arXiv subjects

Zecheng Gan

Publications and source records attributed to Zecheng Gan.

16 recordsLinked to original sources

arXiv2026

Designing Coulombic Contact Interactions between Polarizable Particles through Asymmetry

Polarizable particle systems, including charged colloids, polarizable ions, biomolecular assemblies, and soft nanomaterials, can exhibit contact electrostatic interactions that depart strongly from Coulomb behavior when dielectric mismatch and geometric singularities amplify polarization effects. Here we use charged dielectric spheres as a model system and show that these polarization contributions can be canceled by jointly tuning size, charge, and dielectric asymmetries. By extending a recently developed image-charge formula to contacting dielectric spheres, we derive analytical conditions under which the contact interaction reduces to the bare Coulomb form. Accurate two-sphere calculations validate the resulting contact design rules with relative errors below $3\%$. Strikingly, many-body molecular dynamics simulations reveal that systems satisfying these two-body rules self-assemble into structures that closely match their pure Coulomb references. These results establish asymmetry as a route for turning electrostatic complexity into Coulombic simplicity at contact, with implications for controlled self-assembly and materials design.

cond-mat.soft↗

arXiv2026

LSR-Net: Long-Short-Range Operator Learning for Pattern Dynamics on Manifolds

We propose the Long-Short-Range Neural Network (LSR-Net), an extensible operator-learning framework for predicting pattern dynamics on planar domains, spherical surfaces, and general manifolds. The method decomposes the forward evolution operator into a long-range component, represented by a compact Fourier multiplier constructed via the Sum-of-Exponentials (SOE) approximation, and a short-range component adapted to the underlying geometry and its intrinsic symmetries. For general manifolds represented by irregularly sampled point clouds, the long-range component is implemented by Gaussian gridding onto an auxiliary regular grid, where the Fourier multiplier is efficiently applied in k-space using FFT and the result is interpolated back to the original sample points. We evaluate LSR-Net on several benchmark systems, including the Allen-Cahn, Cahn-Hilliard, Schnakenberg, and Turing systems, over planar domains, spherical surfaces, and a blob-shaped manifold. Numerical results demonstrate that LSR-Net consistently achieves higher accuracy and improved stability compared with baseline operator-learning models. In particular, for Allen-Cahn dynamics on the sphere, the RMSE is reduced by approximately three orders of magnitude compared with the Spherical Fourier Neural Operator (SFNO). Rotation and reflection equivariance tests further confirm that the learned operator is consistent with these geometric transformations. These results indicate that LSR-Net provides an effective and robust approach for learning pattern dynamics on complex geometries.

physics.comp-ph↗

arXiv2026

A spectral-subspace-augmented POD-Galerkin method for parametrized PDEs with limited snapshot data

Parametrized partial differential equations (PDEs) arise in many-query simulation, optimization, control, and uncertainty quantification, where repeated full-order solves restrict the number of high-fidelity snapshots that can be generated. This limitation is particularly pronounced in computational energy science, where multiscale models of porous-media flow, transport, and energy materials often make large snapshot datasets impractical. Proper orthogonal decomposition (POD) constructs compact reduced bases from solution snapshots, but it may exhibit limited out-of-sample predictive capability when the snapshots insufficiently sample the solution manifold. To address this limitation, we propose a spectral-subspace-augmented POD-Galerkin method (SS-POD) tailored to limited-data regimes. SS-POD starts from a problem-adapted spectral approximation space, partitions it into orthogonal subspaces, and performs POD locally on the projected snapshot matrices. An energy-balancing rule determines the spectral partition so that the resulting local POD problems are assigned comparable amounts of snapshot energy. For nonlinear parametrized PDEs, SS-POD is coupled with the discrete empirical interpolation method (DEIM). Numerical experiments show that SS-POD improves out-of-sample accuracy over standard POD-Galerkin while retaining compact reduced bases in limited-snapshot regimes. In particular, for a Laplace-Beltrami problem on the unit sphere with only 5 snapshots, SS-POD achieves a relative error of $3.9*10^{-8}$ using 91 basis functions, whereas the standard POD error saturates at $7.8*10^{-4}$ and the spectral-Galerkin method requires 256 basis functions for comparable accuracy. These results indicate that SS-POD provides an effective strategy for high-fidelity reduced-order modeling from limited snapshot data.

