Explicit analytical expression for the condition number of polynomials in power form

2017 ◽  
Author(s):  
Heinz-Joachim Rack
Keyword(s):  
Condition Number ◽  
Analytical Expression ◽  
Explicit Analytical Expression

The autocorrelation function of the queue length process for the two-server Poisson queue

1978 ◽  
Vol 15 (02) ◽  
pp. 447-451
Author(s):  
James M. Hill ◽  
Keith P. Tognetti
Keyword(s):  
Autocorrelation Function ◽  
Queue Length ◽  
Laplace Transforms ◽  
Analytical Expression ◽  
Explicit Analytical Expression

Using Laplace transforms an explicit analytical expression is obtained for the autocorrelation function of the number in the system for the two-server Poisson queue. The method employed may be extended to Poisson queues with more than two servers.

Explicit Analytical Expression for Solar Flux Distribution on an Undeflected Absorber Tube of Parabolic Trough Concentrator Considering Sun-Shape and Optical Errors

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Sourav Khanna ◽  
Vashi Sharma
Keyword(s):  
Flux Distribution ◽  
Computational Effort ◽  
Solar Flux ◽  
Outer Diameter ◽  
Parabolic Trough ◽  
Analytical Expression ◽  
Explicit Analytical Expression ◽  
Aperture Width ◽  
Design Calculations ◽  
Circumferential Nonuniformity

The absorber tube of the parabolic trough receives the concentrated sun-rays only on the portion facing the reflector. It leads to nonuniformity in the temperature of absorber tube. Thus, the material of tube expands differentially and the tube experiences compression and tension in its different parts. It leads to bending of the tube and the glass cover can be broken. The bending can be reduced by (i) reducing the circumferential nonuniformity in absorber's temperature (using material of high thermal conductivity) and (ii) reducing the nonuniformity in solar flux distribution (using appropriate rim angle of trough). In most of the available studies, Monte Carlo Ray Tracing software has been used to calculate the distribution of solar flux and few studies have used analytical approach. In the present work, an explicit analytical expression is derived for finding the distribution of solar flux accounting for the sun-shape and optical errors. Using it, the design calculations can be carried out in significantly lesser time and lesser computational effort. The explicit expression is also useful in validating the results computed by softwares. The methodology has been verified with the already reported results. The effects of optical errors, rim angle, and aperture width of trough on the solar flux distribution and total flux availability for absorber tube have also been studied. From the calculations, it is found that for Schott 2008 PTR70 receiver (absorber tube with 70 mm outer diameter), 126 deg, 135 deg, and 139 deg, respectively, are the appropriate rim angles corresponding to minimum circumferential nonuniformity in solar flux distribution for 3 m, 6 m, and 9 m aperture width of trough. However, 72 deg, 100 deg, and 112 deg, respectively, are the appropriate rim angles corresponding to the maximum solar flux at absorber tube for 3 m, 6 m, and 9 m aperture width of trough. Considering both the circumferential nonuniformity and the total solar flux availability, 100 deg, 120 deg, and 130 deg, respectively, are the best rim angles.

The autocorrelation function of the queue length process for the two-server Poisson queue

1978 ◽  
Vol 15 (2) ◽  
pp. 447-451
Author(s):  
James M. Hill ◽  
Keith P. Tognetti
Keyword(s):  
Autocorrelation Function ◽  
Queue Length ◽  
Laplace Transforms ◽  
Analytical Expression ◽  
Explicit Analytical Expression

Using Laplace transforms an explicit analytical expression is obtained for the autocorrelation function of the number in the system for the two-server Poisson queue. The method employed may be extended to Poisson queues with more than two servers.

scholarly journals ON THE RELATION BETWEEN THE PROPAGATION CONSTANT OF BLOCH SURFACE WAVES AND THE THICKNESS OF THE UPPER LAYER OF A PHOTONIC CRYSTAL

2018 ◽  
Vol 42 (1) ◽  
pp. 22-27 ◽  
Author(s):  
E. A. Bezus ◽  
D. A. Bykov ◽  
L. L. Doskolovich
Keyword(s):  
Photonic Crystal ◽  
Dispersion Relation ◽  
Surface Waves ◽  
Propagation Constant ◽  
Homogeneous Medium ◽  
One Dimensional ◽  
Analytical Expression ◽  
Dimensional Photonic Crystal ◽  
Explicit Analytical Expression ◽  
The Relationship

We consider the derivation of a dispersion relation of Bloch surface waves supported by interfaces between a semi-infinite one-dimensional photonic crystal and a homogeneous medium. From the derived dispersion relation, we obtain an explicit analytical expression that defines the relationship between the propagation constant and the thickness of the upper layer of the photonic crystal.

On the influence of specimen thickness in TEM images of super-conducting vortices

1996 ◽  
Vol 54 ◽  
pp. 724-725
Author(s):  
J. Bonevich ◽  
D. Capacci ◽  
G. Pozzi ◽  
K. Harada ◽  
H. Kasai ◽  
...  
Keyword(s):  
Flux Line ◽  
Analytical Form ◽  
Realistic Model ◽  
Electron Holography ◽  
Specimen Thickness ◽  
Flux Tubes ◽  
Analytical Expression ◽  
Flux Lines ◽  
Normal Core ◽  
Two Parameters

The successful observation of superconducting flux lines (fluxons) in thin specimens both in conventional and high Tc superconductors by means of Lorentz and electron holography methods has presented several problems concerning the interpretation of the experimental results. The first approach has been to model the fluxon as a bundle of flux tubes perpendicular to the specimen surface (for which the electron optical phase shift has been found in analytical form) with a magnetic flux distribution given by the London model, which corresponds to a flux line having an infinitely small normal core. In addition to being described by an analytical expression, this model has the advantage that a single parameter, the London penetration depth, completely characterizes the superconducting fluxon. The obtained results have shown that the most relevant features of the experimental data are well interpreted by this model. However, Clem has proposed another more realistic model for the fluxon core that removes the unphysical limitation of the infinitely small normal core and has the advantage of being described by an analytical expression depending on two parameters (the coherence length and the London depth).

Contrast From Point Defects in The Infinitesimal Approximation

1980 ◽  
Vol 38 ◽  
pp. 350-351
Author(s):  
L. J. Sykes ◽  
J. J. Hren
Keyword(s):  
Electron Microscope ◽  
Point Defects ◽  
Broad Class ◽  
Stacking Fault ◽  
Crystalline Solids ◽  
Dislocation Loops ◽  
Analytical Expression ◽  
Stacking Fault Tetrahedra

In electron microscope studies of crystalline solids there is a broad class of very small objects which are imaged primarily by strain contrast. Typical examples include: dislocation loops, precipitates, stacking fault tetrahedra and voids. Such objects are very difficult to identify and measure because of the sensitivity of their image to a host of variables and a similarity in their images. A number of attempts have been made to publish contrast rules to help the microscopist sort out certain subclasses of such defects. For example, Ashby and Brown (1963) described semi-quantitative rules to understand small precipitates. Eyre et al. (1979) published a catalog of images for BCC dislocation loops. Katerbau (1976) described an analytical expression to help understand contrast from small defects. There are other publications as well.

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