1,330 research outputs found
Role of hydrodynamic flows in chemically driven droplet division
We study the hydrodynamics and shape changes of chemically active droplets.
In non-spherical droplets, surface tension generates hydrodynamic flows that
drive liquid droplets into a spherical shape. Here we show that spherical
droplets that are maintained away from thermodynamic equilibrium by chemical
reactions may not remain spherical but can undergo a shape instability which
can lead to spontaneous droplet division. In this case chemical activity acts
against surface tension and tension-induced hydrodynamic flows. By combining
low Reynolds-number hydrodynamics with phase separation dynamics and chemical
reaction kinetics we determine stability diagrams of spherical droplets as a
function of dimensionless viscosity and reaction parameters. We determine
concentration and flow fields inside and outside the droplets during shape
changes and division. Our work shows that hydrodynamic flows tends to stabilize
spherical shapes but that droplet division occurs for sufficiently strong
chemical driving, sufficiently large droplet viscosity or sufficiently small
surface tension. Active droplets could provide simple models for prebiotic
protocells that are able to proliferate. Our work captures the key
hydrodynamics of droplet division that could be observable in chemically active
colloidal droplets
Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes
We study the statistics of infima, stopping times and passage probabilities
of entropy production in nonequilibrium steady states, and show that they are
universal. We consider two examples of stopping times: first-passage times of
entropy production and waiting times of stochastic processes, which are the
times when a system reaches for the first time a given state. Our main results
are: (i) the distribution of the global infimum of entropy production is
exponential with mean equal to minus Boltzmann's constant; (ii) we find the
exact expressions for the passage probabilities of entropy production to reach
a given value; (iii) we derive a fluctuation theorem for stopping-time
distributions of entropy production. These results have interesting
implications for stochastic processes that can be discussed in simple colloidal
systems and in active molecular processes. In particular, we show that the
timing and statistics of discrete chemical transitions of molecular processes,
such as, the steps of molecular motors, are governed by the statistics of
entropy production. We also show that the extreme-value statistics of active
molecular processes are governed by entropy production, for example, the
infimum of entropy production of a motor can be related to the maximal
excursion of a motor against the direction of an external force. Using this
relation, we make predictions for the distribution of the maximum backtrack
depth of RNA polymerases, which follows from our universal results for
entropy-production infima.Comment: 30 pages, 13 figure
Sequential pattern formation governed by signaling gradients
Rhythmic and sequential segmentation of the embryonic body plan is a vital
developmental patterning process in all vertebrate species. However, a
theoretical framework capturing the emergence of dynamic patterns of gene
expression from the interplay of cell oscillations with tissue elongation and
shortening and with signaling gradients, is still missing. Here we show that a
set of coupled genetic oscillators in an elongating tissue that is regulated by
diffusing and advected signaling molecules can account for segmentation as a
self-organized patterning process. This system can form a finite number of
segments and the dynamics of segmentation and the total number of segments
formed depend strongly on kinetic parameters describing tissue elongation and
signaling molecules. The model accounts for existing experimental perturbations
to signaling gradients, and makes testable predictions about novel
perturbations. The variety of different patterns formed in our model can
account for the variability of segmentation between different animal species.Comment: 12 pages, 5 figure
Casimir stresses in active nematic films
We calculate the Casimir stresses in a thin layer of active fluid with nematic order. By using a stochastic hydrodynamic approach for an active fluid layer of finite thickness L, we generalize the Casimir stress for nematic liquid crystals in thermal equilibrium to active systems. We show that the active Casimir stress differs significantly from its equilibrium counterpart. For contractile activity, the active Casimir stress, although attractive like its equilibrium counterpart, diverges logarithmically as L approaches a threshold of the spontaneous flow instability from below. In contrast, for small extensile activity, it is repulsive, has no divergence at any L and has a scaling with L different from its equilibrium counterpart
Droplet Ripening in Concentration Gradients
Living cells use phase separation and concentration gradients to organize
chemical compartments in space. Here, we present a theoretical study of droplet
