arXiv subjects

Zhong-Can Ou-Yang

Publications and source records attributed to Zhong-Can Ou-Yang.

16 recordsLinked to original sources

arXiv2026

Anisotropic Electrostatic-Elastic Softening and Stability in Charged Colloidal Crystals

Charged colloidal crystals exhibit a subtle interplay between electrostatic screening and elastic deformation. When an isotropic electrostatic volumetric softening acts on an anisotropic elastic background, the longitudinal acoustic response softens preferentially along specific crystallographic axes. This article provides a self-contained derivation of the long-wavelength acoustic stability condition for cubic crystals subject to a generic electrostatic-elastic coupling. Starting from an effective static elastic tensor renormalized by a scalar coupling constant $λ_g$, we obtain an explicit condition for the onset of a long-wavelength acoustic instability: the direction $\hat{\mathbf{k}}$ that first loses strong ellipticity is determined by the inverse Christoffel matrix evaluated along that direction. Closed-form expressions for the critical coupling $λ_g^c$ are given for the $[100]$, $[110]$, and $[111]$ high-symmetry directions. We further provide a microscopic derivation of $λ_g$ from the Poisson-Boltzmann theory in a spherical Wigner-Seitz cell, linking the phenomenological constant to experimentally accessible parameters such as salt concentration, particle charge, and volume fraction. The analysis reveals that the most fragile direction can be identified without full lattice-dynamical calculations, and the associated unstable strain patterns are discussed. We also compare these acoustic thresholds with the Born stability condition for homogeneous volume change and show that, for a Born-stable reference cubic crystal, the volume mode becomes unstable before any directional acoustic mode, provided homogeneous dilation is admissible. Numerical illustrations using representative modulus values reported for soft colloidal assemblies illustrate how the criterion can be applied to predict directional softening trends. The present framework serves as a diagnostic tool

cond-mat.soft↗

arXiv2026

Electrostatic-Elastic Softening and Ultraviolet Instability Driven by Non-DLVO Interactions in Charged Colloidal Crystals

Colloidal crystals permeated by mobile ions exhibit a coupling between electrostatic and elastic degrees of freedom that renormalizes the effective screening length and induces wave-vector-dependent elastic softening. Building on our recently proposed continuum model, we perform a rigorous Gaussian fluctuation analysis to elucidate the stability limits of the homogeneous phase. By integrating out the electrostatic fluctuations, we derive the effective elastic modulus $Γ(q)$ as a function of wave vector $q$. We show that the modulus in the long-wavelength limit ($q \to 0$) remains identically equal to a bare modulus protected by perfect ionic screening. In contrast, the modulus in the short-wavelength limit ($q \to \infty$) softens as the electrostatic-elastic coupling strength $ξ$ increases, vanishing at a critical value $ξ=1$. For $ξ>1$, the fluctuation spectrum exhibits a negative eigenvalue for all wave vectors $q$ larger than a critical (effective screening) wave vector $q_c$, signaling an ultraviolet instability of the uniform phase. In a real colloidal crystal, this divergence is regulated by the discrete lattice cutoff $q_{\max}\simπ/a$, confining the physical instability to a finite band $q_c < q < q_{\max}$. The macroscopic limit $q\to 0$ remains unconditionally stable for all $ξ$. The transition at $ξ=1$ thus marks the onset of short-wavelength mechanical failure, while macroscopic elastic stiffness remains intact. Our analysis clarifies the proper physical interpretation of the minimal coupling model and provides a consistent picture of how non-DLVO interactions can drive local structural collapse in charged colloidal crystals.

cond-mat.soft↗

arXiv2026

Entropy-Driven Initiation and Cellular Uptake Mediated by Viscoelastic Cytoskeleton: A Kinetic Phase Diagram from Onsager Variational Principle

A fundamental question in receptor-mediated endocytosis remains unanswered: what initial driving force brings ligands and receptors into close proximity? While previous models assume pre-existing contact and overlook this initiation problem, we propose that entropic forces from nanoscale biomolecules in crowded cellular environments provide the essential driving mechanism. We develop a unified continuum model rooted in the Onsager variational principle, where engulfment depth serves as the generalized coordinate and the driving force derives from a free energy landscape of entropic, binding, membrane, and cytoskeleton contributions. The framework naturally incorporates: (i) entropy-driven adhesion as initiation; (ii) ligand-receptor binding as the sustaining force; (iii) membrane deformation via the Helfrich-Canham Hamiltonian; and (iv) cytoskeleton viscoelasticity through the elastic-viscoelastic correspondence principle. The kinetic phase diagram predicts a critical biomolecule concentration for initiation, a lower bound of ligand density for complete engulfment, a finite size window for engulfable particles, and an optimal virus radius of 30--60 nm that decreases with increasing binding energy. The Onsager solubility condition naturally yields the phase boundaries. The model exhibits asymptotic consistency with the classic Asakura-Oosawa result in the large-particle flat-surface limit. Stiffer cells lead to longer engulfment times and narrower size windows. Strikingly, the optimal size matches HIV-1 dimensions under physiologically realistic parameters. This work provides a variational foundation for cellular uptake with implications for virology, nanotechnology, and drug delivery.

