arXiv subjects

Zhongqiang Xiong

Publications and source records attributed to Zhongqiang Xiong.

8 recordsLinked to original sources

arXiv2026

Geometric formulation of state-dependent Langevin dynamics using scalar free energy

Stochastic dynamics with state-dependent diffusion arise broadly in confined, anisotropic, and hydrodynamically coupled systems. The conventional Langevin equation contains a spurious drift associated with multiplicative noise. Since the restricted free energy is generally non-scalar, the covariance is not explicit. Here, we reformulate state-dependent Langevin dynamics using a scalar free energy and a diffusion metric defined by the inverse diffusion tensor. The conventional spurious drift is then expressed as a Christoffel contribution. Although our formulation is mathematically equivalent to the conventional one through the relation between the restricted and scalar free energies, it makes coordinate covariance explicit and enables the phenomenological construction of thermodynamic potentials directly from system symmetries. We demonstrate its consistency in representative examples of state-dependent diffusion arising from coordinate transformations, geometric confinement, and projection from curved to flat spaces.

cond-mat.soft↗

arXiv2026

Covariant Onsager and Onsager-Machlup principles for active and inertial dynamics

The Onsager principle provides a variational route to the phenomenological equations of dissipative dynamics through the minimization of the Rayleighian. We develop a covariant formulation of the Onsager principle for active and inertial systems, ensuring geometric consistency under coordinate transformations. To further incorporate thermal fluctuations, we formulate the Onsager-Machlup principle for active and inertial systems by considering the Onsager-Machlup functional and the corresponding path probability for stochastic trajectories. Requiring that the path probability obeys the detailed fluctuation theorem, we show that the extended Onsager-Machlup theory is consistent with stochastic thermodynamics. The extended OP and OMP offer a unified and useful variational framework for deriving the dynamical equations of active and inertial systems.

cond-mat.soft↗

arXiv2026

Taylor Dispersion in Sedimentation of an Axisymmetric Brownian Particle with Centre Offset

When a non-spherical particle sediments, its velocity generally changes in time as the particle orientation changes in time. This gives extra dispersion of the particle position in addition to the thermal Brownian motion. Brenner [J. Colloid Interf. Sci. 1979, 71(2), 189-208] studied this effect and formulated how to calculate the gravity-induced dispersion (called Taylor dispersion in sedimentation). However, he conducted the explicit calculation only for torque-free particles which keep an isotropic orientational distribution in the steady-state. In this paper, we study the effect of the gravitational torque on the Taylor dispersion. We limit the analysis to particles having uniaxial symmetry. In this case, the gravitational torque is caused by the offset $l_{\mathrm{c}}$, the distance between the hydrodynamic centre and the gravitational force centre. The effect of the gravitational torque is represented by a dimensionless parameter $α$ (called the Langevin parameter by Brenner) which is proportional to $l_{\mathrm{c}}$. We obtain analytical expressions for the Taylor diffusivity for the two limits, $α\ll 1 $ and $α\gg 1$. We show that the offset gives a significant effect on the diffusivity and changes the classical scaling of the Taylor dispersion at a large Péclet number. We also analyze the transient regime of the mean square displacement (MSD) and show how the crossing time from the ballistic regime to the diffusive regime depends on the gravitational torque.

cond-mat.stat-mech↗

arXiv2026

Neural optimization of the most probable paths of 3D active Brownian particles

We develop a variational neural-network framework to determine the most probable path (MPP) of a 3D active Brownian particle (ABP) by directly minimizing the Onsager-Machlup integral (OMI). To obtain the OMI, we use the Onsager-Machlup variational principle for active systems and construct the Rayleighian of the ABP by including its active power. This approach reveals geometric transitions of the MPP from in-plane I- and U-shaped paths to 3D helical paths as the final time and net displacement are varied. We also demonstrate that the initial and final boundary conditions have a significant impact on the MPPs. Our results show that neural optimization combined with the Onsager-Machlup variational principle provides an efficient and versatile framework for exploring optimal transition pathways in active and nonequilibrium systems.

