scholarly journals The system of powers of conformal mappings and biorthogonal to them systems of the functions

2017 ◽  
pp. 31-44
Author(s):  
Halyna Ivasyk
Keyword(s):  
Conformal Mappings ◽  
Exponential Dependence ◽  
Summation Index

In this article we review the methods of power summation of factors. The degree of factors which are arbitrary powers of summation indices are considered. We show that using the Poisson-Abel method only those series can be summarized the order of member increase of which is proportional to the exponent depending on the summation index. At the same time the Gauss-Weierstrass method and other power factors methods can be also applied to the series the terms of which increase in proportion to the exponential dependence of the indices summation.

Behavior of copper in CdGeAs2 crystals

2002 ◽  
Vol 719 ◽  
Author(s):  
Valeriy G. Voevodin ◽  
Olga V. Voevodina ◽  
Svetlana A. Bereznaya ◽  
Zoya V. Korotchenko ◽  
Melvin C. Ohmer ◽  
...  
Keyword(s):  
Exponential Dependence ◽  
Saturation Solubility ◽  
Diffusion Temperature

AbstractWe present an investigation of the diffusion and melt doping of Cu in CdGeAs2. Cu was found to be an acceptor, its introduction in the melt allowed the controlled introduction of holes from ∼8·1016 cm-3 to ∼1·1018 cm -3. Introduction of Cu from the melt was also found to improve the homogeneity of the crystal. The saturation solubility of Cu introduced via diffusion doping was found to have an exponential dependence on the diffusion temperature, from 723 K to 873 K, obeying the equation N = N0 exp (- δH / kT) with the parameters N0 = 6.10+19 cm-3, δH = 0.3 eV, and k equal to Boltzman's constant. From 873 K to 923 K, the saturation solubility was found to decrease exponentially with temperature.

Can the mass balance of the entire glacier area of the Tien Shan be estimated?

1992 ◽  
Vol 16 ◽  
pp. 173-179
Author(s):  
M.B. Dyurgerov ◽  
M.G. Kunakhovitch ◽  
V.N. Mikhalenko ◽  
A. M. Sokalskaya ◽  
V. A. Kuzmichenok
Keyword(s):  
Mass Balance ◽  
Vertical Profile ◽  
River Basins ◽  
Annual Runoff ◽  
Snow Accumulation ◽  
Tien Shan ◽  
Exponential Dependence ◽  
Glacier Area ◽  
Equilibrium Line Altitude ◽  
Boundary Area

The total area of glacierization of the Tien Shan in the boundary area of the USSR is about 8000 km2. The computation of mass balance was determined for this area in 12 river basins.In computation procedure, the vertical profile of snow accumulation in these regions and exponential dependence of variation of ablation with altitude are used. Thus the mass balance in each basin, bn, was calculated on the basis of these curves and represented in its relation with the equilibrium line altitude (ELA). It is shown that the relation ELA = f(bn) is linear when the range of bn values is close to zero, and in all altitude intervals this relation can be described by hypsographic curves, in all basins bn positive up to an ELA elevation of 3450 to 3500 m a.s.l. For average annual altitude of ELA, bn is negative for all regions. So the glaciers of these mountains add about 4 km3 of water to the total annual runoff.

scholarly journals Three-component modelling of C-rich AGB star winds – V. Effects of frequency-dependent radiative transfer including drift★

2020 ◽  
Vol 499 (2) ◽  
pp. 1531-1560
Author(s):  
Christer Sandin ◽  
Lars Mattsson
Keyword(s):  
Radiative Transfer ◽  
Mass Loss ◽  
Density Ratio ◽  
Mie Scattering ◽  
Speed Ratio ◽  
Exponential Dependence ◽  
Frequency Dependent ◽  
Wind Velocities ◽  
Drift Models ◽  
Loss Rates

ABSTRACT Stellar winds of cool carbon stars enrich the interstellar medium with significant amounts of carbon and dust. We present a study of the influence of two-fluid flow on winds where we add descriptions of frequency-dependent radiative transfer (RT). Our radiation hydrodynamic models in addition include stellar pulsations, grain growth and ablation, gas-to-dust drift using one mean grain size, dust extinction based on both the small particle limit (SPL) and Mie scattering, and an accurate numerical scheme. We calculate models at high spatial resolution using 1024 gridpoints and solar metallicities at 319 frequencies, and we discern effects of drift by comparing drift models to non-drift models. Our results show differences of up to 1000 per cent in comparison to extant results. Mass-loss rates and wind velocities of drift models are typically, but not always, lower than in non-drift models. Differences are larger when Mie scattering is used instead of the SPL. Amongst other properties, the mass-loss rates of the gas and dust, dust-to-gas density ratio, and wind velocity show an exponential dependence on the dust-to-gas speed ratio. Yields of dust in the least massive winds increase by a factor 4 when drift is used. We find drift velocities in the range $10\!-\!67\, \mbox{km}\, \mbox{s}^{-1}$, which is drastically higher than in our earlier works that use grey RT. It is necessary to include an estimate of drift velocities to reproduce high yields of dust and low wind velocities.

scholarly journals Analytical Solutions of Upper Convected Maxwell Fluid with Exponential Dependence of Viscosity under the Influence of Pressure

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 334
Author(s):  
Constantin Fetecau ◽  
Dumitru Vieru ◽  
Tehseen Abbas ◽  
Rahmat Ellahi
Keyword(s):  
Fluid Motion ◽  
Maxwell Fluid ◽  
Newtonian Fluids ◽  
Exponential Dependence ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Parallel Plates ◽  
Pressure Dependent Viscosity ◽  
Laplace Transform Technique ◽  
Dependent Viscosity

