arXiv subjects

Zilong Song

Publications and source records attributed to Zilong Song.

At least 19 recordsLinked to original sources

arXiv2026

Multiscale retinal flow on a spherical cap of varying aperture

Modelling retinal haemodynamics is crucial for understanding retinal microcirculation but is computationally demanding because it involves coupling between the vasculature and surrounding tissue across multiple scales. This computational burden has been substantially alleviated by a recent analytic solution on the planar disc that enables lumping the capillary bed and surrounding tissue into an effective resistor. However, that formulation treats the retina as a flat surface, whereas the retina is a curved surface with a finite anterior aperture. In this work, we develop a nontrivial and physiologically necessary extension to spherical-cap tissue domains with varying apertures, where surface curvature and finite-aperture boundaries complicate solving coupled Darcy equations on a curved manifold. Using a stereographic projection and a decoupling transformation, we derive an analytic solution for the capillary-tissue system on the spherical cap that represents flow in both the capillary bed and interstitial tissue more realistically while retaining the efficient resistor formulation, a key advantage of the planar-disc formulation. This solution is coupled to one-dimensional (1D) arteriolar and venular flows to obtain a multiscale description of retinal haemodynamics. Using a vasculature model designed to capture retinal vascular features, we show that the multiscale model's predictions are consistent with experimental data. We further explore aperture effects using both a fixed hemispherical vasculature and aperture-dependent vasculature. The aperture affects retinal haemodynamics mainly through changes in the constructed vasculature itself, whereas the surface-averaged pressures and relative terminal flow distributions remain nearly unchanged. This framework provides a foundation for studying retinal pathophysiology on more anatomically realistic domains.

physics.bio-ph↗

arXiv2025

A novel multiscale modelling for the hemodynamics in retinal microcirculation with an analytic solution for the capillary-tissue coupled system

Mathematical modelling of the microcirculatory hemodynamics in the retina is an essential tool for understanding various diseases of the retina, yet remains challenging due to the multiscale nature of the retinal vasculature and its coupling to surrounding tissue. To address this, we develop a multiscale model that couples retinal vasculature across scales with interstitial tissue. Our model combines the one-dimensional (1D) model for arterioles and venules with the coupled Darcy equations for capillaries and tissue. The model uses an analytic solution for capillary-tissue coupled system that provides a simple interpretation of the results along with much faster computation. The analytic solution implies a dynamic coupling condition that links the capillary bed with upstream arteriolar and downstream venular flows. The model is mathematically robust, demonstrated through analysis of the solution's truncation error and convergence. Its predictive accuracy is validated against experimental data and other models, making it useful in interpreting experimental results. Finally, the role of various parameters in controlling retinal hemodynamics is explored.

physics.bio-ph↗

arXiv2025

PEEL: A Poisoning-Exposing Encoding Theoretical Framework for Local Differential Privacy

Local Differential Privacy (LDP) is a widely adopted privacy-protection model in the Internet of Things (IoT) due to its lightweight, decentralized, and scalable nature. However, it is vulnerable to poisoning attacks, and existing defenses either incur prohibitive resource overheads or rely on domain-specific prior knowledge, limiting their practical deployment. To address these limitations, we propose PEEL, a Poisoning-Exposing Encoding theoretical framework for LDP, which departs from resource- or prior-dependent countermeasures and instead leverages the inherent structural consistency of LDP-perturbed data. As a non-intrusive post-processing module, PEEL amplifies stealthy poisoning effects by re-encoding LDP-perturbed data via sparsification, normalization, and low-rank projection, thereby revealing both output and rule poisoning attacks through structural inconsistencies in the reconstructed space. Theoretical analysis proves that PEEL, integrated with LDP, retains unbiasedness and statistical accuracy, while being robust to expose both output and rule poisoning attacks. Moreover, evaluation results show that LDP-integrated PEEL not only outperforms four state-of-the-art defenses in terms of poisoning exposure accuracy but also significantly reduces client-side computational costs, making it highly suitable for large-scale IoT deployments.

