1,378 research outputs found
A model for the emergence of cooperation, interdependence and structure in evolving networks
Evolution produces complex and structured networks of interacting components
in chemical, biological, and social systems. We describe a simple mathematical
model for the evolution of an idealized chemical system to study how a network
of cooperative molecular species arises and evolves to become more complex and
structured. The network is modeled by a directed weighted graph whose positive
and negative links represent `catalytic' and `inhibitory' interactions among
the molecular species, and which evolves as the least populated species
(typically those that go extinct) are replaced by new ones. A small
autocatalytic set (ACS), appearing by chance, provides the seed for the
spontaneous growth of connectivity and cooperation in the graph. A highly
structured chemical organization arises inevitably as the ACS enlarges and
percolates through the network in a short, analytically determined time scale.
This self-organization does not require the presence of self-replicating
species. The network also exhibits catastrophes over long time scales triggered
by the chance elimination of `keystone' species, followed by recoveries.Comment: 8 pages, 4 figure
Simulating Brownian suspensions with fluctuating hydrodynamics
Fluctuating hydrodynamics has been successfully combined with several
computational methods to rapidly compute the correlated random velocities of
Brownian particles. In the overdamped limit where both particle and fluid
inertia are ignored, one must also account for a Brownian drift term in order
to successfully update the particle positions. In this paper, we present an
efficient computational method for the dynamic simulation of Brownian
suspensions with fluctuating hydrodynamics that handles both computations and
provides a similar approximation as Stokesian Dynamics for dilute and
semidilute suspensions. This advancement relies on combining the fluctuating
force-coupling method (FCM) with a new midpoint time-integration scheme we
refer to as the drifter-corrector (DC). The DC resolves the drift term for
fluctuating hydrodynamics-based methods at a minimal computational cost when
constraints are imposed on the fluid flow to obtain the stresslet corrections
to the particle hydrodynamic interactions. With the DC, this constraint need
only be imposed once per time step, reducing the simulation cost to nearly that
of a completely deterministic simulation. By performing a series of
simulations, we show that the DC with fluctuating FCM is an effective and
versatile approach as it reproduces both the equilibrium distribution and the
evolution of particulate suspensions in periodic as well as bounded domains. In
addition, we demonstrate that fluctuating FCM coupled with the DC provides an
efficient and accurate method for large-scale dynamic simulation of colloidal
dispersions and the study of processes such as colloidal gelation
Lubrication approximation for micro-particles moving along parallel walls
Lubrication expressions for the friction coefficients of a spherical particle
moving in a fluid between and along two parallel solid walls are explicitly
evaluated in the low-Reynolds-number regime. They are used to determine
lubrication expression for the particle free motion under an ambient Poiseuille
flow. The range of validity and the accuracy of the lubrication approximation
is determined by comparing with the corresponding results of the accurate
multipole procedure. The results are applicable for thin, wide and long
microchannels, or quasi-two-dimensional systems.Comment: 4 pages, 5 figure
Lattice-Boltzmann simulations of the drag force on a sphere approaching a superhydrophobic striped plane
By means of lattice-Boltzmann simulations the drag force on a sphere of
radius R approaching a superhydrophobic striped wall has been investigated as a
function of arbitrary separation h. Superhydrophobic (perfect-slip vs. no-slip)
stripes are characterized by a texture period L and a fraction of the gas area
. For very large values of h/R we recover the macroscopic formulae for a
sphere moving towards a hydrophilic no-slip plane. For h/R=O(1) and smaller the
drag force is smaller than predicted by classical theories for hydrophilic
no-slip surfaces, but larger than expected for a sphere interacting with a
uniform perfectly slipping wall. At a thinner gap, the force reduction
compared to a classical result becomes more pronounced, and is maximized by
increasing . In the limit of very small separations our simulation data
are in quantitative agreement with an asymptotic equation, which relates a
correction to a force for superhydrophobic slip to texture parameters. In
addition, we examine the flow and pressure field and observe their oscillatory
character in the transverse direction in the vicinity of the wall, which
reflects the influence of the heterogeneity and anisotropy of the striped
texture. Finally, we investigate the lateral force on the sphere, which is
detectable in case of very small separations and is maximized by stripes with
.Comment: 9 pages, 7 figure
Tilted algebras and short chains of modules
We provide an affirmative answer for the question raised almost twenty years
ago concerning the characterization of tilted artin algebras by the existence
of a sincere finitely generated module which is not the middle of a short
chain
Hydrodynamic orienting of asymmetric microobjects under gravity
It is shown that nonsymmetric microobjects orient while settling under
gravity in a viscous fluid. To analyze this process, a simple shape is chosen:
a non-deformable `chain'. The chain consists of two straight arms, made of
touching solid spheres. In the absence of external torques, the spheres are
free to spin along the arms. The motion of the chain is evaluated by solving
the Stokes equations with the use of the multipole method. It is demonstrated
that the spinning beads speed up sedimentation by a small amount, and increase
the orientation rate significantly in comparison to the corresponding rigid
chain. It is shown that chains orient towards the V-shaped stable stationary
configuration. In contrast, rods and star-shaped microobjects do not rotate.
The hydrodynamic orienting is relevant for efficient swimming of non-symmetric
microobjects, and for sedimenting suspensions.Comment: 9 page
Symmetric three-particle motion in Stokes flow: equilibrium for heavy spheres in contrast to "end-of-world" for point forces
A stationary stable solution of the Stokes equations for three identical
heavy solid spheres falling in a vertical plane is found. It has no analog in
the point-particle approximation. Three spheres aligned horizontally at equal
distances evolve towards the equilibrium relative configuration while the point
particles collapse onto a single point in a finite time.Comment: 4 pages, 7 figure
Jet propulsion without inertia
A body immersed in a highly viscous fluid can locomote by drawing in and
expelling fluid through pores at its surface. We consider this mechanism of jet
propulsion without inertia in the case of spheroidal bodies, and derive both
the swimming velocity and the hydrodynamic efficiency. Elementary examples are
presented, and exact axisymmetric solutions for spherical, prolate spheroidal,
and oblate spheroidal body shapes are provided. In each case, entirely and
partially porous (i.e. jetting) surfaces are considered, and the optimal
jetting flow profiles at the surface for maximizing the hydrodynamic efficiency
are determined computationally. The maximal efficiency which may be achieved by
a sphere using such jet propulsion is 12.5%, a significant improvement upon
traditional flagella-based means of locomotion at zero Reynolds number. Unlike
other swimming mechanisms which rely on the presentation of a small cross
section in the direction of motion, the efficiency of a jetting body at low
Reynolds number increases as the body becomes more oblate, and limits to
approximately 162% in the case of a flat plate swimming along its axis of
symmetry. Our results are discussed in the light of slime extrusion mechanisms
occurring in many cyanobacteria
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