arXiv subjects

Yueheng Lan

Publications and source records attributed to Yueheng Lan.

At least 37 records · Page 2Linked to original sources

arXiv2016

Stochastic Thermodynamics of a Particle in a Box

The piston system (particles in a box) is the simplest and paradigmatic model in traditional thermodynamics. However, the recently established framework of stochastic thermodynamics (ST) fails to apply to this model system due to the embedded singularity in the potential. In this Letter we study the stochastic thermodynamics of a particle in a box by adopting a novel coordinate transformation technique. Through comparing with the exact solution of a breathing harmonic oscillator, we obtain analytical results of work distribution for an arbitrary protocol in the linear response regime, and verify various predictions of the Fluctuation-Dissipation Relation. When applying to the Brownian Szilard's engine model, we obtain the optimal protocol $λ_t = λ_0 2^{t/τ}$ for a given sufficiently long total time $τ$. Our study not only establishes a paradigm for studying ST of a particle in a box, but also bridges the long-standing gap in the development of ST.

cond-mat.stat-mech↗

arXiv2016

Nonlinear waves on circle networks with excitable nodes

Nonlinear wave formation and propagation on a complex network with excitable node dynamics is of fundamental interest in diverse fields in science and engineering. Here, we propose a new model of the Kuramoto type to study nonlinear wave generation and propagation on circular subgraphs of a complex network. On circle networks, in the continuum limit, this model is equivalent to the over-damped Frenkel-Kontorova model. The new model is shown to keep the essential features of those well-known models such as the diffusively coupled Bär-Eiswirth model but with much simplified expression such that analytic analysis becomes possible. We classify traveling wave solutions on circle networks and show the universality of its features with perturbation analysis and numerical computation.

nlin.PS↗

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↗

arXiv2014

SEK: Sparsity exploiting $k$-mer-based estimation of bacterial community composition

Motivation: Estimation of bacterial community composition from a high-throughput sequenced sample is an important task in metagenomics applications. Since the sample sequence data typically harbors reads of variable lengths and different levels of biological and technical noise, accurate statistical analysis of such data is challenging. Currently popular estimation methods are typically very time consuming in a desktop computing environment. Results: Using sparsity enforcing methods from the general sparse signal processing field (such as compressed sensing), we derive a solution to the community composition estimation problem by a simultaneous assignment of all sample reads to a pre-processed reference database. A general statistical model based on kernel density estimation techniques is introduced for the assignment task and the model solution is obtained using convex optimization tools. Further, we design a greedy algorithm solution for a fast solution. Our approach offers a reasonably fast community composition estimation method which is shown to be more robust to input data variation than a recently introduced related method. Availability: A platform-independent Matlab implementation of the method is freely available at http://www.ee.kth.se/ctsoftware; source code that does not require access to Matlab is currently being tested and will be made available later through the above website.

q-bio.GN↗

arXiv2014

The stochastic thermodynamics of a rotating Brownian particle in a gradient flow

We compute the entropy production engendered in the environment from a single Brownian particle which moves in a mean flow, and show that it corresponds in expectation to classical near-equilibrium entropy production in the surrounding fluid with specific mesoscopic transport coefficients. With temperature gradient, extra terms are found which results from the nonlinear interaction between the particle and the non-equilibrated environment. The calculations are carried out in the multi-time formalism and in the advection-dissipation limit where the Stokes number (St) of the flow tends to zero and the Peclet number (Pe) diverges but the combination St times Pe remains constant.

cond-mat.stat-mech↗

arXiv2013

Improved contact prediction in proteins: Using pseudolikelihoods to infer Potts models

Spatially proximate amino acids in a protein tend to coevolve. A protein's three-dimensional (3D) structure hence leaves an echo of correlations in the evolutionary record. Reverse engineering 3D structures from such correlations is an open problem in structural biology, pursued with increasing vigor as more and more protein sequences continue to fill the data banks. Within this task lies a statistical inference problem, rooted in the following: correlation between two sites in a protein sequence can arise from firsthand interaction but can also be network-propagated via intermediate sites; observed correlation is not enough to guarantee proximity. To separate direct from indirect interactions is an instance of the general problem of inverse statistical mechanics, where the task is to learn model parameters (fields, couplings) from observables (magnetizations, correlations, samples) in large systems. In the context of protein sequences, the approach has been referred to as direct-coupling analysis. Here we show that the pseudolikelihood method, applied to 21-state Potts models describing the statistical properties of families of evolutionarily related proteins, significantly outperforms existing approaches to the direct-coupling analysis, the latter being based on standard mean-field techniques. This improved performance also relies on a modified score for the coupling strength. The results are verified using known crystal structures of specific sequence instances of various protein families. Code implementing the new method can be found at http://plmdca.csc.kth.se/.

