arXiv subjects

Xiaoxu Zhong

Publications and source records attributed to Xiaoxu Zhong.

8 recordsLinked to original sources

arXiv2026

A microscopic computational simulation of [18F]FDG transport and metabolism identifies valid regimes for compartmental analysis

18F-fluorodeoxyglucose ([18F]FDG) positron emission tomography (PET), combined with compartmental modeling, is a powerful non-invasive imaging method for assessing cellular metabolism. However, classical two- and three-tissue compartment models assume homogeneous [18F]FDG distribution within the tissue, which needs justification, and the definition and interpretation of rate constants across these models is not always consistent. To address these issues, we develop a finite difference solver to simulate [18F]FDG transport and metabolism within a 1 mm3 tissue volume, representing the smallest volume resolvable by PET. Our simulations reveal sub-millimeter heterogeneity in [18F]FDG distribution and show that the measured PET signal is dependent not only on cellular metabolic activity but also on interstitial [18F]FDG diffusivity, vascular permeability, and vascular architecture. We further demonstrate that our finite-difference simulation reduces to a three-tissue compartment model when interstitial [18F]FDG concentration is homogeneous. Furthermore, this simplified model itself reduces to the two-tissue compartment model when vascular permeability is sufficiently high. This work quantitatively links vascular permeability, vascular architecture, cellular uptake kinetics, [18F]FDG diffusivity, and acquisition time. It also unifies the two- and three-tissue compartment models and identifies their applicable regimes. These findings deepen our understanding of [18F]FDG transport kinetics and enhance the interpretability of dynamic [18F]FDG-PET imaging.

q-bio.TO↗

arXiv2022

Sedimentation of a surfactant-laden drop in a liquid with particles

This project aims to study the sedimentation of a surfactant-laden drop in a liquid with particles. A 2D simulation is performed with MATLAB. The interface is captured by the front-tracking method. The local viscosity depends on the local particle concentration, which follows a power law. The surfactants not only decrease the surface tension but also induce a surface tension gradient. If the surface tension decreases, the settling velocity will decrease due to a larger deformation of the drop (i.e., the drop becomes more flat). Additionally, increasing the Peclet number (ratio of convection to diffusion on the interface) for surfactants will reduce the settling velocity due to a larger surface tension gradient.

physics.flu-dyn↗

arXiv2022

Application of machine learning for predicting the spread of COVID-19

The spread of diseases has been studied for many years, but it receives a particular focus recently due to the outbreak and spread of COVID-19. Studies show that the spread of COVID-19 can be characterized by the Susceptible-Infectious-Recovered-Deceased (SIRD) model with containment coefficients (due to quarantine and keeping social distance). This project aims to apply the machine learning technique to predict the severity of COVID-19 and the effect of quarantine, keeping social distance, working from home, and wearing masks on the transmission of the disease. This work deepens our understanding of disease transmission and reveals the importance of following policies.

cs.LG↗

arXiv2018

On the Limiting Stokes' Wave of Extreme Height in Arbitrary Water Depth

As mentioned by Schwartz (1974) and Cokelet (1977), it was failed to gain convergent results of limiting Stokes' waves in extremely shallow water by means of perturbation methods even with the aid of extrapolation techniques such as Padé approximant. Especially, it is extremely difficult for traditional analytic/numerical approaches to present the wave profile of limiting waves with a sharp crest of $120^\circ$ included angle first mentioned by Stokes in 1880s. Thus, traditionally, different wave models are used for waves in different water depths. In this paper, by means of the homotopy analysis method (HAM), an analytic approximation method for highly nonlinear equations, we successfully gain convergent results (and especially the wave profiles) of the limiting Stokes' waves with this kind of sharp crest in arbitrary water depth, even including solitary waves of extreme form in extremely shallow water, without using any extrapolation techniques. Therefore, in the frame of the HAM, the Stokes' wave can be used as a unified theory for all kinds of waves, including periodic waves in deep and intermediate depth, cnoidal waves in shallow water and solitary waves in extremely shallow water.

