arXiv subjects

Pik-Yin Lai

Publications and source records attributed to Pik-Yin Lai.

At least 19 recordsLinked to original sources

arXiv2026

Time arrow in open-boundary one-dimensional stochastic dynamics

We consider the finite-timestep stochastic dynamics of a single particle confined in one dimension, while the system has a nonuniform temperature profile. Under the open-boundary condition, one cannot observe any net probability current in the nonequilibrium steady state (NESS). On the other hand, the nonequilibrium nature of this system is revealed through the asymmetry in forward and backward transition probabilities, as is reported in this work through the simulation and theoretic analysis. In particular, our result shows prominent time irreversibility nearby the temperature interface. We propose a hidden-gyration scenario that demonstrates the source of irreversibility, while the collapse of gyrations on the one-dimensional coordinate accounts for the absence of probability current.

cond-mat.stat-mech↗

arXiv2026

Mode-locking in a colloidal ring driven by power-modulated optical tweezers

Particles and clusters moving across real-space periodic potentials can become locked to discrete directions or orientations due to competing symmetries. Here, we demonstrate an analogous locking phenomenon within a synthetic frequency space. We drive ring-shaped colloidal clusters using a circular optical tweezer array, where power modulation of the traps generates coexisting, distinct potential waves. Relative displacements between the cluster and these waves trace zigzag trajectories across a synthetic two-dimensional lattice, mirroring directionally locked motion in real-space periodic potentials. By tuning the relative wave amplitudes, both the cluster's direction in synthetic space and its velocity in real space exhibit discrete plateaus, both governed by square-lattice symmetry. Furthermore, the formation of superlattices between the particles and potential wave minima mirrors the characteristic features of kinetically locked two-dimensional clusters, demonstrating the capability to explore driven cluster dynamics within higher-dimensional potentials using lower-dimensional setups. Our findings establish new strategies for controlling transport of particle clusters via power-modulated laser tweezers.

cond-mat.soft↗

arXiv2026

Steady-State Equilibrium and Nonequilibrium Noisy Network Dynamics

The fluctuating dynamics of a network about its stable, noise-free steady state are theoretically investigated. Various causes of non-equilibrium dynamics are identified in terms of the properties and symmetry of the network connections and the noise covariance matrices. Several equivalent conditions are derived for the dynamics of the noisy network at equilibrium. In particular, non-equilibrium steady state (NESS) dynamics are analyzed in terms of the steady-state probability current and the drift velocity relative to the effective potential surface. Conventional physical Brownian dynamics for overdamped fluctuating dynamics is analyzed from the perspective of the linearized fluctuating noisy network dynamics. Connection with the network reconstruction from time-series data is discussed. It is demonstrated that the overdamped Brownian dynamics in the physical system is a special case of the general noisy directed network in a NESS. Furthermore, a general fluctuation-dissipation relation is derived for the general non-equilibrium noisy network dynamics. These theoretical results are verified by numerical simulations.

cond-mat.stat-mech↗

arXiv2024

Coexistence of distinct nonuniform nonequilibrium steady states in Ehrenfest multiurn model on a ring

The recently proposed Ehrenfest M-urn model with interactions on a ring is considered as a paradigm model which can exhibit a variety of distinct nonequilibrium steady states. Unlike the previous three-urn model on a ring which consists of a uniform steady state and a nonuniform nonequilibrium steady state, it is found that for even M>=4, an additional nonequilibrium steady state can coexist with the original ones. Detailed analysis reveals that this additional nonequilibrium steady state emerged via a pitchfork bifurcation which cannot occur if M is odd. Properties of this nonequilibrium steady state, such as stability, and steady-state flux are derived analytically for the four-urn case. The full phase diagram with the phase boundaries is also derived explicitly. The associated thermodynamic stability is also analyzed, confirming its stability. These theoretical results are also explicitly verified by direct Monte Carlo simulations for the three-urn and four-urn ring models.

cond-mat.stat-mech↗

arXiv2024

Non-equilibrium Dynamics and Phase Transitions in Potts model and Interacting Ehrenfest urn model

We show that the recently proposed interacting Ehrenfest M-urn model at equilibrium can be exactly mapped to a mean-field M-state Potts model. By exploiting this correspondence, we show that the M-state Potts model with M >= 3, with transition rates motivated by the non-equilibrium urn model, can exhibit rich non-equilibrium spin dynamics such as non-equilibrium steady states and non-equilibrium periodic states. Monte Carlo simulations of the 3-state Potts model are performed to demonstrate explicitly the first-order transitions for the equilibrium and non-equilibrium steady states, as well as the far-from-equilibrium periodic states.

