arXiv subjects

Liu Hong

Publications and source records attributed to Liu Hong.

At least 37 records · Page 2Linked to original sources

arXiv2021

Stochastic Dynamics, Large Deviations Principle, and Non-equilibrium Thermodynamics

By examining the deterministic limit of a general $ε$-dependent generator for Markovian dynamics, which includes the continuous Fokker-Planck equations and discrete chemical master equations as two special cases, the intrinsic connections among mesoscopic stochastic dynamics, deterministic ODEs or PDEs, large deviations rate function, and macroscopic thermodynamic potential are established. Our result not only solves the long-lasting question on the origin of entropy function in classical irreversible thermodynamics, but also reveals an emergent feature that arises automatically during the deterministic limit, through its large deviations rate function, with both time-reversible dynamics equipped with a Hamiltonian function and time-irreversible dynamics equipped with an entropy function.

math.PR↗

arXiv2021

Recent Advances in Conservation-Dissipation Formalism for Irreversible Processes

The main purpose of this review is to summarize the recent advances of the Conservation-Dissipation Formalism (CDF), a new way for constructing both thermodynamically compatible and mathematically stable and well-posed models for irreversible processes. The contents include but are not restricted to the CDF's physical motivations, mathematical foundations, formulations of several classical models in mathematical physics from master equations and Fokker-Planck equations to Boltzmann equations and quasi-linear Maxwell equations, as well as novel applications in the fields of non-Fourier heat conduction, non-Newtonian viscoelastic fluids, wave propagation/transportation in geophysics and neural science, soft matter physics, \textit{etc.} Connections with other popular theories in the field of non-equilibrium thermodynamics are examined too.

math-ph↗

arXiv2020

Hamiltonian Dynamics of Saturated Elongation in Amyloid Fiber Formation

Elongation is a fundament process in amyloid fiber growth, which is normally characterized by a linear relationship between the fiber elongation rate and the monomer concentration. However, in high concentration regions, a sub-linear dependence was often observed, which could be explained by a universal saturation mechanism. In this paper, we modeled the saturated elongation process through a Michaelis-Menten like mechanism, which is constituted by two sub-steps -- unspecific association and dissociation of a monomer with the fibril end, and subsequent conformational change of the associated monomer to fit itself to the fibrillar structure. Typical saturation concentrations were found to be $7-70μM$ for A$β$40, $α$-synuclein and etc. Furthermore, by using a novel Hamiltonian formulation, analytical solutions valid for both weak and strong saturated conditions were constructed and applied to the fibrillation kinetics of $α$-synuclein and silk fibroin.

q-bio.QM↗

arXiv2020

Revealing hidden dynamics from time-series data by ODENet

To derive the hidden dynamics from observed data is one of the fundamental but also challenging problems in many different fields. In this study, we propose a new type of interpretable network called the ordinary differential equation network (ODENet), in which the numerical integration of explicit ordinary differential equations (ODEs) are embedded into the machine learning scheme to build a general framework for revealing the hidden dynamics buried in massive time-series data efficiently and reliably. ODENet takes full advantage of both machine learning algorithms and ODE modeling. On one hand, the embedding of ODEs makes the framework more interpretable benefiting from the mature theories of ODEs. On the other hand, the schemes of machine learning enable data handling, paralleling, and optimization to be easily and efficiently implemented. From classical Lotka-Volterra equations to chaotic Lorenz equations, the ODENet exhibits its remarkable capability in handling time-series data even in the presence of large noise. We further apply the ODENet to real actin aggregation data, which shows an impressive performance as well. These results demonstrate the superiority of ODENet in dealing with noisy data, data with either non-equal spacing or large sampling time steps over other traditional machine learning algorithms.

math.DS↗

arXiv2020

Epidemic analysis of COVID-19 in China by dynamical modeling

The outbreak of novel coronavirus-caused pneumonia (COVID-19) in Wuhan has attracted worldwide attention. Here, we propose a generalized SEIR model to analyze this epidemic. Based on the public data of National Health Commission of China from Jan. 20th to Feb. 9th, 2020, we reliably estimate key epidemic parameters and make predictions on the inflection point and possible ending time for 5 different regions. According to optimistic estimation, the epidemics in Beijing and Shanghai will end soon within two weeks, while for most part of China, including the majority of cities in Hubei province, the success of anti-epidemic will be no later than the middle of March. The situation in Wuhan is still very severe, at least based on public data until Feb. 15th. We expect it will end up at the beginning of April. Moreover, by inverse inference, we find the outbreak of COVID-19 in Mainland, Hubei province and Wuhan all can be dated back to the end of December 2019, and the doubling time is around two days at the early stage.

