arXiv subjects

Jeff Z. Y. Chen

Publications and source records attributed to Jeff Z. Y. Chen.

12 recordsLinked to original sources

arXiv2026

Run-and-tumble particles in a harmonic external field: constructing the solution of the Fokker-Planck equation from the equations of motion

A method for integrating the Langevin equations of motion for run-and-tumble particles is introduced to compute the joint distribution of their position and active velocity, with and without a harmonic external force field. The key step is the construction of the moments of the distribution and the correlation functions, conditional on the particles being in a specific state at the final time. For one-dimensional run-and-tumble particles in a harmonic external potential, the exact steady-state distributions for the tumble state, as well as for the run state conditional on a specified velocity direction, are obtained. This enables us to demonstrate their equivalence to the exact solutions of the corresponding Fokker-Planck equations.

cond-mat.stat-mech↗

arXiv2026

Defect Organization in Coexisting Hexagonal and Square Lattices on Ellipsoids

Curvature and topology jointly organize defects in two-dimensional crystals, but their combined role remains unresolved when competing lattice symmetries coexist with spatially varying curvature. We use simulated-annealing Langevin dynamics to study Hertzian particles forming coexisting hexagonal (Hex) and square (Sq) lattices on prolate and oblate ellipsoids. Mapping reduced density and aspect ratio reveals a broad sequence of scar and domain-based morphologies in both Hex-dominant and Sq-dominant backgrounds. Latitude-resolved comparisons show that Gaussian curvature biases defects toward its maxima under weak deformation. Strong prolateness, however, confines high curvature to small polar caps that cannot independently accommodate all defect motifs. Defects then spread toward lower-curvature latitudes to relieve defect crowding and elastic repulsion. In the Hex-dominant regime, this competition drives vertex-contacted domains with neutralized corner contacts, and compensating positive defects locate away from the poles. The Sq-dominant regime features Hex-rich triangular domains, bridged states, and linear or open scars similarly reorganized by curvature anisotropy. On oblate ellipsoids, the extended equatorial high-curvature belt allows defects to separate azimuthally while remaining curvature-localized. This work elucidates that nonuniform curvature can engineer rich defect patterns by selecting the spatial distribution of topological charge and the connectivity of finite defect motifs.

cond-mat.soft↗

arXiv2025

Transitional patterns on a spherical surface: from scars to domain defects of mixed lattices

The system of mixed hexagonal and square lattices on a spherical surface is examined, with an emphasis on the exploration of the disclination patterns that form in the square-rich regime. To demonstrate the possible outcomes, the Hertzian potential energy is used as a model for pairwise molecular interactions, which is known to support coexistent hexagonal and square lattices. Through molecular dynamics simulations, we show that at least four different disclination morphologies arise in a square-rich background: triangular defect domains composed of hexagonal lattices arranged in a cubic formation, bridged cubic state, linear scar disclinations with no hexagon content, and open scar disclinations containing a significant amount of hexagonal lattice in the open regions. Order parameters are also introduced to highlight the significance of the bridged and open-scar disclinations, both being the new morphologies reported in this study. The fact that the bridged state is an energetically preferred one is further demonstrated by a separate elastic energy model, which confirms its prevalence over the unbridged cubic state.

cond-mat.soft↗

arXiv2025

Competing Hexagonal and Square Lattices on a Spherical Surface

The structural properties of packed soft-core particles provide a platform to understand the cross-pollinated physical concepts in solid-state- and soft-matter physics. Confined on spherical surface, the traditional differential geometry also dictates the overall defect properties in otherwise regular crystal lattices. Using molecular dynamics simulation of the Hertzian model as a tool, we report here the emergence of new types of disclination patterns: domain and counter-domain defects, when hexagonal and square patterns coexist. A new angle is presented to understand the incompatibility between tiling lattice shapes and the available spherical areal shapes, which is common in nature -- from molecular systems in biology to backbone construction in architectures.

cond-mat.soft↗

arXiv2021

Defect patterns of two-dimensional nematic liquid crystals in confinement

A two-dimensional or quasi-two-dimensional nematic liquid crystal refers to a surface confined system. When such a system is further confined by external line boundaries or excluded from internal line boundaries, the nematic directors form a deformed texture that may display defect points or defect lines, for which winding numbers can be clearly defined. Here, a particular attention is paid to the case when the liquid crystal molecules prefer to form a boundary nematic texture in parallel to the wall surface (i.e., following the homogeneous boundary condition). A general theory, based on geometric argument, is presented for the relationship between the sum of all winding numbers in the system (the total winding number) and the type of confinement angles and curved segments. The conclusion is validated by comparing the theoretical defect rule with existing nematic textures observed experimentally and theoretically in recent years.

