of classical methods or PINNs, in general.

nlin.PS↗

arXiv2025

A positivity-preserving hybrid DDG method for Poisson--Nernst--Planck systems

In earlier work [H. Liu and Z. Wang, J. Comput. Phys., 328(2017)], an arbitrary high-order conservative and energy-dissipative direct discontinuous Galerkin (DDG) scheme was developed. Although this scheme enforced solution positivity using cell averages as reference values, it lacked a theoretical guarantee for the positivity of those cell averages. In this study, we develop a novel arbitrary high-order DDG method with rigorously proven positivity-preserving properties. Specifically, the positivity of the cell averages is ensured through a modified numerical flux in combination with forward Euler time discretization. To achieve point-wise positivity of ion concentrations, we introduce a hybrid algorithm that integrates a positivity-preserving limiter. The proposed method is further extended to higher-dimensional problems with rectangular meshes. Numerical results confirm the scheme's high-order accuracy, guaranteed positivity preservation, and consistent discrete energy dissipation.

math.NA↗

arXiv2025

Clustering-based Low Rank Approximation Method

We propose a clustering-based generalized low rank approximation method, which takes advantage of appealing features from both the generalized low rank approximation of matrices (GLRAM) and cluster analysis. It exploits a more general form of clustering generators and similarity metrics so that it is more suitable for matrix-structured data relative to conventional partitioning methods. In our approach, we first pre-classify the initial matrix collection into several small subset clusters and then sequentially compress the matrices within the clusters. This strategy enhances the numerical precision of the low-rank approximation. In essence, we combine the ideas of GLRAM and clustering into a hybrid algorithm for dimensionality reduction. The proposed algorithm can be viewed as the generalization of both techniques. Theoretical analysis and numerical experiments are established to validate the feasibility and effectiveness of the proposed algorithm.

math.OC↗

arXiv2023

Low rank approximation method for perturbed linear systems with applications to elliptic type stochastic PDEs

In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly reduce the computational load and storage requirements associated with matrix inversion without losing accuracy. To demonstrate the versatility and applicability of our method, we apply it to address two crucial uncertainty quantification problems: stochastic elliptic equations and optimal control problems governed by stochastic elliptic PDE constraints. Based on varying dimension reduction ratios, our algorithm exhibits the capability to yield a high precision numerical solution for stochastic partial differential equations, or provides a rough representation of the exact solutions as a pre-processing phase. Meanwhile, our algorithm for solving stochastic optimal control problems allows a diverse range of gradient-based unconstrained optimization methods, rendering it particularly appealing for computationally intensive large-scale problems. Numerical experiments are conducted and the results provide strong validation of the feasibility and effectiveness of our algorithm.

math.NA↗

arXiv2021

Positivity-preserving third order DG schemes for Poisson--Nernst--Planck equations

In this paper, we design and analyze third order positivity-preserving discontinuous Galerkin (DG) schemes for solving the time-dependent system of Poisson--Nernst--Planck (PNP) equations, which has found much use in diverse applications. Our DG method with Euler forward time discretization is shown to preserve the positivity of cell averages at all time steps. The positivity of numerical solutions is then restored by a scaling limiter in reference to positive weighted cell averages. The method is also shown to preserve steady states. Numerical examples are presented to demonstrate the third order accuracy and illustrate the positivity-preserving property in both one and two dimensions.

math.NA↗

arXiv2020

Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study

We consider the generalized Benjamin-Ono (gBO) equation on the real line, $ u_t + \partial_x (-\mathcal H u_{x} + \tfrac1{m} u^m) = 0, x \in \mathbb R, m = 2,3,4,5$, and perform numerical study of its solutions. We first compute the ground state solution to $-Q -\mathcal H Q^\prime +\frac1{m} Q^m = 0$ via Petviashvili's iteration method. We then investigate the behavior of solutions in the Benjamin-Ono ($m=2$) equation for initial data with different decay rates and show decoupling of the solution into a soliton and radiation, thus, providing confirmation to the soliton resolution conjecture in that equation. In the mBO equation ($m=3$), which is $L^2$-critical, we investigate solutions close to the ground state mass, and, in particular, we observe the formation of stable blow-up above it. Finally, we focus on the $L^2$-supercritical gBO equation with $m=4,5$. In that case we investigate the global vs finite time existence of solutions, and give numerical confirmation for the dichotomy conjecture, in particular, exhibiting blow-up phenomena in the supercritical setting.