q-bio.PE↗

arXiv2020

Identification of hydrodynamic instability by convolutional neural networks

The onset of hydrodynamic instabilities is of great importance in both industry and daily life, due to the dramatic mechanical and thermodynamic changes for different types of flow motions. In this paper, modern machine learning techniques, especially the convolutional neural networks (CNN), are applied to identify the transition between different flow motions raised by hydrodynamic instability, as well as critical non-dimensionalized parameters for characterizing this transit. CNN not only correctly predicts the critical transition values for both Taylor-Couette (TC) flow and Rayleigh- Bénard (RB) convection under various setups and conditions, but also shows an outstanding performance on robustness and noise-tolerance. In addition, key spatial features used for classifying different flow patterns are revealed by the principal component analysis.

physics.comp-ph↗

arXiv2020

When Machine Learning Meets Multiscale Modeling in Chemical Reactions

Due to the intrinsic complexity and nonlinearity of chemical reactions, direct applications of traditional machine learning algorithms may face with many difficulties. In this study, through two concrete examples with biological background, we illustrate how the key ideas of multiscale modeling can help to reduce the computational cost of machine learning a lot, as well as how machine learning algorithms perform model reduction automatically in a time-scale separated system. Our study highlights the necessity and effectiveness of an integration of machine learning algorithms and multiscale modeling during the study of chemical reactions.

q-bio.MN↗

arXiv2020

Representations and Divergences in the Space of Probability Measures and Stochastic Thermodynamics

Radon-Nikodym (RN) derivative between two measures arises naturally in the affine structure of the space of probability measures with densities. Entropy, free energy, relative entropy, and entropy production as mathematical concepts associated with RN derivatives are introduced. We identify a simple equation that connects two measures with densities as a possible mathematical basis of the entropy balance equation that is central in nonequilibrium thermodynamics. Application of this formalism to Gibbsian canonical distribution yields many results in classical thermomechanics. An affine structure based on the canonical represenation and two divergences are introduced in the space of probability measures. It is shown that thermodynamic work, as a conditional expectation, is indictive of the RN derivative between two energy represenations being singular. The entropy divergence and the heat divergence yield respectively a Massieu-Planck potential based and a generalized Carnot inequalities.

cond-mat.stat-mech↗

arXiv2020

Thermodynamics of Markov Processes with Non-extensive Entropy and Free Energy

Statistical thermodynamics of small systems shows dramatic differences from normal systems. Parallel to the recently presented steady-state thermodynamic formalism for master equation and Fokker-Planck equation, we show that a ``thermodynamic'' theory can also be developed based on Tsallis' generalized entropy $S^{(q)}=\sum_{i=1}^N(p_i-p_i^q)/[q(q-1)]$ and Shiino's generalized free energy $F^{(q)}=[\sum_{i=1}^Np_i(p_i/π_i)^{q-1}-1]/[q(q-1)]$, where $π_i$ is the stationary distribution. $dF^{(q)}/dt=-f_d^{(q)}\le 0$ and it is zero iff the system is in its stationary state. $dS^{(q)}/dt-Q_{ex}^{(q)} = f_d^{(q)}$ where $Q_{ex}^{(q)}$ characterizes the heat exchange. For systems approaching equilibrium with detailed balance, $f_d^{(q)}$ is the product of Onsager's thermodynamic flux and force. However, it is discovered that the Onsager's force is non-local. This is a consequence of the particular transformation invariance for zero energy of Tsallis' statistics.

math-ph↗

arXiv2020

The Statistical Foundation of Entropy in Extended Irreversible Thermodynamics

In the theory of extended irreversible thermodynamics (EIT), the flux-dependent entropy function plays a key role and has a fundamental distinction from the usual flux-independent entropy function adopted by classical irreversible thermodynamics (CIT). However, its existence, as a prerequisite for EIT, and its statistical origin have never been justified. In this work, by studying the macroscopic limit of an ε-dependent Langevin dynamics, which admits a large deviations (LD) principle, we show that the stationary LD rate functions of probability density p_ε(x; t) and joint probability density p_ε(x; \dot{x}; t) actually turn out to be the desired fluxindependent entropy function in CIT and flux-dependent entropy function in EIT respectively. The difference of the two entropy functions is determined by the time resolution for Brownian motions times a Lagrangian, the latter arises from the LD Hamilton-Jacobi equation and can be used for constructing conserved Lagrangian/Hamiltonian dynamics.

