arXiv subjects

Lei-Han Tang

Publications and source records attributed to Lei-Han Tang.

At least 19 recordsLinked to original sources

arXiv2026

Spontaneous oscillations and geometric cutoff in confined bacterial swarms

Self-organized dynamic patterns in dense active matter are striking manifestations of non-equilibrium physics. A prominent example is the macroscopic elliptical motion observed in quasi-2D bacterial suspensions, which has lacked a physical explanation. Here, we examine a minimal linear response framework coupling bacterial swimming dynamics with fluid flow, treating long-range hydrodynamic interactions as a macroscopic communication channel. We demonstrate that microscopic swim motion, via Jeffery coupling, manifests as a ``phase-leading'' response to local shear flows. System-wide sustained oscillations, on the other hand, require both a critical bacterial density and strict geometric confinement. By analytically predicting the onset cell density and maximum film thickness, our model achieves excellent quantitative agreement with experiments, establishing a unified physical framework for self-organized periodic motion of elongated body in active fluids.

cond-mat.soft↗

arXiv2025

Magnetization-resolved density of states and quasi-first order transition in the two-dimensional random bond Ising model: an entropic sampling study

Systems with quenched disorder possess complex energy landscapes that are challenging to explore under the conventional Monte Carlo method. In this work, we implement an efficient entropy sampling scheme for accurate computation of the entropy function in low-energy regions. The method is applied to the two-dimensional $\pm J$ random-bond Ising model, where frustration is controlled by the fraction $p$ of ferromagnetic bonds. We investigate the low-temperature paramagnetic--ferromagnetic phase boundary below the multicritical point at $T_N = 0.9530(4)$, $P_N = 0.89078(8)$, as well as the zero-temperature ferromagnetic--spin-glass transition. Finite-size scaling analysis reveals that the phase boundary for $T < T_N$ exhibits reentrant behavior. By analyzing the evolution of the magnetization-resolved density of states $g(E, M)$ and ground-state spin configurations against increasing frustration, we provide strong evidence that the zero-temperature transition is quasi-first order. Finite-size scaling conducted on the spin-glass side supports the validity of $\beta = 0$, with a correlation length exponent $\nu = 1.50(8)$. Our results provide new insights into the nature of the ferromagnetic-to-spin-glass phase transition in an extensively degenerate ground state.

cond-mat.dis-nn↗

arXiv2024

Exact finite-size scaling of the maximum likelihood spectra in the quenched and annealed Sherrington-Kirkpatrick spin glass

Fine resolution of the discrete eigenvalues at the spectral edge of an $N\times N$ random matrix is required in many applications. Starting from a finite-size scaling ansatz for the Stieltjes transform of the maximum likelihood spectrum, we demonstrate that the scaling function satisfies a first-order ODE of the Riccati type. Further transformation yields a linear second-order ODE for the characteristic function, whose nodes determine leading eigenvalues. Using this technique, we examine in detail the spectral crossover of the annealed Sherrington-Kirkpatrick (SK) spin glass model, where a gap develops below a critical temperature. Our analysis provides analytic predictions for the finite-size scaling of the spin condensation phenomenon in the annealed SK model, validated by Monte Carlo simulations. Deviation of scaling amplitudes from their predicted values is observed in the critical region due to eigenvalue fluctuations. More generally, rescaling the spectral axis, adjusted to the distance of neighboring eigenvalues, offers a powerful approach to handling singularities in the infinite size limit.

cond-mat.dis-nn↗

arXiv2024

Balancing reaction-diffusion network for cell polarization pattern with stability and asymmetry