dynamics in gradient systems. We derive the corresponding growth law of
droplets and find that droplets exhibit a drift velocity and position dependent
growth. As a consequence, the dissolution boundary moves through the system,
thereby segregating droplets to one end. We show that for steep enough
gradients, the ripening leads to a transient arrest of droplet growth that is
induced by an narrowing of the droplet size distribution.Comment: 12 pages, 4 figure
Integral Fluctuation Relations for Entropy Production at Stopping Times
A stopping time is the first time when a trajectory of a stochastic
process satisfies a specific criterion. In this paper, we use martingale theory
to derive the integral fluctuation relation for the stochastic entropy production in a
stationary physical system at stochastic stopping times . This fluctuation
relation implies the law , which states
that it is not possible to reduce entropy on average, even by stopping a
stochastic process at a stopping time, and which we call the second law of
thermodynamics at stopping times. This law implies bounds on the average amount
of heat and work a system can extract from its environment when stopped at a
random time. Furthermore, the integral fluctuation relation implies that
certain fluctuations of entropy production are universal or are bounded by
universal functions. These universal properties descend from the integral
fluctuation relation by selecting appropriate stopping times: for example, when
is a first-passage time for entropy production, then we obtain a bound on
the statistics of negative records of entropy production. We illustrate these
results on simple models of nonequilibrium systems described by Langevin
equations and reveal two interesting phenomena. First, we demonstrate that
isothermal mesoscopic systems can extract on average heat from their
environment when stopped at a cleverly chosen moment and the second law at
stopping times provides a bound on the average extracted heat. Second, we
demonstrate that the average efficiency at stopping times of an autonomous
stochastic heat engines, such as Feymann's ratchet, can be larger than the
Carnot efficiency and the second law of thermodynamics at stopping times
provides a bound on the average efficiency at stopping times.Comment: 37 pages, 6 figure
Generic Properties of Stochastic Entropy Production
We derive an Ito stochastic differential equation for entropy production in
nonequilibrium Langevin processes. Introducing a random-time transformation,
entropy production obeys a one-dimensional drift-diffusion equation,
independent of the underlying physical model. This transformation allows us to
identify generic properties of entropy production. It also leads to an exact
uncertainty equality relating the Fano factor of entropy production and the
Fano factor of the random time, which we also generalize to non steady-state
conditions.Comment: 5 pages, 5 figures (contains Supplemental Material, 7 pages
Fluid pumping and active flexoelectricity can promote lumen nucleation in cell assemblies
We discuss the physical mechanisms that promote or suppress the nucleation of
a fluid-filled lumen inside a cell assembly or a tissue. We discuss lumen
formation in a continuum theory of tissue material properties in which the
tissue is described as a two-fluid system to account for its permeation by the
interstitial fluid, and we include fluid pumping as well as active electric
effects. Considering a spherical geometry and a polarized tissue, our work
shows that fluid pumping and tissue flexoelectricity play a crucial role in
lumen formation. We furthermore explore the large variety of long-time states
that are accessible for the cell aggregate and its lumen. Our work reveals a
role of the coupling of mechanical, electrical and hydraulic phenomena in
tissue lumen formation.Comment: Published versio
Cell body rocking is a dominant mechanism for flagellar synchronization in a swimming alga
The unicellular green algae Chlamydomonas swims with two flagella, which can
synchronize their beat. Synchronized beating is required to swim both fast and
straight. A long-standing hypothesis proposes that synchronization of flagella
results from hydrodynamic coupling, but the details are not understood. Here,
we present realistic hydrodynamic computations and high-speed tracking
experiments of swimming cells that show how a perturbation from the
synchronized state causes rotational motion of the cell body. This rotation
feeds back on the flagellar dynamics via hydrodynamic friction forces and
rapidly restores the synchronized state in our theory. We calculate that this
`cell body rocking' provides the dominant contribution to synchronization in
swimming cells, whereas direct hydrodynamic interactions between the flagella
contribute negligibly. We experimentally confirmed the coupling between
flagellar beating and cell body rocking predicted by our theory. This work
appeared also in the Proceedings of the National Academy of Science of the
U.S.A as: Geyer et al., PNAS 110(45), p. 18058(6), 2013.Comment: 40 pages, 15 color figure
- …