SU\G(𝔸)/K·U
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All published works (16)

Avoiding confusion: Modelling image identification surveys with classification errors

2025-01-21
Michael A. Spence , Jon Barry , Thomas Bartos +3 more
Abstract Automated systems driven by machine learning is becoming increasingly used as an environmental monitoring tool. A common approach is to use classification algorithms to identify counts of categories (e.g. … Abstract Automated systems driven by machine learning is becoming increasingly used as an environmental monitoring tool. A common approach is to use classification algorithms to identify counts of categories (e.g. species) from images. However, the classification algorithms can be biased in the presence of classification error. To draw valid conclusions, it is crucial to incorporate these errors into the analysis and interpretation of the classification algorithm results. We introduce a general framework for describing counts with classification errors from classifiers, including data from both the classifier and a confusion matrix. The framework incorporates uncertainty in the classification matrix as well as uncertainty in the generating process. By treating the classification errors as latent variables, our framework allows a wide range of generating processes. We illustrate our methods with three case studies based on simulated data from different generating processes, and data from a machine learning algorithm to identify zooplankton in the Celtic Seas and English Channel. The framework is widely applicable in many subject areas where classification errors occur.

Self-organized intracellular twisters

2023-04-05
Sayantan Dutta , Reza Farhadifar , Wen Lü +7 more
Life in complex systems, such as cities and organisms, comes to a standstill when global coordination of mass, energy, and information flows is disrupted. Global coordination is no less important … Life in complex systems, such as cities and organisms, comes to a standstill when global coordination of mass, energy, and information flows is disrupted. Global coordination is no less important in single cells, especially in large oocytes and newly formed embryos, which commonly use fast fluid flows for dynamic reorganization of their cytoplasm. Here, we combine theory, computing, and imaging to investigate such flows in the Drosophila oocyte, where streaming has been proposed to spontaneously arise from hydrodynamic interactions among cortically anchored microtubules loaded with cargo-carrying molecular motors. We use a fast, accurate, and scalable numerical approach to investigate fluid-structure interactions of 1000s of flexible fibers and demonstrate the robust emergence and evolution of cell-spanning vortices, or twisters. Dominated by a rigid body rotation and secondary toroidal components, these flows are likely involved in rapid mixing and transport of ooplasmic components.
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Self-organized intracellular twisters

2023-01-01
Sayantan Dutta , Reza Farhadifar , Lu Wen +7 more
Life in complex systems, such as cities and organisms, comes to a standstill when global coordination of mass, energy, and information flows is disrupted. Global coordination is no less important … Life in complex systems, such as cities and organisms, comes to a standstill when global coordination of mass, energy, and information flows is disrupted. Global coordination is no less important in single cells, especially in large oocytes and newly formed embryos, which commonly use fast fluid flows for dynamic reorganization of their cytoplasm. Here, we combine theory, computing, and imaging to investigate such flows in the Drosophila oocyte, where streaming has been proposed to spontaneously arise from hydrodynamic interactions among cortically anchored microtubules loaded with cargo-carrying molecular motors. We use a fast, accurate, and scalable numerical approach to investigate fluid-structure interactions of 1000s of flexible fibers and demonstrate the robust emergence and evolution of cell-spanning vortices, or twisters. Dominated by a rigid body rotation and secondary toroidal components, these flows are likely involved in rapid mixing and transport of ooplasmic components.
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Use Adaptive Fast Function Approximator in Motor-Filament Binding Kinetics

2023-01-01
Zihan Zhang , Adam Lamson , Robert Blackwell
The cytoskeleton, consisting of biopolymer filaments, molecular motors, and passive crosslinking proteins, provides the internal structure of cells that facilitate movement, growth, and cell division. Understanding the microscopic motor-filament kinetics … The cytoskeleton, consisting of biopolymer filaments, molecular motors, and passive crosslinking proteins, provides the internal structure of cells that facilitate movement, growth, and cell division. Understanding the microscopic motor-filament kinetics and dynamics is essential for comprehending macroscopic behaviors of reconstituted cytoskeletal assemblies, such as self-organized flow and active stress. In this study, we employ an adaptive fast Chebyshev approximation based on tree search alongside parallel computing to accurately recover the equilibrium distribution of crosslinking proteins, thus satisfying detailed balance in binding through kinetic Monte Carlo sampling, while maintaining cost-effectiveness. Additionally, we offer expandable features, including segregating the simulation process via pre-building and allowing the free-loading of different explicit formulations of the motor's potential energy. This research has the potential to better describe the evolution of cytoskeletal active matter.
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Toward the cellular-scale simulation of motor-driven cytoskeletal assemblies

2022-05-26
Wen Yan , Saad Ansari , Adam Lamson +4 more
The cytoskeleton - a collection of polymeric filaments, molecular motors, and crosslinkers - is a foundational example of active matter, and in the cell assembles into organelles that guide basic … The cytoskeleton - a collection of polymeric filaments, molecular motors, and crosslinkers - is a foundational example of active matter, and in the cell assembles into organelles that guide basic biological functions. Simulation of cytoskeletal assemblies is an important tool for modeling cellular processes and understanding their surprising material properties. Here, we present aLENS (a Living Ensemble Simulator), a novel computational framework designed to surmount the limits of conventional simulation methods. We model molecular motors with crosslinking kinetics that adhere to a thermodynamic energy landscape, and integrate the system dynamics while efficiently and stably enforcing hard-body repulsion between filaments. Molecular potentials are entirely avoided in imposing steric constraints. Utilizing parallel computing, we simulate tens to hundreds of thousands of cytoskeletal filaments and crosslinking motors, recapitulating emergent phenomena such as bundle formation and buckling. This simulation framework can help elucidate how motor type, thermal fluctuations, internal stresses, and confinement determine the evolution of cytoskeletal active matter.
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Kernel aggregated fast multipole method

2021-09-06
Wen Yan , Robert Blackwell
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Kernel Aggregated Fast Multipole Method: Efficient summation of Laplace and Stokes kernel functions