cond-mat.soft↗

arXiv2021

Construction of a pathway map on a complicated energy landscape

How do we search for the entire family tree without unwanted random guesses, starting from a high-index and high-energy stationary state on the energy landscape? Here we introduce a general numerical method that constructs the pathway map clearly connecting all stationary points branched from a single parent state. The map guides our understanding of how a physical system moves on the energy landscape. In particular, the method allows us to identify the transition state between energy minima and the energy barrier associated with such a state. As an example, we solve the Landau-de Gennes energy incorporating the Dirichlet boundary conditions to model a liquid crystal confined in square box; we illustrate the basic concepts by examining the multiple stationary solutions and the connected pathway maps of the model.

physics.comp-ph↗

arXiv2021

Determining the nonequilibrium criticality of a Gardner transition via a hybrid study of molecular simulations and machine learning

Apparent critical phenomena, typically indicated by growing correlation lengths and dynamical slowing-down, are ubiquitous in non-equilibrium systems such as supercooled liquids, amorphous solids, active matter and spin glasses. It is often challenging to determine if such observations are related to a true second-order phase transition as in the equilibrium case, or simply a crossover, and even more so to measure the associated critical exponents. Here, we show that the simulation results of a hard-sphere glass in three dimensions, are consistent with the recent theoretical prediction of a Gardner transition, a continuous non-equilibrium phase transition. Using a hybrid molecular simulation-machine learning approach, we obtain scaling laws for both finite-size and aging effects, and determine the critical exponents that traditional methods fail to estimate. Our study provides a novel approach that is useful to understand the nature of glass transitions, and can be generalized to analyze other non-equilibrium phase transitions.

cond-mat.soft↗

arXiv2018

A machine-learning solver for modified diffusion equations

A feed-forward neural network has a remarkable property which allows the network itself to be a universal approximator for any functions.Here we present a universal, machine-learning based solver for multi-variable partial differential equations. The algorithm approximates the target functions by neural networks and adjusts the network parameters to approach the desirable solutions.The idea can be easily adopted for dealing with multi-variable, coupled integrodifferential equations, such as those in the self-consistent field theory for predicting polymer microphase-separated structures.

cond-mat.dis-nn↗

arXiv2017

Identifying polymer states by machine learning

The ability of a feed-forward neural network to learn and classify different states of polymer configurations is systematically explored. Performing numerical experiments, we find that a simple network model can, after adequate training, recognize multiple structures, including gas-like coil, liquid-like globular, and crystalline anti-Mackay and Mackay structures. The network can be trained to identify the transition points between various states, which compare well with those identified by independent specific-heat calculations. Our study demonstrates that neural network provides an unconventional tool to study the phase transitions in polymeric systems.

cond-mat.soft↗

arXiv2002

Folding dynamics of the helical structures in a minimal model

The folding of a polypeptide is an example of the cooperative effects of the amino-acid residues. Of recent interest is how a secondary structure, such as a helix, spontaneously forms during the collapse of a peptide from an initial denatured state. The Monte Carlo implementation of a recent helix-forming model enables us to study the entire folding process dynamically. As shown by the computer simulations, the foldability and helical propagation are both strongly correlated to the nucleation properties of the sequence.

cond-mat.soft↗

arXiv2002

Statistical Theory of Associating Polymer Solutions: Interfacial Properties

The interfacial structure formed in thermoreversible associating polymer solutions is studied within the density functional approach based on Flory's arguments of tree-like configurations of cluster associations. The unique characteristics of the interfacial region can be described in terms of the monomer density along the interface. For a certain value of the association parameter, which controls thermoreversible chemical reaction between associating functional groups, the density profile is not smooth and undergoes a sudden jump at the point where the number of bonded functional groups is small. Analytical expression for the interfacial tension is given and results of numerical calculations are presented.

cond-mat↗

arXiv2001

Unzipping dsDNA with a force: scaling theory

A double stranded DNA molecule under the stress of a pulling force acting on the strand terminals exhibits a partially denatured structure or can be completely unzipped depending the magnitude of the pulling force. A scaling argument for relationships amongst basic length scales is presented that takes into account the heterogeneity of the sequence. The result agrees with our numerical simulation data, which provides a critical test of the power laws in the unzipping transition region.

cond-mat.stat-mech↗