169 research outputs found
Antispiral waves are sources in oscillatory reaction-diffusion media
Spiral and antispiral waves are studied numerically in two examples of
oscillatory reaction-diffusion media and analytically in the corresponding
complex Ginzburg-Landau equation (CGLE). We argue that both these structures
are sources of waves in oscillatory media, which are distinguished only by the
sign of the phase velocity of the emitted waves. Using known analytical results
in the CGLE, we obtain a criterion for the CGLE coefficients that predicts
whether antispirals or spirals will occur in the corresponding
reaction-diffusion systems. We apply this criterion to the FitzHugh-Nagumo and
Brusselator models by deriving the CGLE near the Hopf bifurcations of the
respective equations. Numerical simulations of the full reaction-diffusion
equations confirm the validity of our simple criterion near the onset of
oscillations. They also reveal that antispirals often occur near the onset and
turn into spirals further away from it. The transition from antispirals to
spirals is characterized by a divergence in the wavelength. A tentative
interpretaion of recent experimental observations of antispiral waves in the
Belousov-Zhabotinsky reaction in a microemulsion is given.Comment: 10 pages, 8 figures, submitted to J. Phys. Chem. B on Feb. 20, 2004.
A short account of the spiral-antispiral criterion has been given in PRL (see
http://link.aps.org/abstract/PRL/v92/e089801
Doppler Effect of Nonlinear Waves and Superspirals in Oscillatory Media
Nonlinear waves emitted from a moving source are studied. A meandering spiral
in a reaction-diffusion medium provides an example, where waves originate from
a source exhibiting a back-and-forth movement in radial direction. The periodic
motion of the source induces a Doppler effect that causes a modulation in
wavelength and amplitude of the waves (``superspiral''). Using the complex
Ginzburg-Landau equation, we show that waves subject to a convective Eckhaus
instability can exhibit monotonous growth or decay as well as saturation of
these modulations away from the source depending on the perturbation frequency.
Our findings allow a consistent interpretation of recent experimental
observations concerning superspirals and their decay to spatio-temporal chaos.Comment: 4 pages, 4 figure
Convective and absolute Eckhaus instability leading to modulated waves in a finite box
We report experimental study of the secondary modulational instability of a
one-dimensional non-linear traveling wave in a long bounded channel. Two
qualitatively different instability regimes involving fronts of spatio-temporal
defects are linked to the convective and absolute nature of the instability.
Both transitions appear to be subcritical. The spatio-temporal defects control
the global mode structure.Comment: 5 pages, 7 figures (ReVTeX 4 and amsmath.sty), final versio
Model evaluation for glycolytic oscillations in yeast biotransformations of xenobiotics
Anaerobic glycolysis in yeast perturbed by the reduction of xenobiotic
ketones is studied numerically in two models which possess the same topology
but different levels of complexity. By comparing both models' predictions for
concentrations and fluxes as well as steady or oscillatory temporal behavior we
answer the question what phenomena require what kind of minimum model
abstraction. While mean concentrations and fluxes are predicted in agreement by
both models we observe different domains of oscillatory behavior in parameter
space. Generic properties of the glycolytic response to ketones are discussed
Quantification of Nematic Cell Polarity in Three-dimensional Tissues
How epithelial cells coordinate their polarity to form functional tissues is
an open question in cell biology. Here, we characterize a unique type of
polarity found in liver tissue, nematic cell polarity, which is different from
vectorial cell polarity in simple, sheet-like epithelia. We propose a
conceptual and algorithmic framework to characterize complex patterns of
polarity proteins on the surface of a cell in terms of a multipole expansion.
