arXiv subjects

Hongxia Guo

Publications and source records attributed to Hongxia Guo.

16 recordsLinked to original sources

arXiv2026

A novel sampling method for reconstruction of a moving point acoustic source in $\mathbb{R}^3$

In this paper, we introduce a novel sampling method to recovering the trajectory of a moving point source in R^3, where both the spatial location and emission moment of the moving point source are unknown. Combining algebraic theory with geometric knowledge, we prove the uniqueness of the source location by using measured data from five observation points. Our sampling method constructs an indicator function based on the property that the residual of the time difference of arrival constraint formula vanishes at the true source location. It achieves the reconstruction of the spatial positions and emission moments of a moving point source only using data from five observation points and their corresponding arrival times. The algorithm not only reduces the required number of observation points, but also improves computational efficiency, stability, and noise resistance. Numerical experiments verify the effectiveness of the method.

math.NA↗

arXiv2026

Reconstruct the ambient noise source from the multi-frequency sparse correlation data

In this paper, we develop a novel multi-frequency factorization method to reconstruct the spatial support of the ambient noise source. The proposed method only requires sparse correlation data and has low computational cost. Numerical experiments in two and three dimensions are presented to demonstrate the effectiveness of the proposed method.

math.NA↗

arXiv2026

A direct sampling method for inverse time-dependent electromagnetic source problems: reconstruction of the radiating time and spatial support

This paper investigates inverse source problems for time-dependent electromagnetic waves governed by Maxwell's equations. After applying the Fourier transform with respect to time, the problem leads to a frequency-domain electromagnetic system with a frequency-dependent source term. We propose a novel direct sampling method for reconstructing such radiating time and spatial space of sources from multi-frequency far-field measurements. By using a pair of multi-frequency data from opposite observation directions, we can obtain the radiating time of the signal. Based on this, the smallest region between two hyperplanes containing the support of source can be reconstructed using multi frequency data from one observation direction. The Theta convex hull of the source support can be reconstructed from multi-frequency data from sparse observation directions. Compared with existing sampling methods that mainly focus on reconstructing the spatial support, the proposed approach allows for the simultaneous reconstruction of both spatial and temporal features of the source.Three-dimensional numerical examples are conducted to validate the effectiveness of the algorithm.

math.NA↗

arXiv2026

A frequency-domain method to inverse moving source problem with unknown radiating moment

This paper introduces a multi-frequency factorization method for imaging a time-dependent source, specifically to recover its spatial support and the associated excitation instants. Using far-field data from two opposite directions, we establish a computational criterion that characterizes both the unknown pulse moments and the narrowest strip (perpendicular to the direction) enclosing the source support. Central to our inversion scheme is the construction of indicator functions, defined pointwise over the spatial and temporal sampling variables. The proposed inversion scheme permits the recovery of the $\Theta$-convex support domain from far-field data at sparse observation directions. Uniqueness in determining the convex hull of the support and the excitation instants-using all observation directions-is also established as a direct consequence of the factorization method. The effectiveness and feasibility of the approach are examined through comprehensive numerical simulations in two and three dimensions.

math.NA↗

arXiv2025

Imaging a moving point source in R^3 from the time of arrival at sparse observation points

In this paper, we introduce a novel numerical method for reconstructing the trajectory within three-dimensional space, where both the emission moment and spatial location of the point source are unknown. Our approach relies solely on measuring the time of arrival at five or seven properly chosen observation points. By utilizing the distinctive geometric configuration of these five or seven observation points, we establish the uniqueness of the trajectory and emission moment of the point source through rigorous mathematical proofs. Moreover, we analyze the stability of our proposed method. The effectiveness of the method is also verified by numerical experiments.

math.NA↗

arXiv2025

PML method for the stochastic acoustic scattering problem driven by an additive Gaussian noise