cond-mat.soft↗

arXiv2026

Brownian motion of a rod threading through a ring with fixed ring-center

We study the Brownian motion of a rigid rod threading through a small fixed ring while the ring can freely rotate. We derive the distribution function for the sliding displacement and the unit vector along the rod both at equilibrium and non-equilibrium. The equilibrium distribution is quadratic in the sliding displacement and is controlled by the moment of inertia (mass distribution). Applying the Onsager variational principle, we derive a Smoluchowski equation in which sliding and rotational diffusion are coupled. The mean square displacement (MSD) of sliding shows a metastable plateau in a certain time range before it approaches the final equilibrium value. The longest sliding relaxation time scales as $α^{-1/2}$, where $α$ is the dimensionless moment of inertia of the rod. The rotational relaxation time obtained from the orientational correlation function is longer than that of a rod with its center fixed but faster than a rod with one end fixed. These results may be useful in understanding the dynamics of polymers connected by sliding rings.

cond-mat.soft↗

arXiv2026

Fokker-Planck description of an active Brownian particle with rotational inertia

We develop a perturbative framework to calculate the mean-squared displacement (MSD) of active Brownian particles (ABPs) with a finite moment of inertia. Starting from the corresponding Fokker-Planck equation, we employ a Fourier transform for the spatial coordinates and Hermite polynomials as eigenfunctions for the angular velocity, which enables a systematic perturbative expansion of the MSD order by order. By resumming the resulting series in Laplace space and performing the inverse transform, we obtain an explicit expression for the MSD as a function of the moment of inertia. The analytical results are further validated by comparison with numerical simulations.

cond-mat.stat-mech↗

arXiv2024

Bending-Rotation coupling in the viscoelasticity of semiflexible polymers -- Rigorous perturbation analysis from the rod limit

Brownian motion and viscoelasticity of semiflexible polymers is a subject that has been studied for many years. Still, rigorous analysis has been hindered due to the difficulty in handling the constraint that polymer chains cannot be stretched along the contour. Here, we show a straightforward method to solve the problem. We consider a stiff polymer that has a persistent length $L_p$ much larger than the contour length $L$. We express the polymer configuration using three types of variables: the position vector of the center of mass $R_c$, the unit vector $n$ along the main axis, and the normal coordinates $u_p$ for bending. Solving the Smoluchowski equation for the distribution function of these variables, we calculate the equilibrium time correlation function $ \langle P(t)\cdot P(0) \rangle$ of the end-to-end vector $P$ and the complex modulus $G^*(ω)$ of dilute solution. They include the bending effect to the first order in $θ\equiv L/L_p$ and reduce to the exact results for the rigid rod in the limit of $θ\to 0$. The rotational diffusion coefficient increases slightly by the semiflexibility because the equilibrium length of the semiflexible polymer is smaller than that of the rigid rod with the same contour length. The storage modulus shows the same asymptotic dependence $G'(ω) \sim ω^{3/4}$ predicted by Shankar, Pasquali, and Morse [J. Rheol. 2002, 46, 1111--1154]. The high-frequency viscosity is predicted to be dependent on the thickness of the semiflexible polymers.

cond-mat.soft↗

arXiv2024

Ridge instability in dense suspensions caused by the second normal stress difference

A dense suspension of the cornstarch flowing on a very inclined wall finally forms some ridge-like patterns of the free surface. The onset of pattern formation is the primary target to elucidate the mechanism. In this work, based on the continuity of fluids and the force balance, we show that the flat free surface is unstable when the second normal stress difference $N_2$ is negatively proportional to shear stress and the gravity component perpendicular to the wall is weak enough. Such instability is inevitable to grow into a ridge-like surface profile oriented parallel to the flow direction. We use the instability criterion to predict the critical slope angle for the formation of ridge patterns. The estimated critical angle was found to be in agreement with experimental observations for a cornstarch suspension.

cond-mat.soft↗