cs.CR↗

arXiv2025

Glymphatic Clearance in the Optic Nerve: A Multidomain Electro-osmostic Model

Effective metabolic waste clearance and maintaining ionic homeostasis are essential for the health and normal function of the central nervous system. To understand its mechanism and the role of fluid flow, we develop a multidomain electro-osmotic model of optic-nerve microcirculation that couples hydrostatic and osmotic fluid transport with electro-diffusive solute movement across axons, glia, the extracellular space, and arterial/venous/capillary perivascular spaces. Cerebrospinal fluid enters the optic nerve via the arterial parivascular space, passes both the glial and ECS before exiting through the venous parivascular space. Exchanges across astrocytic endfeet are essential and they occur in two distinct and coupled paths: through AQP4 on glial membranes and gaps between glial endfeet, thus establishing a mechanistic substrate for two modes of glymphatic transport, at rest and during stimulus-evoked perturbations. Parameter sweeps show that lowering AQP4-mediated fluid permeability or PVS permeability elevates pressure, suppresses radial exchange and slows clearance, effects most pronounced for solutes reliant on PVS V export. The model reproduces baseline and stimulus-evoked flow and demonstrates that PVS-mediated export is the primary clearance route for both small and moderate solutes. Small molecules clear faster because rapid ECS diffusion broadens their distribution and enhances ECS PVS exchange, whereas moderate species have low ECS diffusivity, depend on transendfoot transfer, and clear more slowly via PVS V convection. Our framework can also be used to explain the sleep-wake effect mechanistically: enlarging ECS volume or permeability increases transinterface flux and accelerates waste removal.

q-bio.CB↗

arXiv2025

Pump-driven droplet electrohydrodynamics: deformation, pinch-off and recoalescence

We investigate pump-driven droplet electrohydrodynamics with an emphasis on deformation, pinch-off, and recoalescence. A thermodynamically consistent phase-field framework is developed that couples Nernst--Planck--Poisson electrodiffusion with incompressible Navier--Stokes--Cahn--Hilliard flow, and incorporates interfacial ionic pumps as prescribed surface fluxes. In the pump-free baseline, applied fields merely polarise the droplet and deformation is negligible. By contrast, surface-localised pumping drives the accumulation of positive ions within the droplet, elevates the interior potential, and generates non-uniform electric fields. The resulting Lorentz stresses stretch and displace the droplet, thin interfacial necks, and trigger pinch-off; the daughter droplets subsequently recoalesce, often after wall contact, yielding flattened remnants. In multiple-droplet settings, pump-induced charging produces lateral electrostatic repulsion and asymmetric deformation; under geometric confinement, crescent bending and star-like morphologies emerge. Shear-flow tests further show that a pumped droplet can be immobilised and ruptured while an unpumped neighbour is advected downstream, suggesting a route to sorting. Taken together, the results establish interfacial pumping as an internal actuation mechanism that robustly controls droplet morphology and dynamics across configurations.

physics.flu-dyn↗

arXiv2025

Proper Orthogonal Decomposition-based Model-Order Reduction for Smoothed Particle Hydrodynamics Simulation -- Mass-Spring-Damper System

Model Order Reduction (MOR) based on Proper Orthogonal Decomposition (POD) and Smooth Particle Hydrodynamics (SPH) has proven effective in various applications. Most MOR methods utilizing POD are implemented within a pure Eulerian framework, while significantly less attention has been given to POD in a Lagrangian context. In this paper, we present the POD-MOR of SPH simulations applied to a mass-spring-damper system with two primary objectives: 1. To evaluate the performance of the data-driven POD-MOR approach. 2. To investigate potential methods for accelerating POD-MOR computations. Although the mass-spring-damper system is linear, its SPH implementations are nonlinear, and POD-MOR does not automatically lead to faster computations. Our findings indicate that (1) the POD-MOR effectively reduces the degrees of freedom in the SPH simulations by capturing the essential modes, and (2) in various cases, the acceleration of POD-MOR can be achieved without compromising accuracy. We hope that our results will motivate further investigations into the design of POD-MOR algorithms for nonlinear Lagrangian systems.

physics.comp-ph↗

arXiv2025

Proper Orthogonal Decomposition-based Model-Order Reduction for Smoothed Particle Hydrodynamics Simulation