This paper is concerned with the time-domain stochastic acoustic scattering problem driven by a spatially white additive Gaussian noise. The main contributions of the work are twofold. First, we prove the existence and uniqueness of the pathwise solution to the scattering problem by applying an abstract Laplace transform inversion theorem. The analysis employs the black box scattering theory to investigate the meromorphic continuation of the Helmholtz resolvent defined on rough fields. Second, based on the piecewise constant approximation of the white noise, we construct an approximate wave solution and establish the error estimate. As a consequence, we develop a PML method and establish the convergence analysis with explicit dependence on the PML layer's thickness and medium properties, as well as the piecewise constant approximation of the white noise.

math.NA↗

arXiv2024

Inverse wave-number-dependent source problems for the Helmholtz equation with partial information on radiating period

This paper addresses a factorization method for imaging the support of a wave-number-dependent source function from multi-frequency data measured at a finite pair of symmetric receivers in opposite directions. The source function is given by the inverse Fourier transform of a compactly supported time-dependent source whose initial moment or terminal moment for radiating is unknown. Using the multi-frequency far-field data at two opposite observation directions, we provide a computational criterion for characterizing the smallest strip containing the support and perpendicular to the directions. A new parameter is incorporated into the design of test functions for indicating the unknown moment. The data from a finite pair of opposite directions can be used to recover the $\Theta$-convex polygon of the support. Uniqueness in recovering the convex hull of the support is obtained as a by-product of our analysis using all observation directions. Similar results are also discussed with the multi-frequency near-field data from a finite pair of observation positions in three dimensions. We further comment on possible extensions to source functions with two disconnected supports. Extensive numerical tests in both two and three dimensions are implemented to show effectiveness and feasibility of the approach. The theoretical framework explored here should be seen as the frequency-domain analysis for inverse source problems in the time domain.

math.NA↗

arXiv2023

Inverse wave-number-dependent source problems for the Helmholtz equation

This paper is concerned with the multi-frequency factorization method for imaging the support of a wave-number-dependent source function. It is supposed that the source function is given by the inverse Fourier transform of some time-dependent source with a priori given radiating period. Using the multi-frequency far-field data at a fixed observation direction, we provide a computational criterion for characterizing the smallest strip containing the support and perpendicular to the observation direction. The far-field data from sparse observation directions can be used to recover a $\Theta$-convex polygon of the support. The inversion algorithm is proven valid even with multi-frequency near-field data in three dimensions. The connections to time-dependent inverse source problems are discussed in the near-field case. Numerical tests in both two and three dimensions are implemented to show effectiveness and feasibility of the approach. This paper provides numerical analysis for a frequency-domain approach to recover the support of an admissible class of time-dependent sources.

math.NA↗

arXiv2023

Imaging a moving point source from multi-frequency data measured at one and sparse observation points (part II): near-field case in 3D

In this paper, we introduce a frequency-domain approach to extract information on the trajectory of a moving point source. The method hinges on the analysis of multi-frequency near-field data recorded at one and sparse observation points in three dimensions. The radiating period of the moving point source is supposed to be supported on the real axis and a priori known. In contrast to inverse stationary source problems, one needs to classify observable and non-observable measurement positions. The analogue of these concepts in the far-field regime were firstly proposed in the authors' previous paper (SIAM J. Imag. Sci., 16 (2023): 1535-1571). In this paper we shall derive the observable and non-observable measurement positions for straight and circular motions in $\R^3$. In the near-field case, we verify that the smallest annular region centered at an observable position that contains the trajectory can be imaged for an admissible class of orbit functions. Using the data from sparse observable positions, it is possible to reconstruct the $\Theta$-convex domain of the trajectory. Intensive 3D numerical tests with synthetic data are performed to show effectiveness and feasibility of this new algorithm.

math.NA↗

arXiv2023

Well-posedness and convergence analysis of PML method for time-dependent acoustic scattering problems over a locally rough surface

