arXiv subjects

Chaozhen Wei

Publications and source records attributed to Chaozhen Wei.

17 recordsLinked to original sources

arXiv2026

Efficient primal--dual splitting methods for a Poisson-constrained JKO scheme for Poisson-Nernst-Planck models

The Poisson--Nernst--Planck (PNP) equations strongly couple ionic transport and electrostatic interactions through the Poisson equation, posing substantial numerical challenges under small permittivity and complex potential boundary conditions. Underlying these equations is a natural Wasserstein gradient-flow structure, in which the Poisson equation serves as a local realization of the nonlocal electrostatic interaction energy. Exploiting this structure, we formulate each time step as a constrained convex minimization problem where the ionic continuity equations and the Poisson equation are incorporated as linear constraints, allowing the concentrations, fluxes, and electrostatic potential to be updated simultaneously. The variational structure of the scheme intrinsically guarantees the dissipation of the original free energy, mass conservation, and nonnegativity of ionic concentrations under general electrostatic boundary conditions. Moreover, the framework is structurally modular: extending from classical to modified PNP models with steric interactions and concentration-gradient corrections requires only modifying the energy functional, while all structure-preserving properties are automatically retained. To efficiently solve the resulting large-scale constrained problems, we develop preconditioned and transformed primal--dual algorithms equipped with tailored fast dual solvers, namely DCT-based direct and Schur-complement iterative methods, that exploit the coupled block structure of the PDE constraints. Numerical experiments on classical and modified PNP systems demonstrate the accuracy and structure-preserving properties of the scheme, and show that the proposed algorithms converge reliably in strongly coupled small-permittivity regimes without significant growth in computational cost.

math.NA↗

arXiv2026

Continuum modeling of fluidic and elastic flow during growth-driven wound closure in partial-EMT cell monolayers

Large-scale circular gap closure occurs over a time scale on which cell growth and proliferation become important. Growth is the main driver of the closing process, while cell dynamics such as elongation and intercalation reflect elastic and fluidic contributions to tissue deformation. We develop a novel fluidized growth-elasticity framework as a nonlinear analogue of a Maxwell fluid with growth. The framework decomposes the experimentally observable strain rate into the additive sum of the growth, elastic, and fluidic strain rates, thus enabling the separate quantification of these contributions from tissue kinematics and allowing the roles of tissue elasticity and fluidity (the inverse of viscosity) to be characterized. We apply the model to large circular gaps ($\sim$1.7 mm in diameter) in confluent monolayers of mouse embryonic epicardial cells (MEC1) under two conditions, without and with TGF-$\beta$ treatment. We show that both tissue fluidity and the elastic properties associated with fiber reinforcement are critical for reproducing the closure kinematics. Specifically, we predict that the treated condition has lower fluidity, associated with a lower fluidic deformation rate and a higher elastic deformation rate than the untreated condition, in agreement with the experimental observations.

physics.flu-dyn↗

arXiv2026

A phase-field model for viscoelastic compressible tumor growth

It is well known that growing tumors generate and respond to stress in their local microenvironment. Tissue re-arrangements can relax these mechanical stresses and make the tissue more fluid-like. Further, intricate coupling between mechanotransduction and biochemical signaling leads to complex patterns of growth. To predict the outcomes of these nonlinear interactions, we develop a phase-field model to simulate tumors growing into a surrounding medium taking into account their elastic and viscous properties as well as their compressibilities. We couple continuum modeling of the viscoelastic mechanics to the concentration of a diffusible growth-promoting nutrient in a mass conservative way. The phase-field method is a stable and flexible way to describe the dynamics of arbitrarily shaped tumors. We demonstrate convergence of the phase-field model to a sharp interface model in radially symmetric geometries and can observe progression to stationary tumors. However, our results show that these stationary symmetric tumors are subject to symmetry-breaking instabilities in 2D and 3D driven by two primary mechanisms: (i) elastic buckling instabiliies due to differential growth induced by the nutrient gradient and (ii) instabilities generated by apoptosis-related volumetric loss. Further, tissue fluidity and compressibility can lead to changes in tumor topologies. Our modeling framework provides a robust methodology for investigating how tissue mechanics and growth factor signaling influence the progression and invasive potential of solid tumors.