To rigorously quantify previously observed tissue-level patterns of nematic
cell polarity (Morales-Navarette et al., eLife 8:e44860, 2019), we introduce
the concept of co-orientational order parameters, which generalize the known
biaxial order parameters of the theory of liquid crystals. Applying these
concepts to three-dimensional reconstructions of single cells from
high-resolution imaging data of mouse liver tissue, we show that the axes of
nematic cell polarity of hepatocytes exhibit local coordination and are aligned
with the biaxially anisotropic sinusoidal network for blood transport. Our
study characterizes liver tissue as a biological example of a biaxial liquid
crystal. The general methodology developed here could be applied to other
tissues or in-vitro organoids.Comment: 27 pages, 9 color figure
Flat Spacetime Vacuum in Loop Quantum Gravity
We construct a state in the loop quantum gravity theory with zero
cosmological constant, which should correspond to the flat spacetime vacuum
solution. This is done by defining the loop transform coefficients of a flat
connection wavefunction in the holomorphic representation which satisfies all
the constraints of quantum General Relativity and it is peaked around the flat
space triads. The loop transform coefficients are defined as spin foam state
sum invariants of the spin networks embedded in the spatial manifold for the
SU(2) quantum group. We also obtain an expression for the vacuum wavefunction
in the triad represntation, by defining the corresponding spin networks
functional integrals as SU(2) quantum group state sums.Comment: 20 pages, 6 figure
Mutual Zonated Interactions of Wnt and Hh Signaling Are Orchestrating the Metabolism of the Adult Liver in Mice and Human
The Hedgehog (Hh) and Wnt/β-Catenin (Wnt) cascades are morphogen pathways whose pronounced influence on adult liver metabolism has been identified in recent years. How both pathways communicate and control liver metabolic functions are largely unknown. Detecting core components of Wnt and Hh signaling and mathematical modeling showed that both pathways in healthy liver act largely complementary to each other in the pericentral (Wnt) and the periportal zone (Hh) and communicate mainly by mutual repression. The Wnt/Hh module inversely controls the spatiotemporal operation of various liver metabolic pathways, as revealed by transcriptome, proteome, and metabolome analyses. Shifting the balance to Wnt (activation) or Hh (inhibition) causes pericentralization and periportalization of liver functions, respectively. Thus, homeostasis of the Wnt/Hh module is essential for maintaining proper liver metabolism and to avoid the development of certain metabolic diseases. With caution due to minor species-specific differences, these conclusions may hold for human liver as well
Accelerated cell divisions drive the outgrowth of the regenerating spinal cord in axolotls
Axolotls are unique in their ability to regenerate the spinal cord. However, the mechanisms that underlie this phenomenon remain poorly understood. Previously, we showed that regenerating stem cells in the axolotl spinal cord revert to a molecular state resembling embryonic neuroepithelial cells and functionally acquire rapid proliferative divisions (Rodrigo Albors et al., 2015). Here, we refine the analysis of cell proliferation in space and time and identify a high- proliferation zone in the regenerating spinal cord that shifts posteriorly over time. By tracking sparsely-labeled cells, we also quantify cell influx into the regenerate. Taking a mathematical modeling approach, we integrate these quantitative datasets of cell proliferation, neural stem cell activation and cell influx, to predict regenerative tissue outgrowth. Our model shows that while cell influx and neural stem cell activation play a minor role, the acceleration of the cell cycle is the major driver of regenerative spinal cord outgrowth in axolotls.Facultad de Ciencias ExactasInstituto de FĂsica de LĂquidos y Sistemas BiolĂłgico
Forecasting the SST space-time variability of the Alboran Sea with genetic algorithms
We propose a nonlinear ocean forecasting technique based on a combination of
genetic algorithms and empirical orthogonal function (EOF) analysis. The method
is used to forecast the space-time variability of the sea surface temperature
(SST) in the Alboran Sea. The genetic algorithm finds the equations that best
describe the behaviour of the different temporal amplitude functions in the EOF
decomposition and, therefore, enables global forecasting of the future
time-variability.Comment: 15 pages, 3 figures; latex compiled with agums.st
SPIRAL INSTABILITIES IN PERIODICALLY FORCED EXTENDED OSCILLATORY MEDIA
We investigate two instabilities of spiral waves in oscillatory media subject to different types of forcing using the complex Ginzburg-Landau equation. First, the transition of spiral waves via so-called superspirals to spatio-temporal chaos is related to a coexistence of the Eckhaus instability of the wave field and the intrinsic oscillatory meandering instability of the spiral core. Second, resonantly forced oscillatory media are shown to possess a novel scenario of spiral breakup. Bifurcation analysis and linear stability analysis yield explanations for the phenomenology observed by direct simulations
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