arXiv subjects

Yuhai Tu

Publications and source records attributed to Yuhai Tu.

At least 55 records · Page 3Linked to original sources

arXiv2016

A framework towards understanding mesoscopic phenomena: Emergent unpredictability, symmetry breaking and dynamics across scales

By integrating 4 lines of thoughts: symmetry breaking originally advanced by Anderson, bifurcation from nonlinear dynamics, Landau's theory of phase transition, and the mechanism of emergent rare events studied by Kramers, we introduce a possible framework for understanding mesoscopic dynamics that links (i) fast lower level microscopic motions, (ii) movements within each basin at the mid-level, and (iii) higher-level rare transitions between neighboring basins, which have rates that decrease exponentially with the size of the system. In this mesoscopic framework, multiple attractors arise as emergent properties of the nonlinear systems. The interplay between the stochasticity and nonlinearity leads to successive jump-like transitions among different basins. We argue each transition is a dynamic symmetry breaking, with the potential of exhibiting Thom-Zeeman catastrophe as well as phase transition with the breakdown of ergodicity (e.g., cell differentiation). The slow-time dynamics of the nonlinear mesoscopic system is not deterministic, rather it is a discrete stochastic jump process. The existence of these discrete states and the Markov transitions among them are both emergent phenomena. This emergent stochastic jump dynamics then serves as the stochastic element for the nonlinear dynamics of a higher level aggregates on an even larger spatial and slower time scales (e.g., evolution). This description captures the hierarchical structure outlined by Anderson and illustrates two distinct types of limit of a mesoscopic dynamics: A long-time ensemble thermodynamics in terms of time $t$ tending infinity followed by the size of the system $N$ tending infinity, and a short-time trajectory steady state with $N$ tending infinity followed by $t$ tending infinity. With these limits, symmetry breaking and cusp catastrophe are two perspectives of the same mesoscopic system on different time scales.

cond-mat.stat-mech↗

arXiv2015

The free energy cost of accurate biochemical oscillations

Oscillation is an important cellular process that regulates timing of different vital life cycles. However, in the noisy cellular environment, oscillations can be highly inaccurate due to phase fluctuations. It remains poorly understood how biochemical circuits suppress phase fluctuations and what is the incurred thermodynamic cost. Here, we study four different types of biochemical oscillations representing three basic oscillation motifs shared by all known oscillatory systems. We find that the phase diffusion constant follows the same inverse dependence on the free energy dissipation per period for all systems studied. This relationship between the phase diffusion and energy dissipation is shown analytically in a model of noisy oscillation. Microscopically, we find that the oscillation is driven by multiple irreversible cycles that hydrolyze the fuel molecules such as ATP; the number of phase coherent periods is proportional to the free energy consumed per period. Experimental evidence in support of this universal relationship and testable predictions are also presented.

physics.bio-ph↗

arXiv2015

The free energy cost of reducing noise while maintaining a high sensitivity

Living systems need to be highly responsive, and also to keep fluctuations low. These goals are incompatible in equilibrium systems due to the Fluctuation Dissipation Theorem (FDT). Here, we show that biological sensory systems, driven far from equilibrium by free energy consumption, can reduce their intrinsic fluctuations while maintaining high responsiveness. By developing a continuum theory of the E. coli chemotaxis pathway, we demonstrate that adaptation can be understood as a non-equilibrium phase transition controlled by free energy dissipation, and it is characterized by a breaking of the FDT. We show that the maximum response at short time is enhanced by free energy dissipation. At the same time, the low frequency fluctuations and the adaptation error decrease with the free energy dissipation algebraically and exponentially, respectively.

physics.bio-ph↗

arXiv2011

Noise Filtering Strategies of Adaptive Signaling Networks: The Case of E. Coli Chemotaxis

Two distinct mechanisms for filtering noise in an input signal are identified in a class of adaptive sensory networks. We find that the high frequency noise is filtered by the output degradation process through time-averaging; while the low frequency noise is damped by adaptation through negative feedback. Both filtering processes themselves introduce intrinsic noises, which are found to be unfiltered and can thus amount to a significant internal noise floor even without signaling. These results are applied to E. coli chemotaxis. We show unambiguously that the molecular mechanism for the Berg-Purcell time-averaging scheme is the dephosphorylation of the response regulator CheY-P, not the receptor adaptation process as previously suggested. The high frequency noise due to the stochastic ligand binding-unbinding events and the random ligand molecule diffusion is averaged by the CheY-P dephosphorylation process to a negligible level in E.coli. We identify a previously unstudied noise source caused by the random motion of the cell in a ligand gradient. We show that this random walk induced signal noise has a divergent low frequency component, which is only rendered finite by the receptor adaptation process. For gradients within the E. coli sensing range, this dominant external noise can be comparable to the significant intrinsic noise in the system. The dependence of the response and its fluctuations on the key time scales of the system are studied systematically. We show that the chemotaxis pathway may have evolved to optimize gradient sensing, strong response, and noise control in different time scales

q-bio.CB↗

arXiv2010

The Effects of Stator Compliance, Backs Steps, Temperature, and Clockwise Rotation on the Torque-Speed Curve of Bacterial Flagellar Motor