Cell polarization is a critical process that separates molecular species into two distinct regions in prokaryotic and eukaryotic cells, guiding biological processes such as cell division and cell differentiation. Although several underlying antagonistic reaction-diffusion networks capable of setting up cell polarization have been identified experimentally and theoretically, our understanding of how to manipulate pattern stability and asymmetry remains incomplete, especially when only a subset of network components are known. Here we present numerical results to show that the polarized pattern of an antagonistic 2-node network collapses into a homogeneous state when subjected to single-sided self-regulation, single-sided additional regulation, or unequal system parameters. However, polarity restoration can be achieved by combining two modifications with opposing effects. Additionally, spatially inhomogeneous parameters favoring respective domains stabilize their interface at designated locations. To connect our findings to cell polarity studies of the nematode Caenorhabditis elegans zygote, we reconstituted a 5-node network where a 4-node circuit with full mutual inhibitions between anterior and posterior is modified by a mutual activation in the anterior and an additional mutual inhibition between the anterior and the posterior. Once again, a generic set of kinetic parameters moves the interface towards either the anterior or posterior end, yet a polarized pattern can be stabilized through spatial tuning of one or more parameters coupled to intracellular or extracellular cues. A user-friendly software, PolarSim, is introduced to facilitate the exploration of networks with alternative node numbers, parameter values, and regulatory pathways.

q-bio.MN↗

arXiv2022

Finite-size scaling and double-crossover critical behavior in two-dimensional incompressible polar active fluids

We study the order-disorder transition in two-dimensional incompressible systems of motile particles with alignment interactions through extensive numerical simulations of the incompressible Toner-Tu (ITT) field theory and a detailed finite-size scaling (FSS) analysis. The transition looks continuous in the explored parameter space, but the effective susceptibility exponent $\gamma/\nu$ and the dynamic exponent $z$ exhibit a strong, non-monotonic variation on the system size in the form of double crossovers. At small sizes, mean-field exponents are observed for the homogeneous $k=0$ mode whereas spatial fluctuations follow Gaussian statistics. A first crossover marks the departure from this regime to one where the system behaves like the equilibrium XY model with long-ranged dipolar interaction and vortex excitations. At larger sizes, scaling deviates from the dipolar XY behavior and a second crossover is observed, to presumably the asymptotic ITT universality class. At this crossover to genuinely off-equilibrium behavior, advection comes in to expedite transport of fluctuations, suppress large-scale fluctuations and help stabilize long-range order. We obtain estimates and bounds of the universal Binder cumulant and exponents of the ITT class. We propose a reduced hydrodynamic theory, previously overlooked, that quantitatively describes the first scaling regime. By providing a relatively comprehensive numerical picture and a novel analytical description, our results help elucidate finite-size effects in critical active matter systems, which have been argued to be relevant for understanding scale-free behavior in real flocks or swarms.

cond-mat.stat-mech↗

arXiv2021

Speed and fate diversity tradeoff in nematode's early embryogenesis

Nematode species are well-known for their invariant cell lineage pattern during development. Combining knowledge about the fate specification induced by asymmetric division and the anti-correlation between cell cycle length and cell volume in Caenorhabditis elegans, we propose a model to simulate lineage initiation by altering cell volume segregation ratio in each division, and quantify the derived pattern's performance in proliferation speed, fate diversity and space robustness. The stereotypic pattern in C. elegans embryo is found to be one of the most optimal solutions taking minimum time to achieve the cell number before gastrulation, by programming asymmetric division as a strategy.

q-bio.CB↗

arXiv2020

Calibrated Intervention and Containment of the COVID-19 Pandemic

Within a short period of time, COVID-19 grew into a world-wide pandemic. Transmission by pre-symptomatic and asymptomatic viral carriers rendered intervention and containment of the disease extremely challenging. Based on reported infection case studies, we construct an epidemiological model that focuses on transmission around the symptom onset. The model is calibrated against incubation period and pairwise transmission statistics during the initial outbreaks of the pandemic outside Wuhan with minimal non-pharmaceutical interventions. Mathematical treatment of the model yields explicit expressions for the size of latent and pre-symptomatic subpopulations during the exponential growth phase, with the local epidemic growth rate as input. We then explore reduction of the basic reproduction number R_0 through specific disease control measures such as contact tracing, testing, social distancing, wearing masks and sheltering in place. When these measures are implemented in combination, their effects on R_0 multiply. We also compare our model behaviour to the first wave of the COVID-19 spreading in various affected regions and highlight generic and less generic features of the pandemic development.