2020-10-28
Wen Yan , Robert Blackwell
Many different simulation methods for Stokes flow problems involve a common computationally intense task---the summation of a kernel function over $O(N^2)$ pairs of points. One popular technique is the Kernel … Many different simulation methods for Stokes flow problems involve a common computationally intense task---the summation of a kernel function over $O(N^2)$ pairs of points. One popular technique is the Kernel Independent Fast Multipole Method (KIFMM), which constructs a spatial adaptive octree and places a small number of equivalent multipole and local points around each octree box, and completes the kernel sum with $O(N)$ performance. However, the KIFMM cannot be used directly with nonlinear kernels, can be inefficient for complicated linear kernels, and in general is difficult to implement compared to less-efficient alternatives such as Ewald-type methods. Here we present the Kernel Aggregated Fast Multipole Method (KAFMM), which overcomes these drawbacks by allowing different kernel functions to be used for specific stages of octree traversal. In many cases a simpler linear kernel suffices during the most extensive stage of octree traversal, even for nonlinear kernel summation problems. The KAFMM thereby improves computational efficiency in general and also allows efficient evaluation of some nonlinear kernel functions such as the regularized Stokeslet. We have implemented our method as an open-source software library STKFMM with support for Laplace kernels, the Stokeslet, regularized Stokeslet, Rotne-Prager-Yamakawa (RPY) tensor, and the Stokes double-layer and traction operators. Open and periodic boundary conditions are supported for all kernels, and the no-slip wall boundary condition is supported for the Stokeslet and RPY tensor. The package is designed to be ready-to-use as well as being readily extensible to additional kernels. Massive parallelism is supported with mixed OpenMP and MPI.
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Statistical Mechanics of an Elastically Pinned Membrane: Equilibrium Dynamics and Power Spectrum

2019-07-09
Josip Augustin Janeš , Daniel Schmidt , Robert Blackwell +2 more
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Two Heads Are (Sometimes) Better Than One: How Rate Formulations Impact Molecular Motor Dynamics

2018-01-01
Robert Blackwell , David H. Jung , Mona Bukenberger +1 more
Cells are complex structures which require considerable amounts of organization via transport of large intracellular cargo. While passive diffusion is often sufficiently fast for the transport of smaller cargo, active … Cells are complex structures which require considerable amounts of organization via transport of large intracellular cargo. While passive diffusion is often sufficiently fast for the transport of smaller cargo, active transport is necessary to organize large structures on short timescales. The main mechanism of this transport is by cargo attachment to motors which walk in a directed fashion along intracellular filaments. There are a number of models which seek to describe the motion of motors with attached cargo, from detailed microscopic to coarse phenomenological descriptions. We focus on the intermediate-detailed discrete stochastic hopping models, and explore how cargo transport changes depending on the number of motors, motor interaction, system constraints and rate formulations which are derived from common thermodynamic assumptions. We find that, despite obeying the same detailed balance constraint, the choice of rate formulation considerably affects the characteristics of the overall motion of the system, with one rate formulation exhibiting novel behavior of loaded motor groups moving faster than a single unloaded motor.
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Contributions of Microtubule Dynamic Instability and Rotational Diffusion to Kinetochore Capture

2016-09-30
Robert Blackwell , Oliver Sweezy-Schindler , C. J. Edelmaier +7 more
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Hysteresis, reentrance, and glassy dynamics in systems of self-propelled rods

2015-12-31
Hui-Shun Kuan , Robert Blackwell , Loren E. Hough +2 more
Nonequilibrium active matter made up of self-driven particles with short-range repulsive interactions is a useful minimal system to study active matter as the system exhibits collective motion and nonequilibrium order-disorder … Nonequilibrium active matter made up of self-driven particles with short-range repulsive interactions is a useful minimal system to study active matter as the system exhibits collective motion and nonequilibrium order-disorder transitions. We studied high-aspect-ratio self-propelled rods over a wide range of packing fractions and driving to determine the nonequilibrium state diagram and dynamic properties. Flocking and nematic-laning states occupy much of the parameter space. In the flocking state, the average internal pressure is high and structural and mechanical relaxation times are long, suggesting that rods in flocks are in a translating glassy state despite overall flock motion. In contrast, the nematic-laning state shows fluidlike behavior. The flocking state occupies regions of the state diagram at both low and high packing fraction separated by nematic-laning at low driving and a history-dependent region at higher driving; the nematic-laning state transitions to the flocking state for both compression and expansion. We propose that the laning-flocking transitions are a type of glass transition that, in contrast to other glass-forming systems, can show fluidization as density increases. The fluid internal dynamics and ballistic transport of the nematic-laning state may promote collective dynamics of rod-shaped micro-organisms.
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Multiscale modeling and simulation of microtubule–motor-protein assemblies

2015-12-10
Tong Gao , Robert Blackwell , Matthew A. Glaser +2 more
Microtubules and motor proteins self-organize into biologically important assemblies including the mitotic spindle and the centrosomal microtubule array. Outside of cells, microtubule-motor mixtures can form novel active liquid-crystalline materials driven … Microtubules and motor proteins self-organize into biologically important assemblies including the mitotic spindle and the centrosomal microtubule array. Outside of cells, microtubule-motor mixtures can form novel active liquid-crystalline materials driven out of equilibrium by adenosine triphosphate--consuming motor proteins. Microscopic motor activity causes polarity-dependent interactions between motor proteins and microtubules, but how these interactions yield larger-scale dynamical behavior such as complex flows and defect dynamics is not well understood. We develop a multiscale theory for microtubule-motor systems in which Brownian dynamics simulations of polar microtubules driven by motors are used to study microscopic organization and stresses created by motor-mediated microtubule interactions. We identify polarity-sorting and crosslink tether relaxation as two polar-specific sources of active destabilizing stress. We then develop a continuum Doi-Onsager model that captures polarity sorting and the hydrodynamic flows generated by these polar-specific active stresses. In simulations of active nematic flows on immersed surfaces, the active stresses drive turbulent flow dynamics and continuous generation and annihilation of disclination defects. The dynamics follow from two instabilities, and accounting for the immersed nature of the experiment yields unambiguous characteristic length and time scales. When turning off the hydrodynamics in the Doi-Onsager model, we capture formation of polar lanes as observed in the Brownian dynamics simulation.
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Multiscale Polar Theory of Microtubule and Motor-Protein Assemblies

2015-01-27
Tong Gao , Robert Blackwell , Matthew A. Glaser +2 more
Microtubules and motor proteins are building blocks of self-organized subcellular biological structures such as the mitotic spindle and the centrosomal microtubule array. These same ingredients can form new ``bioactive'' liquid-crystalline … Microtubules and motor proteins are building blocks of self-organized subcellular biological structures such as the mitotic spindle and the centrosomal microtubule array. These same ingredients can form new ``bioactive'' liquid-crystalline fluids that are intrinsically out of equilibrium and which display complex flows and defect dynamics. It is not yet well understood how microscopic activity, which involves polarity-dependent interactions between motor proteins and microtubules, yields such larger-scale dynamical structures. In our multiscale theory, Brownian dynamics simulations of polar microtubule ensembles driven by cross-linking motors allow us to study microscopic organization and stresses. Polarity sorting and cross-link relaxation emerge as two polar-specific sources of active destabilizing stress. On larger length scales, our continuum Doi-Onsager theory captures the hydrodynamic flows generated by polarity-dependent active stresses. The results connect local polar structure to flow structures and defect dynamics.
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Jamming at the laning-flocking transition in systems of self-propelled rods