cond-mat.soft↗

arXiv2026

Liquid Crystal Theory of Biomembranes

Biomembranes, primarily composed of lipid bilayers, are not merely passive barriers but dynamic and complex materials whose shapes are governed by the principles of soft matter physics. This review explores the shape problem in biomembranes through the lens of material science and liquid crystal theory. Beginning with classical analogies to crystals and soap bubbles, it details the application of the Helfrich elastic model to explain the biconcave shape of red blood cells. The discussion extends to multi-layer systems, drawing parallels between the focal conic structures of smectic liquid crystals, the geometries of fullerenes and carbon nanotubes, and the reversible transitions in peptide assemblies. Furthermore, it examines icosahedral self-assemblies and shape formation in two-dimensional lipid monolayers at air/water interfaces. At the end of the paper, we find that the shapes such as cylinders, spheres, tori, biconcave discoids and Delaunay surfaces form a group. This result is merely an intrinsic geometric feature of these shapes and is independent of the biomembrane equation. When the pressure on the membrane, surface tension, and bending modules meet certain conditions, the biomembrane will take on these shapes. The review concludes by highlighting the unifying power of continuum elastic theories in describing a vast array of membrane morphologies across biological and synthetic systems.

physics.comp-ph↗

arXiv2025

Continuum theory of electrostatic-elastic coupling interactions in colloidal crystals

A mobile Coulomb gas permeating a fixed background crystalline lattice of charged colloidal crystals is subject to an electrostatic-elastic coupling, which we study on the continuum level by introducing a minimal coupling between electrostatic and displacement fields. We derive linearized, Debye-Hückel-like mean-field equations that can be analytically solved, incorporating the minimal coupling between electrostatic and displacement fields leading to an additional effective attractive interaction between mobile charges that depends in general on the strength of the coupling between the electrostatic and displacement fields. By analyzing the Gaussian fluctuations around the mean-field solution we also identify and quantify the region of its stability in terms of the electrostatic-elastic screening length. This detailed continuum theory incorporating the standard lattice elasticity and electrostatics of mobile charges provides a baseline to investigate the electrostatic-elastic coupling for microscopic models in colloid science and materials science.

cond-mat.soft↗

arXiv2020

A critical survey on the kinetic assays of DNA polymerase fidelity from a new theoretical perspective

The high fidelity of DNA polymerase is critical for the faithful replication of genomic DNA. Several approaches were proposed to quantify the fidelity of DNA polymerase. Direct measurements of the error frequency of the replication products definitely give the true fidelity but turn out very hard to implement. Two biochemical kinetic approaches, the steady-state assay and the transient-state assay, were then suggested and widely adopted. In these assays, the error frequency is indirectly estimated by using the steady-state or the transient-state kinetic theory combined with the measured kinetic rates. However, whether these indirectly estimated fidelities are equivalent to the true fidelity has never been clarified theoretically, and in particular there are different strategies to quantify the proofreading efficiency of DNAP but often lead to inconsistent results. The reason for all these confusions is that it's mathematically challenging to formulate a rigorous and general theory of the true fidelity. Recently we have succeeded to establish such a theoretical framework. In this paper, we develop this theory to make a comprehensive examination on the theoretical foundation of the kinetic assays and the relation between fidelities obtained by different methods. We conclude that while the steady-state assay and the transient-state assay can always measure the true fidelity of exonuclease-deficient DNA polymerases, they only do so for exonuclease-efficient DNA polymerases conditionally (the proper way to use these assays to quantify the proofreading efficiency is also suggested). We thus propose a new kinetic approach, the single-molecule assay, which indirectly but precisely characterizes the true fidelity of either exonuclease-deficient or exonuclease-efficient DNA polymerases.