math.AP↗

arXiv2020

Structure-Preserving and Efficient Numerical Methods for Ion Transport

Ion transport, often described by the Poisson--Nernst--Planck (PNP) equations, is ubiquitous in electrochemical devices and many biological processes of significance. In this work, we develop conservative, positivity-preserving, energy dissipating, and implicit finite difference schemes for solving the multi-dimensional PNP equations with multiple ionic species. A central-differencing discretization based on harmonic-mean approximations is employed for the Nernst--Planck (NP) equations. The backward Euler discretization in time is employed to derive a fully implicit nonlinear system, which is efficiently solved by a newly proposed Newton's method. The improved computational efficiency of the Newton's method originates from the usage of the electrostatic potential as the iteration variable, rather than the unknowns of the nonlinear system that involves both the potential and concentration of multiple ionic species. Numerical analysis proves that the numerical schemes respect three desired analytical properties (conservation, positivity preserving, and energy dissipation) fully discretely. Based on advantages brought by the harmonic-mean approximations, we are able to establish estimate on the upper bound of condition numbers of coefficient matrices in linear systems that are solved iteratively. The solvability and stability of the linearized problem in the Newton's method are rigorously established as well. Numerical tests are performed to confirm the anticipated numerical accuracy, computational efficiency, and structure-preserving properties of the developed schemes. Adaptive time stepping is implemented for further efficiency improvement. Finally, the proposed numerical approaches are applied to characterize ion transport subject to a sinusoidal applied potential.

math.NA↗

arXiv2017

A Modified Poisson--Nernst--Planck Model with Excluded Volume Effect: Theory and Numerical Implementation

The Poisson--Nernst--Planck (PNP) equations have been widely applied to describe ionic transport in ion channels, nanofluidic devices, and many electrochemical systems. Despite their wide applications, the PNP equations fail in predicting dynamics and equilibrium states of ionic concentrations in confined environments, due to the ignorance of the excluded volume effect. In this work, a simple but effective modified PNP (MPNP) model with the excluded volume effect is derived, based on a modification of diffusion coefficients of ions. At the steady state, a modified Poisson--Boltzmann (MPB) equation is obtained with the help of the Lambert-W special function. The existence and uniqueness of a weak solution to the MPB equation are established. Further analysis on the limit of weak and strong electrostatic potential leads to two modified Debye screening lengths, respectively. A numerical scheme that conserves total ionic concentration and satisfies energy dissipation is developed for the MPNP model. Numerical analysis is performed to prove that our scheme respects ionic mass conservation and satisfies a corresponding discrete free energy dissipation law. Positivity of numerical solutions is also discussed and numerically investigated. Numerical tests are conducted to demonstrate that the scheme is of second-order accurate in spatial discretization and has expected properties. Extensive numerical simulations reveal that the excluded volume effect has pronounced impacts on the dynamics of ionic concentration and flux. In addition, the effect of volume exclusion on the timescales of charge diffusion is systematically investigated by studying the evolution of free energies and diffuse charges.

cond-mat.stat-mech↗

arXiv2017

Computational Study on Hysteresis of Ion Channels: Multiple Solutions to Steady-State Poisson--Nernst--Planck Equations

The steady-state Poisson-Nernst-Planck (ssPNP) equations are an effective model for the description of ionic transport in ion channels. It is observed that an ion channel exhibits voltage-dependent switching between open and closed states. Different conductance states of a channel imply that the ssPNP equations probably have multiple solutions with different level of currents. We propose numerical approaches to study multiple solutions to the ssPNP equations with multiple ionic species. To find complete current-voltage (I-V ) and current-concentration (I-C) curves, we reformulate the ssPNP equations into four different boundary value problems (BVPs). Numerical continuation approaches are developed to provide good initial guesses for iteratively solving algebraic equations resulting from discretization. Numerical continuations on V , I, and boundary concentrations result in S-shaped and double S-shaped (I-V and I-C) curves for the ssPNP equations with multiple species of ions. There are five solutions to the ssPNP equations with five ionic species, when an applied voltage is given in certain intervals. Remarkably, the current through ion channels responds hysteretically to varying applied voltages and boundary concentrations, showing a memory effect. In addition, we propose a useful computational approach to locate turning points of an I-V curve. With obtained locations, we are able to determine critical threshold values for hysteresis to occur and the interval for V in which the ssPNP equations have multiple solutions. Our numerical results indicate that the developed numerical approaches have a promising potential in studying hysteretic conductance states of ion channels.

math.NA↗

arXiv2016

A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson--Nernst--Planck systems

We design an arbitrary-order free energy satisfying discontinuous Galerkin (DG) method for solving time-dependent Poisson-Nernst-Planck systems. Both the semi-discrete and fully discrete DG methods are shown to satisfy the corresponding discrete free energy dissipation law for positive numerical solutions. Positivities of numerical solutions are enforced by an accuracy-preserving limiter in reference to positive cell averages. Numerical examples are presented to demonstrate the high resolution of the numerical algorithm and to illustrate the proven properties of mass conservation, free energy dissipation, as well as the preservation of steady states.

math.NA↗

arXiv2016

An entropy satisfying discontinuous Galerkin method for nonlinear Fokker-Planck equations

We propose a high order discontinuous Galerkin (DG) method for solving nonlinear Fokker-Planck equations with a gradient flow structure. For some of these models it is known that the transient solutions converge to steady-states when time tends to infinity. The scheme is shown to satisfy a discrete version of the entropy dissipation law and preserve steady-states, therefore providing numerical solutions with satisfying long-time behavior. The positivity of numerical solutions is enforced through a reconstruction algorithm, based on positive cell averages. For the model with trivial potential, a parameter range sufficient for positivity preservation is rigorously established. For other cases, cell averages can be made positive at each time step by tuning the numerical flux parameters. A selected set of numerical examples is presented to confirm both the high-order accuracy and the efficiency to capture the large-time asymptotic.