q-bio.PE↗

arXiv2019

Emergence of collective oscillations in adaptive cells

Collective oscillation of cells in a population has been reported under diverse biological contexts and with vastly different molecular constructs. Could there be common principles similar to those that govern spontaneous oscillation in mechanical or electrical systems? Here, we answer this question in the affirmative by categorising the response of individual cells against a time-varying signal. A positive intracellular signal relay of sufficient gain from participating cells is required to sustain the oscillations, together with phase matching. The two conditions yield quantitative predictions for the onset cell density and frequency in terms of measured single-cell and signal response functions. Through mathematical constructions, we show that cells that adapt to a constant stimulus fulfil the phase requirement by developing a leading phase in an "active" frequency window that enables cell-to-signal energy flow. Analysis of dynamical quorum sensing in several cellular systems with increasing biological complexity reaffirms the pivotal role of adaptation in powering oscillations in an otherwise dissipative cell-to-cell communication channel. The physical conditions identified can be used to design synthetic oscillatory systems

q-bio.CB↗

arXiv2016

Extracting energy from non-equilibrium fluctuations without using information

Extracting energy from fluctuations has been an everlasting endeavor. An important strategy is to use information-based operation, which allows energy extraction even from thermal fluctuations. However, it remains unclear whether a blind external operation, ignorant of such fluctuations, will also work. Assuming such a small operation, we find that energy extraction requires a negative response spectrum in a certain frequency region, which inevitably requires an internal power source to maintain. Energy is then extracted by operating the system at these frequencies. Negative response is intrinsic to any system that adapts to a slow external operation, which could be realized through integral feedback control. These are demonstrated through a solvable model.

cond-mat.stat-mech↗

arXiv2016

Nonequilibrium fluctuation response relation in a time scale separated system

We present a theoretical framework to analyze the violation of fluctuation-response relation (FRR) for any observable from a finite Markov system with two well-separated time scales. We find that, generally for both slow and fast observables, a broad plateau exists in the intermediate frequency region, which contributes to a finite hidden entropy production. Assuming that non-equilibrium behavior arises only from coupling of slow and fast processes, we find that, at large observation time scae, the effective temperature for a slow observable deviates only slightly from the bath temperature, accompanied by an emerging well-defined effective potential landscape, while the deviation is significant for a fast observable. Our study also identifies a wider range of applicability of the Harada-Sasa equality in Markov jumping systems.

cond-mat.stat-mech↗

arXiv2016

Entropy production of nano systems with timescale separation

Energy flow in bio-molecular motors and machines are vital to their function. Yet experimental observations are often limited to a small subset of variables that participate in energy transport and dissipation. Here we show, through a solvable Langevin model, that the seemingly hidden entropy production is measurable through the violation spectrum of the fluctuation-response relation of a slow observable. For general Markov systems with timescale separation, we prove that the violation spectrum exhibits a characteristic plateau in the intermediate frequency region. Despite its vanishing height, the plateau can account for energy dissipation over a broad timescale. Our findings suggest a general possibility to probe hidden entropy production in nano systems without direct observation of fast variables.

cond-mat.stat-mech↗

arXiv2015

Sample-dependent first-passage time distribution in a disordered medium

Above two dimensions, diffusion of a particle in a medium with quenched random traps is believed to be well-described by the annealed continuous time random walk (CTRW). We propose an approximate expression for the first-passage-time (FPT) distribution in a given sample that enables detailed comparison of the two problems. For a system of finite size, the number and spatial arrangement of deep traps yield significant sample-to-sample variations in the FPT statistics. Numerical simulations of a quenched trap model with power-law sojourn times confirm the existence of two characteristic time scales and a non-self-averaging FPT distribution, as predicted by theory.

cond-mat.stat-mech↗

arXiv2015

Finite-size scaling, dynamic fluctuations, and hyperscaling relation in the Kuramoto model

We revisit the Kuramoto model to explore the finite-size scaling (FSS) of the order parameter and its dynamic fluctuations near the onset of the synchronization transition, paying particular attention to effects induced by the randomness of the intrinsic frequencies of oscillators. For a population of size $N$, we study two ways of sampling the intrinsic frequencies according to the {\it same} given unimodal distribution $g(ω)$. In the `{\em random}' case, frequencies are generated independently in accordance with $g(ω)$, which gives rise to oscillator number fluctuation within any given frequency interval. In the `{\em regular}' case, the $N$ frequencies are generated in a deterministic manner that minimizes the oscillator number fluctuations, leading to quasi-uniformly spaced frequencies in the population. We find that the two samplings yield substantially different finite-size properties with clearly distinct scaling exponents. Moreover, the hyperscaling relation between the order parameter and its fluctuations is valid in the regular case, but is violated in the random case. In this last case, a self-consistent mean-field theory that completely ignores dynamic fluctuations correctly predicts the FSS exponent of the order parameter but not its critical amplitude.