physics.bio-ph↗

arXiv2019

Magnetic deformation theory of a vesicle

We have extended the Helfrich's spontaneous curvature model [M. Iwamoto and Z. C. Ou-Yang. Chem. Phys. Lett. \textbf{590}(2013)183; Y. X. Deng, et.al., EPL. \textbf{123}(2018)68002] of the equilibrium vesicle shapes by adding the interaction between magnetic field and the constituent molecules to explain the phenomena of the reversibly deformation of artificial stomatocyte[P. G. van Rhee, et.al., Nat. Commun. \textbf{Sep 24;5:5010}(2014)doi: 10.1038/ncomms6010.] and the anharmonic deformation of a self-assembled nanocapsules of bola-amphiphilic molecules and the linear birefringence[O.V. Manyuhina, et.al., Phys. Rev. Lett. \textbf{98}(2007)146101.]. However, the sophistic mathematics in differential geometry is still covered. Here, we present the derivations of formulas in detailed to reveal the perturbation of deformation $ψ$ under two cases.

cond-mat.soft↗

arXiv2019

The template-specific fidelity of DNA replication with high-order neighbor effects: a first-passage approach

DNA replication fidelity is a critical issue in molecular biology. Biochemical experiments have provided key insights on the mechanism of fidelity control by DNAP in the past decades, whereas systematic theoretical studies on this issue began only recently. Because of the underlying difficulties of mathematical treatment, comprehensive surveys on the template-specific replication kinetics are still rare. Here we proposed a first-passage approach to address this problem, in particular the positional fidelity, for complicated processes with high-order neighbor effects. Under biologically-relevant conditions, we derived approximate analytical expressions of the positional fidelity which shows intuitively how some key kinetic pathways are coordinated to guarantee the high fidelity, as well as the high velocity, of the replication processes. It was also shown that the fidelity at any template position is dominantly determined by the nearest-neighbor template sequences, which is consistent with the idea that replication mutations are randomly distributed in the genome.

cond-mat.stat-mech↗

arXiv2016

The Mechanism Behind Beauty: Golden Ratio Appears in Red Blood Cell Shape

In the past two decades, under the conditions that both the osmotic pressure $Δp$ and tensile stress $λ$ equal zero, a rigorous solution (RS) of human red blood cell (RBC) with a minus spontaneous curvature $c_{0}$ has been derived with Helfrich model. And, by fitting with observed shapes of RBC, $c_{0}R_{0}$ has been predicted to be -1.62 as minus golden ratio, where $R_{0}$ is the radius of a sphere with the same area of RBC. In this Lett., it is also found $ρ_{max}$ /$ρ_{B}\approx$ 1.6 shows a approximately beautiful golden cross section of RBC, where $ρ_{max}$ is the radius of RBC and $ρ_{B}$ is the radius at maximal thickness of RBC. With a complete numerical calculation, we find the mechanism behind the beauty that minus golden ratio of $c_{0}R_{0}$ is the balance between economical surface area and enough deformability to pass spleen, the so called "physical fitness test".

physics.bio-ph↗

arXiv2016

Proofreading of DNA Polymerase: a new kinetic model with higher-order terminal effects

The fidelity of DNA replication by DNA polymerase (DNAP) has long been an important issue in biology. While numerous experiments have revealed details of the molecular structure and working mechanism of DNAP which consists of both a polymerase site and an exonuclease (proofreading) site, there were quite few theoretical studies on the fidelity issue. The first model which explicitly considered both sites was proposed in 1970s' and the basic idea was widely accepted by later models. However, all these models did not systematically and rigorously investigate the dominant factor on DNAP fidelity, i.e, the higher-order terminal effects through which the polymerization pathway and the proofreading pathway coordinate to achieve high fidelity. In this paper, we propose a new and comprehensive kinetic model of DNAP based on some recent experimental observations, which includes previous models as special cases. We present a rigorous and unified treatment of the corresponding steady-state kinetic equations of any-order terminal effects, and derive analytical expressions for fidelity in terms of kinetic parameters under bio-relevant conditions. These expressions offer new insights on how the the higher-order terminal effects contribute substantially to the fidelity in an order-by-order way, and also show that the polymerization-and-proofreading mechanism is dominated only by very few key parameters. We then apply these results to calculate the fidelity of some real DNAPs, which are in good agreements with previous intuitive estimates given by experimentalists.

q-bio.SC↗

arXiv2015

Reweighted ensemble dynamics simulations: theory, improvement, and application

Based on multiple parallel short molecular dynamics simulation trajectories, we designed the reweighted ensemble dynamics (RED) method to more efficiently sample complex (biopolymer) systems, and to explore their hierarchical metastable states. Here we further present an improvement to depress statistical errors of the RED and we discuss a few keys in practical application of the RED, provides schemes on selection of basis functions, determination of free parameter in the RED. We illustrate the application of the improvements in two toy models and in the solvated alanine dipeptide. The results show the RED enable to capture the topology of multiple-state transition networks, to detect the diffusion-like dynamical behavior in entropy-dominated system, and to identify solvent effects in the solvated peptides. The illustrations serve as general applications of the RED in more complex biopolymer systems.

