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From discrete to continuum models of three-dimensional deformations in epithelial sheets
International audienceEpithelial tissue, in which cells adhere tightly to each other and to theunderlying substrate, is one of the four major tissue types in adultorganisms. In embryos, epithelial sheets serve as versatile substratesduring the formation of developing organs. Some aspects of epithelialmorphogenesis can be adequately described using vertex models, in which thetwo-dimensional arrangement of epithelial cells is approximated by apolygonal lattice with an energy that has contributions reflecting theproperties of individual cells and their interactions. Previous studieswith such models have largely focused on dynamics confined to two spatialdimensions and analyzed them numerically. We show how these models can beextended to account for three-dimensional deformations and studiedanalytically. Starting from the extended model, we derive a continuumplate description of cell sheets, in which the effective tissue properties,such as bending rigidity, are related explicitly to the parameters of thevertex model. To derive the continuum plate model, we duly take intoaccount a microscopic shift between the two sublattices of the hexagonalnetwork, which has been ignored in previous work. As an application of thecontinuum model, we analyze tissue buckling by a line tension applied alonga circular contour, a simplified set-up relevant to several situations inthe developmental context. The buckling thresholds predicted by thecontinuum description are in good agreement with the results of directstability calculations based on the vertex model. Our results establish adirect connection between discrete and continuum descriptions of cellsheets and can be used to probe a wide range of morphogenetic processes inepithelial tissues
Effect of Distributed Photovoltaic Generation on the Voltage Magnitude in a Self-Contained Power Supply System
A promising way to increase the technical and economic characteristics of standalone power supply systems is to incorporate renewable energy installations in their structure. This saves fuel and extends the operational life of diesel power stations. The most common option is a hybrid system with photovoltaic power stations incorporated into the local network of the diesel power station. This paper deals with the dependence of the deflection voltage and power losses in the electric power transmission line on the graphs of electrical loads, the parameters of elements of the power supply system, connection points and the capacity of distributed photovoltaic power stations. Research has been carried out on the common low-voltage power supply systems of the radial type (0.4 kV) with an installed capacity of up to 100 kW. The studies have been conducted by simulating the operating modes of hybrid power systems of various configurations. As a result of these studies recommendations to reduce losses and voltage variations in the network by selecting the power and photovoltaic power connection points have been put forward
Trans-sonic propeller stage
We follow the approach used by Davies and Pringle (1981) and discuss the
trans-sonic substage of the propeller regime. This substage is intermediate
between the supersonic and subsonic propeller substages. In the trans-sonic
regime an envelope around a magnetosphere of a neutron star passes through a
kind of a reorganization process. The envelope in this regime consists of two
parts. In the bottom one turbulent motions are subsonic. Then at some distance
the turbulent velocity becomes equal to the sound velocity.
During this substage the boundary propagates outwards till it
reaches the outer boundary, and so the subsonic regime starts.
We found that the trans-sonic substage is unstable, so the transition between
supersonic and subsonic substages proceeds on the dynamical time scale. For
realistic parameters this time is in the range from weeks to years.Comment: 8 pages with figures, submitted to Astron. Astroph. Transaction
Self-similar dynamics of morphogen gradients
We discovered a class of self-similar solutions in nonlinear models
describing the formation of morphogen gradients, the concentration fields of
molecules acting as spatial regulators of cell differention in developing
tissues. These models account for diffusion and self-induced degration of
locally produced chemical signals. When production starts, the signal
concentration is equal to zero throughout the system. We found that in the
limit of infinitely large signal production strength the solution of this
problem is given by the product of the steady state concentration profile and a
function of the diffusion similarity variable. We derived a nonlinear boundary
value problem satisfied by this function and used a variational approach to
prove that this problem has a unique solution in a natural setting. Using the
asymptotic behavior of the solutions established by the analysis, we
constructed these solutions numerically by the shooting method. Finally, we
demonstrated that the obtained solutions may be easily approximated by simple
analytical expressions, thus providing an accurate global characterization of
the dynamics in an important class of non-linear models of morphogen gradient
formation. Our results illustrate the power of analytical approaches to
studying nonlinear models of biophysical processes.Comment: 17 pages, 5 figure
Stellar-Mass Black Holes in the Solar Neighborhood
We search for nearby, isolated, accreting, ``stellar-mass'' (3 to
) black holes. Models suggest a synchrotron spectrum in visible
wavelengths and some emission in X-ray wavelengths. Of 3.7 million objects in
the Sloan Digital Sky Survey Early Data Release, about 150,000 objects have
colors and properties consistent with such a spectrum, and 87 of these objects
are X-ray sources from the ROSAT All Sky Survey. Thirty-two of these have been
confirmed not to be black-holes using optical spectra. We give the positions
and colors of these 55 black-hole candidates, and quantitatively rank them on
their likelihood to be black holes. We discuss uncertainties the expected
number of sources, and the contribution of blackholes to local dark matter.Comment: Replaced with version accepted by ApJ. 40 pages, 8 figure
Effect of Distributed Photovoltaic Generation on the Voltage Magnitude in a Self-Contained Power Supply System
A promising way to increase the technical and economic characteristics of standalone power supply systems is to incorporate renewable energy installations in their structure. This saves fuel and extends the operational life of diesel power stations. The most common option is a hybrid system with photovoltaic power stations incorporated into the local network of the diesel power station. This paper deals with the dependence of the deflection voltage and power losses in the electric power transmission line on the graphs of electrical loads, the parameters of elements of the power supply system, connection points and the capacity of distributed photovoltaic power stations. Research has been carried out on the common low-voltage power supply systems of the radial type (0.4 kV) with an installed capacity of up to 100 kW. The studies have been conducted by simulating the operating modes of hybrid power systems of various configurations. As a result of these studies recommendations to reduce losses and voltage variations in the network by selecting the power and photovoltaic power connection points have been put forward
Spherically Symmetric Accretion Flows: Minimal Model with MHD Turbulence
The first spherical accretion model was developed 55 years ago, but the
theory is yet far from being complete. The real accretion flow was found to be
time-dependent and turbulent. This paper presents the minimal MHD spherical
accretion model that separately deals with turbulence. Treatment of turbulence
is based on simulations of several regimes of collisional MHD. The effects of
freezing-in amplification, dissipation, dynamo action, isotropization, and
constant magnetic helicity are self-consistently included. The assumptions of
equipartition and magnetic field isotropy are released. Correct dynamics of
magnetized flow is calculated. Diffusion, convection, and radiation are not
accounted for. Two different types of Radiatively Inefficient accretion flows
are found: a transonic non-rotating flow (I), a flow with effective transport
of angular momentum outward (II). Non-rotating flow has an accretion rate
several times smaller than Bondi rate, because turbulence inhibits accretion.