q-bio.QM↗

arXiv2011

A resolution of the turbulence paradox: numerical implementation

Sommerfeld paradox (turbulence paradox) roughly says that mathematically the Couette linear shear flow is linearly stable for all values of the Reynolds number, but experimentally transition from the linear shear to turbulence occurs under perturbations of any size when the Reynolds number is large enough. In [Li, Lin 2011], we offered a resolution of this paradox. The aim of this paper is to provide a numerical implementation of the resolution. The main idea of the resolution is that even though the linear shear is linearly stable, slow orbits (also called quasi-steady states) in arbitrarily small neighborhoods of the linear shear can be linearly unstable. The key is that in infinite dimensions, smallness in one norm does not mean smallness in all norms. Our study here focuses upon a sequence of 2D oscillatory shears which are the Couette linear shear plus small amplitude and high frequency sinusoidal shear perturbations. In the fluid velocity variable, the sequence approaches the Couette linear shear (e.g. in $L^2$ norm of velocity), thus it can be viewed as Couette linear shear plus small noises; while in the fluid vorticity variable, the sequence does not approaches the Couette linear shear (e.g. in $H^1$ norm of velocity). Unlike the Couette linear shear, the sequence of oscillatory shears has inviscid linear instability; furthermore, with the sequence of oscillatory shears as potentials, the Orr-Sommerfeld operator has unstable eigenvalues when the Reynolds number is large enough, this should lead to transient nonlinear growth which manifests as transient turbulence as observed in experiments. The main result of this paper verifies this transient growth.

math.AP↗

arXiv2011

Accelerating cycle expansions by dynamical conjugacy

Periodic orbit theory provides two important functions---the dynamical zeta function and the spectral determinant for the calculation of dynamical averages in a nonlinear system. Their cycle expansions converge rapidly when the system is uniformly hyperbolic but greatly slowed down in the presence of non-hyperbolicity. We find that the slow convergence can be associated with singularities in the natural measure. A properly designed coordinate transformation may remove these singularities and results in a dynamically conjugate system where fast convergence is restored. The technique is successfully demonstrated on several examples of one-dimensional maps and some remaining challenges are discussed.

nlin.CD↗

arXiv2009

Analyzing intramolecular dynamics by Fast Lyapunov Indicators

We report an analysis of intramolecular dynamics of the highly excited planar carbonyl sulfide (OCS) below and at the dissociation threshold by the Fast Lyapunov Indicator (FLI) method. By mapping out the variety of dynamical regimes in the phase space of this molecule, we obtain the degree of regularity of the system versus its energy. We combine this stability analysis with a periodic orbit search, which yields a family of elliptic periodic orbits in the regular part of phase space an a family of in-phase collinear hyperbolic orbits associated with the chaotic regime.

nlin.CD↗

arXiv2008

Chaotic Spin Dynamics of a Long Nanomagnet Driven by a Current

We study the spin dynamics of a long nanomagnet driven by an electrical current. In the case of only DC current, the spin dynamics has a sophisticated bifurcation diagram of attractors. One type of attractors is a weak chaos. On the other hand, in the case of only AC current, the spin dynamics has a rather simple bifurcation diagram of attractors. That is, for small Gilbert damping, when the AC current is below a critical value, the attractor is a limit cycle; above the critical value, the attractor is chaotic (turbulent). For normal Gilbert damping, the attractor is always a limit cycle in the physically interesting range of the AC current. We also developed a Melnikov integral theory for a theoretical prediction on the occurrence of chaos. Our Melnikov prediction seems performing quite well in the DC case. In the AC case, our Melnikov prediction seems predicting transient chaos. The sustained chaotic attractor seems to have extra support from parametric resonance leading to a turbulent state.

nlin.CD↗

arXiv2008

Unstable recurrent patterns in Kuramoto-Sivashinsky dynamics

We undertake a systematic exploration of recurrent patterns in a 1-dimensional Kuramoto-Sivashinsky system. For a small, but already rather turbulent system, the long-time dynamics takes place on a low-dimensional invariant manifold. A set of equilibria offers a coarse geometrical partition of this manifold. A variational method enables us to determine numerically a large number of unstable spatiotemporally periodic solutions. The attracting set appears surprisingly thin - its backbone are several Smale horseshoe repellers, well approximated by intrinsic local 1-dimensional return maps, each with an approximate symbolic dynamics. The dynamics appears decomposable into chaotic dynamics within such local repellers, interspersed by rapid jumps between them.