In this paper, we present a projection-based model-order reduction (MOR) technique for smoothed particle hydrodynamics (SPH) simulations, which is a mesh-free approach within the Lagrangian framework. Our approach utilizes the proper orthogonal decomposition (POD) technique to generate a subspace basis for the reduction process. The main objective of this study is to conduct an initial exploration of the feasibility of employing POD-based MOR (POD-MOR) in SPH simulations and to quantify the associated POD error. To illustrate the effectiveness of this approach, we consider the friction stir spot welding problem, which involves the coupling of flow equations and heat equation. Our findings reveal that, with the same degrees of freedom, POD-MOR significantly reduces computational error compared to the uniform reduction of particle numbers in SPH simulations. Additionally, the acceleration technique of POD-MOR for SPH simulation via linearization and freezing coefficients has been shown to be effective while keeping the error small. We have also showed the effectiveness of POD-MOR in predictive settings in SPH simulations with different parameter values.

physics.comp-ph↗

arXiv2025

Micro-Macro Modeling of Polymeric Fluids with Multi-Bead Polymer Chain

This work extends the classical dumbbell (two-bead) model of polymer chains to a more detailed multi-bead representation, where each polymer chain consists of $N$ beads connected by $N-1$ springs. We develop a thermodynamically consistent micro-macro model based on the energy variational method to describe the coupled dynamics of polymer configurations and fluid flow. The resulting framework captures complex microscopic behaviors, such as bond stretching and alignment under flow, and links them to macroscopic stress responses.

cond-mat.soft↗

arXiv2024

Multidomain Model for Optic Nerve Potassium Clearance: Roles of Glial Cells and Perivascular Spaces

The accumulation of potassium in the extracellular space surrounding nerve cells is a fundamental aspect of biophysics that has garnered significant attention in recent research. This phenomenon holds implications for various neurological conditions, including spreading depression, migraine, certain types of epilepsy, and potentially, learning processes. A quantitative analysis is essential for understanding the dynamics of potassium clearance following a series of action potentials. This clearance process involves multiple structures along the nerve, including glia, the extracellular space, axons, and the perivascular space, necessitating a spatially distributed systems approach akin to the cable equations of nerve physiology. In this study, we propose a multi-domain model for the optic nerve to investigate potassium accumulation and clearance dynamics. The model accounts for the convection, diffusion, and electrical migration of fluid and ions, revealing the significant roles of glia and the perivascular space in potassium buffering. Specifically, our findings suggest that potassium clearance primarily occurs through convective flow within the syncytia of glia, driven by osmotic pressure differences. Additionally, the perivascular space serves as a crucial pathway for potassium buffering and fluid circulation, further contributing to the overall clearance process. Importantly, our model's adaptability allows for its application to diverse structures with distinct channel and transporter distributions across the six compartments, extending its utility beyond the optic nerve.

physics.bio-ph↗

arXiv2024

FedFixer: Mitigating Heterogeneous Label Noise in Federated Learning

Federated Learning (FL) heavily depends on label quality for its performance. However, the label distribution among individual clients is always both noisy and heterogeneous. The high loss incurred by client-specific samples in heterogeneous label noise poses challenges for distinguishing between client-specific and noisy label samples, impacting the effectiveness of existing label noise learning approaches. To tackle this issue, we propose FedFixer, where the personalized model is introduced to cooperate with the global model to effectively select clean client-specific samples. In the dual models, updating the personalized model solely at a local level can lead to overfitting on noisy data due to limited samples, consequently affecting both the local and global models' performance. To mitigate overfitting, we address this concern from two perspectives. Firstly, we employ a confidence regularizer to alleviate the impact of unconfident predictions caused by label noise. Secondly, a distance regularizer is implemented to constrain the disparity between the personalized and global models. We validate the effectiveness of FedFixer through extensive experiments on benchmark datasets. The results demonstrate that FedFixer can perform well in filtering noisy label samples on different clients, especially in highly heterogeneous label noise scenarios.

cs.LG↗

arXiv2024

A multi-domain model for microcirculation in optic nerve: blood flow and oxygen transport

