95 research outputs found
Efficient Mixing at low Reynolds numbers using polymer additives
Mixing in fluids is a rapidly developing field of fluid mechanics
\cite{Sreen,Shr,War}, being an important industrial and environmental problem.
The mixing of liquids at low Reynolds numbers is usually quite weak in simple
flows, and it requires special devices to be efficient. Recently, the problem
of mixing was solved analytically for a simple case of random flow, known as
the Batchelor regime \cite{Bat,Kraich,Fal,Sig,Fouxon}. Here we demonstrate
experimentally that very viscous liquids at low Reynolds number, . Here we
show that very viscous liquids containing a small amount of high molecular
weight polymers can be mixed quite efficiently at very low Reynolds numbers,
for a simple flow in a curved channel. A polymer concentration of only 0.001%
suffices. The presence of the polymers leads to an elastic instability
\cite{LMS} and to irregular flow \cite{Ours}, with velocity spectra
corresponding to the Batchelor regime \cite{Bat,Kraich,Fal,Sig,Fouxon}. Our
detailed observations of the mixing in this regime enable us to confirm sevearl
important theoretical predictions: the probability distributions of the
concentration exhibit exponential tails \cite{Fal,Fouxon}, moments of the
distribution decay exponentially along the flow \cite{Fouxon}, and the spatial
correlation function of concentration decays logarithmically.Comment: 11 pages, 5 figure
Characterising epithelial tissues using persistent entropy
In this paper, we apply persistent entropy, a novel topological statistic,
for characterization of images of epithelial tissues. We have found out that
persistent entropy is able to summarize topological and geometric information
encoded by \alpha-complexes and persistent homology. After using some
statistical tests, we can guarantee the existence of significant differences in
the studied tissues.Comment: 12 pages, 7 figures, 4 table
Mechanical Stress Inference for Two Dimensional Cell Arrays
Many morphogenetic processes involve mechanical rearrangement of epithelial
tissues that is driven by precisely regulated cytoskeletal forces and cell
adhesion. The mechanical state of the cell and intercellular adhesion are not
only the targets of regulation, but are themselves likely signals that
coordinate developmental process. Yet, because it is difficult to directly
measure mechanical stress {\it in vivo} on sub-cellular scale, little is
understood about the role of mechanics of development. Here we present an
alternative approach which takes advantage of the recent progress in live
imaging of morphogenetic processes and uses computational analysis of high
resolution images of epithelial tissues to infer relative magnitude of forces
acting within and between cells. We model intracellular stress in terms of bulk
pressure and interfacial tension, allowing these parameters to vary from cell
to cell and from interface to interface. Assuming that epithelial cell layers
are close to mechanical equilibrium, we use the observed geometry of the two
dimensional cell array to infer interfacial tensions and intracellular
pressures. Here we present the mathematical formulation of the proposed
Mechanical Inverse method and apply it to the analysis of epithelial cell
layers observed at the onset of ventral furrow formation in the {\it
Drosophila} embryo and in the process of hair-cell determination in the avian
cochlea. The analysis reveals mechanical anisotropy in the former process and
mechanical heterogeneity, correlated with cell differentiation, in the latter
process. The method opens a way for quantitative and detailed experimental
tests of models of cell and tissue mechanics
Fluid Particle Accelerations in Fully Developed Turbulence
The motion of fluid particles as they are pushed along erratic trajectories
by fluctuating pressure gradients is fundamental to transport and mixing in
turbulence. It is essential in cloud formation and atmospheric transport,
processes in stirred chemical reactors and combustion systems, and in the
industrial production of nanoparticles. The perspective of particle
trajectories has been used successfully to describe mixing and transport in
turbulence, but issues of fundamental importance remain unresolved. One such
issue is the Heisenberg-Yaglom prediction of fluid particle accelerations,
based on the 1941 scaling theory of Kolmogorov (K41). Here we report
acceleration measurements using a detector adapted from high-energy physics to
track particles in a laboratory water flow at Reynolds numbers up to 63,000. We
find that universal K41 scaling of the acceleration variance is attained at
high Reynolds numbers. Our data show strong intermittency---particles are
observed with accelerations of up to 1,500 times the acceleration of gravity
(40 times the root mean square value). Finally, we find that accelerations
manifest the anisotropy of the large scale flow at all Reynolds numbers
studied.Comment: 7 pages, 4 figure
Algebraic charge liquids
High temperature superconductivity emerges in the cuprate compounds upon
changing the electron density of an insulator in which the electron spins are
antiferromagnetically ordered. A key characteristic of the superconductor is
that electrons can be extracted from them at zero energy only if their momenta
take one of four specific values (the `nodal points'). A central enigma has
been the evolution of the zero energy electrons in the metallic state between
the antiferromagnet and the superconductor, and recent experiments yield
apparently contradictory results. The oscillation of the resistance in this
metal as a function of magnetic field indicate that the zero energy electrons
carry momenta which lie on elliptical `Fermi pockets', while ejection of
electrons by high intensity light indicates that the zero energy electrons have
momenta only along arc-like regions. We present a theory of new states of
matter, which we call `algebraic charge liquids', which arise naturally between
the antiferromagnet and the superconductor, and reconcile these observations.