2014-07-17
Hui-Shun Kuan , Robert Blackwell , Matthew A. Glaser +1 more
Non-equilibrium active matter made up of self-driven particles exhibits collective motion and nonequilibrium order-disorder transitions. Self-propelled rod models with short-range repulsive interactions are a useful minimal system to study active … Non-equilibrium active matter made up of self-driven particles exhibits collective motion and nonequilibrium order-disorder transitions. Self-propelled rod models with short-range repulsive interactions are a useful minimal system to study active matter. We simulated high-aspect-ratio self-propelled rods with varying packing fraction and driving. Two characteristic phases, the flocking and laning phases, occupy much of the phase diagram. We study the laning-flocking transition and the emergence of the laning state from the equilibrium nematic. For low packing fraction, driving induces formation of a clustered flocking phase, as observed previously. In flocks the average pressure is high and structural and mechanical relaxation times are long. These results suggest that rods in flocks are in a translating jammed state with an internal structure similar to a jammed solid despite overall flock motion. For higher packing fraction, a laning state emerges in response to driving, with polar domains that vary in size with the driving force. The average pressure is relatively low and structural and mechanical relaxation times are short, showing fluid-like behavior. Both structural and mechanical properties vary rapidly upon lowering the packing fraction from the laning to flocking regime, suggesting an abrupt dynamic phase transition occurs in this system. We propose that the laning-flocking transition is a type of jamming transition which, in contrast to other jamming systems, occurs as density is decreased. In contrast, the laning state appears to emerge continuously from the equilibrium nematic as driving is increased.

A multiscale active nematic theory of microtubule/motor-protein assemblies

2014-01-31
Tong Gao , Robert Blackwell , Matthew A. Glaser +2 more
Microtubules and motor proteins are building blocks of self-organized subcellular biological structures such as the mitotic spindle and the centrosomal microtubule array. These same ingredients can form new bioactive liquid-crystalline … Microtubules and motor proteins are building blocks of self-organized subcellular biological structures such as the mitotic spindle and the centrosomal microtubule array. These same ingredients can form new bioactive liquid-crystalline fluids that are intrinsically out of equilibrium and which display complex flows and defect dynamics. It is not yet well understood how microscopic activity, which involves polarity-dependent interactions between motor proteins and microtubules, yields such larger scale dynamical structures. In our multiscale theory, Brownian dynamics simulations of polar microtubule ensembles driven by crosslinking motors allow us to study microscopic organization and stresses. Polarity sorting and crosslink relaxation emerge as two polar-specific sources of active destabilizing stress. On larger length scales, our continuum Doi-Onsager theory captures the hydrodynamic flows generated by polarity-dependent active stresses. The results connect local polar structure to flow structures and defect dynamics.
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Two-dimensional monad theory

1989-07-01
Robert Blackwell , G. M. Kelly , John Power

Common Coauthors

Coauthor Papers Together
Matthew A. Glaser 7
Meredith D. Betterton 7
Michael Shelley 6
Tong Gao 3
Wen Yan 3
Vladimir I. Gelfand 2
Gökberk Kabacaoğlu 2
Reza Farhadifar 2
David B. Stein 2
Sayantan Dutta 2
Margot Lakonishok 2
Hui-Shun Kuan 2
Stanislav Y. Shvartsman 2
Ana‐Sunčana Smith 2
Adam Lamson 2
Loren E. Hough 1
John Power 1
J. Richard McIntosh 1
Zachary R. Gergely 1
Lu Wen 1
Zihan Zhang 1
David H. Jung 1
Patrick Flynn 1
Daniel Schmidt 1
Saad Ansari 1
Sophie Pitois 1
Alireza Doostan 1
Wen Lü 1
Salvador Montes 1
Michael A. Spence 1
G. M. Kelly 1
C. J. Edelmaier 1
Thomas Bartos 1
Jon Barry 1
Mona Bukenberger 1
Josip Augustin Janeš 1
Oliver Sweezy-Schindler 1
Ammon Crapo 1
James D. Scott 1
Udo Seifert 1

Commonly Cited References

A scalable computational platform for particulate Stokes suspensions

2020-05-13
Wen Yan , Eduardo Corona , Dhairya Malhotra +2 more
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Spontaneous motion in hierarchically assembled active matter

2012-11-01
Tim Sanchez , Daniel T. N. Chen , Stephen J. DeCamp +2 more
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Multiscale Polar Theory of Microtubule and Motor-Protein Assemblies

2015-01-27
Tong Gao , Robert Blackwell , Matthew A. Glaser +2 more
Microtubules and motor proteins are building blocks of self-organized subcellular biological structures such as the mitotic spindle and the centrosomal microtubule array. These same ingredients can form new ``bioactive'' liquid-crystalline … Microtubules and motor proteins are building blocks of self-organized subcellular biological structures such as the mitotic spindle and the centrosomal microtubule array. These same ingredients can form new ``bioactive'' liquid-crystalline fluids that are intrinsically out of equilibrium and which display complex flows and defect dynamics. It is not yet well understood how microscopic activity, which involves polarity-dependent interactions between motor proteins and microtubules, yields such larger-scale dynamical structures. In our multiscale theory, Brownian dynamics simulations of polar microtubule ensembles driven by cross-linking motors allow us to study microscopic organization and stresses. Polarity sorting and cross-link relaxation emerge as two polar-specific sources of active destabilizing stress. On larger length scales, our continuum Doi-Onsager theory captures the hydrodynamic flows generated by polarity-dependent active stresses. The results connect local polar structure to flow structures and defect dynamics.
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Instabilities and topological defects in active nematics

2014-01-01
Sumesh P. Thampi , Ramin Golestanian , Julia M. Yeomans
We study a continuum model of an extensile active nematic to show that mesoscale turbulence develops in two stages: (i) ordered regions undergo an intrinsic hydrodynamic instability generating walls, lines … We study a continuum model of an extensile active nematic to show that mesoscale turbulence develops in two stages: (i) ordered regions undergo an intrinsic hydrodynamic instability generating walls, lines of stong bend deformations, (ii) the walls relax by forming oppositely charged pairs of defects. Both creation and annihilation of defect pairs reinstate nematic regions which undergo further instabilities, leading to a dynamic steady state. We compare this with the development of active turbulence in a contractile active nematic.
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RPYFMM: Parallel adaptive fast multipole method for Rotne–Prager–Yamakawa tensor in biomolecular hydrodynamics simulations

