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Raymond E. Goldstein

Publications and source records attributed to Raymond E. Goldstein.

At least 37 records · Page 2Linked to original sources
arXiv2021

Turing's diffusive threshold in random reaction-diffusion systems

Turing instabilities of reaction-diffusion systems can only arise if the diffusivities of the chemical species are sufficiently different. This threshold is unphysical in most systems with $N=2$ diffusing species, forcing experimental realizations of the instability to rely on fluctuations or additional nondiffusing species. Here we ask whether this diffusive threshold lowers for $N>2$ to allow "true" Turing instabilities. Inspired by May's analysis of the stability of random ecological communities, we analyze the probability distribution of the diffusive threshold in reaction-diffusion systems defined by random matrices describing linearized dynamics near a homogeneous fixed point. In the numerically tractable cases $N\leqslant 6$, we find that the diffusive threshold becomes more likely to be smaller and physical as $N$ increases and that most of these many-species instabilities cannot be described by reduced models with fewer species.

cond-mat.soft↗
arXiv2021

Comment on "Faceting and Flattening of Emulsion Droplets: A Mechanical Model"

García-Aguilar et al. [Phys. Rev. Lett 126, 038001 (2021)] have shown that the deformations of "shape-shifting droplets" are consistent with an elastic model, that, unlike previous models, includes the intrinsic curvature of the frozen surfactant layer. In this Comment, we show that the interplay between surface tension and intrinsic curvature in their model is in fact mathematically equivalent to a physically very different phase-transition mechanism of the same process that we developed previously [Phys. Rev. Lett. 118, 088001 (2017); Phys. Rev. Res. 1, 023017 (2019)]. The mathematical models cannot therefore distinguish between the two mechanisms, and hence it is not possible to claim that one mechanism underlies all observed shape-shifting phenomena without a much more detailed comparison of experiment and theory.

cond-mat.soft↗
arXiv2020

Morphoelasticity of Large Bending Deformations of Cell Sheets during Development

Deformations of cell sheets during morphogenesis are driven by developmental processes such as cell division and cell shape changes. In morphoelastic shell theories of development, these processes appear as variations of the intrinsic geometry of a thin elastic shell. However, morphogenesis often involves large bending deformations that are outside the formal range of validity of these shell theories. Here, by asymptotic expansion of three-dimensional incompressible morphoelasticity in the limit of a thin shell, we derive a shell theory for large intrinsic bending deformations and emphasise the resulting geometric material anisotropy and the elastic role of cell constriction. Taking the invagination of the green alga Volvox as a model developmental event, we show how results for this theory differ from those for a classical shell theory that is not formally valid for these large bending deformations and reveal how these geometric effects stabilise invagination.

cond-mat.soft↗
arXiv2020

The fluid dynamics of collective vortex structures of plant-animal worms

Circular milling, a stunning manifestation of collective motion, is found across the natural world, from fish shoals to army ants. It has been observed recently that the plant-animal worm $Symsagittifera~roscoffensis$ exhibits circular milling behaviour, both in shallow pools at the beach and in Petri dishes in the laboratory. Here we investigate this phenomenon, through experiment and theory, from a fluid dynamical viewpoint, focusing on the effect that an established circular mill has on the surrounding fluid. Unlike systems such as confined bacterial suspensions and collections of molecular motors and filaments that exhibit spontaneous circulatory behaviour, and which are modelled as force dipoles, the front-back symmetry of individual worms precludes a stresslet contribution. Instead, singularities such as source dipoles and Stokes quadrupoles are expected to dominate. A series of models is analyzed to understand the contributions of these singularities to the azimuthal flow fields generated by a mill, in light of the particular boundary conditions that hold for flow in a Petri dish. A model that treats a circular mill as a rigid rotating disc that generates a Stokes flow is shown to capture basic experimental results well, and gives insights into the emergence and stability of multiple mill systems.

cond-mat.soft↗
arXiv2020

Direct Measurement of Unsteady Microscale Stokes Flow Using Optically Driven Microspheres