nlin.PS↗

arXiv2006

On the Dynamics of Navier-Stokes and Euler Equations

This is a rather comprehensive study on the dynamics of Navier-Stokes and Euler equations via a combination of analysis and numerics. We focus upon two main aspects: (a). zero viscosity limit of the spectra of linear Navier-Stokes operator, (b). heteroclinics conjecture for Euler equation, its numerical verification, Melnikov integral, and simulation and control of chaos. Besides Navier-Stokes and Euler equations, we also study two models of them.

nlin.CD↗

arXiv2006

The interplay between discrete noise and nonlinear chemical kinetics in a signal amplification cascade

We used various analytical and numerical techniques to elucidate signal propagation in a small enzymatic cascade which is subjected to external and internal noise. The nonlinear character of catalytic reactions, which underlie protein signal transduction cascades, renders stochastic signaling dynamics in cytosol biochemical networks distinct from the usual description of stochastic dynamics in gene regulatory networks. For a simple 2-step enzymatic cascade which underlies many important protein signaling pathways, we demonstrated that the commonly used techniques such as the linear noise approximation and the Langevin equation become inadequate when the number of proteins becomes too low. Consequently, we developed a new analytical approximation, based on mixing the generating function and distribution function approaches, to the solution of the master equation that describes nonlinear chemical signaling kinetics for this important class of biochemical reactions. Our techniques work in a much wider range of protein number fluctuations than the methods used previously. We found that under certain conditions the burst-phase noise may be injected into the downstream signaling network dynamics, resulting possibly in unusually large macroscopic fluctuations. In addition to computing first and second moments, which is the goal of commonly used analytical techniques, our new approach provides the full time-dependent probability distributions of the colored non-Gaussian processes in a nonlinear signal transduction cascade.

q-bio.MN↗

arXiv2006

A variational approach to the stochastic aspects of cellular signal transduction

Cellular signaling networks have evolved to cope with intrinsic fluctuations, coming from the small numbers of constituents, and the environmental noise. Stochastic chemical kinetics equations govern the way biochemical networks process noisy signals. The essential difficulty associated with the master equation approach to solving the stochastic chemical kinetics problem is the enormous number of ordinary differential equations involved. In this work, we show how to achieve tremendous reduction in the dimensionality of specific reaction cascade dynamics by solving variationally an equivalent quantum field theoretic formulation of stochastic chemical kinetics. The present formulation avoids cumbersome commutator computations in the derivation of evolution equations, making more transparent the physical significance of the variational method. We propose novel time-dependent basis functions which work well over a wide range of rate parameters. We apply the new basis functions to describe stochastic signaling in several enzymatic cascades and compare the results so obtained with those from alternative solution techniques. The variational ansatz gives probability distributions that agree well with the exact ones, even when fluctuations are large and discreteness and nonlinearity are important. A numerical implementation of our technique is many orders of magnitude more efficient computationally compared with the traditional Monte Carlo simulation algorithms or the Langevin simulations.

q-bio.QM↗

arXiv2006

Variational method for locating invariant tori

We formulate a variational fictitious-time flow which drives an initial guess torus to a torus invariant under given dynamics. The method is general and applies in principle to continuous time flows and discrete time maps in arbitrary dimension, and to both Hamiltonian and dissipative systems.

nlin.CD↗

arXiv2005

Experimental evidence for the Volume Conjecture for the simplest hyperbolic non-2-bridge knot

Loosely speaking, the Volume Conjecture states that the limit of the n-th colored Jones polynomial of a hyperbolic knot, evaluated at the primitive complex n-th root of unity is a sequence of complex numbers that grows exponentially. Moreover, the exponential growth rate is proportional to the hyperbolic volume of the knot. We provide an efficient formula for the colored Jones function of the simplest hyperbolic non-2-bridge knot, and using this formula, we provide numerical evidence for the Hyperbolic Volume Conjecture for the simplest hyperbolic non-2-bridge knot.

math.GT↗

arXiv2003

Variational method for finding periodic orbits in a general flow

A variational principle for determining unstable periodic orbits of flows as well as unstable spatio-temporally periodic solutions of extended systems is proposed and implemented. An initial loop approximating a periodic solution is evolved in the space of loops toward a true periodic solution by a minimization of local errors along the loop. The ``\descent'' partial differential equation that governs this evolution is an infinitesimal step version of the damped Newton-Raphson iteration. The feasibility of the method is demonstrated by its application to the Hénon-Heiles system, the circular restricted three-body problem, and the Kuramoto-Sivashinsky system in a weakly turbulent regime.

nlin.CD↗

arXiv2003

Turbulent fields and their recurrences

We introduce a new variational method for finding periodic orbits of flows and spatio-temporally periodic solutions of classical field theories, a generalization of the Newton method to a flow in the space of loops. The feasibility of the method is demonstrated by its application to several dynamical systems, including the Kuramoto-Sivashinsky system.

nlin.CD↗