math.NA↗

arXiv2026

Reformulating Neural Operators in $d+1$ Dimensions for Embedding Evolution

Neural Operators (NOs) are powerful architectures for learning mappings between function spaces. While most advances focus on refining kernel parameterizations over the $d$-dimensional physical domain, the evolution of lifted embeddings remains underexplored, which often drives models toward computationally expensive embedding-scaling designs to improve approximation. In this paper, we introduce an auxiliary function dimension that models embedding evolution in operator form, thereby reformulating the NO pipeline in $d+1$ dimensions. We instantiate this framework via Fourier-based operators acting jointly on the physical and auxiliary domains, yielding a basis-diversified auxiliary evolution module as an alternative to brute-force embedding scaling. Across more than ten increasingly challenging benchmarks, ranging from the 1D heat equation to the highly nonlinear 3D Rayleigh-Taylor instability, our model consistently achieves the lowest relative $L_2$ error among the evaluated baselines. Crucially, this advantage is empirically supported by (1) controlled budget-aware comparisons against scaled and ablated baselines; (2) robustness under mixed-resolution training and super-resolution inference; and (3) zero-shot generalization to unseen temporal regimes. In addition, we present a broader set of design choices for lifting and recovery operators, demonstrating their impact on our model's predictive performance.

cs.LG↗

arXiv2026

An O(N) quasi-Ewald splitting method for nanoconfined electrostatics

Simulating the dynamics of charged particles in quasi-two-dimensional (quasi-2D) nanoconfined systems presents a significant computational challenge due to the long-range nature of electrostatic interactions and the geometric anisotropy. To address this, we introduce a novel quasi-Ewald splitting strategy tailored for particle-based simulations in such geometry. Our splitting strategy seamlessly integrates a collection of advanced numerical techniques, including optimal quadrature rules [L. N. Trefethen, SIAM Rev. 64(1)(2022), pp.132-150], fast pairwise kernel summation methods [S. Jiang and L. Greengard, Commun. Comput. Phys. 31(1)(2022), pp.1-26], and the random batch method with importance sampling in k-space [S. Jin, L. Li, Z. Xu et al., SIAM J. Sci. Comput. 43(4)(2021), pp.B937-B960]. The resulting algorithm achieves an O(N) overall computational complexity, where N denotes the total number of confined particles. Simulations of several prototype systems validate the accuracy and efficiency of our method. Furthermore, we present numerical observations specifically related to nanoconfined charged many-body systems, highlighting phenomena such as dielectric boundary effects, anisotropic diffusion, and the structure of the electrical double layer (EDL) under conditions of charge asymmetry.

cond-mat.soft↗

arXiv2025

Accurate Error Estimates and Optimal Parameter Selection in Ewald Summation for Dielectrically Confined Coulomb Systems

Dielectrically confined Coulomb systems are widely employed in molecular dynamics (MD) simulations. Despite extensive efforts in developing efficient and accurate algorithms for these systems, rigorous and accurate error estimates, which are crucial for optimal parameter selection for simulations, is still lacking. In this work, we present a rigorous error analysis in Ewald summation for electrostatic interactions in systems with two dielectric planar interfaces, where the polarization contribution is modeled by an infinitely reflected image charge series. Accurate error estimate is provided for the truncation error of image charge series, as well as decay rates of energy and force correction terms, as functions of system parameters such as vacuum layer thickness, dielectric contrasts, and image truncation levels. Extensive numerical tests conducted across several prototypical parameter settings validate our theoretical predictions. Additionally, our analysis elucidates the non-monotonic error convergence behavior observed in previous numerical studies. Finally, we provide an optimal parameter selection strategy derived from our theoretical insights, offering practical guidance for efficient and accurate MD simulations of dielectric-confined systems.