Our theory also explains a puzzling dependence of the density of
superconducting electrons on the total electron density, and makes a number of
unique predictions for future experiments.Comment: 6+8 pages, 2 figures; (v2) Rewritten for broader accessibility; (v3)
corrected numerical error in Eq. (5
Modeling and Inferring Cleavage Patterns in Proliferating Epithelia
The regulation of cleavage plane orientation is one of the key mechanisms driving
epithelial morphogenesis. Still, many aspects of the relationship between local
cleavage patterns and tissue-level properties remain poorly understood. Here we
develop a topological model that simulates the dynamics of a 2D proliferating
epithelium from generation to generation, enabling the exploration of a wide
variety of biologically plausible cleavage patterns. We investigate a spectrum
of models that incorporate the spatial impact of neighboring cells and the
temporal influence of parent cells on the choice of cleavage plane. Our findings
show that cleavage patterns generate “signature” equilibrium
distributions of polygonal cell shapes. These signatures enable the inference of
local cleavage parameters such as neighbor impact, maternal influence, and
division symmetry from global observations of the distribution of cell shape.
Applying these insights to the proliferating epithelia of five diverse
organisms, we find that strong division symmetry and moderate neighbor/maternal
influence are required to reproduce the predominance of hexagonal cells and low
variability in cell shape seen empirically. Furthermore, we present two distinct
cleavage pattern models, one stochastic and one deterministic, that can
reproduce the empirical distribution of cell shapes. Although the proliferating
epithelia of the five diverse organisms show a highly conserved cell shape
distribution, there are multiple plausible cleavage patterns that can generate
this distribution, and experimental evidence suggests that indeed plants and
fruitflies use distinct division mechanisms
Rule-based modelling provides an extendable framework for comparing candidate mechanisms underpinning clathrin polymerisation
Abstract Polymerisation of clathrin is a key process that underlies clathrin-mediated endocytosis. Clathrin-coated vesicles are responsible for cell internalization of external substances required for normal homeostasis and life –sustaining activity. There are several hypotheses describing formation of closed clathrin structures. According to one of the proposed mechanisms cage formation may start from a flat lattice buildup on the cellular membrane, which is later transformed into a curved structure. Creation of the curved surface requires rearrangement of the lattice, induced by additional molecular mechanisms. Different potential mechanisms require a modeling framework that can be easily modified to compare between them. We created an extendable rule-based model that describes polymerisation of clathrin molecules and various scenarios of cage formation. Using Global Sensitivity Analysis (GSA) we obtained parameter sets describing clathrin pentagon closure and the emergence/production and closure of large-size clathrin cages/vesicles. We were able to demonstrate that the model can reproduce budding of the clathrin cage from an initial flat array
On residual stresses and homeostasis: an elastic theory of functional adaptation in living matter
Living matter can functionally adapt to external physical factors by developing internal tensions, easily revealed by cutting experiments. Nonetheless, residual stresses intrinsically have a complex spatial distribution, and destructive techniques cannot be used to identify a natural stress-free configuration. This work proposes a novel elastic theory of pre-stressed materials. Imposing physical compatibility and symmetry arguments, we define a new class of free energies explicitly depending on the internal stresses. This theory is finally applied to the study of arterial remodelling, proving its potential for the non-destructive determination of the residual tensions within biological materials
Mechanisms and mechanics of cell competition in epithelia
When fast-growing cells are confronted with slow-growing cells in a mosaic tissue, the slow-growing cells are often progressively eliminated by apoptosis through a process known as cell competition. The underlying signalling pathways remain unknown, but recent findings have shown that cell crowding within an epithelium leads to the eviction of cells from the epithelial sheet. This suggests that mechanical forces could contribute to cell elimination during cell competition
Mechanics rules cell biology
Cells in the musculoskeletal system are subjected to various mechanical forces in vivo. Years of research have shown that these mechanical forces, including tension and compression, greatly influence various cellular functions such as gene expression, cell proliferation and differentiation, and secretion of matrix proteins. Cells also use mechanotransduction mechanisms to convert mechanical signals into a cascade of cellular and molecular events. This mini-review provides an overview of cell mechanobiology to highlight the notion that mechanics, mainly in the form of mechanical forces, dictates cell behaviors in terms of both cellular mechanobiological responses and mechanotransduction
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