math.NA↗

arXiv2015

Accurate Estimation of Quantitative Trait Locus Effects with Epistatic by Improved Variational Linear Regression

Bayesian approaches to variable selection have been widely used for quantitative trait locus (QTL) mapping. The Markov chain Monte Carlo (MCMC) algorithms for that aim are often difficult to be implemented for high-dimensional variable selection problems, such as the ones arising in epistatic analysis. Variational approximation is an alternative to MCMC, and variational linear regression (VLR) is an effective solution for the variable selection problems, but lacks accuracy in some QTL mapping problems where there are many more variables than samples. In this paper, we propose an effective method with aim to improve the accuracy of VLR in the case of above by dynamically reducing components (variable or markers) with known effects (zero or fixed). We show that the proposed method can greatly improve the accuracy of VLR with little increase in computational cost. The method is compared with several other variational methods used for QTL mapping, and simulation results show that its performance is higher than those methods when applied in high-dimensional cases.

q-bio.QM↗

arXiv2014

A free energy satisfying finite difference method for Poisson--Nernst--Planck equations

In this work we design and analyze a free energy satisfying finite difference method for solving Poisson-Nernst-Planck equations in a bounded domain. The algorithm is of second order in space, with numerical solutions satisfying all three desired properties: i) mass conservation, ii) positivity preserving, and iii) free energy satisfying in the sense that these schemes satisfy a discrete free energy dissipation inequality. These ensure that the computed solution is a probability density, and the schemes are energy stable and preserve the equilibrium solutions. Both one and two-dimensional numerical results are provided to demonstrate the good qualities of the algorithm, as well as effects of relative size of the data given.

math.NA↗

arXiv2007

Rhodium Mossbauer Supperadiance Induced by Liquid-Nitrogen Cooling

In the previous report, we have demonstrated cascade branching channels of the multipolar E3 transition of rhodium Mossbauer gamma via the time- and energy-resolved spectroscopy. Moreover, superradiance in the Borrmann channel from inverted nuclei gives gamma entanglement. In this letter, we report further four observations of superradiance and its associated gamma entanglement at the liquid-nitrogen temperature, i.e. (i) speed-up decay, (ii) immediate recovery of the speed-up decay after quenching, (iii) simultaneous suppression of gamma and K lines, and (iv) enhanced multiple ionizations. Anisotropic superradiant channels open by quenching and recover back immediately after quenching. Enhanced K satellites and K hypersatellites induced by cooling are attributed to the inelastic scattering of more than three entangled gammas.

quant-ph↗

arXiv2006

Possible Stimulated Emission of Entangled Rhodium Mossbauer Gammas

Observation of possible stimulated emission of Mossbauer gamma is reported by liquid-nitrogen quenching of rhodium sample from room temperature to 77K in the time-resolved Mossbauer spectroscopy. Recently, we have demonstrated the anomalous emission of three entangled gammas of the E3 Mossbauer transition generated by bremsstrahlung irradiation. In this work, we further report the high-speed decay of excited state. We conjecture that cooling shrinkage, gravitational redshift and crystal lattice collimate entangled gammas in a linear cavity. This opens up a new approach towards gamma lasing, if the stimulated emission occurs at this obtained low excitation density.

quant-ph↗

arXiv2006

Resonant Propagation of Entangled Rhodium Mossbauer Gammas

We report the resonant propagation of the long-lived Mossbauer gamma in the time-resolved Mossbauer spectroscopy. Recently, three entangled gammas emitted from the E3 rhodium Mossbauer transition has been proposed to interpret the extraordinary observations in the previous report. Further observation reported here is the dynamic beat of these entangled gammas at room temperature and 77K. Apparent beat anisotropy reveals their long-distance resonant propagation, which leads to suppressed Doppler shift of entangled photon transport in the Borrmann channel.

quant-ph↗

arXiv2006

Inelastic Scatterings of Entangled Mossbauer Gammas

We report the observation of the temperature-dependent inelastic scattering of three entangled Mossbauer gammas in the time-resolved Mossbauer spectroscopy. Recently, the long-lived E3 Mossbauer transition of rhodium generated by bremsstrahlung irradiation has been reported. Two kinds of X-rays with the fast decay are attributed to the tri-photon effect. They are tri-photon pile-up of rhodium K X-rays and the high-Z impurity K X-rays. Energy of the particular K emission is higher than the sum energy of two Mossbauer gammas. This letter reports new discoveries by cooling down the sample using liquid nitrogen, namely the collective anomalous emission of entangled Mossbauer gammas. The enhancement of inelastic scatterings at low temperature such as rhodium K satellites is attributed to this entanglement.

nucl-ex↗