cond-mat.stat-mech↗

arXiv2023

Theory of Non-equilibrium Asymptotic State Thermodynamics: Interacting Ehrenfest Urn Ring as an Example

A generalized class of non-equilibrium state, called non-equilibrium asymptotic state (NEAS), is proposed. The NEAS is constructed within the framework of the Fokker-Planck equations in thermodynamic limit. Besides the usual equilibrium state and non-equilibrium steady state (NESS), the class of NEAS could also cover non-equilibrium periodic state (NEPS) in which its dynamics shows periodicity, non-equilibrium quasi-periodic state (NEQPS), and non-equilibrium chaotic state (NECS) in which its dynamics becomes chaotic. Based on the theory of NEAS thermodynamics, the corresponding thermodynamics of different NEAS could also be determined. Finally the interacting Ehrenfest urn ring model is used as an example to illustrate how different kinds of NEAS (equilibrium state, uniform NESS, non-uniform NESS, NEPS) in three-urn case are identified in our framework. In particular, the thermodynamics of NEPS and its phase transitions to other types of NEAS are studied.

cond-mat.stat-mech↗

arXiv2022

Activity-assisted barrier-crossing of self-propelled colloids over parallel microgrooves

We report a systematic study of the dynamics of self-propelled particles (SPPs) over a one-dimensional periodic potential landscape, which is fabricated on a microgroove-patterned polydimethylsiloxane (PDMS) substrate. From the measured non-equilibrium probability density function of the SPPs, we find that the escape dynamics of the slow-rotating SPPs across the potential landscape can be described by an effective potential, once the self-propulsion force is included into the potential under the fixed angle approximation. This work demonstrates that the parallel microgrooves provide a versatile platform for a quantitative understanding of the interplay among the self-propulsion force, spatial confinement by the potential landscape, and thermal noise, as well as its effects on activity-assisted escape dynamics and transport of the SPPs.

cond-mat.soft↗

arXiv2022

Revealing directed effective connectivity of cortical neuronal networks from measurements

In the study of biological networks, one of the major challenges is to understand the relationships between network structure and dynamics. In this paper, we model in vitro cortical neuronal cultures as stochastic dynamical systems and apply a method that reconstructs directed networks from dynamics [Ching and Tam, Phys. Rev. E 95, 010301(R), 2017] to reveal directed effective connectivity, namely the directed links and synaptic weights, of the neuronal cultures from voltage measurements recorded by a multielectrode array. The effective connectivity so obtained reproduces several features of cortical regions in rats and monkeys and has similar network properties as the synaptic network of the nematode C. elegans, the only organism whose entire nervous system has been mapped out as of today. The distribution of the incoming degree is bimodal and the distributions of the average incoming and outgoing synaptic strength are non-Gaussian with long tails. The effective connectivity captures different information from the commonly studied functional connectivity, estimated using statistical correlation between spiking activities. The average synaptic strengths of excitatory incoming and outgoing links are found to increase with the spiking activity in the estimated effective connectivity but not in the functional connectivity estimated using the same sets of voltage measurements. These results thus demonstrate that the reconstructed effective connectivity can capture the general properties of synaptic connections and better reveal relationships between network structure and dynamics.

q-bio.NC↗

arXiv2021

Regulatory Feedback Effects on Tissue Growth Dynamics in a Two-Stage Cell Lineage Model

Identifying the mechanism of intercellular feedback regulation is critical for the basic understanding of tissue growth control in organisms. In this paper, we analyze a tissue growth model consisting of a single lineage of two cell types regulated by negative feedback signalling molecules that undergo spatial diffusion. By deriving the fixed points for the uniform steady states and carrying out linear stability analysis, phase diagrams are obtained analytically for arbitrary parameters of the model. Two different generic growth modes are found: blow-up growth and final-state controlled growth which are governed by the non-trivial fixed point and the trivial fixed point respectively, and can be sensitively switched by varying the negative feedback regulation on the proliferation of the stem cells. Analytic expressions for the characteristic time scales for these two growth modes are also derived. Remarkably, the trivial and non-trivial uniform steady states can coexist and a sharp transition occurs in the bistable regime as the relevant parameters are varied. Furthermore, the bi-stable growth properties allows for the external control to switch between these two growth modes. In addition, the condition for an early accelerated growth followed by a retarded growth can be derived. These analytical results are further verified by numerical simulations and provide insights on the growth behavior of the tissue. Our results are also discussed in the light of possible realistic biological experiments and tissue growth control strategy. Furthermore, by external feedback control of the concentration of regulatory molecules, it is possible to achieve a desired growth mode, as demonstrated with an analysis of boosted growth, catch-up growth and the design for the target of a linear growth dynamic.

