We construct schemes for self-replicating clusters of spherical particles, validated with computer simulations in a finite-temperature heat bath. Each particle has stickers uniformly distributed over its surface, and the rules for self-replication are encoded into the specificity and strength of interactions. Geometrical constraints imply that a compact cluster can copy itself only with help of a catalyst, a smaller cluster that increases the surface area to form a template. Replication efficiency requires optimizing interaction energies to destabilize all kinetic traps along the reaction pathway, as well as initiating a trigger event that specifies when the new cluster disassociates from its parent. Although there is a reasonably wide parameter range for self-replication, there is a subtle balance between the speed of the reaction, and the error rate. As a proof of principle, we construct interactions that self-replicate an octahedron, requiring a two-particle dimer for a catalyst. The resulting self-replication scheme is a hypercycle, and computer simulations confirm the exponential growth of both octahedron and catalyst replicas.

The striking diversity of bird beak shapes is an outcome of natural selection, yet the relative importance of the limitations imposed by the process of beak development on generating such variation is unclear. Untangling these factors requires mapping developmental mechanisms over a phylogeny far exceeding model systems studied thus far. We address this issue with a comparative morphometric analysis of beak shape in a diverse group of songbirds. Here we show that the dynamics of the proliferative growth zone must follow restrictive rules to explain the observed variation, with beak diversity constrained to a three parameter family of shapes, parameterized by length, depth and the degree of shear. We experimentally verify these predictions by analysing cell proliferation in the developing embryonic beaks of the zebra finch. Our findings indicate that beak shape variability in many songbirds is strongly constrained by shared properties of the developmental programme controlling the growth zone.

We establish size limitations for assembling structures of controlled size and shape out of colloidal particles with short-ranged interactions. Through simulations we show that structures with highly variable shapes made out of dozens of particles can form with high yield, as long as each particle in the structure binds only to the particles in their local environment. To understand this, we identify the excited states that compete with the ground-state structure and demonstrate that these excited states have a completely topological characterization, valid when the interparticle interactions are short-ranged. This allows complete enumeration of the energy landscape and gives bounds on how large a colloidal structure can assemble with high yield. For large structures the yield can be significant, even with hundreds of particles.

The forcibly ejected spores of ascomycete fungi must penetrate several millimetres of nearly still air surrounding sporocarps to reach dispersive airflows, and escape is facilitated when a spore is launched with large velocity. To launch, the spores of thousands of species are ejected through an apical ring, a small elastic pore. The startling diversity of apical ring and spore shapes and dimensions make them favoured characters for both species descriptions and the subsequent inference of relationships among species. However, the physical constraints shaping this diversity and the adaptive benefits of specific morphologies are not understood. Here, we develop an elastohydrodynamic theory of the spore's ejection through the apical ring and demonstrate that to avoid enormous energy losses during spore ejection, the four principal morphological dimensions of spore and apical ring must cluster within a nonlinear one-dimensional subspace. We test this prediction using morphological data for 45 fungal species from two different classes and 18 families. Our sampling encompasses multiple loss and gain events and potentially independent origins of this spore ejection mechanism. Although the individual dimensions of the spore and apical ring are only weakly correlated with each other, they collapse into the predicted subspace with high accuracy. The launch velocity appears to be within 2 per cent of the optimum for over 90 per cent of all forcibly ejected species. Although the morphological diversity of apical rings and spores appears startlingly diverse, a simple principle can be used to organize it.

We present a method for calculating the asymptotic shape of interacting vortex filaments in incompressible Euler flows using delay differential equations. Neglecting the filaments' core-size, the asymptotic shape of the filaments is self-similar up to logarithmic corrections, albeit non-universal. We demonstrate explicitly that the asymptotic geometry of the collapse of two interacting filaments depends on the pre-factor of the scaling law of their separation distance, the angle between the tangent vectors at their approaching tips, and the ratio of their circulations. We then explore the validity of the filament approximation in the limit of approaching the singularity. We show that a sufficiently fast stretching-rate to maintain this approximation is inconsistent with all collapse geometries. This suggests that a singular solution to the Euler equations based on stretching of vortex filaments is unlikely to exist for any initial conditions. (C) 2013 The Authors. Published by Elsevier B.V. Selection and/or peer-review under responsibility of the Isaac Newton Institute for Mathematical Sciences, University of Cambridge

Individuals can function as integrated organisms only when information and resources are shared across a body. Signals and substrates are commonly moved using fluids, often channeled through a network of tubes. Peristalsis is one mechanism for fluid transport and is caused by a wave of cross-sectional contractions along a tube. We extend the concept of peristalsis from the canonical case of one tube to a random network. Transport is maximized within the network when the wavelength of the peristaltic wave is of the order of the size of the network. The slime mold Physarum polycephalum grows as a random network of tubes, and our experiments confirm peristalsis is used by the slime mold to drive internal cytoplasmic flows. Comparisons of theoretically generated contraction patterns with the patterns exhibited by individuals of P. polycephalum demonstrate that individuals maximize internal flows by adapting patterns of contraction to size, thus optimizing transport throughout an organism. This control of fluid flow may be the key to coordinating growth and behavior, including the dynamic changes in network architecture seen over time in an individual.