math.NA↗

arXiv2025

Quantitative Theory for Critical Conditions of Like-Charge Attraction Between Polarizable Spheres

Despite extensive experimental and theoretical efforts, a concise quantitative theory to predict the occurrence of like-charge attraction (LCA) between polarizable spheres remains elusive. In this work, we first derive a novel three-point image formula, based on a key observation that connects the classical Neumann's image principle with the incomplete beta function. This approach naturally yields simple yet precise critical conditions for LCA, with a relative discrepancy of less than $1\%$ compared to numerical simulations, validated across diverse parameter settings. The obtained critical conditions may provide physical insights into various processes potentially involving LCA, such as self-assembly, crystallization, and phase separation across different length scales. Additionally, the new image formula is directly applicable to enhance the efficiency of polarizable force field calculations involving polarizable spheres.

cond-mat.soft↗

arXiv2025

Fast Algorithm for Quasi-2D Coulomb Systems

Quasi-2D Coulomb systems are of fundamental importance and have attracted much attention in many areas nowadays. Their reduced symmetry gives rise to interesting collective behaviors, but also brings great challenges for particle-based simulations. Here, we propose a novel algorithm framework to address the $O(N^2)$ simulation complexity associated with the long-range nature of Coulomb interactions. First, we introduce an efficient Sum-of-Exponentials (SOE) approximation for the long-range kernel associated with Ewald splitting, achieving uniform convergence in terms of inter-particle distance, which reduces the complexity to $O(N^{7/5})$. We then introduce a random batch sampling method in the periodic dimensions, the stochastic approximation is proven to be both unbiased and with reduced variance via a tailored importance sampling strategy, further reducing the computational cost to $O(N)$. The performance of our algorithm is demonstrated via various numerical examples. Notably, it achieves a speedup of $2\sim 3$ orders of magnitude comparing with Ewald2D method, enabling molecular dynamics (MD) simulations with up to $10^6$ particles on a single core. The present approach is therefore well-suited for large-scale particle-based simulations of Coulomb systems under confinement, making it possible to investigate the role of Coulomb interaction in many practical situations.

math.NA↗

arXiv2025

Mechanisms of electrostatic interactions between two charged dielectric spheres inside a polarizable medium: An effective-dipole analysis

The mechanisms of electrostatic interactions between two charged dielectric spheres inside a polarizable medium have been investigated, in terms of hypothetical effective dipoles that depict how the positive and negative charge in each particle are separated. Our findings, which revealed that it is possible for polarization-induced opposite-charge repulsion to occur at short interparticle separations if the dielectric constant of the medium is greater than the dielectric constants of both spheres, provide insights into the physics of charge separation in each sphere and of polarization in the medium behind such counterintuitive behaviour.

cond-mat.soft↗

arXiv2024

Broken Symmetries in Quasi-2D Charged Systems via Negative Dielectric Confinement

We report spontaneous symmetry breaking (SSB) phenomena in symmetrically charged binary particle systems under planar nanoconfinement with negative dielectric constants.The SSB is triggered $solely$ via the dielectric confinement effect, without any external fields. The mechanism of SSB is found to be caused by the strong polarization field enhanced by nanoconfinement, giving rise to charge/field oscillations in the transverse directions. Interestingly, dielectric contrast can even determine the degree of SSB in transverse and longitudinal dimensions, forming charge-separated interfacial liquids and clusters on square lattices. Furthermore, we analytically show that the formed lattice constant is determined by the dielectric mismatch and the length scale of confinement, which is validated via molecular dynamics simulations. The novel broken symmetry mechanism may provide new insights in the study of quasi-2D systems and the design of future nanodevices.