2018-02-16
Wen-hua Guan , Xiaolin Cheng , Jingfang Huang +4 more
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Collective Langevin dynamics of flexible cytoskeletal fibers

2007-11-30
François Nédélec , Dietrich Foethke
We develop a numerical method to simulate mechanical objects in a viscous medium at a scale where inertia is negligible. Fibers, spheres and other voluminous objects are represented with points. … We develop a numerical method to simulate mechanical objects in a viscous medium at a scale where inertia is negligible. Fibers, spheres and other voluminous objects are represented with points. Different types of connections are used to link the points together and in this way create composite mechanical structures. The motion of such structures in a Brownian environment is described by a first-order multivariate Langevin equation. We propose a computationally efficient method to integrate the equation, and illustrate the applicability of the method to cytoskeletal modeling with several examples.
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Fast Ewald summation for Green’s functions of Stokes flow in a half-space

2018-08-13
Shriram Srinivasan , Anna‐Karin Tornberg
Recently, Gimbutas et al derived an elegant representation for the Green's functions of Stokes flow in a half-space. We present a fast summation method for sums involving these half-space Green's … Recently, Gimbutas et al derived an elegant representation for the Green's functions of Stokes flow in a half-space. We present a fast summation method for sums involving these half-space Green's functions (stokeslets, stresslets and rotlets) that consolidates and builds on the work by Klinteberg et al for the corresponding free-space Green's functions. The fast method is based on two main ingredients: The Ewald decomposition and subsequent use of FFTs. The Ewald decomposition recasts the sum into a sum of two exponentially decaying series: one in real-space (short-range interactions) and one in Fourier-space (long-range interactions) with the convergence of each series controlled by a common parameter. The evaluation of short-range interactions is accelerated by restricting computations to neighbours within a specified distance, while the use of FFTs accelerates the computations in Fourier-space thus accelerating the overall sum. We demonstrate that while the method incurs extra costs for the half-space in comparison to the free-space evaluation, greater computational savings is also achieved when compared to their respective direct sums.
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Generalization of the Rotne–Prager–Yamakawa mobility and shear disturbance tensors

2013-08-28
Eligiusz Wajnryb , Krzysztof A. Mizerski , Paweł J. Żuk +1 more
Abstract The Rotne–Prager–Yamakawa approximation is one of the most commonly used methods of including hydrodynamic interactions in modelling of colloidal suspensions and polymer solutions. The two main merits of this … Abstract The Rotne–Prager–Yamakawa approximation is one of the most commonly used methods of including hydrodynamic interactions in modelling of colloidal suspensions and polymer solutions. The two main merits of this approximation are that it includes all long-range terms (i.e. decaying as ${R}^{- 3} $ or slower in interparticle distances) and that the diffusion matrix is positive definite, which is essential for Brownian dynamics modelling. Here, we extend the Rotne–Prager–Yamakawa approach to include both translational and rotational degrees of freedom, and derive the regularizing corrections to account for overlapping particles. Additionally, we show how the Rotne–Prager–Yamakawa approximation can be generalized for other geometries and boundary conditions.
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Flexibly imposing periodicity in kernel independent FMM: A multipole-to-local operator approach

2017-11-16
Wen Yan , Michael Shelley
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Fast Ewald summation for free-space Stokes potentials

2017-01-16
Ludvig af Klinteberg , Davoud Saffar Shamshirgar , Anna‐Karin Tornberg
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Emergent states in dense systems of active rods: from swarming to turbulence

2012-10-31
H. H. Wensink , Hartmut Löwen
Dense suspensions of self-propelled rod-like particles exhibit a fascinating variety of non-equilibrium phenomena. By means of computer simulations of a minimal model for rigid self-propelled colloidal rods with variable shape … Dense suspensions of self-propelled rod-like particles exhibit a fascinating variety of non-equilibrium phenomena. By means of computer simulations of a minimal model for rigid self-propelled colloidal rods with variable shape we explore the generic diagram of emerging states over a large range of rod densities and aspect ratios. The dynamics is studied using a simple numerical scheme for the overdamped noiseless frictional dynamics of a many-body system in which steric forces are dominant over hydrodynamic ones. The different emergent states are identified by various characteristic correlation functions and suitable order parameter fields. At low density and aspect ratio, a disordered phase with no coherent motion precedes a highly-cooperative swarming state at large aspect ratio. Conversely, at high densities weakly anisometric particles show a distinct jamming transition whereas slender particles form dynamic laning patterns. In between there is a large window corresponding to strongly vortical, turbulent flow. The different dynamical states should be verifiable in systems of swimming bacteria and artificial rod-like micro-swimmers.
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Universal image systems for non-periodic and periodic Stokes flows above a no-slip wall

2018-08-27
Wen Yan , Michael Shelley
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The Ewald sums for singly, doubly and triply periodic electrostatic systems

2015-06-26
Anna‐Karin Tornberg
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Velocity Correlations in an Active Nematic

2013-09-10
Sumesh P. Thampi , Ramin Golestanian , Julia M. Yeomans
The flow properties of a continuum model for an active nematic is studied and compared with recent experiments on suspensions of microtubule bundles and molecular motors. The velocity correlation length … The flow properties of a continuum model for an active nematic is studied and compared with recent experiments on suspensions of microtubule bundles and molecular motors. The velocity correlation length is found to be independent of the strength of the activity while the characteristic velocity scale increases monotonically as the activity is increased, both in agreement with the experimental observations. We interpret our results in terms of the creation and annihilation dynamics of a gas of topological defects.
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Scale-free correlations in starling flocks

2010-06-14
Andrea Cavagna , Alessio Cimarelli , Irene Giardina +4 more
From bird flocks to fish schools, animal groups often seem to react to environmental perturbations as if of one mind. Most studies in collective animal behavior have aimed to understand … From bird flocks to fish schools, animal groups often seem to react to environmental perturbations as if of one mind. Most studies in collective animal behavior have aimed to understand how a globally ordered state may emerge from simple behavioral rules. Less effort has been devoted to understanding the origin of collective response, namely the way the group as a whole reacts to its environment. Yet, in the presence of strong predatory pressure on the group, collective response may yield a significant adaptive advantage. Here we suggest that collective response in animal groups may be achieved through scale-free behavioral correlations. By reconstructing the 3D position and velocity of individual birds in large flocks of starlings, we measured to what extent the velocity fluctuations of different birds are correlated to each other. We found that the range of such spatial correlation does not have a constant value, but it scales with the linear size of the flock. This result indicates that behavioral correlations are scale free: The change in the behavioral state of one animal affects and is affected by that of all other animals in the group, no matter how large the group is. Scale-free correlations provide each animal with an effective perception range much larger than the direct interindividual interaction range, thus enhancing global response to perturbations. Our results suggest that flocks behave as critical systems, poised to respond maximally to environmental perturbations.
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Nonequilibrium structure and dynamics in a microscopic model of thin-film active gels