A promising mechanism for generating a finite-time singularity in the incompressible Euler equations is the stretching of vortex filaments. Here, we argue that interacting vortex filaments cannot generate a singularity by analysing the asymptotic dynamics of their collapse. We use the separation of the dynamics of the filament shape, from that of its core, to derive constraints that must be satisfied for a singular solution to remain self-consistent uniformly in time. Our only assumption is that the length scales characterizing filament shape obey scaling laws set by the dimension of circulation as the singularity is approached. The core radius necessarily evolves on a different length scale. We show that a self-similar ansatz for the filament shapes cannot induce singular stretching, due to the logarithmic prefactor in the self-interaction term for the filaments. More generally, there is an antagonistic relationship between the stretching rate of the filaments and the requirement that the radius of curvature of filament shape obeys the dimensional scaling laws. This suggests that it is unlikely that solutions in which the core radii vanish sufficiently fast to maintain the filament approximation exist.

We show that time-oscillating electric fields applied to plasmas present in flames create steady flows of gas. Ions generated within the flame move in the field and migrate a distance delta before recombining; the net flow of ions away from the flame creates a time-averaged force that drives the steady flows observed experimentally. A quantitative model describes the response of the flame and reveals how delta decreases as the frequency of the applied field increases. Interestingly, above a critical frequency, ac fields can be used to manipulate flames at a distance without the need for proximal electrodes.

The astonishing variation in the shape and size of bird beaks reflects a wide range of dietary specializations that played an important role in avian diversification. Among Darwin's finches, ground finches (Geospiza spp.) have beaks that represent scaling variations of the same shape, which are generated by alterations in the signaling pathways that regulate growth of the two skeletal components of the beak: the prenasal cartilage (pnc) and the premaxillary bone (pmx). Whether this developmental mechanism is responsible for variation within groups of other closely related bird species, however, has remained unknown. Here, we report that the Caribbean bullfinches (Loxigilla spp.), which are closely related to Darwin's finches, have independently evolved beaks of a novel shape, different from Geospiza, but also varying from each other only in scaling. However, despite sharing the same beak shape, the signaling pathways and tissues patterning Loxigilla beaks differ among the three species. In Loxigilla noctis, as in Geospiza, the pnc develops first, shaped by Bmp4 and CaM signaling, followed by the development of the pmx, regulated by TGF beta IIr, beta-catenin, and Dkk3 signaling. In contrast, beak morphogenesis in Loxigilla violacea and Loxigilla portoricensis is generated almost exclusively by the pmx through a mechanism in which Ihh and Bmp4 synergize to promote expansion of bone tissue. Together, our results demonstrate high flexibility in the relationship between morphology and underlying developmental causes, where different developmental programs can generate identical shapes, and similar developmental programs can pattern different shapes.

Using a theoretical analysis of the ion beam sputtering dynamics, we demonstrate how ion bombardment on an initially sloped surface can create knife-edge-like ridges on the surface. These ridges arise as nonclassical shocklike solutions that are undercompressive on both sides and appear to control the dynamics over a large range of initial conditions. The slope of the ridges is selected uniquely by the dynamics and can be up to 30 or more depending on the orientation dependence of the sputtering yield. For 1 keV Ar+ on Si(001), the scale of the ridge is similar to 2 nm. This is much smaller than the most unstable length scale and suggests a method for creating very steep, very sharp features on a surface spontaneously, by prepatterning the surface to contain relatively modest slopes on the macroscale.

We demonstrate in both laboratory and numerical experiments that ion bombardment of a modestly sloped surface can create knife-edge like ridges with extremely high slopes. Small pre-fabricated pits expand under ion bombardment, and the collision of two such pits creates knife-edge ridges. Both laboratory and numerical experiments show that the pit propagation speed and the precise shape of the knife edge ridges are universal, independent of initial conditions, as has been predicted theoretically. These observations suggest a method of fabrication in which a surface is pre-patterned so that it dynamically evolves to a desired target pattern made of knife-edge ridges. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4755838]

Particles interacting with short-ranged potentials have attracted increasing interest, partly for their ability to model mesoscale systems such as colloids interacting via DNA or depletion. We consider the free-energy landscape of such systems as the range of the potential goes to zero. In this limit, the landscape is entirely defined by geometrical manifolds, plus a single control parameter. These manifolds are fundamental objects that do not depend on the details of the interaction potential and provide the starting point from which any quantity characterizing the system-equilibrium or nonequilibrium-can be computed for arbitrary potentials. To consider dynamical quantities we compute the asymptotic limit of the Fokker-Planck equation and show that it becomes restricted to the low-dimensional manifolds connected by ``sticky'' boundary conditions. To illustrate our theory, we compute the low-dimensional manifolds for n <= 8 identical particles, providing a complete description of the lowest-energy parts of the landscape including floppy modes with up to 2 internal degrees of freedom. The results can be directly tested on colloidal clusters. This limit is a unique approach for understanding energy landscapes, and our hope is that it can also provide insight into finite-range potentials.