We aim to analyze and calculate time-dependent acoustic wave scattering by a bounded obstacle and a locally perturbed non-selfintersecting curve. The scattering problem is equivalently reformulated as an initial-boundary value problem of the wave equation in a truncated bounded domain through a well-defined transparent boundary condition. Well-posedness and stability of the reduced problem are established. Numerically, we adopt the perfect matched layer (PML) scheme for simulating the propagation of perturbed waves. By designing a special absorbing medium in a semi-circular PML, we show well-posedness and stability of the truncated initial-boundary value problem. Finally, we prove that the PML solution converges exponentially to the exact solution in the physical domain. Numerical results are reported to verify the exponential convergence with respect to absorbing medium parameters and thickness of the PML.

math.NA↗

arXiv2022

Imaging a moving point source from multi-frequency data measured at one and sparse observation directions (part I): far-field case

We propose a multi-frequency algorithm for imaging the trajectory of a moving point source from one and sparse far-field observation directions in the frequency domain. The starting and terminal time points of the moving source are both supposed to be known. We introduce the concept of observable directions (angles) in the far-field region and derive all observable directions (angles) for straight and circular motions. At an observable direction, it is verified that the smallest trip containing the trajectory and perpendicular to the direction can be imaged, provided the orbit function possesses a certain monotonical property. Without the monotonicity one can only expect to recover a thinner strip. The far-field data measured at sparse observable directions can be used to recover the $\Theta$-convex domain of the trajectory. Both two- and three-dimensional numerical examples are implemented to show effectiveness and feasibility of the approach.

math.NA↗

arXiv2022

Direct sampling method to inverse wave-number-dependent source problems (part I): determination of the support of a stationary source

This paper is concerned with a direct sampling method for imaging the support of a frequency-dependent source term embedded in a homogeneous and isotropic medium. The source term is given by the Fourier transform of a time-dependent source whose radiating period in the time domain is known. The time-dependent source is supposed to be stationary in the sense that its compact support does not vary along the time variable. Via a multi-frequency direct sampling method, we show that the smallest strip containing the source support and perpendicular to the observation direction can be recovered from far-field patterns at a fixed observation angle. With multiple but sparse observation directions, the shape of the convex hull of the source support can be recovered. The frequency-domain analysis performed here can be used to handle inverse time-dependent source problems. Our algorithm has low computational overhead and is robust against noise. Numerical experiments in both two and three dimensions have proved our theoretical findings.

math.NA↗

arXiv2019

$B_{(s)}\to D^*_{s0}(2317)P(V)$ decays in perturbative QCD approach

In this work, we use pQCD approach to calculate 20 $B_{(s)}\to D^*_{s0}(2317)P(V)$ two body decays by assuming $D^*_{s0}(2317)$ as a $\bar cs$ scalar meson, where $P(V)$ denotes a pseudoscalar (vector) meson. These $B_{(s)}$ decays can serve as an ideal platform to probe the valuable information on the inner structure of the charmed-strange meson $D^*_{s0}(2317)$, and to explore the dynamics of strong interactions and signals of new physics. These considered decays can be divided into two types: the CKM favored decays and the CKM suppressed decays. The former are induced by $b\to c$ transition, whose branching ratios are larger than $10^{-5}$. The branching fraction of the decay $\bar B^0_s\to D^{*+}_{s0}(2317)\rho^{-}$ is the largest and reaches about $1.8\times 10^{-3}$, while the branching ratios for the decay $\bar B^0_s\to D^{*+}_{s0}(2317)K^{*-}$ and other two pure annihilation decays $\bar B^0\to D^{*+}_{s0}(2317)K^-, D^{*+}_{s0}(2317)K^{*-}$ are only at $10^{-5}$ order. Our predictions are consistent well with the results given by the light cone sum rules approach. These decays are most likely to be measured at the running LHCb and the forthcoming SuperKEKB. The latter are induced by $b\to u$ transition, among of which the channel $\bar B^0\to D^{*-}(2317)\rho^+$ has the largest branching fraction, reaching up to $10^{-5}$ order. Again the pure annihilation decays $B^-\to D^{*-}_{s0}(2317)\phi, \bar B^0\to D^{*-}_{s0}(2317)K^+(K^{*+}), B^-\to D^{*-}_{s0}(2317)K^0(K^{*0})$, have the smallest branching ratios, which drop to as low as $10^{-10}\sim10^{-8}$.