cond-mat.soft↗

arXiv2025

A Primal-dual Forward-backward Splitting Method for Cross-diffusion Gradient Flows with General Mobility Matrices

In this work, we construct a primal-dual forward-backward (PDFB) splitting method for computing a class of cross-diffusion systems that can be formulated as gradient flows under transport distances induced by matrix mobilities. By leveraging their gradient flow structure, we use minimizing movements as the variational formulation and compute these cross-diffusion systems by solving the minimizing movements as optimization problems at the fully discrete level. Our strategy to solve the optimization problems is the PDFB splitting method outlined in our previous work \cite{PDFB2024}. The efficiency of the proposed PDFB splitting method is demonstrated on several challenging cross-diffusion equations from the literature.

math.NA↗

arXiv2025

Variable-preconditioned transformed primal-dual method for generalized Wasserstein Gradient Flows

We propose a Variable-Preconditioned Transformed Primal-Dual (VPTPD) method for solving generalized Wasserstein gradient flows based on the structure-preserving JKO scheme. This is a nontrivial extension of the TPD method [Chen et al. (2025) SIAM J. Sci. Comput.] incorporating proximal splitting techniques to address the challenges arising from the nonsmoothness of the objective function. Our key contributions include: (i) a semi-implicit-explicit iterative scheme that combines proximal gradient steps with explicit gradient steps to treat the nonsmooth and smooth terms respectively; (ii) variable-dependent preconditioners constructed from the Hessian of a regularized objective to balance iteration count and per-iteration cost; (iii) a proof of existence and uniqueness of bounded solutions for the generalized proximal operator with the chosen preconditioner, along with a convergent and bound-preserving Newton solver; and (iv) an adaptive step-size strategy to improve robustness and accelerate convergence under poor Lipschitz conditions of the energy derivative. Comprehensive numerical experiments spanning from 1D to 3D settings demonstrate that our method achieves superior computational efficiency--achieving up to a 20$\times$ speedup over existing methods-thereby highlighting its broad applicability through several challenging simulations.

math.NA↗

arXiv2025

Inferring Exocytosis Profiles from Cell Shapes Using a Dual-Configuration Model of Walled Cell Tip Growth

Tip growth in filamentous cells, such as root hairs, moss protonemata, and fungal hyphae, depends on coordinated cell wall extension driven by turgor pressure, wall mechanics, and exocytosis. We introduce a dual-configuration model that incorporates both turgid and unturgid states to describe cell wall growth as the combined effect of elastic deformation and irreversible extension. This framework infers exocytosis profiles directly from cell morphology and elastic stretches, formulated as an initial value problem based on the self-similarity condition. Applying the model to Medicago truncatula root hairs, moss Physcomitrium patens protonemata, and hyphoid-like shapes, we find that exocytosis peaks at the tip in tapered cells but shifts to an annular region away from the apex in flatter-tip cells beyond a threshold. The model generalizes previous fluid models and provides a mechanistic link between exocytosis distribution and cell shape, explaining observed variations in tip-growing cells across species.

q-bio.CB↗

arXiv2025

Primal-dual splitting methods for phase-field surfactant model with moving contact lines

Surfactants have important effects on the dynamics of droplets on solid surfaces, which has inspired many industrial applications. Phase-field surfactant model with moving contact lines (PFS-MCL) has been employed to investigate the complex droplet dynamics with surfactants, while its numerical simulation remains challenging due to the coupling of gradient flows with respect to transport distances involving nonlinear and degenerate mobilities. We propose a novel structure-preserving variational scheme for PFS-MCL model with the dynamic boundary condition based on the minimizing movement scheme and optimal transport theory for Wasserstein gradient flows. The proposed scheme consists of a series of convex minimization problems and can be efficiently solved by our proposed primal-dual splitting method and its accelerated versions. By respecting the underlying PDE's variational structure with respect to the transport distance, the proposed scheme is proved to inherits the desirable properties including original energy dissipation, bound-preserving, and mass conservation. Through a suite of numerical simulations, we validate the performance of the proposed scheme and investigate the effects of surfactants on the droplet dynamics.