2014-03-10
David Head , W. J. Briels , Gerhard Gompper
In the presence of adenosine triphosphate, molecular motors generate active force dipoles that drive suspensions of protein filaments far from thermodynamic equilibrium, leading to exotic dynamics and pattern formation. Microscopic … In the presence of adenosine triphosphate, molecular motors generate active force dipoles that drive suspensions of protein filaments far from thermodynamic equilibrium, leading to exotic dynamics and pattern formation. Microscopic modeling can help to quantify the relationship between individual motors plus filaments to organization and dynamics on molecular and supramolecular length scales. Here, we present results of extensive numerical simulations of active gels where the motors and filaments are confined between two infinite parallel plates. Thermal fluctuations and excluded-volume interactions between filaments are included. A systematic variation of rates for motor motion, attachment, and detachment, including a differential detachment rate from filament ends, reveals a range of nonequilibrium behavior. Strong motor binding produces structured filament aggregates that we refer to as asters, bundles, or layers, whose stability depends on motor speed and differential end detachment. The gross features of the dependence of the observed structures on the motor rate and the filament concentration can be captured by a simple one-filament model. Loosely bound aggregates exhibit superdiffusive mass transport, where filament translocation scales with lag time with nonunique exponents that depend on motor kinetics. An empirical data collapse of filament speed as a function of motor speed and end detachment is found, suggesting a dimensional reduction of the relevant parameter space. We conclude by discussing the perspectives of microscopic modeling in the field of active gels.
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Emergence of macroscopic directed motion in populations of motile colloids

2013-11-01
Antoine Bricard , Jean-Baptiste Caussin , Nicolas Desreumaux +2 more
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Excitable Patterns in Active Nematics

2011-05-25
Luca Giomi , L. Mahadevan , Bulbul Chakraborty +1 more
We analyze a model of mutually propelled filaments suspended in a two-dimensional solvent. The system undergoes a mean-field isotropic-nematic transition for large enough filament concentrations, and the nematic order parameter … We analyze a model of mutually propelled filaments suspended in a two-dimensional solvent. The system undergoes a mean-field isotropic-nematic transition for large enough filament concentrations, and the nematic order parameter is allowed to vary in space and time. We show that the interplay between nonuniform nematic order, activity, and flow results in spatially modulated relaxation oscillations, similar to those seen in excitable media. In this regime the dynamics consists of nearly stationary periods separated by ``bursts'' of activity in which the system is elastically distorted and solvent is pumped throughout. At even higher activity, the dynamics becomes chaotic.
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A fast platform for simulating semi-flexible fiber suspensions applied to cell mechanics

2016-10-19
Ehssan Nazockdast , Abtin Rahimian , Denis Zorin +1 more
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The Spectral Ewald method for singly periodic domains

2017-07-11
Davoud Saffar Shamshirgar , Anna‐Karin Tornberg
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Regularized Stokeslet segments

2018-09-06
Ricardo Cortez
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Bridging the microscopic and the hydrodynamic in active filament solutions

2005-02-10
Tanniemola B. Liverpool , M. C. Marchetti
Hydrodynamic equations for an isotropic solution of active polar filaments are derived from a microscopic mean-field model of the forces exchanged between motors and filaments. We find that a spatial … Hydrodynamic equations for an isotropic solution of active polar filaments are derived from a microscopic mean-field model of the forces exchanged between motors and filaments. We find that a spatial dependence of the motor stepping rate along the filament is essential to drive bundle formation. A number of differences arise as compared to hydrodynamics derived (earlier) from a mesoscopic model where relative filament velocities were obtained on the basis of symmetry considerations. Due to the anisotropy of filament diffusion, motors are capable of generating net filament motion relative to the solvent. The effect of this new term on the stability of the homogeneous state is investigated.
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Spontaneous flow transition in active polar gels

2005-04-05
Raphaël Voituriez , Jean‐François Joanny , Jacques Prost
We study theoretically the effects of confinement on active polar gels such as the actin network of eukaryotic cells. Using generalized hydrodynamics equations derived for active gels, we predict, in … We study theoretically the effects of confinement on active polar gels such as the actin network of eukaryotic cells. Using generalized hydrodynamics equations derived for active gels, we predict, in the case of quasi one-dimensional geometry, a spontaneous flow transition from a homogeneously polarized immobile state for small thicknesses, to a perturbed flowing state for larger thicknesses. The transition is not driven by an external field but by the activity of the system. We suggest several possible experimental realizations.
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A Kernel-Independent Treecode for General Rotne-Prager-Yamakawa Tensor

2020-12-18
Lei Wang

Complex dynamics of long, flexible fibers in shear

2019-06-19
John LaGrone , Ricardo Cortez , Wen Yan +1 more
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Meso-scale turbulence in living fluids

2012-08-20
H. H. Wensink , Jörn Dunkel , Sebastian Heidenreich +4 more
Turbulence is ubiquitous, from oceanic currents to small-scale biological and quantum systems. Self-sustained turbulent motion in microbial suspensions presents an intriguing example of collective dynamical behavior among the simplest forms … Turbulence is ubiquitous, from oceanic currents to small-scale biological and quantum systems. Self-sustained turbulent motion in microbial suspensions presents an intriguing example of collective dynamical behavior among the simplest forms of life and is important for fluid mixing and molecular transport on the microscale. The mathematical characterization of turbulence phenomena in active nonequilibrium fluids proves even more difficult than for conventional liquids or gases. It is not known which features of turbulent phases in living matter are universal or system-specific or which generalizations of the Navier–Stokes equations are able to describe them adequately. Here, we combine experiments, particle simulations, and continuum theory to identify the statistical properties of self-sustained meso-scale turbulence in active systems. To study how dimensionality and boundary conditions affect collective bacterial dynamics, we measured energy spectra and structure functions in dense Bacillus subtilis suspensions in quasi-2D and 3D geometries. Our experimental results for the bacterial flow statistics agree well with predictions from a minimal model for self-propelled rods, suggesting that at high concentrations the collective motion of the bacteria is dominated by short-range interactions. To provide a basis for future theoretical studies, we propose a minimal continuum model for incompressible bacterial flow. A detailed numerical analysis of the 2D case shows that this theory can reproduce many of the experimentally observed features of self-sustained active turbulence.
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Active nematic materials with substrate friction