cond-mat.stat-mech↗

arXiv2014

Network cluster detecting in associated bi-graph view

We find there is relationship between the associated bigraph and the cluster (or community) detecting on network. By imbedding the associated bigraph of some network (suppose it has cluster structures) into some space, we can identify the clusters on this network, which is a new method for network cluster detecting. And this method, of which the physical meaning is clear and the time complexity is acceptable, may provide us a new point to understand the structure and character of networks. In this paper, We test the methods on serval computer-generated networks and real networks. A computer-generated network with 128 vertexes and the Zachary Network, which presents the structure of a karate club, can be partitioned correctly by these methods. And the Dolphin Network, which presents the relationship between 62 dolphins on the coast of New Zealand, is partitioned reasonably.

physics.soc-ph↗

arXiv2012

Diffusion-limited aggregation with polygon particles

Diffusion-limited aggregation (DLA) assumes that particles perform pure random walk at a finite temperature and aggregate when they come close enough and stick together. Although it is well known that DLA in two dimensions results in a ramified fractal structure, how the particle shape influences the formed morphology is still unclear. In this work, we perform the off-lattice two-dimensional DLA simulations with different particle shapes of triangle, quadrangle, pentagon, hexagon, and octagon, respectively, and compared with the results for circular particles. Our results indicate that different particle shapes only change the local structure, but have no effects on the global structure of the formed fractal cluster. The local compactness decreases as the number of polygon edges increases.

cond-mat.stat-mech↗

arXiv2009

Temperature dependence of circular DNA topological states

Circular double stranded DNA has different topological states which are defined by their linking numbers. Equilibrium distribution of linking numbers can be obtained by closing a linear DNA into a circle by ligase. Using Monte Carlo simulation, we predict the temperature dependence of the linking number distribution of small circular DNAs. Our predictions are based on flexible defect excitations resulted from local melting or unstacking of DNA base pairs. We found that the reduced bending rigidity alone can lead to measurable changes of the variance of linking number distribution of short circular DNAs. If the defect is accompanied by local unwinding, the effect becomes much more prominent. The predictions can be easily investigated in experiments, providing a new method to study the micromechanics of sharply bent DNAs and the thermal stability of specific DNA sequences. Furthermore, the predictions are directly applicable to the studies of binding of DNA distorting proteins that can locally reduce DNA rigidity, form DNA kinks, or introduce local unwinding.

q-bio.BM↗

arXiv2008

Simulating the collapse transition of a two-dimensional semiflexible lattice polymer

It has been revealed by mean-field theories and computer simulations that the nature of the collapse transition of a polymer is influenced by its bending stiffness $ε_{\rm b}$. In two dimensions, a recent analytical work demonstrated that the collapse transition of a partially directed lattice polymer is always first-order as long as $ε_{\rm b}$ is positive [H. Zhou {\em et al.}, Phys. Rev. Lett. {\bf 97}, 158302 (2006)]. Here we employ Monte Carlo simulation to investigate systematically the effect of bending stiffness on the static properties of a 2D lattice polymer. The system's phase-diagram at zero force is obtained. Depending on $ε_{\rm b}$ and the temperature $T$, the polymer can be in one of three phases: crystal, disordered globule, or swollen coil. The crystal-globule transition is discontinuous, the globule-coil transition is continuous. At moderate or high values of $ε_{\rm b}$ the intermediate globular phase disappears and the polymer has only a discontinuous crystal-coil transition. When an external force is applied, the force-induced collapse transition will either be continuous or discontinuous, depending on whether the polymer is originally in the globular or the crystal phase at zero force. The simulation results also demonstrate an interesting scaling behavior of the polymer at the force-induced globule-coil transition.

cond-mat.soft↗

arXiv2007

Collapse Transition of Two-Dimensional Flexible and Semiflexible Polymers

The nature of the globule-coil transition of surface-confined polymers has been an issue of debate. Here this 2D collapse transition is studied through a partially directed lattice model. In the general case of polymers with positive bending stiffness ($Δ>0$), the collapse transition is {\em first-order}; it becomes {\em second-order} only in the limiting case of zero bending stiffness ($Δ\equiv 0$). These analytical results are confirmed by Monte Carlo simulations. We also suggest some possible future experiments.

cond-mat.soft↗