1,174 research outputs found
Viscous evolution of point vortex equilibria: The collinear state
When point vortex equilibria of the 2D Euler equations are used as initial
conditions for the corre- sponding Navier-Stokes equations (viscous), typically
an interesting dynamical process unfolds at short and intermediate time scales,
before the long time single peaked, self-similar Oseen vortex state dom-
inates. In this paper, we describe the viscous evolution of a collinear three
vortex structure that cor- responds to an inviscid point vortex fixed
equilibrium. Using a multi-Gaussian 'core-growth' type of model, we show that
the system immediately begins to rotate unsteadily, a mechanism we attribute to
a 'viscously induced' instability. We then examine in detail the qualitative
and quantitative evolution of the system as it evolves toward the long-time
asymptotic Lamb-Oseen state, showing the sequence of topological bifurcations
that occur both in a fixed reference frame, and in an appropriately chosen
rotating reference frame. The evolution of passive particles in this viscously
evolving flow is shown and interpreted in relation to these evolving streamline
patterns.Comment: 17 pages, 15 figure
Coronavirus peplomer charge heterogeneity
Recent advancements in viral hydrodynamics afford the calculation of the transport properties of particle suspensions from first principles, namely, from the detailed particle shapes. For coronavirus suspensions, for example, the shape can be approximated by beading (i) the spherical capsid and (ii) the radially protruding peplomers. The general rigid bead-rod theory allows us to assign Stokesian hydrodynamics to each bead. Thus, viral hydrodynamics yields the suspension rotational diffusivity, but not without first arriving at a configuration for the cationic peplomers. Prior work considered identical peplomers charged identically. However, a recent pioneering experiment uncovers remarkable peplomer size and charge heterogeneities. In this work, we use energy minimization to arrange the spikes, charged heterogeneously to obtain the coronavirus spike configuration required for its viral hydrodynamics. For this, we use the measured charge heterogeneity. We consider 20 000 randomly generated possibilities for cationic peplomers with formal charges ranging from 30 to 55. We find the configurations from energy minimization of all of these possibilities to be nearly spherically symmetric, all slightly oblate, and we report the corresponding breadth of the dimensionless rotational diffusivity, the transport property around which coronavirus cell attachment revolves.journal articl
Discrete Lie Advection of Differential Forms
In this paper, we present a numerical technique for performing Lie advection
of arbitrary differential forms. Leveraging advances in high-resolution finite
volume methods for scalar hyperbolic conservation laws, we first discretize the
interior product (also called contraction) through integrals over Eulerian
approximations of extrusions. This, along with Cartan's homotopy formula and a
discrete exterior derivative, can then be used to derive a discrete Lie
derivative. The usefulness of this operator is demonstrated through the
numerical advection of scalar fields and 1-forms on regular grids.Comment: Accepted version; to be published in J. FoC
A Geometric Approach Towards Momentum Conservation
In this work, a geometric discretization of the Navier-Stokes equations is
sought by treating momentum as a covector-valued volume-form. The novelty of
this approach is that we treat conservation of momentum as a tensor equation
and describe a higher order approximation to this tensor equation. The
resulting scheme satisfies mass and momentum conservation laws exactly, and
resembles a staggered-mesh finite-volume method. Numerical test-cases to which
the discretization scheme is applied are the Kovasznay flow, and lid-driven
cavity flow
Coronavirus pleomorphism
The coronavirus is always idealized as a spherical capsid with radially protruding spikes. However, histologically, in the tissues of infected patients, capsids in cross section are elliptical, and only sometimes spherical [Neuman et al., “Supramolecular architecture of severe acute respiratory syndrome coronavirus revealed by electron cryomicroscopy,” J Virol, 80, 7918 (2006)]. This capsid ellipticity implies that coronaviruses are oblate or prolate or both. We call this diversity of shapes, pleomorphism. Recently, the rotational diffusivity of the spherical coronavirus in suspension was calculated, from first principles, using general rigid bead-rod theory [Kanso et al., “Coronavirus rotational diffusivity,” Phys Fluids 32, 113101 (2020)]. We did so by beading the spherical capsid and then also by replacing each of its bulbous spikes with a single bead. In this paper, we use energy minimization for the spreading of the spikes, charged identically, over the oblate or prolate capsids. We use general rigid bead-rod theory to explore the role of such coronavirus cross-sectional ellipticity on its rotational diffusivity, the transport property around which its cell attachment revolves. We learn that coronavirus ellipticity drastically decreases its rotational diffusivity, be it oblate or prolate.journal articl
A Simple Attack on Some Clock-Controlled Generators
We present a new approach to edit distance attacks on certain
clock-controlled generators, which applies basic concepts of Graph Theory to
simplify the search trees of the original attacks in such a way that only the
most promising branches are analyzed. In particular, the proposed improvement
is based on cut sets defined on some graphs so that certain shortest paths
provide the edit distances. The strongest aspects of the proposal are that the
obtained results from the attack are absolutely deterministic, and that many
inconsistent initial states of the target registers are recognized beforehand
and avoided during search
Teamwork in the viscous oceanic microscale
© The Author(s), 2021. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Kanso, E. A., Lopes, R. M., Strickler, J. R., Dabiri, J. O., & Costello, J. H. Teamwork in the viscous oceanic microscale. Proceedings of the National Academy of Sciences of the United States of America, 118(29), (2021): e2018193118, https://doi.org/10.1073/pnas.2018193118.Nutrient acquisition is crucial for oceanic microbes, and competitive solutions to solve this challenge have evolved among a range of unicellular protists. However, solitary solutions are not the only approach found in natural populations. A diverse array of oceanic protists form temporary or even long-lasting attachments to other protists and marine aggregates. Do these planktonic consortia provide benefits to their members? Here, we use empirical and modeling approaches to evaluate whether the relationship between a large centric diatom, Coscinodiscus wailesii, and a ciliate epibiont, Pseudovorticella coscinodisci, provides nutrient flux benefits to the host diatom. We find that fluid flows generated by ciliary beating can increase nutrient flux to a diatom cell surface four to 10 times that of a still cell without ciliate epibionts. This cosmopolitan species of diatom does not form consortia in all environments but frequently joins such consortia in nutrient-depleted waters. Our results demonstrate that symbiotic consortia provide a cooperative alternative of comparable or greater magnitude to sinking for enhancement of nutrient acquisition in challenging environments.We are grateful to Y. Garcia for help with organism sampling and sorting. E.A.K. is funded by NSF-2100209, NSF RAISE IOS-2034043 and NIH R01 HL 153622-01A1. R.M.L. is a CNPq research fellow (grant # 310642/2017-5). J.H.C. and J.O.D. are funded by Grant NSF-2100705
The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation
We consider the motion of a planar rigid body in a potential flow with
circulation and subject to a certain nonholonomic constraint. This model is
related to the design of underwater vehicles.
The equations of motion admit a reduction to a 2-dimensional nonlinear
system, which is integrated explicitly. We show that the reduced system
comprises both asymptotic and periodic dynamics separated by a critical value
of the energy, and give a complete classification of types of the motion. Then
we describe the whole variety of the trajectories of the body on the plane.Comment: 25 pages, 7 figures. This article uses some introductory material
from arXiv:1109.321
- …