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 $r_\mathrm{s}$ the turbulent velocity becomes equal to the sound velocity. During this substage the boundary $r_\mathrm{s}$ 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 $100M_\odot$) 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 $e^+e^-$ 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