268 research outputs found
Linear response to leadership, effective temperature and decision making in flocks
Large collections of autonomously moving agents, such as animals or
micro-organisms, are able to 'flock' coherently in space even in the absence of
a central control mechanism. While the direction of the flock resulting from
this critical behavior is random, this can be controlled by a small subset of
informed individuals acting as leaders of the group. In this article we use the
Vicsek model to investigate how flocks respond to leadership and make
decisions. Using a combination of numerical simulations and continuous modeling
we demonstrate that flocks display a linear response to leadership that can be
cast in the framework of the fluctuation-dissipation theorem, identifying an
'effective temperature' reflecting how promptly the flock reacts to the
initiative of the leaders. The linear response to leadership also holds in the
presence of two groups of informed individuals with competing interests,
indicating that the flock's behavioral decision is determined by both the
number of leaders and their degree of influence.Comment: 8 pages (incl. supplementary information), 8 figures, Supplementary
movies can be found at
http://wwwhome.lorentz.leidenuniv.nl/~giomi/sup_mat/20151108
Excitable Patterns in Active Nematics
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 non-uniform 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.Comment: 4 pages, 4 figure
Dislocation screening in crystals with spherical topology
Whereas disclination defects are energetically prohibitive in two-dimensional
flat crystals, their existence is necessary in crystals with spherical
topology, such as viral capsids, colloidosomes or fullerenes. Such a
geometrical frustration gives rise to large elastic stresses, which render the
crystal unstable when its size is significantly larger than the typical lattice
spacing. Depending on the compliance of the crystal with respect to stretching
and bending deformations, these stresses are alleviated by either a local
increase of the intrinsic curvature in proximity of the disclinations or by the
proliferation of excess dislocations, often organized in the form of
one-dimensional chains known as "scars". The associated strain field of the
scars is such to counterbalance the one resulting from the isolated
disclinations. Here, we develop a continuum theory of dislocation screening in
two-dimensional closed crystals with genus one. Upon modeling the flux of scars
emanating from a given disclination as an independent scalar field, we
demonstrate that the elastic energy of closed two-dimensional crystals with
various degrees of asphericity can be expressed as a simple quadratic function
of the screened topological charge of the disclinations, both at zero and
finite temperature. This allows us to predict the optimal density of the excess
dislocations as well as the minimal stretching energy attained by the crystal
Molecular Tilt on Monolayer-Protected Nanoparticles
The structure of the tilted phase of monolayer-protected nanoparticles is investigated by means of a simple Ginzburg-Landau model. The theory contains two dimensionless parameters representing the preferential tilt angle and the ratio (epsilon) between the energy cost due to spatial variations in the tilt of the coating molecules and that of the van der Waals interactions which favors uniform tilt. We analyze the model for both spherical and octahedral particles. On spherical particles, we find a transition from a tilted phase, at small (epsilon), to a phase where the molecules spontaneously align along the surface normal and tilt disappears. Octahedral particles have an additional phase at small characterized by the presence of six topological defects. These defective configurations provide preferred sites for the chemical functionalization of monolayer-protected nanoparticles via place-exchange reactions and their consequent linking to form molecules and\ud
bulk materials
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The Dynamics of Sperm Cooperation in a Competitive Environment
Sperm cooperation has evolved in a variety of taxa and is often considered a response to sperm competition, yet the benefit of this form of collective movement remains unclear. Here we use fine-scale imaging and a minimal mathematical model to study sperm aggregation in the rodent genus Peromyscus. We demonstrate that as the number of sperm cells in an aggregate increase, the group moves with more persistent linearity but without increasing speed; this benefit, however, is offset in larger aggregates as the geometry of the group forces sperm to swim against one another. The result is a non-monotonic relationship between aggregate size and average velocity with both a theoretically predicted and empirically observed optimum of 6-7 sperm/aggregate. To understand the role of sexual selection in driving these sperm group dynamics, we compared two sister-species with divergent mating systems and find that sperm of P. maniculatus (highly promiscuous), which have evolved under intense competition, form optimal-sized aggregates more often than sperm of P. polionotus (strictly monogamous), which lack competition. Our combined mathematical and experimental study of coordinated sperm movement reveals the importance of geometry, motion and group size on sperm velocity and suggests how these physical variables interact with evolutionary selective pressures to regulate cooperation in competitive environments.Engineering and Applied SciencesOrganismic and Evolutionary Biolog
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The dynamics of sperm cooperation in a competitive environment
Sperm cooperation has evolved in a variety of taxa and is often considered a response to sperm competition, yet the benefit of this form of collective movement remains unclear. Here, we use fine-scale imaging and a minimal mathematical model to study sperm aggregation in the rodent genus Peromyscus. We demonstrate that as the number of sperm cells in an aggregate increase, the group moves with more persistent linearity but without increasing speed. This benefit, however, is offset in larger aggregates as the geometry of the group forces sperm to swim against one another. The result is a non-monotonic relationship between aggregate size and average velocity with both a theoretically predicted and empirically observed optimum of six to seven sperm per aggregate. To understand the role of sexual selection in driving these sperm group dynamics, we compared two sister-species with divergent mating systems. We find that sperm of Peromyscus maniculatus (highly promiscuous), which have evolved under intense competition, form optimal-sized aggregates more often than sperm of Peromyscus polionotus (strictly monogamous), which lack competition. Our combined mathematical and experimental study of coordinated sperm movement reveals the importance of geometry, motion and group size on sperm velocity and suggests how these physical variables interact with evolutionary selective pressures to regulate cooperation in competitive environments
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