arXiv subjects

Mingxin Wang

Publications and source records attributed to Mingxin Wang.

At least 37 records · Page 2Linked to original sources

arXiv2025

On a reaction-diffusion virus model with general boundary conditions in heterogeneous environments

To describe the propagation of West Nile virus and/or Zika virus, in this paper, we propose and study a time-periodic reaction-diffusion model with general boundary conditions in heterogeneous environments and with four unknowns: susceptible host, infectious host, susceptible vector and infectious vector. We can prove that such problem has a positive time periodic solution if and only if host and vector persist and the basic reproduction ratio is greater than one, and moreover the positive time periodic solution is unique and globally asymptotically stable when it exists.

math.AP↗

arXiv2025

Longtime behaviors of a reducible cooperative system with nonlocal diffusions and free boundaries

This paper aims at understanding the longtime behaviors of a reducible cooperative system with nonlocal diffusions and different free boundaries, describing the interactions of two mutually beneficial species. Compared with the irreducible and monostable cooperative system, the system we care about here has many nonnegative steady states, leading to much different and rich longtime behaviors. Moreover, since the possible nonnegative steady states on half space are non-constant, we need to employ more detailed analysis to understand the corresponding steady state problems which in turn helps us to derive a complete classification for the longtime behaviors of our problem. The spreading speeds of free boundaries and more accurate limits of $(u,v)$ as $t\to\infty$ are also discussed, and accelerated spreading can happen if some threshold conditions are violated by kernel functions.

math.AP↗

arXiv2024

Longtime behaviors of an epidemic model with nonlocal diffusions and a free boundary: rate of accelerated spreading

This is the third part of our series of work devoted to the dynamics of an epidemic model with nonlocal diffusions and free boundary. This part is concerned with the rate of accelerated spreading for three types of kernel functions when spreading happens. By constructing the suitable upper and lower solutions, we get the rate of the accelerated spreading of free boundary, which is closely related to the behavior of kernel functions near infinity. Our results indicate that the heavier the tail of the kernel functions are, the faster the rate of accelerated spreading is. Moreover, more accurate spreading profiles for solution component $(u,v)$ are also obtained.

math.AP↗

arXiv2024

Spreading dynamics of a Fisher-KPP nonlocal diffusion model with a free boundary

This paper concerns the spreading speed and asymptotical behaviors, which was left as an open problem in \cite{LLW22}, of a Fisher-KPP nonlocal diffusion model with a free boundary. Using a new lower solution, we get the exact finite spreading speed of free boundary that is proved to be the asymptotical spreading speed of solution component $u$. Moreover, for the algebraic decay kernels, we derive the rates of accelerated spreading and the corresponding asymptotical behaviors of solution component $u$. Especially, for the level set $E^λ(t)$ with $λ\in(0,u^*)$, we find an interesting propagation phenomenon different from the double free boundary problem.

math.AP↗

arXiv2024

Dynamics for a diffusive epidemic model with a free boundary: sharp asymptotic profile

This paper concerns the sharp asymptotic profiles of the solution of a diffusive epidemic model with one free boundary and one fixed boundary which is subject to the homogeneous Dirichlet boundary condition and Neumann boundary condition, respectively. The longtime behaviors has been proved to be governed by a spreading-vanishing dichotomy in \cite{LL}, and when spreading happens, the spreading speed is determined in \cite{LLW}. In this paper, by constructing some subtle upper and lower solutions, as well as employing some detailed analysis, we improve the results in \cite{LLW} and obtain the sharp asymptotic spreading profiles, which show the homogeneous Dirichlet boundary condition and Neumann boundary condition imposed at the fixed boundary $x=0$ lead to the same asymptotic behaviors of $h(t)$ and $(u,v)$ near the spreading front $h(t)$.

math.AP↗

arXiv2024

Dynamics for a diffusive epidemic model with a free boundary: spreading speed

We study the spreading speed of a diffusive epidemic model proposed by Li et al. \cite{LL}, where the Stefan boundary condition is imposed at the right boundary, and the left boundary is subject to the homogeneous Dirichlet and Neumann condition, respectively. A spreading-vanishing dichotomy and some sharp criteria were obtained in \cite{LL}. In this paper, when spreading happens, we not only obtain the exact spreading speed of the spreading front described by the right boundary, but derive some sharp estimates on the asymptotical behavior of solution component $(u,v)$. Our arguments depend crucially on some detailed understandings for a corresponding semi-wave problem and a steady state problem.

math.AP↗

arXiv2024

Note on a vector-host epidemic model with spatial structure

Magal, Webb and Wu [Nonlinearity 31, 5589-5614 (2018)] studied the model describing outbreak of Zika in Rio De Janerio, and provided a complete analysis of dynamical properties for the solutions. In this note we first use a very simple approach to prove their results, and then investigate the modified version of the model concerned in their paper, with Neumann boundary condition replaced by Dirichlet boundary condition.

math.AP↗

arXiv2024

The free boundary problem of an epidemic model with nonlocal diffusions and nonlocal reactions: spreading-vanishing dichotomy