math.NA↗

arXiv2025

Efficient Primal-dual Forward-backward Splitting Method for Wasserstein-like Gradient Flows with General Nonlinear Mobilities

We construct an efficient primal-dual forward-backward (PDFB) splitting method for computing a class of minimizing movement schemes with nonlinear mobility transport distances, and apply it to computing Wasserstein-like gradient flows. This approach introduces a novel saddle point formulation for the minimizing movement schemes, leveraging a support function form from the Benamou-Brenier dynamical formulation of optimal transport. The resulting framework allows for flexible computation of Wasserstein-like gradient flows by solving the corresponding saddle point problem at the fully discrete level, and can be easily extended to handle general nonlinear mobilities. We also provide a detailed convergence analysis of the PDFB splitting method, along with practical remarks on its implementation and application. The effectiveness of the method is demonstrated through several challenging numerical examples.

math.NA↗

arXiv2024

Chemomechanical regulation of growing tissues from a thermodynamically-consistent framework and its application to tumor spheroid growth

It is widely recognized that reciprocal interactions between cells and their microenvironment, via mechanical forces and biochemical signaling pathways, regulate cell behaviors during normal development, homeostasis and disease progression such as cancer. However, it is still not well understood how complex patterns of tissue growth emerge. Here, we propose a framework for the chemomechanical regulation of growth based on thermodynamics of continua and growth-elasticity to predict growth patterns. Combining the elastic and chemical energies, we use an energy variational approach to derive a novel formulation that incorporates an energy-dissipating stress relaxation and biochemomechanical regulation of the volumetric growth rate. We validate the model using experimental data from growth of tumor spheroids in confined environments. We also investigate the influence of model parameters, including tissue rearrangement rate, tissue compressibility, strength of mechanical feedback and external mechanical stimuli, on the growth patterns of tumor spheroids.

physics.bio-ph↗

arXiv2023

Structure preserving primal dual methods for gradient flows with nonlinear mobility transport distances

We develop structure preserving schemes for a class of nonlinear mobility continuity equation. When the mobility is a concave function, this equation admits a form of gradient flow with respect to a Wasserstein-like transport metric. Our numerical schemes build upon such formulation and utilize modern large scale optimization algorithms. There are two distinctive features of our approach compared to previous ones. On one hand, the essential properties of the solution, including positivity, global bounds, mass conservation and energy dissipation are all guaranteed by construction. On the other hand, it enjoys sufficient flexibility when applies to a large variety of problems including different free energy functionals, general wetting boundary conditions and degenerate mobilities. The performance of our methods are demonstrated through a suite of examples.

math.NA↗

arXiv2022

Inferring relative surface elastic moduli in thin-wall models of single cells

There is a growing interest in measuring the cell wall mechanical property at different locations in single walled cells. We present an inference scheme that maps relative surface elastic modulus distributions along the cell wall based on tracking the location of material marker points along the turgid and relaxed cell wall outline. A primary scheme provides a step-function inference of surface elastic moduli by computing the tensions and elastic stretches between material marker points. We perform stability analysis for the primary scheme against perturbations on the marker-point locations, which may occur due to image acquisition and processing from experiments. The perturbation analysis shows that the primary scheme is more stable to noise when the spacing between the marker points is coarser, and has been confirmed by the numerical experiments where we apply the primary scheme to synthetic cell outlines from simulations of hyper-elastic membrane deformation with random noise on the marker-point locations. To improve the spatial resolution of elastic modulus distribution of the primary scheme with noise, we propose two optimization schemes that convert the step-function inferences of elastic moduli into smooth-curve inferences. The first scheme infers a canonical elastic modulus distribution based on marker-point locations from multiple cell samples of the same cell type. The second scheme is a simplified cost-effective version that infers the elastic moduli based on marker-point locations from a single cell. The numerical experiments show that the first scheme significantly improves the inference precision for the underlying canonical elastic modulus distributions and can even capture some degree of nonlinearity when the underlying elastic modulus gradients are nonlinear. The second cost-effective scheme can predict the trend of the elastic modulus gradients consistently.