q-bio.TO↗

arXiv2021

Optimized two-dimensional Networks with edge crossing cost: frustrated anti-ferromagnetic spin system

We consider a quasi two-dimensional network connection growth model that minimizes the wiring cost while maximizing the network connections, but at the same time edge crossings are penalized or forbidden. This model is mapped to a dilute anti-ferromagnetic Ising spin system with frustrations. We obtain analytic results for the order-parameter or mean degree of the optimized network using mean field theories. The cost landscape is analyzed in detail showing complex structures due to frustration as the crossing penalty increases. For the case of strictly no edge crossing is allowed, the mean-field equations lead to a new algorithm that can effectively find the (near) optimal solution even for this strongly frustrated system. All these results are also verified by Monte Carlo simulations and numerical solution of the mean-field equations. Possible applications and relation to the planar triangulation problem is also discussed.

cond-mat.stat-mech↗

arXiv2021

Instantaneous equilibrium Transport for Brownian systems under time-dependent temperature and potential variations: Reversibility, Heat and work relations, and Fast Isentropic process

The theory of constructing instantaneous equilibrium (ieq) transition under arbitrary time-dependent temperature and potential variation for a Brownian particle is developed. It is shown that it is essential to consider the underdamped dynamics for temperature-changing transitions. The ieq is maintained by a time-dependent auxiliary position and momentum potential, which can be calculated for given time-dependent transition protocols. Explicit analytic results are derived for the work and heat statistics, energy, and entropy changes for harmonic and non-harmonic trapping potential with arbitrary time-dependent potential parameters and temperature protocols. Numerical solutions of the corresponding Langevin dynamics are computed to confirm the theoretical results. Although ieq transition of the reverse process is not the time-reversal of the ieq transition of the forward process due to the odd-parity of controlling parameters, their phase-space distribution functions restore the time-reversal symmetry, and hence the energy and entropy changes of the ieq of the reverse process are simply the negative of that of the forward process. Furthermore, it is shown that it is possible to construct an ieq transition that has zero entropy production at a finite transition rate, i.e., a fast ieq isentropic process, and is further demonstrated by explicit Langevin dynamics simulations. Our theory provides fundamental building blocks for designing controlled microscopic heat engine cycles. Implications for constructing an efficient Brownian heat engine are also discussed.

cond-mat.stat-mech↗

arXiv2021

Non-equilibrium thermodynamics and Phase transition of Ehrenfest urns with interactions

Ehrenfest urns with interaction that are connected in a ring is considered as a paradigm model for non-equilibrium thermodynamics and is shown to exhibit two distinct non-equilibrium steady states (NESS) of uniform and non-uniform particle distributions. As the inter-particle attraction varies, a first order non-equilibrium phase transition occurs between these two NESSs characterized by a coexistence regime. The phase boundaries, the NESS particle distributions near saddle points and the associated particle fluxes, average urn population fractions, and the relaxational dynamics to the NESSs are obtained analytically and verified numerically. A generalized non-equilibrium thermodynamics law is also obtained, which explicitly identifies the heat, work, energy and entropy of the system.

cond-mat.stat-mech↗

arXiv2021

Phase Transitions in Ehrenfest Urns Model with Interactions: Coexistence of uniform and non-uniform states

A model based on the classic non-interacting Ehrenfest urn model with two-urns is generalized to $M$ urns with the introduction of interactions for particles within the same urn. As the inter-particle interaction strength is varied, phases of different levels of non-uniformity emerge and their stabilities are calculated analytically. In particular, coexistence of locally stable uniform and non-uniform phases connected by first-order transition occurs. The phase transition threshold and energy barrier can be derived exactly together with the phase diagram obtained analytically. These analytic results are further confirmed by Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2021