cond-mat.soft↗

arXiv2024

Random Batch Ewald Method for Dielectrically Confined Coulomb Systems

Quasi two-dimensional Coulomb systems have drawn widespread interest. The reduced symmetry of these systems leads to complex collective behaviors, yet simultaneously poses significant challenges for particle-based simulations. In this paper, a novel method is presented for efficiently simulate a collection of charges confined in doubly-periodic slabs, with the extension to scenarios involving dielectric jumps at slab boundaries. Unlike existing methods, the method is insensitive to the aspect ratio of simulation box, and it achieves optimal O(N) complexity and strong scalability, thanks to the random batch Ewald (RBE) approach. Moreover, the additional cost for polarization contributions, represented as image reflection series, is reduced to a negligible cost via combining the RBE with an efficient structure factor coefficient re-calibration technique in k-space. Explicit formulas for optimal parameter choices of the algorithm are provided through error estimates, together with a rigorous proof. Finally, we demonstrate the accuracy, efficiency and scalability of our method, called RBE2D, via numerical tests across a variety of prototype systems. An excellent agreement between the RBE2D and the PPPM method is observed, with a significant reduction in the computational cost and strong scalability, demonstrating that it is a promising method for a broad range of charged systems under quasi-2D confinement.

math.NA↗

arXiv2023

Computing hydrodynamic interactions in confined doubly-periodic geometries in linear time

We develop a linearly-scaling variant of the Force Coupling Method [K. Yeo and M. R. Maxey, J. Fluid Mech. 649, 205-231 (2010)] for computing hydrodynamic interactions among particles confined to a doubly-periodic geometry with either a single bottom wall or two walls (slit channel) in the aperiodic direction. Our spectrally-accurate Stokes solver uses the Fast Fourier Transform (FFT) in the periodic $xy$ plane and Chebyshev polynomials in the aperiodic $z$ direction normal to the wall(s). We decompose the problem into two problems. The first is a doubly-periodic subproblem in the presence of particles (source terms) with free-space boundary conditions in the $z$ direction, which we solve by borrowing ideas from a recent method for rapid evaluation of electrostatic interactions in doubly-periodic geometries [O. Maxian, R. P. Peláez, L. Greengard and A. Donev, J. Chem. Phys. 154, 204107 (2021)]. The second is a correction subproblem to impose the boundary conditions on the wall(s). Instead of the traditional Gaussian kernel, we use the exponential of a semicircle kernel to model the source terms (body force) due to the presence of particles, and provide optimum values for the kernel parameters that ensure a given hydrodynamic radius with at least two digits of accuracy and rotational and translational invariance. The computation time of our solver, which is implemented in graphical processing units, scales linearly with the number of particles, and allows computations with about a million particles in less than a second for a sedimented layer of colloidal microrollers. We find that in a slit channel, a driven dense suspension of microrollers maintains the same two-layer structure as above a single wall, but moves at a substantially lower collective speed due to increased confinement.

physics.comp-ph↗

arXiv2020

Harmonic surface mapping algorithm for electrostatic potentials in an atomistic/continuum hybrid model for electrolyte solutions

Simulating charged many-body systems has been a computational demanding task due to the long-range nature of electrostatic interaction. For the multi-scale model of electrolytes which combines the strengths of atomistic/continuum electrolyte representations, a harmonic surface mapping algorithm is developed for fast and accurate evaluation of the electrostatic reaction potentials. Our method reformulates the reaction potential into a sum of image charges for the near-field, and a charge density on an auxiliary spherical surface for the far-field, which can be further discretized into point charges. Fast multipole method is used to accelerate the pairwise Coulomb summation. The accuracy and efficiency of our algorithm, as well as the choice of relevant numerical parameters are demonstrated in detail. As a concrete example, for charges close to the dielectric interface, our method can improve the accuracy by two orders of magnitudes compared to the Kirkwood series expansion method.