physics.bio-ph↗

arXiv2021

An Eulerian nonlinear elastic model for compressible and fluidic tissue with radially symmetric growth

Cell proliferation, apoptosis, and myosin-dependent contraction can generate elastic stress and strain in living tissues, which may be dissipated by internal rearrangement through cell topological transition and cytoskeletal reorganization. Moreover, cells and tissues can change their sizes in response to mechanical cues. The present work demonstrates the role of tissue compressibility and internal rearranging activities on its size and mechanics regulation in the context of differential growth induced by a field of growth-promoting chemical factors. We develop a mathematical model based on finite elasticity and growth theory and the reference map techniques to describe the coupled tissue growth and mechanics in the Eulerian frame. We incorporate the tissue rearrangement by introducing a rearranging rate to the reference map evolution, leading to elastic-energy dissipation when tissue growth and deformation are in radial symmetry. By linearizing the model, we show that the stress follows the Maxwell-type viscoelastic relaxation. The rearrangement rate, which we call tissue fluidity, sets the stress relaxation time, and the ratio between the shear modulus and the fluidity sets the tissue viscosity. By nonlinear simulation of growing tissue spheroids and discs with graded growth rates along the radius, we find that the tissue compressibility and fluidity influence their equilibrium size. By comparing the nonlinear simulations with the linear analytical solutions, we show the size change as a nonlinear effect due to the advection of the tissue density flow, which only occurs when both tissue compressibility and fluidity are small. We apply the model to study tumor spheroid growth and epithelial disc growth when a reaction-diffusion process determines the growth-promoting factor field.

physics.bio-ph↗

arXiv2019

Grain boundary triple junction dynamics: a continuum disconnection model

The microstructure of polycrystalline materials consists of networks of grain boundaries (GBs) and triple junctions (TJs), along which three GBs meet. The evolution of such microstructures may be driven by surface tension (capillarity), applied stresses, or other means that lead to a jump in chemical potential across the GBs. Here, we develop a model for the concurrent evolution of the GB/TJ network based upon the microscopic mechanism of motion; the motion of line defects (disconnections) in the GB that have both dislocation and step character. The evolution involves thermally-activated disconnection formation/annihilation and migration of multiple disconnections modes/types. We propose this crystallography-respecting continuum model for the disconnection mechanism of GB/TJ dynamics derived with a variational approach based on the principle of maximum energy dissipation. The resultant TJ dynamics is reduced to an optimization problem with constraints that account for local microstructure geometry, conservation of Burgers vectors, and thermal-kinetic limitations on disconnection fluxes. We present analysis of and numerical simulations based upon our model to demonstrate the dependence of the GB and TJ mobilities and the TJ drag effect on the disconnection properties, and compare the predictions with molecular dynamics and experimental observations.

physics.comp-ph↗

arXiv2019

A Continuum Multi-Disconnection-Mode Model for Grain Boundary Migration

We study the Grain Boundary (GB) migration based on the underlying disconnection structure and mechanism. Disconnections are line defects that lie solely within a GB and are characterized by both a Burgers vector and a step height, as set by the GB bicrystallography. Multiple disconnection modes can nucleate, as determined by their formation energy barriers and temperature, and move along the GB under different kinds of competing driving forces including shear stress and chemical potential jumps across the GBs. We present a continuum model in two dimensions for GB migration where the GB migrates via the thermally-activated nucleation and kinetically-driven motion of disconnections. We perform continuum numerical simulations for investigating the GB migration behavior in single and multi-mode disconnection limits in both a bicrystal (under two types of boundary conditions) and for a finite-length GB with pinned ends. The results clearly demonstrate the significance of including the coupling and competing between different disconnection modes and driving forces for describing the complex and diverse phenomena of GB migration within polycyrstalline microstructures.