This paper concerns the free boundary problem of an epidemic model. The spatial movements of the infectious agents and the infective humans are approximated by nonlocal diffusion operators. Especially, both the growth rate of the agents and the infective rate of humans are represented by nonlocal reaction terms. Thus our model has four integral terms which bring some diffculties for the study of the corresponding principal eigenvalue problem. Firstly, using some elementray analysis instead of Krein-Rutman theorem and the variational characteristic, we obtain the existence and asymptotic behaviors of principal eigenvalue. Then a spreading-vanishing dichotomy is proved to hold, and the criteria for spreading and vanishing are derived. Lastly, comparing our results with those in the existing works, we discuss the effect of nonlocal reaction term on spreading and vanishing, finding that the more nonlocal reaction terms a model has, the harder spreading happens.

math.AP↗

arXiv2024

Front-end electronics development of large-area SiPM arrays for high-precision single-photon time measurement

TRopIcal DEep-sea Neutrino Telescope (TRIDENT) plans to incorporate silicon photomultipliers (SiPMs) with superior time resolution in addition to photomultiplier tubes (PMTs) into its detection units, namely hybrid Digital Optical Modules (hDOMs), to improve its angular resolution. However, the time resolution significantly degrades for large-area SiPMs due to the large detector capacitance, posing significant challenges for the readout electronics of SiPMs in hDOM. We analyzed the influences of series and parallel connections when constructing a large-area SiPM array and designed a series-parallel connection SiPM array with differential output. We also designed a high-speed pre-amplifier based on transformers (MABA-007159) and radio frequency amplifiers (BGA2803), and an analog multi-channel summing circuit based on operational amplifiers (LMH6629). We measured the single photon time resolution (SPTR) of a $4\times4$ SiPM (Hamamatsu S13360-3050PE) array ($12\times12~\mathrm{mm}^2$) of approximately 300 ps FWHM. This front-end readout design enables the large-area SiPM array to achieve high-precision single photon time measurement in one readout channel.

physics.ins-det↗

arXiv2024

Life span of solutions to a semilinear parabolic equation on locally finite graphs

Let $G=(V,E)$ be a locally finite connected graph. We develop the first eigenvalue method on $G$ introduced in 1963 by Kaplan \cite{Kaplan} on Euclidean space, the discrete Phragmén-Lindelöf principle of parabolic equations and upper and lower solutions method on $G$. Using these methods, we establish the estimates and asymptotic behaviour of the life span of solutions to a semilinear heat equation with initial data $λψ(x)$ for different scales of $λ$ on $G$ under some different conditions. Our results are different from the continuous case, which is related to the structure of the graph $G$.

math.AP↗

arXiv2024

Dynamics of a nonlinear infection viral propagation model with one fixed boundary and one free boundary

In this paper we study a nonlinear infection viral propagation model with diffusion, in which, the left boundary is fixed and with homogeneous Dirichlet boundary conditions, while the right boundary is free. We find that the habitat always expands to the half line $[0, \infty)$, and that the virus and infected cells always die out when the {\it Basic Reproduction Number} $\mathcal{R}_0\le 1$, while the virus and infected cells have persistence properties when $\mathcal{R}_0>1$. To obtain the persistence properties of virus and infected cells when $\mathcal{R}_0>1$, the most work of this paper focuses on the existence and uniqueness of positive equilibrium solutions for subsystems and the existence of positive equilibrium solutions for the entire system.

math.AP↗

arXiv2024

Qualitative properties of solutions to nonlocal infectious SIR epidemic models

This paper studies qualitative properties of solutions of nonlocal infectious SIR epidemic models (1.3)-(1.5), with the homogeneous Neumann boundary conditions, Dirichlet boundary conditions and free boundary, respectively. We first use the upper and lower solutions method and the Lyapunov function method to prove the global asymptotically stabilities of the disease-free equilibrium and the unique positive equilibrium of (1.3). Then we use the theory of topological degree in cones to study the positive equilibrium solutions of (1.4), including the necessary and sufficient conditions for the existence, and the uniqueness in some special case. At last, for the free boundary problem (1.5), we study the longtime behaviors of solutions and criteria for spreading and vanishing. The highlights are to overcome failures of the Lyapunov functional method and comparison principle, and difficulties in the maximum principle and Hopf boundary lemma of boundary value problems caused by nonlocal terms.

math.AP↗

arXiv2024

Dynamics of an epidemic model with nonlocal di?usion and a free boundary

An epidemic model, where the dispersal is approximated by nonlocal diffusion operator and spatial domain has one ?xed boundary and one free boundary, is considered in this paper. Firstly, using some elementary analysis instead of variational characterization, we show the existence and asymptotic behaviors of the principal eigenvalue of a cooperative system which can be used to characterize more epidemic models, not just ours. Then we study the existence, uniqueness and stability of a related steady state problem. Finally, we obtain a rather complete understanding for long time behaviors, spreading-vanishing dichotomy, criteria for spreading and vanishing, and spreading speed. Particularly, we prove that the asymptotic spreading speed of solution component (u; v) is equal to the spreading speed of free boundary which is ?nite if and only if a threshold condition holds for kernel functions.