A growing body of work on the dynamics of eukaryotic flagella has noted that their oscillation frequencies are sufficiently high that the viscous penetration depth of unsteady Stokes flow is comparable to the scales over which flagella synchronize. Incorporating these effects into theories of synchronization requires an understanding of the global unsteady flows around oscillating bodies. Yet, there has been no precise experimental test on the microscale of the most basic aspects of such unsteady Stokes flow: the orbits of passive tracers and the position-dependent phase lag between the oscillating response of the fluid at a distant point and that of the driving particle. Here, we report the first such direct Lagrangian measurement of this unsteady flow. The method uses an array of $30$ submicron tracer particles positioned by a time-shared optical trap at a range of distances and angular positions with respect to a larger, central particle, which is then driven by an oscillating optical trap at frequencies up to $400$ Hz. In this microscale regime, the tracer dynamics is considerably simplified by the smallness of both inertial effects on particle motion and finite-frequency corrections to the Stokes drag law. The tracers are found to display elliptical Lissajous figures whose orientation and geometry are in agreement with a low-frequency expansion of the underlying dynamics, and the experimental phase shift between motion parallel and orthogonal to the oscillation axis exhibits a predicted scaling form in distance and angle. Possible implications of these results for synchronization dynamics are discussed.

cond-mat.soft↗
arXiv2020

Swirling Instability of the Microtubule Cytoskeleton

In the cellular phenomena of cytoplasmic streaming, molecular motors carrying cargo along a network of microtubules entrain the surrounding fluid. The piconewton forces produced by individual motors are sufficient to deform long microtubules, as are the collective fluid flows generated by many moving motors. Studies of streaming during oocyte development in the fruit fly $D.~melanogaster$ have shown a transition from a spatially-disordered cytoskeleton, supporting flows with only short-ranged correlations, to an ordered state with a cell-spanning vortical flow. To test the hypothesis that this transition is driven by fluid-structure interactions we study a discrete-filament model and a coarse-grained continuum theory for motors moving on a deformable cytoskeleton, both of which are shown to exhibit a $swirling~instability$ to spontaneous large-scale rotational motion, as observed.

cond-mat.soft↗
arXiv2020

Stress-Induced Dinoflagellate Bioluminescence at the Single Cell Level

One of the characteristic features of many marine dinoflagellates is their bioluminescence, which lights up nighttime breaking waves or seawater sliced by a ship's prow. While the internal biochemistry of light production by these microorganisms is well established, the manner by which fluid shear or mechanical forces trigger bioluminescence is still poorly understood. We report controlled measurements of the relation between mechanical stress and light production at the single-cell level, using high-speed imaging of micropipette-held cells of the marine dinoflagellate $Pyrocystis~lunula$ subjected to localized fluid flows or direct indentation. We find a viscoelastic response in which light intensity depends on both the amplitude and rate of deformation, consistent with the action of stretch-activated ion channels. A phenomenological model captures the experimental observations.

cond-mat.soft↗
arXiv2020

Optimal Design of Multi-Layer Fog Collectors

The growing concerns over desertification have spurred research into technologies aimed at acquiring water from non-traditional sources such as dew, fog, and water vapor. Some of the most promising developments have focused on improving designs to collect water from fog. However, the absence of a shared framework to predict, measure and compare the water collection efficiencies of new prototypes is becoming a major obstacle to progress in the field. We address this problem by providing a general theory to design efficient fog collectors as well as a concrete experimental protocol to furnish our theory with all the necessary parameters to quantify the effective water collection efficiency. We show in particular that multi-layer collectors are required for high fog collection efficiency and that all efficient designs are found within a narrow range of mesh porosity. We support our conclusions with measurements on simple multi-layer harp collectors.

physics.flu-dyn↗
arXiv2020

Stability of dancing Volvox

Biflagellate algal cells of the genus Volvox form spherical colonies that propel themselves, vertically upwards in still fluid, by the coordinated beating of thousands of flagella, that also cause the colonies to rotate about their vertical axes. When they are swimming in a chamber of finite depth, pairs (or more) of Volvox carteri colonies were observed by Drescher et al. [Phys. Rev. Lett. 102, 168101 (2009)] to exhibit hydrodynamic bound states when they are close to a rigid horizontal boundary. When the boundary is above, the colonies are attracted to each other and orbit around each other in a `waltz'; when the boundary is below they perform more complex `minuet' motions. These dances are simulated in the present paper, using a novel `spherical squirmer' model of a colony in which, instead of a time-independent but $θ$-dependent tangential velocity being imposed on the spherical surface (radius $a$; $θ$ is the polar angle), a time-independent and uniform tangential shear stress is applied to the fluid on a sphere of radius $(1+ε)a, ε\ll 1$, where $εa$ represents the length of the flagella. The fluid must satisfy the no-slip condition on the sphere at radius $a$. In addition to the shear stress, the motions depend on two dimensionless parameters that describe the effect of gravity on a colony: $F_g$, proportional to the ratio of the sedimentation speed of a non-swimming colony to its swimming speed, and $G_{bh}$, that represents the fact that colonies are bottom-heavy...