math.PR↗

arXiv2019

Linear and nonlinear electromagnetic waves in modulated honeycomb media

Wave dynamics in topological materials has been widely studied recently. A striking feature is the existence of robust and chiral wave propagations that have potential applications in many fields. A common way to realize such wave patterns is to utilize Dirac points which carry topological indices and is supported by the symmetries of the media. In this work, we investigate these phenomena in photonic media. Starting with Maxwell's equations with a honeycomb material weight as well as the nonlinear Kerr effect, we first prove the existence of Dirac points in the dispersion surfaces of transverse electric and magnetic Maxwell operators under very general assumptions of the material weight. Our assumptions on the material weight are almost the minimal requirements to ensure the existence of Dirac points in a general hexagonal photonic crystal. We then derive the associated wave packet dynamics in the scenario where the honeycomb structure is weakly modulated. It turns out the reduced envelope equation is generally a two-dimensional nonlinear Dirac equation with a spatially varying mass. By studying the reduced envelope equation with a domain-wall-like mass term, we realize the subtle wave motions which are chiral and immune to local defects. The underlying mechanism is the existence of topologically protected linear line modes, also referred to as edge states. However, we show that these robust linear modes do not survive with nonlinearity. We demonstrate the existence of nonlinear line modes, which can propagate in the nonlinear media based on high-accuracy numerical computations. Moreover, we also report a new type of nonlinear modes which are localized in both directions.

math-ph↗

arXiv2019

Conservation-Dissipation Formalism for Soft Matter Physics: I. Equivalence with Doi's Variational Approach

In this paper, we proved that by choosing the proper variational function and variables, the variational approach proposed by M. Doi in soft matter physics was equivalent to the Conservation-Dissipation Formalism. To illustrate the correspondence between these two theories, several novel examples in soft matter physics, including particle diffusion in dilute solutions, polymer phase separation dynamics and nematic liquid crystal flows, were carefully examined. Based on our work, a deep connection among the generalized Gibbs relation, the second law of thermodynamics and the variational principle in non-equilibrium thermodynamics was revealed.

cond-mat.stat-mech↗

arXiv2019

Conservation-Dissipation Formalism for Soft Matter Physics: II. Application to Non-isothermal Nematic Liquid Crystals

To most existing non-equilibrium theories, the modeling of non-isothermal processes was a hard task. Intrinsic difficulties involved the non-equilibrium temperature, the coexistence of conserved energy and dissipative entropy, etc. In this paper, by taking the non-isothermal flow of nematic liquid crystals as a typical example, we illustrated that thermodynamically consistent models in either vectorial or tensorial forms could be constructed within the framework of Conservation-Dissipation Formalism (CDF). And the classical isothermal Ericksen-Leslie model and Qian-Sheng model were shown to be special cases of our new vectorial and tensorial models in the isothermal, incompressible and stationary limit. Most importantly, from above examples, it was learnt that mathematical modeling based on CDF could easily solve the issues relating with non-isothermal situations in a systematic way. The first and second laws of thermodynamics were satisfied simultaneously. The non-equilibrium temperature was defined self-consistently through the partial derivative of entropy function. Relaxation-type constitutive relations were constructed, which gave rise to the classical linear constitutive relations, like Newton's law and Fourier's law, in stationary limits. Therefore, CDF was expected to have a broad scope of applications in soft matter physics, especially under the complicated situations, such as non-isothermal, compressible and nanoscale systems.

cond-mat.soft↗

arXiv2018

Phase Transition Dynamics and Stochastic Resonance in Topologically Confined Nematic Liquid Crystals