2014-12-15
Sumesh P. Thampi , Ramin Golestanian , Julia M. Yeomans
Active turbulence in dense active systems is characterized by high vorticity on a length scale that is large compared to that of individual entities. We describe the properties of active … Active turbulence in dense active systems is characterized by high vorticity on a length scale that is large compared to that of individual entities. We describe the properties of active turbulence as momentum propagation is screened by frictional damping. As friction is increased, the spacing between the walls in the nematic director field decreases as a consequence of the more rapid velocity decays. This leads to, first, a regime with more walls and an increased number of topological defects, and then to a jammed state in which the walls deliminate bands of opposing flow, analogous to the shear bands observed in passive complex fluids.
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Fast and spectrally accurate Ewald summation for 2-periodic electrostatic systems

2012-04-26
Dag Lindbo , Anna‐Karin Tornberg
A new method for Ewald summation in planar/slablike geometry, i.e., systems where periodicity applies in two dimensions and the last dimension is “free” (2P), is presented. We employ a spectral … A new method for Ewald summation in planar/slablike geometry, i.e., systems where periodicity applies in two dimensions and the last dimension is “free” (2P), is presented. We employ a spectral representation in terms of both Fourier series and integrals. This allows us to concisely derive both the 2P Ewald sum and a fast particle mesh Ewald (PME)-type method suitable for large-scale computations. The primary results are: (i) close and illuminating connections between the 2P problem and the standard Ewald sum and associated fast methods for full periodicity; (ii) a fast, O(N log N), and spectrally accurate PME-type method for the 2P k-space Ewald sum that uses vastly less memory than traditional PME methods; (iii) errors that decouple, such that parameter selection is simplified. We give analytical and numerical results to support this.
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Swimmers in Thin Films: From Swarming to Hydrodynamic Instabilities

2010-12-02
Marco Leoni , Tanniemola B. Liverpool
We investigate theoretically the collective dynamics of a suspension of low Reynolds number swimmers that are confined to two dimensions by a thin fluid film. Our model swimmer is characterized … We investigate theoretically the collective dynamics of a suspension of low Reynolds number swimmers that are confined to two dimensions by a thin fluid film. Our model swimmer is characterized by internal degrees of freedom which locally exert active stresses on the fluid. We find that hydrodynamic interactions mediated by the film can give rise to spontaneous continuous symmetry breaking (swarming), to states with either polar or nematic homogeneous order. For dipolar swimmers, the stroke averaged dynamics are enough to determine the leading contributions to the collective behavior. In contrast, for quadrupolar swimmers, details of the internal dynamics are important in determining the bulk behavior. In the broken symmetry phases, fluctuations of hydrodynamic variables destabilize order. Interestingly, this instability is not generic and depends on the length scale.
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Defect Annihilation and Proliferation in Active Nematics

2013-05-29
Luca Giomi , Mark J. Bowick , Xu Ma +1 more
Liquid crystals inevitably possess topological defect excitations generated through boundary conditions, through applied fields, or in quenches to the ordered phase. In equilibrium, pairs of defects coarsen and annihilate as … Liquid crystals inevitably possess topological defect excitations generated through boundary conditions, through applied fields, or in quenches to the ordered phase. In equilibrium, pairs of defects coarsen and annihilate as the uniform ground state is approached. Here we show that defects in active liquid crystals exhibit profoundly different behavior, depending on the degree of activity and its contractile or extensile character. While contractile systems enhance the annihilation dynamics of passive systems, extensile systems act to drive defects apart so that they swarm around in the manner of topologically well-characterized self-propelled particles. We develop a simple analytical model for the defect dynamics which reproduces the key features of both the numerical solutions and recent experiments on microtubule-kinesin assemblies.
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Actively Contracting Bundles of Polar Filaments

2000-08-21
Karsten Kruse , Frank Jülicher
We introduce a phenomenological model to study the properties of bundles of polar filaments which interact via active elements. The stability of the homogeneous state, the attractors of the dynamics … We introduce a phenomenological model to study the properties of bundles of polar filaments which interact via active elements. The stability of the homogeneous state, the attractors of the dynamics in the unstable regime, and the tensile stress generated in the bundle are discussed. We find that the interaction of parallel filaments can induce unstable behavior and is responsible for active contraction and tension in the bundle. The interaction between antiparallel filaments leads to filament sorting. Our model could apply to simple contractile structures in cells such as stress fibers.
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Multiscale modeling and simulation of microtubule–motor-protein assemblies

2015-12-10
Tong Gao , Robert Blackwell , Matthew A. Glaser +2 more
Microtubules and motor proteins self-organize into biologically important assemblies including the mitotic spindle and the centrosomal microtubule array. Outside of cells, microtubule-motor mixtures can form novel active liquid-crystalline materials driven … Microtubules and motor proteins self-organize into biologically important assemblies including the mitotic spindle and the centrosomal microtubule array. Outside of cells, microtubule-motor mixtures can form novel active liquid-crystalline materials driven out of equilibrium by adenosine triphosphate--consuming motor proteins. Microscopic motor activity causes polarity-dependent interactions between motor proteins and microtubules, but how these interactions yield larger-scale dynamical behavior such as complex flows and defect dynamics is not well understood. We develop a multiscale theory for microtubule-motor systems in which Brownian dynamics simulations of polar microtubules driven by motors are used to study microscopic organization and stresses created by motor-mediated microtubule interactions. We identify polarity-sorting and crosslink tether relaxation as two polar-specific sources of active destabilizing stress. We then develop a continuum Doi-Onsager model that captures polarity sorting and the hydrodynamic flows generated by these polar-specific active stresses. In simulations of active nematic flows on immersed surfaces, the active stresses drive turbulent flow dynamics and continuous generation and annihilation of disclination defects. The dynamics follow from two instabilities, and accounting for the immersed nature of the experiment yields unambiguous characteristic length and time scales. When turning off the hydrodynamics in the Doi-Onsager model, we capture formation of polar lanes as observed in the Brownian dynamics simulation.
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Cytoplasmic streaming in plant cells emerges naturally by microfilament self-organization

2013-08-12
Francis G. Woodhouse , Raymond E. Goldstein
Many cells exhibit large-scale active circulation of their entire fluid contents, a process termed cytoplasmic streaming. This phenomenon is particularly prevalent in plant cells, often presenting strikingly regimented flow patterns. … Many cells exhibit large-scale active circulation of their entire fluid contents, a process termed cytoplasmic streaming. This phenomenon is particularly prevalent in plant cells, often presenting strikingly regimented flow patterns. The driving mechanism in such cells is known: myosin-coated organelles entrain cytoplasm as they process along actin filament bundles fixed at the periphery. Still unknown, however, is the developmental process which constructs the well-ordered actin configurations required for coherent cell-scale flow. Previous experimental works on streaming regeneration in cells of Characean algae, whose longitudinal flow is perhaps the most regimented of all, hint at an autonomous process of microfilament self-organization driving the formation of streaming patterns during morphogenesis. Working from first principles, we propose a robust model of streaming emergence that combines motor dynamics with both micro- and macroscopic hydrodynamics to explain how several independent processes, each ineffectual on its own, can reinforce to ultimately develop the patterns of streaming observed in the Characeae and other streaming species.
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The Mechanics and Statistics of Active Matter