Autonomous Brownian gyrators: a study on gyrating characteristics

We study the nonequilibrium steady-state (NESS) dynamics of two-dimensional Brownian gyrators under harmonic and nonharmonic potentials via computer simulations and analyses based on the Fokker-Planck equation, while our nonharmonic cases feature a double-well potential and an isotropic quartic potential. In particular, we report two simple methods that can help understand gyrating patterns. For harmonic potentials, we use the Fokker-Planck equation to survey the NESS dynamical characteristics, i.e., the NESS currents gyrate along the equiprobability contours and the stationary point of flow coincides with the potential minimum. As a contrast, the NESS results in our nonharmonic potentials show that these properties are largely absent, as the gyrating patterns are much distinct from those of corresponding probability distributions. Furthermore, we observe a critical case of the double-well potential, where the harmonic contribution to the gyrating pattern becomes absent, and the NESS currents do not circulate about the equiprobability contours nearby the potential minima even at low temperatures.

cond-mat.stat-mech↗

arXiv2016

Positive Feedback and Synchronized Bursts in Neuronal Cultures

Synchronized bursts (SBs) with complex structures are common in neuronal cultures. Although the origin of SBs is still unclear, they have been studied for their information processing capabilities. Here, we investigate the properties of these SBs in a culture on multi-electrode array system. We find that structures of these SBs are related to the different developmental stages of the cultures. A model based on short term synaptic plasticity, recurrent connections and astrocytic recycling of neurotransmitters has been developed successfully to understand these structures. A phase diagram obtained from this model shows that networks exhibiting SBs are in an oscillatory state due to large enough positive feedback provided by synaptic facilitation and recurrent connections. In this model, the structures of the SBs are the results of intrinsic synaptic interactions; not information stored in the network.

q-bio.NC↗

arXiv2015

Adaptive Synchronization and Anticipatory Dynamical System

Many biological systems can sense periodical variations in a stimulus input and produce well-timed, anticipatory responses after the input is removed. Such systems show memory effects for retaining timing information in the stimulus and cannot be understood from traditional synchronization consideration of passive oscillatory systems. To understand this anticipatory phenomena, we consider oscillators built from excitable systems with the addition of an adaptive dynamics. With such systems, well-timed post-stimulus responses similar to those from experiments can be obtained. Furthermore, a well-known model of working memory is shown to possess similar anticipatory dynamics when the adaptive mechanism is identified with synaptic facilitation. The last finding suggests that this type of oscillators can be common in neuronal systems with plasticity.

q-bio.NC↗

arXiv2014

Reconstruction of network structures from repeating spike patterns in simulated bursting dynamics

Repeating patterns of spike sequences from a neuronal network have been proposed to be useful in the reconstruction of the network topology. Reverberations in a physiologically realistic model with various physical connection topologies (from random to scale-free) have been simulated to study the effectiveness of the pattern-matching method in the reconstruction of network topology from network dynamics. Simulation results show that functional networks reconstructed from repeating spike patterns can be quite different from the original physical networks; even global properties, such as the degree distribution, cannot always be recovered. However, the pattern-matching method can be effective in identifying hubs in the network. Since the form of reverberations are quite different for networks with and without hubs, the form of reverberations together with the reconstruction by repeating spike patterns might provide a reliable method to detect hubs in neuronal cultures.

q-bio.NC↗

arXiv2014

Electric field shielding in dielectric nanosolutions

To gain some insight into electrochemical activity of dielectric colloids of technical and biomedical interest we investigate a model of dielectric nanosolution whose micro-constitution is dominated by dipolarions -- positively and negatively charged spherically symmetric nano-structures composed of ionic charge surrounded by cloud of radially polarized dipoles of electrically neutral molecules of solvent. Combing the standard constitutive equations of an isotropic dielectric liquid with Maxwell equation of electrostatics and presuming the Boltzmann shape of the particle density of bound-charge we derive equation for the in-medium electrostatic field. Particular attention is given to numerical analysis of obtained analytic solutions of this equation describing the exterior fields of dipolarions with dipolar atmospheres of solvent molecules endowed with either permanent or field-induced dipole moments radially polarized by central symmetric field of counterions. The presented computations show that the electric field shielding of dipolarions in dielectric nanosolutions is quite different from that of counterionic nano-complexes of Debye-Hückel theory of electrolytes.

cond-mat.soft↗