Microcirculation of blood and oxygen transport play important roles in biological function of optic nerve and are directly affected by damages or pathologies. This work develops a multi-domain model for optic nerve, that includes important biological structures and various physical mechanisms in blood flow and oxygen delivery. The two sets of vasculature network are treated as five domains in the same geometric region, with various exchanges among them (such as Darcy's law for fluid flow) and with the tissue domain (such as water leak, diffusion). The numerical results of the coupled model for a uniform case of vasculature distribution show mechanisms and scales consistent with literature and intuition. The effects of various important model parameters (relevant to pathological conditions) are investigated to provide insights into the possible implications. The vasculature distribution (resting volume fractions here) has significant impacts on the blood circulation and could lead to insufficient blood supply in certain local region and in turn affect the oxygen delivery. The water leak across the capillary wall will have nontrivial effects after the leak coefficients pass a threshold. The periodic arterial pressure conditions lead to expected periodic patterns and stable spatial profiles, and the uniform case is almost the averaged version of periodic case. The effects of viscosity, the stiffness of blood vessel wall, oxygen demand, etc. have also been analyzed. The framework can be extended to include ionic transport or to study the retina when more biological structural information is available.

physics.bio-ph↗

arXiv2023

Coupled Chemical Reactions: Effects of Electric Field, Diffusion and Boundary Control

Chemical reactions involve the movement of charges, and this work presents a mathematical model for describing chemical reactions in electrolytes. The model is developed using an energy variational method that aligns with classical thermodynamics principles. It encompasses both electrostatics and chemical reactions within consistently defined energetic and dissipative functionals. Furthermore, the energy variation method is extended to account for open systems that involve the input and output of charge and mass. Such open systems have the capability to convert one form of input energy into another form of output energy. In particular, a two-domain model is developed to study a reaction system with self-regulation and internal switching, which plays a vital role in the electron transport chain of mitochondria responsible for ATP generation crucial process for sustaining life. Simulations are conducted to explore the influence of electric potential on reaction rates and switching dynamics within the two-domain system. It shows that the electric potential inhibits the oxidation reaction while accelerating the reduction reaction.

physics.chem-ph↗

arXiv2023

Micro-Macro Modeling of Polymeric Fluids and Shear-Induced Microscopic Behaviors

This article delves into the micro-macro modeling of polymeric fluids, considering various microscopic potential energies, including the classical Hookean potential, as well as newly proposed modified Morse and Elastic-plastic potentials. These proposed potentials encompass microscopic-scale bond-breaking processes. The development of a thermodynamically consistent micro-macro model is revisited, employing the energy variational method. To validate the model's predictions, we conduct numerical simulations utilizing a deterministic particle-FEM method. Our numerical findings shed light on the distinct behaviors exhibited by polymer chains at the micro-scale in comparison to the macro-scale velocity and induced shear stresses of fluids under shear flow. Notably, we observe that polymer elongation, rotation, and bond breaking contribute to the zero polymer-induced stress in the micro-macro model when employing Morse and Elastic-plastic potentials. Furthermore, at high shear rates, polymer rotation is found to induce shear-thinning behavior in the model employing the classical Hookean potential.

cond-mat.soft↗

arXiv2023

A phase field model for droplets suspended in viscous liquids under the influence of electric fields

In this paper, we propose a Poisson-Nernst-Planck-Navier-Stokes-Cahn-Hillard (PNP-NS-CH)model for an electrically charged droplet suspended in a viscous fluid subjected to an external electric field. Our model incorporates spatial variations of electric permittivity and diffusion constants, as well as interfacial capacitance. Based on a time scale analysis, we derive two approximations of the original model, namely a dynamic model for the net charge and a leaky-dielectric model. For the leaky-dielectric model, we conduct a detailed asymptotic analysis to demonstrate the convergence of the diffusive-interface leaky-dielectric model to the sharp interface model as the interface thickness approaches zero. Numerical computations are performed to validate the asymptotic analysis and demonstrate the model's effectiveness in handling topology changes, such as electrocoalescence. Our numerical results of these two approximation models reveal that the polarization force, which is induced by the spatial variation of electric permittivity in the direction perpendicular to the external electric field, consistently dominates the Lorentz force, which arises from the net charge. The equilibrium shape of droplets is determined by the interplay between these two forces along the direction of the electric field. Furthermore, in the presence of the interfacial capacitance, a local variation of effective permittivity leads to an accumulation of counter-ions near the interface, resulting in a reduction in droplet deformation. Our numerical solutions also confirm that the leaky dielectric model serves as a reasonable approximation of the original PNP-NS-CH model when the electric relaxation time is sufficiently short. The Lorentz force and droplet deformation both decrease when the diffusion of net charge is significant.