cond-mat.stat-mech↗

arXiv2015

Energy dissipation in an adaptive molecular circuit

The ability to monitor nutrient and other environmental conditions with high sensitivity is crucial for cell growth and survival. Sensory adaptation allows a cell to recover its sensitivity after a transient response to a shift in the strength of extracellular stimulus. The working principles of adaptation have been established previously based on rate equations which do not consider fluctuations in a thermal environment. Recently, G. Lan et al. (Nature Phys., 8:422-8, 2012) performed a detailed analysis of a stochastic model for the E. coli sensory network. They showed that accurate adaptation is possible only when the system operates in a nonequilibrium steady-state (NESS). They further proposed an energy-speed-accuracy (ESA) trade-off relation. We present here analytic results on the NESS of the model through a mapping to a one-dimensional birth-death process. An exact expression for the entropy production rate is also derived. Based on these results, we are able to discuss the ESA relation in a more general setting. Our study suggests that the adaptation error can be reduced exponentially as the methylation range increases. Finally, we show that a nonequilibrium phase transition exists in the infinite methylation range limit, despite the fact that the model contains only two discrete variables.

q-bio.SC↗

arXiv2013

Phase transitions of the q-state Potts model on multiply-laced Sierpinski gaskets

We present an exact solution of the q-state Potts model on a class of generalized Sierpinski fractal lattices. The model is shown to possess an ordered phase at low temperatures and a continuous transition to the high temperature disordered phase at any q>=1. Multicriticality is observed in the presence of a symmetry-breaking field. Exact renormalization group analysis yields the phase diagram of the model and a complete set of critical exponents at various transitions.

cond-mat.dis-nn↗

arXiv2012

Stripe formation in bacterial systems with density-suppressed motility

Engineered bacteria in which motility is reduced by local cell density generate periodic stripes of high and low density when spotted on agar plates. We study theoretically the origin and mechanism of this process in a kinetic model that includes growth and density-suppressed motility of the cells. The spreading of a region of immotile cells into an initially cell-free region is analyzed. From the calculated front profile we provide an analytic ansatz to determine the phase boundary between the stripe and the no-stripe phases. The influence of various parameters on the phase boundary is discussed.

cond-mat.soft↗

arXiv2010

To synchronize or not to synchronize, that is the question: finite-size scaling and fluctuation effects in the Kuramoto model

The entrainment transition of coupled random frequency oscillators presents a long-standing problem in nonlinear physics. The onset of entrainment in populations of large but finite size exhibits strong sensitivity to fluctuations in the oscillator density at the synchronizing frequency. This is the source for the unusual values assumed by the correlation size exponent $ν'$. Locally coupled oscillators on a $d$-dimensional lattice exhibit two types of frequency entrainment: symmetry-breaking at $d > 4$, and aggregation of compact synchronized domains in three and four dimensions. Various critical properties of the transition are well captured by finite-size scaling relations with simple yet unconventional exponent values.

nlin.CD↗

arXiv2009

Gauge glass in two dimensions

The gauge glass model offers an interesting example of a randomly frustrated system with a continuous O(2) symmetry. In two dimensions, the existence of a glass phase at low temperatures has long been disputed among numerical studies. To resolve this controversy, we examine the behavior of vortices whose movement generates phase slips that destroy phase rigidity at large distances. Detailed analytical and numerical studies of the corresponding Coulomb gas problem in a random potential establish that the ground state, with a finite density of vortices, is polarizable with a scale-dependent dielectric susceptibility. Screening by vortex/antivortex pairs of arbitrarily large size is present to eliminate the logarithmic divergence of the Coulomb energy of a single vortex. The observed power-law decay of the Coulomb interaction between vortices with distance in the ground state leads to a power-law divergence of the glass correlation length with temperature $T$. It is argued that free vortices possess a bound excitation energy and a nonzero diffusion constant at any $T>0$.

cond-mat.dis-nn↗