Topological defects resulted from boundary constraints in confined liquid crystals have attracted extensive research interests. In this paper, we use numerical simulation to study the phase transition dynamics in the context of stochastic resonance in a bistable liquid crystal device containing defects. This device is made of nematic liquid crystals confined in a shallow square well, and is described by the planar Lebwohl-Lasher model. The stochastic phase transition processes of the system in the presence of a weak oscillating potential is simulated using an over-damped Langevin dynamics. Our simulation results reveal that, depending on system size, the phase transition may follow two distinct pathways: in small systems the pre-existing defect structures at the corners hold until the last stage and there is no newly formed defect point in the bulk during the phase transition, In large systems new defect points appear spontaneously in the bulk and eventually merge with the pre-existing defects at the corners. For both transition pathways stochastic resonance can be observed, but show dramatic difference in their responses to the boundary anchoring strength. In small systems we observe a "sticky-boundary" effect for a certain range of anchoring strength in which the phase transition gets stuck and stochastic resonance becomes de-activated. Our work demonstrates the dynamical interplay among defects, noises, and boundary conditions in confined liquid crystals.

cond-mat.soft↗

arXiv2017

The Markov Process Admits a Consistent Steady-State Thermodynamic Formalism

The seek for a new universal formulation for describing various non-equilibrium processes is a central task of modern non-equilibrium thermodynamics. In this paper, a novel steady-state thermodynamic formalism was established for general Markov processes described by the Chapman-Kolmogorov equation. Furthermore, corresponding formalisms of steady-state thermodynamics for master equation and Fokker-Planck equation could be rigorously derived in mathematics. To be concrete, we proved that: 1) in the limit of continuous time, the steady-state thermodynamic formalism for the Chapman-Kolmogorov equation fully agrees with that for the master equation; 2) a similar one-to-one correspondence could be established rigorously between the master equation and Fokker-Planck equation in the limit of large system size; 3) when a Markov process is restrained to one-step jump, the steady-state thermodynamic formalism for the Fokker-Planck equation with discrete state variables also goes to that for master equations, as the discretization step gets smaller and smaller. Our analysis indicated that, with respect to the steady state, general Markov processes admit a unified and self-consistent non-equilibrium thermodynamic formulation, regardless of underlying detailed models.

cond-mat.stat-mech↗

arXiv2017

Hamiltonian and Godunov Structures of the Grad Hierarchy

The time evolution governed by the Boltzmann kinetic equation is compatible with mechanics and thermodynamics. The former compatibility is mathematically expressed in the Hamiltonian and Godunov structures, the latter in the structure of gradient dynamics guaranteeing the growth of entropy and consequently the approach to equilibrium. We carry all three structures to the Grad reformulation of the Boltzmann equation (to the Grad hierarchy). First, we recognize the structures in the infinite Grad hierarchy and then in several examples of finite hierarchies representing extended hydrodynamic equations. In the context of Grad's hierarchies we also investigate relations between Hamiltonian and Godunov structures.

cond-mat.stat-mech↗

arXiv2016

Statistical Mechanics and Kinetics of Amyloid Fibrillation

Amyloid fibrillation is a protein self-assembly phenomenon that is intimately related to well-known human neurodegenerative diseases. During the past few decades, striking advances have been achieved in our understanding of the physical origin of this phenomenon and they constitute the contents of this review. Starting from a minimal model of amyloid fibrils, we explore systematically the equilibrium and kinetic aspects of amyloid fibrillation in both dilute and semi-dilute limits. We then incorporate further molecular mechanisms into the analyses. We also discuss the mathematical foundation of kinetic modeling based on chemical mass-action equations, the quantitative linkage with experimental measurements, as well as the procedure to perform global fitting.

q-bio.BM↗

arXiv2015

A Novel Dissipation Property of the Master Equation

Recent studies have shown that the entropy production rate for the master equation consists of two nonnegative terms: the adiabatic and non-adiabatic parts, where the non-adiabatic part is also known as the dissipation rate of a Boltzmann-Shannon relative entropy. In this paper, we provide some nonzero lower bounds for the relative entropy, the entropy production rate, and its adiabatic and non-adiabatic parts. These nonzero lower bounds not only reveal some novel dissipative properties for general nonequilibrium processes which are much stronger than the second law of thermodynamics, but also impose some new constraints on thermodynamic constitutive relations. Moreover, we also provide a mathematical application of these nonzero lower bounds by studying the long-time behavior of the master equation. Extensions to the Tsallis statistics are also discussed, including the nonzero lower bounds for the Tsallis-type relative entropy and its dissipation rate.

physics.chem-ph↗