cond-mat.mtrl-sci↗

arXiv2019

Primal dual methods for Wasserstein gradient flows

Combining the classical theory of optimal transport with modern operator splitting techniques, we develop a new numerical method for nonlinear, nonlocal partial differential equations, arising in models of porous media, materials science, and biological swarming. Our method proceeds as follows: First, we discretize in time, either via the classical JKO scheme or via a novel Crank-Nicolson type method we introduce. Next, we use the Benamou-Brenier dynamical characterization of the Wasserstein distance to reduce computing the solution of the discrete time equations to solving fully discrete minimization problems, with strictly convex objective functions and linear constraints. Third, we compute the minimizers by applying a recently introduced, provably convergent primal dual splitting scheme for three operators [Yan 2018]. By leveraging the PDEs' underlying variational structure, our method overcomes stability issues present in previous numerical work built on explicit time discretizations, which suffer due to the equations' strong nonlinearities and degeneracies. Our method is also naturally positivity and mass preserving and, in the case of the JKO scheme, energy decreasing. We prove that minimizers of the fully discrete problem converge to minimizers of the spatially continuous, discrete time problem as the spatial discretization is refined. We conclude with simulations of nonlinear PDEs and Wasserstein geodesics in one and two dimensions that illustrate the key properties of our approach, including higher order convergence our novel Crank-Nicolson type method, when compared to the classical JKO method.

math.NA↗

arXiv2017

Bound states in the continuum of fractional Schr\"odinger equation in the Earth's gravitational field and their effects in the presence of a minimal length: applications to distinguish ultralight particles

In this paper, the influence of the fractional dimensions of the L\'evy path under the Earth's gravitational field is studied, and the phase transitions of energy and wave functions are obtained: the energy changes from discrete to continuous and wave functions change from non-degenerate to degenerate when dimension of L\'evy path becomes from integer to non-integer. By analyzing the phase transitions, we solve two popular problems. First, we find an exotic way to produce the bound states in the continuum (BICs), our approach only needs a simple potential, and does not depend on interactions between particles. Second, we address the continuity of the energy will become strong when the mass of the particle becomes small. By deeply analyze, it can provide a way to distinguish ultralight particles from others types in the Earth's gravitational field, and five popular particles are discussed. In addition, we obtain analytical expressions for the wave functions and energy in the Earth's gravitational field in the circumstance of a fractional fractal dimensional L\'evy path. Moreover, to consider the influence of the minimal length, we analyze the phase transitions and the BICs in the presence of the minimal length. We find the phenomenon energy shift do not exist, which is a common phenomenon in the presence of the minimal length, and hence such above phenomena can still be found. Finally, relations between our results and existing results are discussed.

quant-ph↗

arXiv2017

A Fokker-Planck reaction model for the epitaxial growth and shape transition of quantum dots

We construct a Fokker-Planck reaction model to investigate the dynamics of the coupled epitaxial growth and shape transition process of an array of quantum dots. The Fokker-Planck reaction model is based on a coupled system of Fokker-Planck equations wherein the distribution of each island type is governed by its own Fokker-Planck equation for growth, with reaction terms describing the shape transitions between islands of different types including asymmetric shapes. The reaction terms for the shape transitions depend on the island size and are determined from explicit calculations of the lowest-barrier pathway for each shape transition. This mean-field model enables us to consider the kinetics of asymmetric shape transitions and study the evolution of island shape distributions during the coupled growth and transition process. Through numerical simulations over a range of growth parameters, we find multimodal and unimodal evolution modes of the shape distribution of island arrays, which depend on the external deposition flux rate and temperature rather than the shape transition rate. However, the shape transition rate governs the kinetics of shape transitions and determines the fraction of islands that form via asymmetric states, which has implications for the development of asymmetric composition profiles within alloy islands.

cond-mat.stat-mech↗