physics.flu-dyn↗

arXiv2022

Mathematical Model for Chemical Reactions in Electrolyte Applied to Cytochrome $c$ Oxidase: an Electro-osmotic Approach

A mathematical model for chemical reactions in electrolytes is developed using an Energy variational method consistent with classical thermodynamics. Electrostatics and chemical reactions are included in properly defined energetic and dissipative functionals. The energy variation method is generalized to deal with open systems with inputs of charge, mass, and energy. The open systems can transform input energy of one type into output energy of another type. The generalized method is used to analyze the conversion of electrical current into proton flow by cytochrome c oxidase, an important enzyme in mitochondria that helps generate the 'energetic currency of life' ATP. The structure of the oxidase guides flows of current and mass that interact according to the energetic and dissipative functionals of the generalized theory. Kirchhoff's current law provides important coupling when the enzyme is in its natural setting in the mitochondrial membrane. The natural function of the enzyme is the result. Electron flows are converted into proton flows and gradients.

physics.chem-ph↗

arXiv2022

A Bubble Model for the Gating of Kv Channels

Voltage-gated Kv channels play fundamental roles in many biological processes, such as the generation of the action potential. The gating mechanism of Kv channels is characterized experimentally by single-channel recordings and ensemble properties of the channel currents. In this work, we propose a bubble model coupled with a Poisson-Nernst-Planck (PNP) system to capture the key characteristics, particularly the delay in the opening of channels. The coupled PNP system is solved numerically by a finite-difference method and the solution is compared with an analytical approximation. We hypothesize that the stochastic behaviour of the gating phenomenon is due to randomness of the bubble and channel sizes. The predicted ensemble average of the currents under various applied voltages across the channels is consistent with experimental observations, and the Cole-Moore delay is captured by varying the holding potential.

physics.bio-ph↗

arXiv2019

An energy stable $C^0$ finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density

In this paper, we focus on modeling and simulation of two-phase flow with moving contact lines and variable density. A thermodynamically consistent phase-field model with General Navier Boundary Condition is developed based on the concept of quasi-incompressibility and the energy variational method. Then a mass conserving and energy stable C0 finite element scheme is developed to solve the PDE system. Various numerical simulation results show that the proposed schemes are mass conservative, energy stable and the 2nd order for P1 element and 3rd order for P2 element convergence rate in the sense of L2 norm.

math.NA↗

arXiv2019

Analytical study on phase transition of shape memory alloy wire under uniaxial tension

This paper considers the stress-induced phase transitions of shape memory alloy slender cylinder, and analytically studies the phase transition process and the associated instability. A three-dimensional (3D) phenomenological model with an internal variable is adopted, which is simplified to a 1D system of two strains in three regions (austenite, martensite and phase transition regions). Suitable boundary conditions and interface conditions are proposed. Theoretically, it is a free boundary problem, as the position and shape of phase interfaces are unknown. We then focus on planar interfaces (which are energetically favored), and a symmetric case when phase transition occurs in the middle. For given applied stress, two-region solutions, three-region solutions and the connecting solutions between them are obtained analytically or semi-analytically, including many period-k solutions. Two-region solutions show that phase transition does not take place at one point, but simultaneously in a small region. The width of phase transition region is found analytically, revealing the roles of the material and geometrical parameters. Three-region solutions represent localized inhomogeneous deformations in experiments, and capture that the stress stays almost at the Maxwell stress during propagation of transformation front. For displacement-controlled process, the transition process is demonstrated by the stress-strain curve, which captures the stress drop/rise and the transition from homogeneous deformations to period-1 localized inhomogeneous deformations. When the radius is smaller than a critical value (given by material constants), the stress drop is very sharp due to transition of solutions in a snap-back bifurcation. These features show good agreement with experimental observations and shed light on the difficulties of numerical simulations.

cond-mat.soft↗