physics.flu-dyn↗

arXiv2018

A singularity-free analytic solution of rise dynamics of a liquid in a vertical cylindrical capillary

Capillary driven flow is a famous problem in fluid dynamics which dates back to Leonardo da Vinci. In this paper, we apply an analytic approximation method for highly nonlinear problem, namely the homotopy analysis method (HAM), to a model of the meniscus movement in a uniform vertical circular tube. Convergent explicit series solution is successfully obtained. Our results agree well with the numerical results given by the symbolic computing software Mathematica using six-order Runge-Kutta methods. More importantly, our analytic solution is valid in the whole region of physical parameters, and therefore can predict whether the path of liquid is monotonic or oscillatory. This kind of solution, to the best knowledge of the authors, has never been reported in the past, which might greatly deepen our understandings about capillarity.

physics.flu-dyn↗

arXiv2016

On the homotopy analysis method for backward/forward-backward stochastic differential equations

In this paper, an analytic approximation method for highly nonlinear equations, namely the homotopy analysis method (HAM), is employed to solve some backward stochastic differential equations (BSDEs) and forward-backward stochastic differential equations (FBSDEs), including one with high dimensionality (up to 12 dimensions). By means of the HAM, convergent series solutions can be quickly obtained with high accuracy for a FBSDE in a 6 dimensional case, within less than $1\%$ CPU time used by a currently reported numerical method for the same case [34]. Especially, as dimensionality enlarges, the increase of computational complexity for the HAM is not as dramatic as this numerical method. All of these demonstrate the validity and high efficiency of the HAM for the backward/forward-backward stochastic differential equations in science, engineering and finance.

math.NA↗

arXiv2016

Analytic Solutions of Von Karman Plate under Arbitrary Uniform Pressure --- Equations in Differential Form

The large deflection of a circular thin plate under uniform external pressure is a classic problem in solid mechanics, dated back to Von K{á}rm{á}n \cite{Karman}. {This problem is reconsidered in this paper using an analytic approximation method, namely the homotopy analysis method (HAM).} Convergent series solutions are obtained for four types of boundary conditions with rather high nonlinearity, even in the case of $w(0)/h>20$, where $w(0)/h$ denotes the ratio of central deflection to plate thickness. Especially, we prove that the previous perturbation methods for an arbitrary perturbation quantity (including the Vincent's [2] and Chien's [3] methods) and the modified iteration method [4] are only the special cases of the HAM. However, the HAM works well even when the perturbation methods become invalid. All of these demonstrate the validity and potential of the HAM for the Von K{á}rm{á}n's plate equations, and show the superiority of the HAM over perturbation methods for highly nonlinear problems

math.AP↗

arXiv2016

Analytic Solutions of Von Karman Plate under Arbitrary Uniform Pressure (II): Equations in Integral Form

In this paper, the homotopy analysis method (HAM) is successfully applied to solve the Von Karman's plate equations in the integral form for a circular plate with the clamped boundary under an arbitrary uniform external pressure. Two HAM-based approaches are proposed. One is for a given external load Q, the other for a given central deflection. Both of them are valid for an arbitrary uniform external pressure by means of choosing a proper value of the so-called convergence-control parameters c_1 and c_2 in the frame of the HAM. Besides, it is found that iteration can greatly accelerate the convergence of solution series. In addition, we prove that the interpolation iterative method is a special case of the HAM-based 1st-order iteration approach for a given external load Q when c_1=-theta and c_2=-1, where theta denotes the interpolation parameter of the interpolation iterative method. Therefore, like Zheng and Zhou}, one can similarly prove that the HAM-based approaches are valid for an arbitrary uniform external pressure, at least in some special cases such as c_1=-theta and c_2=-1. Furthermore, it is found that the HAM-based iteration approaches converge much faster than the interpolation iterative method. All of these illustrate the validity and potential of the HAM for the famous Von Karman's plate equations, and show the superiority of the HAM over perturbation methods.

math.AP↗