Many bacteria on earth exist in surface-attached communities known as biofilms. These films are responsible for manifold problems, including hospital-acquired infections and biofouling, but they can also be beneficial. Biofilm growth depends on the transport of nutrients and waste, for which diffusion is thought to be the main source of transport. However, diffusion is ineffective for transport over large distances and thus should limit growth. Nevertheless, biofilms can grow to be very large. Here we report the presence of a remarkable network of well-defined channels that form in wildtype Bacillus subtilis biofilms and provide a system for enhanced transport. We observe that these channels have high permeability to liquid flow and facilitate the transport of liquid through the biofilm. In addition, we find that spatial variations in evaporative flux from the surface of these biofilms provide a driving force for the flow of liquid in the channels. These channels offer a remarkably simple system for liquid transport, and their discovery provides insight into the physiology and growth of biofilms.

Bacterial biofilms are organized communities of cells living in association with surfaces. The hallmark of biofilm formation is the secretion of a polymeric matrix rich in sugars and proteins in the extracellular space. In Bacillus subtilis, secretion of the exopolysaccharide (EPS) component of the extracellular matrix is genetically coupled to the inhibition of flagella-mediated motility. The onset of this switch results in slow expansion of the biofilm on a substrate. Different strains have radically different capabilities in surface colonization: Flagella-null strains spread at the same rate as wild type, while both are dramatically faster than EPS mutants. Multiple functions have been attributed to the EPS, but none of these provides a physical mechanism for generating spreading. We propose that the secretion of EPS drives surface motility by generating osmotic pressure gradients in the extracellular space. A simple mathematical model based on the physics of polymer solutions shows quantitative agreement with experimental measurements of biofilm growth, thickening, and spreading. We discuss the implications of this osmotically driven type of surface motility for nutrient uptake that may elucidate the reduced fitness of the matrix-deficient mutant strains.

Sequencing by Hybridization (SBH) reconstructs an n-long target DNA sequence from its biochemically determined l-long subsequences. In the standard approach, the length of a uniformly random sequence that can be unambiguously reconstructed is limited to n=O(2(l)) due to repetitive subsequences causing reconstruction degeneracies. We present a modified sequencing method that overcomes this limitation without the need for different types of biochemical assays and is robust to error.

The commonly accepted description of drops impacting on a surface typically ignores the essential role of the air that is trapped between the impacting drop and the surface. Here we describe a new imaging modality that is sensitive to the behavior right at the surface. We show that a very thin film of air, only a few tens of nanometers thick, remains trapped between the falling drop and the surface as the drop spreads. The thin film of air serves to lubricate the drop enabling the fluid to skate on the air film laterally outward at surprisingly high velocities, consistent with theoretical predictions. Eventually this thin film of air breaks down as the fluid wets the surface via a spinodal-like mechanism. Our results show that the dynamics of impacting drops are much more complex than previously thought, with a rich array of unexpected phenomena that require rethinking classic paradigms.

Microfluidic technology has revolutionized the control of flows at small scales giving rise to new possibilities for assembling complex structures on the microscale. We analyze different possible algorithms for assembling arbitrary structures, and demonstrate that a sequential assembly algorithm can manufacture arbitrary 3D structures from identical constituents. We illustrate the algorithm by showing that a modified Hele-Shaw cell with 7 controlled flow rates can be designed to construct the entire English alphabet from particles that irreversibly stick to each other.

Microfluidic technology has revolutionized the control of flows at small scales giving rise to new possibilities for assembling complex structures on the microscale. We analyze different possible algorithms for assembling arbitrary structures, and demonstrate that a sequential assembly algorithm can manufacture arbitrary 3D structures from identical constituents. We illustrate the algorithm by showing that a modified Hele-Shaw cell with 7 controlled flow rates can be designed to construct the entire English alphabet from particles that irreversibly stick to each other.

Bacterial biofilms are interface-associated colonies of bacteria embedded in an extracellular matrix that is composed primarily of polymers and proteins. They can be viewed in the context of soft matter physics: the rigid bacteria are analogous to colloids, and the extracellular matrix is a cross-linked polymer gel. This perspective is beneficial for understanding the structure, mechanics, and dynamics of the biofilm. Bacteria regulate the water content of the biofilm by controlling the composition of the extracellular matrix, and thereby controlling the mechanical properties. The mechanics of well-defined soft materials can provide insight into the mechanics of biofilms and, in particular, the viscoelasticity. Furthermore, spatial heterogeneities in gene expression create heterogeneities in polymer and surfactant production. The resulting concentration gradients generate forces within the biofilm that are relevant for biofilm spreading and survival.