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

Three-Dimensional Magnetohydrodynamic Simulations of Spherical Accretion

We present three-dimensional numerical magnetohydrodynamic simulations of radiatively inefficient spherical accretion onto a black hole. The simulations are initialized with a Bondi flow, and with a weak, dynamically unimportant, large-scale magnetic field. The magnetic field is amplified as the gas flows in. When the magnetic pressure approaches equipartition with the gas pressure, the field begins to reconnect and the gas is heated up. The heated gas is buoyant and moves outward, causing line stretching of the frozen-in magnetic field. This leads to further reconnection, and more heating and buoyancy-induced motions, so that the flow makes a transition to a state of self-sustained convection. The radial structure of the flow changes dramatically from its initial Bondi profile, and the mass accretion rate onto the black hole decreases significantly. Motivated by the numerical results, we develop a simplified analytical model of a radiatively inefficient spherical flow in which convective transport of energy to large radii plays an important role. In this "convection-dominated Bondi flow" the accretion velocity is highly subsonic and the density varies with radius as ~R^{-1/2} rather than the standard Bondi scaling ~R^{-3/2}. We estimate that the mass accretion rate onto the black hole is significantly less than the Bondi accretion rate. Convection-dominated Bondi flows may be relevant for understanding many astrophysical phenomena, e.g. post-supernova fallback and radiatively inefficient accretion onto supermassive black holes, stellar-mass black holes and neutron stars.Comment: 23 pages, 6 figures, submitted to Ap

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

A variational approach to the stochastic aspects of cellular signal transduction

Cellular signaling networks have evolved to cope with intrinsic fluctuations, coming from the small numbers of constituents, and the environmental noise. Stochastic chemical kinetics equations govern the way biochemical networks process noisy signals. The essential difficulty associated with the master equation approach to solving the stochastic chemical kinetics problem is the enormous number of ordinary differential equations involved. In this work, we show how to achieve tremendous reduction in the dimensionality of specific reaction cascade dynamics by solving variationally an equivalent quantum field theoretic formulation of stochastic chemical kinetics. The present formulation avoids cumbersome commutator computations in the derivation of evolution equations, making more transparent the physical significance of the variational method. We propose novel time-dependent basis functions which work well over a wide range of rate parameters. We apply the new basis functions to describe stochastic signaling in several enzymatic cascades and compare the results so obtained with those from alternative solution techniques. The variational ansatz gives probability distributions that agree well with the exact ones, even when fluctuations are large and discreteness and nonlinearity are important. A numerical implementation of our technique is many orders of magnitude more efficient computationally compared with the traditional Monte Carlo simulation algorithms or the Langevin simulations.Comment: 15 pages, 11 figure

Regularity properties of optimal controls for problems with time-varying state and control constraints

Accepted versio

Magnetic Field Limitations on Advection Dominated Flows

Recent papers discussing advection dominated accretion flows (ADAF) as a solution for astrophysical accretion problems should be treated with some caution because of their uncertain physical basis. The suggestions underlying ADAF involve ignoring the magnetic field reconnection in heating of the plasma flow, assuming electron heating due only to binary Coulomb collisions with ions. Here, we analyze the physical processes in optically thin accretion flows at low accretion rates including the influence of an equipartition turbulent magnetic field. For these conditions there is continuous destruction of magnetic flux by reconnection. The reconnection is expected to significantly heat the electrons which can efficiently emit magnetobremstrahlung radiation. Because of this electron emission, the radiative efficiency of the ADAF is not small. We suggest that the small luminosities of nearby galactic black holes is due to outflows rather than ADAF accretion.Comment: 7 pages, 3 figures, Submitted to Ap

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

Ultra-light Axions: Degeneracies with Massive Neutrinos and Forecasts for Future Cosmological Observations

A generic prediction of string theory is the existence of many axion fields. It has recently been argued that many of these fields should be light and, like the well known QCD axion, lead to observable cosmological consequences. In this paper we study in detail the effect of the so-called string axiverse on large scale structure, focusing on the morphology and evolution of density perturbations, anisotropies in the cosmic microwave background and weak gravitational lensing of distant galaxies. We quantify specific effects that will arise from the presence of the axionic fields and highlight possible degeneracies that may arise in the presence of massive neutrinos. We take particular care understanding the different physical effects and scales that come into play. We then forecast how the string axiverse may be constrained and show that with a combination of different observations, it should be possible to detect a fraction of ultralight axions to dark matter of a few percent.Comment: 24 pages, 16 figures, this version: corrected typos, some comments added, matches published versio

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.