Flow with angular momentum transport has accretion rate about 10-100 times
smaller than Bondi rate. The effects of highly helical turbulence, states of
outer magnetization, and different equations of state are discussed. The flows
were found to be convectively stable on average, despite gas entropy increases
inward. The proposed model has a small number of free parameters and the
following attractive property. Inner density in the non-rotating magnetized
flow was found to be several times lower than density in a non-magnetized
accretion. Still several times lower density is required to explain the
observed low IR luminosity and low Faraday rotation measure of accretion onto
Sgr A*.Comment: Accepted for publication in ApJS. 52 pages, 7 figure
THE PECULIARITIES OF CEREBRAL BLOOD FLOW IN PATIENTS WITH CHRONIC HEPATITIS
Aim. To study extra- and intracranial hemodynamics in patients with chronic hepatitis of different activity.Material and methods. Ultrasonography of the cerebral blood flow was performed in 576 patients with chronic hepatitis.Results. Contralateral hemyspherical asymmetry (more than 30 %) of the maximum linear rate of blood flow in the medium cerebral arteries and decrease in resistance index (0,55±0,09) and pulsativity index (1,34±0,66) were found in 33,8 % of patients with chronic hepatitis of high activity. Collateral blood flow reduction through connecting arteries of Willis circle was revealed in 13,8 % of patients. The tortuosity of arteries and thickening of intima-media complex was found in patients with chronic hepatitis (mainly of high activity). It leads to decline of cerebral blood flow.Conclusion. Symptomatic and asymptomatic cerebral blood flow disturbances were observed in 23,2% and 38,8% of patients with active chronic hepatitis respectively
On the structure of the burst and afterglow of Gamma-Ray Bursts I: the radial approximation
We have proposed three paradigms for the theoretical interpretation of
gamma-ray bursts (GRBs). (1) The relative space-time transformation (RSTT)
paradigm emphasizes how the knowledge of the entire world-line of the source
from the moment of gravitational collapse is a necessary condition to interpret
GRB data. (2) The interpretation of the burst structure (IBS) paradigm
differentiates in all GRBs between an injector phase and a beam-target phase.
(3) The GRB-supernova time sequence (GSTS) paradigm introduces the concept of
induced supernova explosion in the supernovae-GRB association. These three
paradigms are illustrated using our theory based on the vacuum polarization
process occurring around an electromagnetic black hole (EMBH theory) and using
GRB 991216 as a prototype. We illustrate the five fundamental eras of the EMBH
theory: the self acceleration of the pair-electromagnetic plasma (PEM
pulse), its interaction with the baryonic remnant of the progenitor star (PEMB
pulse). We then study the approach of the PEMB pulse to transparency, the
emission of the proper GRB (P-GRB) and its relation to the ``short GRBs''.
Finally the three different regimes of the afterglow are described within the
fully radiative and radial approximations. The best fit of the theory leads to
an unequivocal identification of the ``long GRBs'' as extended emission
occurring at the afterglow peak (E-APE). The relative intensities, the time
separation and the hardness ratio of the P-GRB and the E-APE are used as
distinctive observational test of the EMBH theory and the excellent agreement
between our theoretical predictions and the observations are documented. The
afterglow power-law indexes in the EMBH theory are compared and contrasted with
the ones in the literature, and no beaming process is found for GRB 991216.Comment: 96 pages, 40 figures, to appear on Int. Journ. Mod. Phys.
Three-dimensional MHD Simulations of Radiatively Inefficient Accretion Flows
We present three-dimensional MHD simulations of rotating radiatively
inefficient accretion flows onto black holes. In the simulations, we
continuously inject magnetized matter into the computational domain near the
outer boundary, and we run the calculations long enough for the resulting
accretion flow to reach a quasi-steady state. We have studied two limiting
cases for the geometry of the injected magnetic field: pure toroidal field and
pure poloidal field. In the case of toroidal field injection, the accreting
matter forms a nearly axisymmetric, geometrically-thick, turbulent accretion
disk. The disk resembles in many respects the convection-dominated accretion
flows found in previous numerical and analytical investigations of viscous
hydrodynamic flows. Models with poloidal field injection evolve through two
distinct phases. In an initial transient phase, the flow forms a relatively
flattened, quasi-Keplerian disk with a hot corona and a bipolar outflow.
However, when the flow later achieves steady state, it changes in character
completely. The magnetized accreting gas becomes two-phase, with most of the
volume being dominated by a strong dipolar magnetic field from which a thermal
low-density wind flows out. Accretion occurs mainly via narrow slowly-rotating
radial streams which `diffuse' through the magnetic field with the help of
magnetic reconnection events.Comment: 35 pages including 3 built-in plots and 14 separate jpg-plots;
version accepted by Ap
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