2010-07-29
Sriraṁ Ramaswamy
Active particles contain internal degrees of freedom with the ability to take in and dissipate energy and, in the process, execute systematic movement. Examples include all living organisms and their … Active particles contain internal degrees of freedom with the ability to take in and dissipate energy and, in the process, execute systematic movement. Examples include all living organisms and their motile constituents such as molecular motors. This article reviews recent progress in applying the principles of nonequilibrium statistical mechanics and hydrodynamics to form a systematic theory of the behaviour of collections of active particles -- active matter -- with only minimal regard to microscopic details. A unified view of the many kinds of active matter is presented, encompassing not only living systems but inanimate analogues. Theory and experiment are discussed side by side.
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Spectral Ewald Acceleration of Stokesian Dynamics for polydisperse suspensions

2015-12-02
Mu Wang , John F. Brady
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Invasion-wave-induced first-order phase transition in systems of active particles

2013-10-18
Thomas Ihle
An instability near the transition to collective motion of self-propelled particles is studied numerically by Enskog-like kinetic theory. While hydrodynamics breaks down, the kinetic approach leads to steep solitonlike waves. … An instability near the transition to collective motion of self-propelled particles is studied numerically by Enskog-like kinetic theory. While hydrodynamics breaks down, the kinetic approach leads to steep solitonlike waves. These supersonic waves show hysteresis and lead to an abrupt jump of the global order parameter if the noise level is changed. Thus they provide a mean-field mechanism to change the second-order character of the phase transition to first order. The shape of the wave is shown to follow a scaling law and to quantitatively agree with agent-based simulations.
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Active jamming: Self-propelled soft particles at high density

2011-10-12
Silke Henkes , Yaouen Fily , M. Cristina Marchetti
We study numerically the phases and dynamics of a dense collection of self-propelled particles with soft repulsive interactions in two dimensions. The model is motivated by recent in vitro experiments … We study numerically the phases and dynamics of a dense collection of self-propelled particles with soft repulsive interactions in two dimensions. The model is motivated by recent in vitro experiments on confluent monolayers of migratory epithelial and endothelial cells. The phase diagram exhibits a liquid phase with giant number fluctuations at low packing fraction and high self-propulsion speed and a jammed phase at high packing fraction and low self-propulsion speed. The dynamics of the jammed phase is controlled by the low frequency modes of the jammed packing.
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Living liquid crystals

2014-01-13
Shuang Zhou , Andrey Sokolov , Oleg D. Lavrentovich +1 more
Collective motion of self-propelled organisms or synthetic particles, often termed "active fluid," has attracted enormous attention in the broad scientific community because of its fundamentally nonequilibrium nature. Energy input and … Collective motion of self-propelled organisms or synthetic particles, often termed "active fluid," has attracted enormous attention in the broad scientific community because of its fundamentally nonequilibrium nature. Energy input and interactions among the moving units and the medium lead to complex dynamics. Here, we introduce a class of active matter--living liquid crystals (LLCs)--that combines living swimming bacteria with a lyotropic liquid crystal. The physical properties of LLCs can be controlled by the amount of oxygen available to bacteria, by concentration of ingredients, or by temperature. Our studies reveal a wealth of intriguing dynamic phenomena, caused by the coupling between the activity-triggered flow and long-range orientational order of the medium. Among these are (i) nonlinear trajectories of bacterial motion guided by nonuniform director, (ii) local melting of the liquid crystal caused by the bacteria-produced shear flows, (iii) activity-triggered transition from a nonflowing uniform state into a flowing one-dimensional periodic pattern and its evolution into a turbulent array of topological defects, and (iv) birefringence-enabled visualization of microflow generated by the nanometers-thick bacterial flagella. Unlike their isotropic counterpart, the LLCs show collective dynamic effects at very low volume fraction of bacteria, on the order of 0.2%. Our work suggests an unorthodox design concept to control and manipulate the dynamic behavior of soft active matter and opens the door for potential biosensing and biomedical applications.
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Cooperative cargo transport by several molecular motors

2005-11-15
Stefan Klumpp , Reinhard Lipowsky
The transport of cargo particles that are pulled by several molecular motors in a cooperative manner is studied theoretically in this article. The transport properties depend primarily on the maximal … The transport of cargo particles that are pulled by several molecular motors in a cooperative manner is studied theoretically in this article. The transport properties depend primarily on the maximal number N of motor molecules that may pull simultaneously on the cargo particle. Because each motor must unbind from the filament after a finite number of steps but can also rebind to it again, the actual number of pulling motors is not constant but varies with time between zero and N . An increase in the maximal number N leads to a strong increase of the average walking distance (or run length) of the cargo particle. If the cargo is pulled by up to N kinesin motors, for example, the walking distance is estimated to be 5 N –1 / N micrometers, which implies that seven or eight kinesin molecules are sufficient to attain an average walking distance in the centimeter range. If the cargo particle is pulled against an external load force, this force is shared between the motors, which provides a nontrivial motor–motor coupling and a generic mechanism for nonlinear force–velocity relationships. With increasing load force, the probability distribution of the instantaneous velocity is shifted toward smaller values, becomes broader, and develops several peaks. Our theory is consistent with available experimental data and makes quantitative predictions that are accessible to systematic in vitro experiments.
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Pressure is not a state function for generic active fluids

2015-06-29
Alexandre Solon , Yaouen Fily , Aparna Baskaran +4 more
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Traffic Jams, Gliders, and Bands in the Quest for Collective Motion of Self-Propelled Particles

2011-03-21
Fernando Peruani , Tobias Klauß , Andreas Deutsch +1 more
We study a simple swarming model on a two-dimensional lattice where the self-propelled particles exhibit a tendency to align ferromagnetically. Volume exclusion effects are present: particles can only hop to … We study a simple swarming model on a two-dimensional lattice where the self-propelled particles exhibit a tendency to align ferromagnetically. Volume exclusion effects are present: particles can only hop to a neighboring node if the node is empty. Here we show that such effects lead to a surprisingly rich variety of self-organized spatial patterns. As particles exhibit an increasingly higher tendency to align to neighbors, they first self-segregate into disordered particle aggregates. Aggregates turn into traffic jams. Traffic jams evolve toward gliders, triangular high density regions that migrate in a well-defined direction. Maximum order is achieved by the formation of elongated high density regions - bands - that transverse the entire system. Numerical evidence suggests that below the percolation density the phase transition associated to orientational order is of first-order, while at full occupancy it is of second-order. The model highlights the (pattern formation) importance of a coupling between local density, orientation, and local speed.
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Complex Spontaneous Flows and Concentration Banding in Active Polar Films

