arXiv subjects

Cheng-Tai Lee

Publications and source records attributed to Cheng-Tai Lee.

7 recordsLinked to original sources

arXiv2026

Elastodynamics from Eulerian Poisson-bracket formalism: application to chiral odd solids

The Poisson-bracket (PB) formalism is widely used to derive dynamics of coarse-grained (CG) fields to capture large-scale physics, extending the role of PBs in classical particle mechanics to macroscopic fields. It has been applied to fluctuations in critical phenomena, hydrodynamics of liquid crystals, liquid crystal elastomers, tissues, and the emergence of odd viscosity from spinning particles. The PB formalism can be formulated in either the Lagrangian framework, using reference space, or the Eulerian framework, using real space. Conventionally, the Lagrangian formulation is used for elastic solids, and the Eulerian one for fluids. However, growing interest in Eulerian descriptions of solids has emerged for phenomena naturally defined in real space, such as viscoelastic responses, moving interfaces, and field-induced structural changes in particles. Here we develop a systematic formulation for applying the Eulerian PB formalism to elastic systems with potentials typically written in Lagrangian space, and clarify its consistency with the Lagrangian counterpart. We show that the Eulerian formulation generates additional nonlinearities absent in the Lagrangian framework. Such nonlinearities originate from CG volume changes under coordinate transformation and from particle flow across neighboring CG volumes. They must be retained when nonlinear effects are important. To illustrate, we study chiral active solids of finite-sized particles, where active torques drive internal particle rotations and generate geometric nonlinearities. These nonlinearities give rise to the odd elastic modulus, which non-reciprocally couples two different shear modes in stress-strain response. By recovering this modulus directly from the Eulerian PB formalism, we demonstrate its ability to capture emergent nonlinear elastic behavior in driven active solids, whose stresses are naturally measured in real space.

cond-mat.soft↗

arXiv2026

Non-Hermitian chiral surface waves in disordered odd solids

Chiral surface waves are surface-localized modes that propagate unidirectionally along a boundary, enabling directed transport and minimal back-scattering. While first identified in quantum systems, they were recently shown to emerge in classical metamaterials in the presence of `odd elasticity'. Owing to the non-reciprocality of odd elasticity, these waves exhibit growing amplitudes during propagation, reminiscent of the non-Hermitian skin effect. To date, studies of odd elastic systems have mainly focused on ordered structures. Whether structurally-disordered materials can host non-Hermitian chiral surface waves (NHCSW) remains unexplored. We address this question using a minimal model of torque-driven disordered odd solids. Such solids are abundant, from biological gels such as the cytoskeleton driven by motor-proteins to synthesized systems such as magnetic colloidal gels. We find that torque-driven disordered odd solids have unique NHCSW with stronger surface localization and stable boundary velocity, in contrast to previous lattice models of odd solids. These distinct features stem from an intrinsic interplay between boundary torques and odd elasticity in torque-driven odd solids. Our results offer a new strategy to control NHCSW using active torques.

cond-mat.soft↗

arXiv2025

Odd elasticity in disordered chiral active materials

Chiral active materials are abundant in nature, including the cytoskeleton with attached motor proteins, rotary clusters of bacterial flagella, and self-spinning starfish embryos. These materials break both time reversal and mirror-image (parity) symmetries due to injection of torques at the microscale. It was recently discovered that chiral active materials show a new type of elastic response termed `odd' elasticity. Currently, odd elasticity is understood microscopically only in ordered structures, e.g., lattice designs of metamaterials. It remains to explore how odd elasticity emerges in natural or biological systems, which are usually disordered. To address this, we propose a minimal generic model for disordered `odd solids', using micropolar (Cosserat) elasticity in the presence of local active torques. We find that odd elasticity naturally emerges as a nonlinear effect of internal particle rotations. Exploring the viscoelasticity of such a solid, when immersed in an odd fluid, we discover new dynamically unstable regions driven by the odd solid-fluid coupling, and, in the underdamped regime, also by inertia. Remarkably, in the overdamped limit, this odd solid-fluid coupling allows for bulk wave propagation near these unstable regions.