physics.comp-ph↗

arXiv2019

On-node lattices construction using $\textit{partial}$ Gauss-Hermite quadrature for the lattice Boltzmann method

A concise theoretical framework, the $\textit{partial}$ Gauss-Hermite quadrature (pGHQ), is established for constructing on-node lattices of the lattice Boltzmann (LB) method under a Cartesian coordinate system. Comparing with existing approaches, the pGHQ scheme has the following advantages: $\textbf{a).}$ extremely concise algorithm, $\textbf{b).}$ unifying the constructing procedure of symmetric and asymmetric on-node lattices, $\textbf{c).}$ covering full-range quadrature degree of a given discrete velocity set. We employ it to search the local optimal and asymmetric lattices for $\left\{ {n = 3,4,5,6,7} \right\}$ moment degree equilibrium distribution discretization on range $\left[ { - 10,10} \right]$. The search reveals a surprising abundance of available lattices. Through a brief analysis, the discrete velocity set shows a significant influence on the positivity of equilibrium distributions, which is considered as one major impact to the numerical stability of the LB method. Hence the results of the pGHQ scheme lay a foundation for further investigations on improving the numerical stability of the LB method by modifying the discrete velocity set. It also worths noting that pGHQ can be extended into the entropic LB model though it was proposed for the Hermite polynomial expansion LB theory.

physics.comp-ph↗

arXiv2013

Efficient Implementation of the Barnes-Hut Octree Algorithm for Monte Carlo Simulations of Charged Systems

Computer simulation with Monte Carlo is an important tool to investigate the function and equilibrium properties of many systems with biological and soft matter materials solvable in solvents. The appropriate treatment of long-range electrostatic interaction is essential for these charged systems, but remains a challenging problem for large-scale simulations. We have developed an efficient Barnes-Hut treecode algorithm for electrostatic evaluation in Monte Carlo simulations of Coulomb many-body systems. The algorithm is based on a divide-and-conquer strategy and fast update of the octree data structure in each trial move through a local adjustment procedure. We test the accuracy of the tree algorithm, and use it to perform computer simulations of electric double layer near a spherical interface. It has been shown that the computational cost of the Monte Carlo method with treecode acceleration scales as $\log N$ in each move. For a typical system with ten thousand particles, by using the new algorithm, the speed has been improved by two orders of magnitude from the direct summation.

physics.comp-ph↗

arXiv2012

Effects of image charges, interfacial charge discreteness, and surface roughness on the zeta potential of spherical electric double layers

We investigate the effects of image charges, interfacial charge discreteness, and surface roughness on spherical electric double layers in electrolyte solutions with divalent counter-ions in the setting of the primitive model. By using Monte Carlo simulations and the image charge method, the zeta potential profile and the integrated charge distribution function are computed for varying surface charge strengths and salt concentrations. Systematic comparisons were carried out between three distinct models for interfacial charges: 1) SURF1 with uniform surface charges, 2) SURF2 with discrete point charges on the interface, and 3) SURF3 with discrete interfacial charges and finite excluded volume. By comparing the integrated charge distribution function (ICDF) and potential profile, we argue that the potential at the distance of one ion diameter from the macroion surface is a suitable location to define the zeta potential. In SURF2 model, we find that image charge effects strongly enhance charge inversion for monovalent interfacial charges, and strongly suppress charge inversion for multivalent interfacial charges. For SURF3, the image charge effect becomes much smaller. Finally, with image charges in action, we find that excluded volumes (in SURF3) suppress charge inversion for monovalent interfacial charges and enhance charge inversion for multivalent interfacial charges. Overall, our results demonstrate that all these aspects, i.e., image charges, interfacial charge discreteness, their excluding volumes have significant impacts on the zeta potential, and thus the structure of electric double layers.

cond-mat.soft↗