physics.flu-dyn↗
arXiv2019

Subpopulations and Stability in Microbial Communities

In microbial communities, each species often has multiple, distinct phenotypes, but studies of ecological stability have largely ignored this subpopulation structure. Here, we show that such implicit averaging over phenotypes leads to incorrect linear stability results. We then analyze the effect of phenotypic switching in detail in an asymptotic limit and partly overturn classical stability paradigms: abundant phenotypic variation is linearly destabilizing but, surprisingly, a rare phenotype such as bacterial persisters has a stabilizing effect. Finally, we extend these results by showing how phenotypic variation modifies the stability of the system to large perturbations such as antibiotic treatments.

q-bio.PE↗
arXiv2019

Motility and Phototaxis of $Gonium$, the Simplest Differentiated Colonial Alga

Green algae of the $Volvocine$ lineage, spanning from unicellular $Chlamydomonas$ to vastly larger $Volvox$, are models for the study of the evolution of multicellularity, flagellar dynamics, and developmental processes. Phototactic steering in these organisms occurs without a central nervous system, driven solely by the response of individual cells. All such algae spin about a body-fixed axis as they swim; directional photosensors on each cell thus receive periodic signals when that axis is not aligned with the light. The flagella of $Chlamydomonas$ and $Volvox$ both exhibit an adaptive response to such signals in a manner that allows for accurate phototaxis, but in the former the two flagella have distinct responses, while the thousands of flagella on the surface of spherical $Volvox$ colonies have essentially identical behaviour. The planar 16-cell species $Gonium~pectorale$ thus presents a conundrum, for its central 4 cells have a $Chlamydomonas$-like beat that provide propulsion normal to the plane, while its 12 peripheral cells generate rotation around the normal through a $Volvox$-like beat. Here, we combine experiment, theory, and computations to reveal how $Gonium$, perhaps the simplest differentiated colonial organism, achieves phototaxis. High-resolution cell tracking, particle image velocimetry of flagellar driven flows, and high-speed imaging of flagella on micropipette-held colonies show how, in the context of a recently introduced model for $Chlamydomonas$ phototaxis, an adaptive response of the peripheral cells alone leads to photo-reorientation of the entire colony. The analysis also highlights the importance of local variations in flagellar beat dynamics within a given colony, which can lead to enhanced reorientation dynamics.

cond-mat.soft↗
arXiv2019

A theory for the slip and drag of superhydrophobic surfaces with surfactant

Superhydrophobic surfaces (SHSs) have the potential to reduce drag at solid boundaries. However, multiple independent studies have recently shown that small amounts of surfactant, naturally present in the environment, can induce Marangoni forces that increase drag, at least in the laminar regime. To obtain accurate drag predictions, one must solve the mass, momentum, bulk surfactant and interfacial surfactant conservation equations. This requires expensive simulations, thus preventing surfactant from being widely considered in SHS studies. To address this issue, we propose a theory for steady, pressure-driven, laminar, two-dimensional flow in a periodic SHS channel with soluble surfactant. We linearise the coupling between flow and surfactant, under the assumption of small concentration, finding a scaling prediction for the local slip length. To obtain the drag reduction and interfacial shear, we find a series solution for the velocity field by assuming Stokes flow in the bulk and uniform interfacial shear. We find how the slip and drag depend on the nine dimensionless groups that together characterize the surfactant transport near SHSs, the gas fraction and the normalized interface length. Our model agrees with numerical simulations spanning orders of magnitude in each dimensionless group. The simulations also provide the constants in the scaling theory. Our model significantly improves predictions relative to a surfactant-free one, which can otherwise overestimate slip and underestimate drag by several orders of magnitude. Our slip length model can provide the boundary condition in other simulations, thereby accounting for surfactant effects without having to solve the full problem.