hep-ph↗

arXiv2018

Three body radiative decay $B_s\to \phi \bar K^0 \gamma$ in the PQCD approach

We study the three body radiative decay $B_s\to \phi \bar K^0 \gamma$ by introducing the $\phi K$ pair distribution amplitudes (DAs) in the perturbative QCD approach. This nonperturbative inputs, the two meson DAs, is very important to simplify the calculations. Besides the dominant electromagnetic penguin operator $O_{7\gamma}$, the subleading contributions from chromomagnetic penguin operator $O_{8g}$, quark-loop corrections and annihilation type amplitudes are also considered. We find that the branching ratio for the decay $B_s\to \phi \bar K^0 \gamma$ is about $(9.26^{+1.79+3.12+0.64}_{-1.61-3.86-0.49})\times10^{-8}$, which is much smaller compared with that for the decay $B^0\to \phi K^0\gamma$. It is mainly because that the former decay induces by $b\to d\gamma$ with small CKM matrix element being proportional to $\lambda^3$. The prediction for the direct CP asymmetry is $A^{dir}_{CP}(B_s\to \phi \bar K^0 \gamma)=(-4.1^{+0.4+1.7+0.2}_{-0.6-1.2-0.1})\%$, which is well consistent with the result from the U-spin symmetry approach. we also predict the $B_s \to\phi \bar K^0\gamma$ decay spectrum, which exhibits a maximu at the $\phi K$ invariant masss around 1.95 GeV.

hep-ph↗

arXiv2018

Multiple solutions and their asymptotics for laminar flows through a porous channel with different permeabilities

The existence and multiplicity of similarity solutions for the steady, incompressible and fully developed laminar flows in a uniformly porous channel with two permeable walls are investigated. We shall focus on the so-called asymmetric case where the upper wall is with an amount of flow injection and the lower wall with a different amount of suction. We show that there exist three solutions designated as type $I$, type $II$ and type $III$ for the asymmetric case. The numerical results suggest that a unique solution exists for the Reynolds number $0\leq R<14.10$ and two additional solutions appear for $R>14.10$. The corresponding asymptotic solution for each of the multiple solutions is constructed by the method of boundary layer correction or matched asymptotic expansion for the most difficult high Reynolds number case. Asymptotic solutions are all verified by their corresponding numerical solutions.

math.CA↗

arXiv2017

Study of the $K_1(1270)-K_1(1400)$ mixing in the decays $B\to J/\Psi K_1(1270), J/\Psi K_1(1400)$

We studied the B meson decays $B\to J/\Psi K_1(1270,1400)$ in the pQCD approach beyond the leading order. With the vertex corrections and the NLO Wilson coefficients included, the branching ratios of the considered decays are $Br(B^+\to J/\Psi K_1(1270)^+)=1.76^{+0.65}_{-0.69}\times10^{-3}, Br(B^+\to J/\Psi K_1(1400)^+)=7.03^{+2.70}_{-2.52}\times10^{-4}$, and $Br(B^0\to J/\Psi K_1(1270)^0)=(1.63^{+0.60}_{-0.64})\times10^{-3}$ with the mixing angle $\theta_{K_1}=33^\circ$, which can agree well with the data or the present experimental upper limit within errors. So we support the opinion that $\theta_{K_1}\sim33^\circ$ is much more favored than $58^{\circ}$. Furthermore, we also give the predictions for the polarization fractions, direct CP violations from the different polarization components, the relative phase angles for the considered decays with the mixing angle $\theta_{K_1}=33^\circ$ and $58^\circ$, respectively. The direct CP violations of the two charged decays $B^+\to J/\Psi K_1(1270,1400)^+$ are very small $(10^{-4}\sim10^{-5})$, because there is no weak phase until up to $\mathcal{O}(\lambda^4)$ with the Wolfenstein parameter $\lambda=0.22537$. These results can be tested at the running LHCb and forthcoming Super-B experiments.

hep-ph↗