cond-mat.soft↗

arXiv2023

Partition sum of thermal, under-constrained systems

Athermal (i.e. zero-temperature) under-constrained systems are typically floppy, but they can be rigidified by the application of external strain. Following our recently developed analytical theory for the athermal limit, here and in the companion paper, we extend this theory to under-constrained systems at finite temperatures. Close to the athermal transition point, we derive from first principles the partition sum for a broad class of under-constrained systems, from which we obtain analytic expressions for elastic material properties such as isotropic tension $t$ and shear modulus $G$ in terms of isotropic strain $\varepsilon$, shear strain $\gamma$, and temperature $T$. These expressions contain only three parameters, entropic rigidity $\kappa_S$, energetic rigidity $\kappa_E$, and a parameter $b_\varepsilon$ describing the interaction between isotropic and shear strain. We provide analytical expressions for these parameters based on the microscopic structure of the system. Our work unifies the physics of systems as diverse as polymer fibers & networks, membranes, and vertex models for biological tissues.

cond-mat.soft↗

arXiv2023

Generic elasticity of thermal, under-constrained systems

Athermal (i.e. zero-temperature) under-constrained systems are typically floppy, but they can be rigidified by the application of external strain, which is theoretically well understood. Here and in the companion paper, we extend this theory to finite temperatures for a very broad class of under-constrained systems. In the vicinity of the athermal transition point, we derive from first principles expressions for elastic properties such as isotropic tension $t$ and shear modulus $G$ on temperature $T$, isotropic strain $\varepsilon$, and shear strain $\gamma$, which we confirm numerically. These expressions contain only three parameters, entropic rigidity $\kappa_S$, energetic rigidity $\kappa_E$, and a parameter $b_\varepsilon$ describing the interaction between isotropic and shear strain, which can be determined from the microstructure of the system. Our results imply that in under-constrained systems, entropic and energetic rigidity interact like two springs in series. This also allows for a simple explanation of the previously numerically observed scaling relation $t\sim G\sim T^{1/2}$ at $\varepsilon=\gamma=0$. Our work unifies the physics of systems as diverse as polymer fibers & networks, membranes, and vertex models for biological tissues.

cond-mat.soft↗

arXiv2022

Stiffening of under-constrained spring networks under isotropic strain

Disordered spring networks are a useful paradigm to examine macroscopic mechanical properties of amorphous materials. Here, we study the elastic behavior of under-constrained spring networks, i.e.\ networks with more degrees of freedom than springs. While such networks are usually floppy, they can be rigidified by applying external strain. Recently, an analytical formalism has been developed to predict the mechanical network properties close to this rigidity transition. Here we numerically show that these predictions apply to many different classes of spring networks, including phantom triangular, Delaunay, Voronoi, and honeycomb networks. The analytical predictions further imply that the shear modulus $G$ scales linearly with isotropic stress $T$ close to the rigidity transition; however, this seems to be at odds with recent numerical studies suggesting an exponent between $G$ and $T$ that is smaller than one for some network classes. Using increased numerical precision and shear stabilization, we demonstrate here that close to the transition linear scaling, $G\sim T$, holds independent of the network class. Finally, we show that our results are not or only weakly affected by finite-size effects, depending on the network class.

cond-mat.soft↗

arXiv2017

Mechanisms and Rates of Nucleation of Amyloid Fibrils

The classical nucleation theory finds the rate of nucleation proportional to the monomer concentration raised to the power, which is the `critical nucleaus size', ${n_c}$. The implicit assumption, that amyloids nucleate in the same way, has been recently challenged by an alternative two-step mechanism, when the soluble monomers first form a metastable aggregate (micelle), and then undergo conversion into the conformation rich in $β$-strands that are able to form a stable growing nucleus for the protofilament. Here we put together the elements of extensive knowledge about aggregation and nucleation kinetics, using a specific case of A${β_{1\mathrm{-}42}}$ amyloidogenic peptide for illustration, to find theoretical expressions for the effective rate of amyloid nucleation. We find that at low monomer concentration in solution, and also at low interaction energy between two peptide conformations in the micelle, the nucleation occurs via the classical route. At higher monomer concentration, and a range of other interaction parameters between peptides, the two-step `aggregation-conversion' mechanism of nucleation takes over. In this regime, the effective rate of the process can be interpreted as a power of monomer concentration in a certain range of parameters, however, the exponent is determined by a complicated interplay of interaction parameters and is not related to the minimum size of the growing nucleus (which we find to be ${\sim}$ 7-8 for A${β_{1-42}}$).

cond-mat.soft↗