math.AP↗

arXiv2023

The PMT System of the TRIDENT Pathfinder Experiment

Next generation neutrino telescopes are highly anticipated to boost the development of neutrino astronomy. A multi-cubic-kilometer neutrino telescope, TRopIcal DEep-sea Neutrino Telescope (TRIDENT), was proposed to be built in the South China Sea. The detector aims to achieve ~ 0.1 degree angular resolution for track-like events at energy above 100 TeV by using hybrid digital optical modules, opening new opportunities for neutrino astronomy. In order to measure the water optical properties and marine environment of the proposed TRIDENT site, a pathfinder experiment was conducted, in which a 100-meter-long string consisting of three optical modules was deployed at a depth of 3420 m to perform in-situ measurements. The central module emits light by housing LEDs, whereas the other two modules detect light with two independent and complementary systems: the PMT and the camera systems. By counting the number of detected photons and analyzing the photon arrival time distribution, the PMT system can measure the absorption and scattering lengths of sea water, which serve as the basic inputs for designing the neutrino telescope. In this paper, we present the design concept, calibration and performance of the PMT system in the pathfinder experiment.

hep-ex↗

arXiv2023

A fast tunable driver of light source for the TRIDENT Pathfinder experiment

TRIDENT (The tRopIcal DEep-sea Neutrino Telescope) is a proposed next-generation neutrino telescope to be constructed in the South China Sea. In September 2021, the TRIDENT Pathfinder experiment (TRIDENT EXplorer, T-REX for short) was conducted to evaluate the in-situ optical properties of seawater. The T-REX experiment deployed three digital optical modules at a depth of 3420 meters, including a light emitter module (LEM) and two light receiver modules (LRMs) equipped with photomultiplier tubes (PMTs) and cameras to detect light signals. The LEM emits light in pulsing and steady modes. It features a fast tunable driver to activate light-emitting diodes (LEDs) that emit nanosecond-width light pulses with tunable intensity. The PMTs in the LRM receive single photo-electron (SPE) signals with an average photon number of approximately 0.3 per 1-microsecond time window, which is used to measure the arrival time distribution of the SPE signals. The fast tunable driver can be remotely controlled in real-time by the data acquisition system onboard the research vessel, allowing for convenient adjustments to the driver's parameters and facilitating the acquisition of high-quality experimental data. This paper describes the requirements, design scheme, and test results of the fast tunable driver, highlighting its successful implementation in the T-REX experiment and its potential for future deep-sea experiments.

physics.ins-det↗

arXiv2023

Global bifurcation of coexistence states for a prey-taxis system with Dirichlet conditions

This paper is concerned with positive solutions of boundary value problems \begin{equation*} \left\{\begin{array}{ll} {\rm div}\left(d(v)\nabla u-uχ(v)\nabla v\right)+λu-u^2 +γu F(v)=0, & x \in Ω,\\[1mm] D Δv+μv-v^2-u F(v)=0, & x \in Ω,\\[1mm] u=v=0, & x \in \partial Ω. \end{array}\right. \end{equation*} This is the stationary problem associated with the predator-prey system with prey-taxis, and $u$ (resp. $v$) denotes the population density of predator (resp. prey). In particular, the presence of $χ(v)$ represents the tendency of predators to move toward the increasing preys gradient direction. Regarding $λ$ as a bifurcation parameter, we make a detailed description for the global bifurcation structure of the set of positive solutions. So that ranges of parameters are found for which the system admits positive solutions.

math.AP↗

arXiv2023

The nonlocal dispersal equation with seasonal succession

In this paper, we focus on the nonlocal dispersal monostable equation with seasonal succession, which can be used to describe the dynamics of species in an environment alternating between bad and good seasons. We first prove the existence and uniqueness of global positive solution, and then discuss the long time behaviors of solution. It is shown that its dynamics is completely determined by the sign of the principal eigenvalue, i.e., the time periodic problem has no positive solution and the solution of the initial value problem tends to zero when principal eigenvalue is non-negative, while the time periodic positive solution exists uniquely and is globally asymptotically stable when principal eigenvalue is negative.

math.DS↗

arXiv2022

The diffusive eco-epidemiological prey-predator model with infectious diseases in prey

This paper focus on the diffusive eco-epidemiological prey-predator model with infectious diseases in prey, and with the homogeneous Neumann and Dirichlet boundary conditions, respectively. When boundary conditions are homogeneous Neumann boundary conditions, we give a complete conclusion about the stabilities of nonnegative constant equilibrium solutions. The results show that such a problem has neither periodic solutions nor Turing patterns. When boundary conditions are homogeneous Dirichlet boundary conditions, we first establish the necessary and sufficient conditions for the existence of positive equilibrium solutions, and prove that the positive equilibrium solution is unique when it exists. Then we study the global asymptotic stabilities of trivial and semi-trivial nonnegative equilibrium solutions.

math.AP↗