Some unsteady motions of incompressible upper-convected Maxwell (UCM) fluids with exponential dependence of viscosity on the pressure are analytically studied. The fluid motion between two infinite horizontal parallel plates is generated by the lower plate, which applies time-dependent shear stresses to the fluid. Exact expressions, in terms of standard Bessel functions, are established both for the dimensionless velocity fields and the corresponding non-trivial shear stresses using the Laplace transform technique and suitable changes of the unknown function and the spatial variable in the transform domain. They represent the first exact solutions for unsteady motions of non-Newtonian fluids with pressure-dependent viscosity. The similar solutions corresponding to the flow of the same fluids due to an exponential shear stress on the boundary as well as the solutions of ordinary UCM fluids performing the same motions are obtained as limiting cases of present results. Furthermore, known solutions for unsteady motions of the incompressible Newtonian fluids with/without pressure-dependent viscosity induced by oscillatory or constant shear stresses on the boundary are also obtained as limiting cases. Finally, the influence of physical parameters on the fluid motion is graphically illustrated and discussed. It is found that fluids with pressure-dependent viscosity flow are slower when compared to ordinary fluids.

Shear degradation resistance of star poly(ethyleneimine) - polyacrylamides during elongational flow

e-Polymers ◽  
2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Ming Duan ◽  
Shenwen Fang ◽  
Liehui Zhang ◽  
Fuxiao Wang ◽  
Peng Zhang ◽  
...  
Keyword(s):  
Shear Rate ◽  
Aqueous Solutions ◽  
Relative Viscosity ◽  
Reduction Rate ◽  
Elongational Flow ◽  
Exponential Dependence ◽  
Distilled Water ◽  
Shear Stability ◽  
Low Viscosity ◽  
Shear Degradation

AbstractAn experimental study of the flow-induced scission behaviour of four star hydrolyzed polyacrylamides (HPMA) with different arms during planar elongational flow in a cross-slot flow cell is described. The results showed that the shear stability of linear HPAM in distilled water was not essentially different from star HPAM. Polymer scission was not observed in either system in a shear rate range from 20,000 to 100,000s-1, which can be attributed to the strong polyelectrolyte behaviour of HPAM in distilled water. However, at the same shear rate, the star HPAMs exhibited superior shear stability in comparison to the linear HPAMs in aqueous solutions containing NaCl (CNaCl=0.2-1.0%wt) and, in particular, the initial reduction rate of relative viscosity (R) decreased with the degree of branching of the HPAMs. In addition, it was found that the R of five HPAMs in NaCl aqueous solutions exhibited an exponential dependence on shear rate, in which the coefficient C1 can be used to quantitatively evaluate shear stability. In star HPAM NaCl aqueous solutions, the increase of R with shear rate is very likely due to the decrease of the hydrodynamic radius (Rh) of these HPAMs, while the increase of R with NaCl concentrations can be attributed to the relatively low viscosity of these polymers at high NaCl concentrations.

scholarly journals Conformal mapping of the Misner–Sharp mass from gravitational collapse

2016 ◽  
Vol 25 (07) ◽  
pp. 1650081 ◽  
Author(s):  
Fayçal Hammad
Keyword(s):  
Conformal Mapping ◽  
Gravitational Collapse ◽  
Conformal Transformation ◽  
Conformal Mappings ◽  
Conformal Transformations ◽  
Theories Of Gravity ◽  
Definition Of ◽  
Geometric Definition

The conformal transformation of the Misner–Sharp mass is reexamined. It has recently been found that this mass does not transform like usual masses do under conformal mappings of spacetime. We show that when it comes to conformal transformations, the widely used geometric definition of the Misner–Sharp mass is fundamentally different from the original conception of the latter. Indeed, when working within the full hydrodynamic setup that gave rise to that mass, i.e. the physics of gravitational collapse, the familiar conformal transformation of a usual mass is recovered. The case of scalar–tensor theories of gravity is also examined.

Wavelength and threshold current variation in inhomogeneously pumped InGaAs/AlGaAs single and double quantum well ridge wave-guide lasers

1992 ◽  
Vol 70 (10-11) ◽  
pp. 908-913
Author(s):  
K. A. McGreer ◽  
D. Moss ◽  
R. L. Williams ◽  
M. Dion ◽  
D. Landheer
Keyword(s):  
Quantum Well ◽  
Threshold Current ◽  
Wave Guide ◽  
Double Quantum ◽  
Wavelength Shift ◽  
Exponential Dependence ◽  
Lasing Wavelength ◽  
Output Wavelength ◽  
Double Quantum Well ◽  
Current Variation

We investigate the wavelength and threshold current variation with passive wave-guide length in inhomogeneously pumped single and double quantum well InGaAs/AlGaAs strained layer ridge wave-guide lasers. We observe a linear and extremely low increase in threshold current with unpumped length, both for single and double quantum well lasers. A large red shift in the lasing wavelength as the unpumped length is increased is also observed. We present a model, based on absorption saturation in the unpumped section, which describes both the wavelength shift and the threshold current variation. The increase in threshold current that we observe is much smaller than results reported in the literature for GaAs/AlGaAs lasers, where a large exponential dependence was attributed to gain saturation in the pumped section. Because the threshold current does not dramatically vary with unpumped length for our lasers, this is a potentially useful technique for shifting the output wavelength of the laser. Finally, we investigate the wavelength tuning behavior of lasers having two segments pumped with different currents. A wavelength tunability of ~13 nm for the DQW laser was observed.

Conformal mappings of a once-holed torus

1995 ◽  
Vol 66 (1) ◽  
pp. 117-136 ◽  
Author(s):  
Makoto Masumoto
Keyword(s):  
Conformal Mappings
Sign in / Sign up

Export Citation Format

Share Document