Rotation of a single bacterial flagellar motor is powered by multiple stators tethered to the cell wall. In a "power-stroke" model the observed independence of the speed at low load on the number of stators is explained by a torque-dependent stepping mechanism independent of the strength of the stator tethering spring. On the other hand, in models that depend solely on the stator spring to explain the observed behavior, exceedingly small stator spring constants are required. To study the dynamics of the motor driven by external forces (such as those exerted by an optical tweezer), back-stepping is introduced when stators are driven far out of equilibrium. Our model with back-stepping reproduces the observed absence of a barrier to backward rotation, as well the behaviors in the high-speed negative-torque regime. Recently measured temperature dependence of the motor speed near zero load (Yuan & Berg 2010 Biophys J) is explained quantitatively by the thermally activated stepping rates in our model. Finally, we suggest that the general mechanical properties of all molecular motors (linear and rotary), characterized by their force(torque)-speed curve, can be determined by their power-stroke potentials and the dependence of the stepping rates on the mechanical state of the motor (force or speed). The torque-speed curve for the clockwise rotating flagellar motor has been observed for the first time recently (Yuan et al. 2010 PNAS). Its quasi-linear behavior is quantitatively reproduced by our model. In particular, we show that concave and convex shapes of the torque-speed curve can be achieved by changing the interaction potential from linear to quadratic form. We also show that reversing the stepping rate dependence on force (torque) can lead to non-monotonicity in the speed-load dependency.

q-bio.SC↗

arXiv2004

Moving and staying together without a leader

A microscopic, stochastic, minimal model for collective and cohesive motion of identical self-propelled particles is introduced. Even though the particles interact strictly locally in a very noisy manner, we show that cohesion can be maintained, even in the zero-density limit of an arbitrarily large flock in an infinite space. The phase diagram spanned by the two main parameters of our model, which encode the tendencies for particles to align and to stay together, contains non-moving "gas", "liquid"' and "solid" phases separated from their moving counterparts by the onset of collective motion. The "gas/liquid" and "liquid/solid" are shown to be first-order phase transitions in all cases. In the cohesive phases, we study also the diffusive properties of individuals and their relation to the macroscopic motion and to the shape of the flock.

cond-mat.stat-mech↗

arXiv1999

Structure and energetics of the Si-SiO_2 interface

Silicon has long been synonymous with semiconductor technology. This unique role is due largely to the remarkable properties of the Si-SiO_2 interface, especially the (001)-oriented interface used in most devices. Although Si is crystalline and the oxide is amorphous, the interface is essentially perfect, with an extremely low density of dangling bonds or other electrically active defects. With the continual decrease of device size, the nanoscale structure of the silicon/oxide interface becomes more and more important. Yet despite its essential role, the atomic structure of this interface is still unclear. Using a novel Monte Carlo approach, we identify low-energy structures for the interface. The optimal structure found consists of Si-O-Si "bridges" ordered in a stripe pattern, with very low energy. This structure explains several puzzling experimental observations.

cond-mat.mtrl-sci↗

arXiv1998

Properties of a continuous-random-network model for amorphous systems

We use a Monte Carlo bond-switching method to study systematically the thermodynamic properties of a "continuous random network" model, the canonical model for such amorphous systems as a-Si and a-SiO$_2$. Simulations show first-order "melting" into an amorphous state, and clear evidence for a glass transition in the supercooled liquid. The random-network model is also extended to study heterogeneous structures, such as the interface between amorphous and crystalline Si.

cond-mat.stat-mech↗

arXiv1998

Stability of Solid State Reaction Fronts

We analyze the stability of a planar solid-solid interface at which a chemical reaction occurs. Examples include oxidation, nitridation, or silicide formation. Using a continuum model, including a general formula for the stress-dependence of the reaction rate, we show that stress effects can render a planar interface dynamically unstable with respect to perturbations of intermediate wavelength.

cond-mat.mtrl-sci↗

arXiv1998

Clustering Kinetics of Granular Media in Three Dimensions

Three-dimensional molecular dynamics simulations of dissipative particles (~ 10^6) are carried out for studying the clustering kinetics of granular media during cooling. The inter-connected high particle density regions are identified, showing tube-like structures. The energy decay rates as functions of the particle density and the restitution coefficient are obtained. It is found that the probability density function of the particle density obeys an exponential distribution at late stages. Both the fluctuation of density and the mean cluster size of the particle density have power law relations against time during the inelastic coalescing process.