2008-11-04
Luca Giomi , M. Cristina Marchetti , Tanniemola B. Liverpool
We study the dynamical properties of active polar liquid crystalline films. Like active nematic films, active polar films undergo a dynamical transition to spontaneously flowing steady states. Spontaneous flow in … We study the dynamical properties of active polar liquid crystalline films. Like active nematic films, active polar films undergo a dynamical transition to spontaneously flowing steady states. Spontaneous flow in polar fluids is, however, always accompanied by strong concentration inhomogeneities or ``banding'' not seen in nematics. In addition, a spectacular property unique to polar active films is their ability to generate spontaneously oscillating and banded flows even at low activity. The oscillatory flows become increasingly complicated for strong polarity.
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Elementary observations on 2-categorical limits

1989-04-01
G. M. Kelly
With a view to further applications, we give a self-contained account of indexed limits for 2-categories, including necessary and sufficient conditions for 2-categorical completeness. Many important 2-categories fail to be … With a view to further applications, we give a self-contained account of indexed limits for 2-categories, including necessary and sufficient conditions for 2-categorical completeness. Many important 2-categories fail to be complete but do admit a wide class of limits. Accordingly, we introduce a variety of particular 2-categorical limits of practical importance, and show that certain of these suffice for the existence of indexed lax- and pseudo-limits. Other important 2-categories fail to admit even pseudo-limits, but do admit the weaker bilimits; we end by discussing these.
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Pressure and Phase Equilibria in Interacting Active Brownian Spheres

2015-05-11
Alexandre Solon , Joakim Stenhammar , Raphael Wittkowski +4 more
We derive a microscopic expression for the mechanical pressure P in a system of spherical active Brownian particles at density ρ. Our exact result relates P, defined as the force … We derive a microscopic expression for the mechanical pressure P in a system of spherical active Brownian particles at density ρ. Our exact result relates P, defined as the force per unit area on a bounding wall, to bulk correlation functions evaluated far away from the wall. It shows that (i) P(ρ) is a state function, independent of the particle-wall interaction; (ii) interactions contribute two terms to P, one encoding the slow-down that drives motility-induced phase separation, and the other a direct contribution well known for passive systems; and (iii) P is equal in coexisting phases. We discuss the consequences of these results for the motility-induced phase separation of active Brownian particles and show that the densities at coexistence do not satisfy a Maxwell construction on P.
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Collective Motion of Vibrated Polar Disks

2010-08-23
Julien Deseigne , Olivier Dauchot , Hugues Chaté
We experimentally study a monolayer of vibrated disks with a built-in polar asymmetry which enables them to move quasi-balistically on a large persistence length. Alignment occurs during collisions as a … We experimentally study a monolayer of vibrated disks with a built-in polar asymmetry which enables them to move quasi-balistically on a large persistence length. Alignment occurs during collisions as a result of self-propulsion and hard core repulsion. Varying the amplitude of the vibration, we observe the onset of large-scale collective motion and the existence of giant number fluctuations with a scaling exponent in agreement with the predicted theoretical value.
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Hydrodynamics of self-propelled hard rods

2008-01-25
Aparna Baskaran , M. Cristina Marchetti
Motivated by recent simulations and by experiments on aggregation of gliding bacteria, we study a model of the collective dynamics of self-propelled hard rods on a substrate in two dimensions. … Motivated by recent simulations and by experiments on aggregation of gliding bacteria, we study a model of the collective dynamics of self-propelled hard rods on a substrate in two dimensions. The rods have finite size, interact via excluded volume and their dynamics is overdamped by the interaction with the substrate. Starting from a microscopic model with non-thermal noise sources, a continuum description of the system is derived. The hydrodynamic equations are then used to characterize the possible steady states of the systems and their stability as a function of the particles packing fraction and the speed of self propulsion.
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Novel Type of Phase Transition in a System of Self-Driven Particles

1995-08-07
Tamás Vicsek , András Czirók , Eshel Ben‐Jacob +2 more
A simple model with a novel type of dynamics is introduced in order to investigate the emergence of self-ordered motion in systems of particles with biologically motivated interaction. In our … A simple model with a novel type of dynamics is introduced in order to investigate the emergence of self-ordered motion in systems of particles with biologically motivated interaction. In our model particles are driven with a constant absolute velocity and at each time step assume the average direction of motion of the particles in their neighborhood with some random perturbation ($\eta$) added. We present numerical evidence that this model results in a kinetic phase transition from no transport (zero average velocity, $| {\bf v}_a | =0$) to finite net transport through spontaneous symmetry breaking of the rotational symmetry. The transition is continuous since $| {\bf v}_a |$ is found to scale as $(\eta_c-\eta)^\beta$ with $\beta\simeq 0.45$.
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Totally asymmetric simple exclusion process with Langmuir kinetics

2004-10-06
Andrea Parmeggiani , Thomas Franosch , Erwin Frey
We discuss a class of driven lattice gas obtained by coupling the one-dimensional totally asymmetric simple exclusion process to Langmuir kinetics. In the limit where these dynamics are competing, the … We discuss a class of driven lattice gas obtained by coupling the one-dimensional totally asymmetric simple exclusion process to Langmuir kinetics. In the limit where these dynamics are competing, the resulting nonconserved flow of particles on the lattice leads to stationary regimes for large but finite systems. We observe unexpected properties such as localized boundaries (domain walls) that separate coexisting regions of low and high density of particles (phase coexistence). A rich phase diagram, with high and low density phases, two and three phase coexistence regions, and a boundary independent "Meissner" phase is found. We rationalize the average density and current profiles obtained from simulations within a mean-field approach in the continuum limit. The ensuing analytic solution is expressed in terms of Lambert W functions. It allows one to fully describe the phase diagram and extract unusual mean-field exponents that characterize critical properties of the domain wall. Based on the same approach, we provide an explanation of the localization phenomenon. Finally, we elucidate phenomena that go beyond mean-field such as the scaling properties of the domain wall.
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Transport of organelles by elastically coupled motor proteins

2016-07-01
Deepak Bhat , Manoj Gopalakrishnan
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Introduction to bicategories

1967-01-01
Jean Bénabou