physics.flu-dyn↗
arXiv2019

Swimming eukaryotic microorganisms exhibit a universal speed distribution

One approach to quantifying biological diversity consists of characterizing the statistical distribution of specific properties of a taxonomic group or habitat. Microorganisms living in fluid environments, and for whom motility is key, exploit propulsion resulting from a rich variety of shapes, forms, and swimming strategies. Here, we explore the variability of swimming speed for unicellular eukaryotes based on published data. The data naturally partitions into that from flagellates (with a small number of flagella) and from ciliates (with tens or more). Despite the morphological and size differences between these groups, each of the two probability distributions of swimming speed are accurately represented by log-normal distributions, with good agreement holding even to fourth moments. Scaling of the distributions by a characteristic speed for each data set leads to a collapse onto an apparently universal distribution. These results suggest a universal way for ecological niches to be populated by abundant microorganisms.

cond-mat.soft↗
arXiv2019

Interkinetic nuclear migration in the zebrafish retina as a diffusive process

A major hallmark of neural development is the oscillatory movement of nuclei between the apical and basal surfaces of the neuroepithelium during the process of interkinetic nuclear migration (IKNM). Here, we employ long-term, rapid lightsheet and two-photon imaging of zebrafish retinas $in~vivo$ during early development to uncover the physical processes that govern the behavior of nuclei during IKNM. These images allow the capture of reliable tracks of nuclear movements and division during early retinogenesis for many tightly packed nuclei. These tracks are then used to create and test a theory of retinal IKNM as a diffusive process across a nuclear concentration gradient generated by the addition of new nuclei at the apical surface. The analysis reveals the role of nuclear packing at the apical surface on the migration dynamics of nuclei, provides a robust quantitative explanation for the distribution of nuclei across the retina, and may have implications for stochastic fate choice in this system.

physics.bio-ph↗
arXiv2019

Shape-Shifting Polyhedral Droplets

Cooled oil emulsion droplets in aqueous surfactant solution have been observed to flatten into a remarkable host of polygonal shapes with straight edges and sharp corners, but different driving mechanisms - (i) a partial phase transition of the liquid bulk oil into a plastic rotator phase near the droplet interface and (ii) buckling of the interfacially frozen surfactant monolayer enabled by drastic lowering of surface tension - have been proposed. Here, combining experiment and theory, we analyse the hitherto unexplored initial stages of the evolution of these 'shape-shifting' droplets, during which a polyhedral droplet flattens into a polygonal platelet under cooling and gravity. Using reflected-light microscopy, we reveal how icosahedral droplets evolve through an intermediate octahedral stage to flatten into hexagonal platelets. This behaviour is reproduced by a theoretical model of the phase transition mechanism, but the buckling mechanism can only reproduce the flattening if surface tension decreases by several orders of magnitude during cooling so that the flattening is driven by buoyancy. The analysis thus provides further evidence that the first mechanism underlies the 'shape-shifting' phenomena.

cond-mat.soft↗
arXiv2018

Nonlinear and Nonlocal Elasticity in Coarse-Grained Differential-Tension Models of Epithelia

The shapes of epithelial tissues result from a complex interplay of contractile forces in the cytoskeleta of the cells in the tissue, and adhesion forces between them. A host of discrete, cell-based models describe these forces by assigning different surface tensions to the apical, basal, and lateral sides of the cells. These differential-tension models have been used to describe the deformations of epithelia in different living systems, but the underlying continuum mechanics at the scale of the epithelium are still unclear. Here, we derive a continuum theory for a simple differential-tension model of a two-dimensional epithelium and study the buckling of this epithelium under imposed compression. The analysis reveals how the cell-level properties encoded in the differential-tension model lead to linear, nonlinear as well as nonlocal elastic behavior at the continuum level.

cond-mat.soft↗
arXiv2018

Embryonic Inversion in $Volvox~carteri$: The Flipping and Peeling of Elastic Lips

The embryos of the green alga $Volvox~carteri$ are spherical sheets of cells that turn themselves inside out at the close of their development through a programme of cell shape changes. This process of inversion is a model for morphogenetic cell sheet deformations; it starts with four lips opening up at the anterior pole of the cell sheet, flipping over and peeling back to invert the embryo. Experimental studies have revealed that inversion is arrested if some of these cell shape changes are inhibited, but the mechanical basis for these observations has remained unclear. Here, we analyse the mechanics of this inversion by deriving an averaged elastic theory for these lips and we interpret the experimental observations in terms of the mechanics and evolution of inversion.

cond-mat.soft↗