cond-mat.mtrl-sci↗

arXiv1998

Flocks, herds, and schools: A quantitative theory of flocking

We present a quantitative continuum theory of ``flocking'': the collective coherent motion of large numbers of self-propelled organisms. Our model predicts the existence of an ``ordered phase'' of flocks, in which all members of the flock move together with the same mean velocity. This coherent motion of the flock is an example of spontaneously broken symmetry. The ``Goldstone modes'' associated with this ``spontaneously broken rotational symmetry'' are fluctuations in the direction of motion of a large part of the flock away from the mean direction. These ``Goldstone modes'' mix with modes associated with conservation of bird number to produce propagating sound modes. These sound modes lead to enormous fluctuations of the density of the flock. Our model is similar in many ways to the Navier-Stokes equations for a simple compressible fluid; in other ways, it resembles a relaxational time dependent Ginsburg-Landau theory for an $n = d$ component isotropic ferromagnet. In spatial dimensions $d > 4$, the long distance behavior is correctly described by a linearized theory. For $d < 4$, non-linear fluctuation effects radically alter the long distance behavior, making it different from that of any known equilibrium model. In particular, we find that in $d = 2$, where we can calculate the scaling exponents \underline{exactly}, flocks exhibit a true, long-range ordered, spontaneously broken symmetry state, in contrast to equilibrium systems, which cannot spontaneously break a continuous symmetry in $d = 2$ (the ``Mermin-Wagner'' theorem). We make detailed predictions for various correlation functions that could be measured either in simulations, or by quantitative imaging of real flocks.

cond-mat.stat-mech↗

arXiv1997

Sound waves and the absence of Galilean invariance in flocks

We study a model of flocking for a very large system (N=320,000) numerically. We find that in the long wavelength, long time limit, the fluctuations of the velocity and density fields are carried by propagating sound modes, whose dispersion and damping agree quantitatively with the predictions of our previous work using a continuum equation. We find that the sound velocity is anisotropic and characterized by its speed $c$ for propagation perpendicular to the mean velocity $<\vec{v}>$, $<\vec{v}>$ itself, and a third velocity $λ<\vec{v}>$, arising explicitly from the lack of Galilean invariance in flocks.

cond-mat.stat-mech↗

arXiv1997

Worm Structure in Modified Swift-Hohenberg Equation for Electroconvection

A theoretical model for studying pattern formation in electroconvection is proposed in the form of a modified Swift-Hohenberg equation. A localized state is found in two dimension, in agreement with the experimentally observed ``worm" state. The corresponding one dimensional model is also studied, and a novel stationary localized state due to nonadiabatic effect is found. The existence of the 1D localized state is shown to be responsible for the formation of the two dimensional ``worm" state in our model.

patt-sol↗

arXiv1996

Systems with Multiplicative Noise: Critical Behavior from KPZ Equation and Numerics

We show that certain critical exponents of systems with multiplicative noise can be obtained from exponents of the KPZ equation. Numerical simulations in 1d confirm this prediction, and yield other exponents of the multiplicative noise problem. The numerics also verify an earlier prediction of the divergence of the susceptibility over an entire range of control parameter values, and show that the exponent governing the divergence in this range varies continuously with control parameter.

adap-org↗

arXiv1996

Phase Structure of Systems with Multiplicative Noise

The phase diagrams and transitions of nonequilibrium systems with multiplicative noise are studied theoretically. We show the existence of both strong and weak-coupling critical behavior, of two distinct active phases, and of a nonzero range of parameter values over which the susceptibility is infinite in any dimension. A scaling theory of the strong-coupling transition is constructed.

adap-org↗

arXiv1995

Front Stability in Mean Field Models of Diffusion Limited Growth

We present calculations of the stability of planar fronts in two mean field models of diffusion limited growth. The steady state solution for the front can exist for a continuous family of velocities, we show that the selected velocity is given by marginal stability theory. We find that naive mean field theory has no instability to transverse perturbations, while a threshold mean field theory has such a Mullins-Sekerka instability. These results place on firm theoretical ground the observed lack of the dendritic morphology in naive mean field theory and its presence in threshold models. The existence of a Mullins-Sekerka instability is related to the behavior of the mean field theories in the zero-undercooling limit.

patt-sol↗

arXiv1995

How birds fly together: Long-range order in a two-dimensional dynamical XY model

We propose a non-equilibrium continuum dynamical model for the collective motion of large groups of biological organisms (e.g., flocks of birds, slime molds, etc.) Our model becomes highly non-trivial, and different from the equilibrium model, for $d<d_c=4$; nonetheless, we are able to determine its scaling exponents {\it exactly} in $d=2$, and show that, unlike equilibrium systems, our model exhibits a broken continuous symmetry even in $d=2$. Our model describes a large universality class of microscopic rules, including those recently simulated by Viscek et. al.

adap-org↗

arXiv1995

Mean Field Theory of the Morphology Transition in Stochastic Diffusion Limited Growth

We propose a mean-field model for describing the averaged properties of a class of stochastic diffusion-limited growth systems. We then show that this model exhibits a morphology transition from a dense-branching structure with a convex envelope to a dendritic one with an overall concave morphology. We have also constructed an order parameter which describes the transition quantitatively. The transition is shown to be continuous, which can be verified by noting the non-existence of any hysteresis.

patt-sol↗