239,381 research outputs found
On the Inverse Problem Relative to Dynamics of the w Function
In this paper we shall study the inverse problem relative to dynamics of the
w function which is a special arithmetic function and shall get some results.Comment: 11 page
Local molecular field theory for effective attractions between like charged objects in systems with strong Coulomb interactions
Strong short ranged positional correlations involving counterions can induce
a net attractive force between negatively charged strands of DNA, and lead to
the formation of ion pairs in dilute ionic solutions. But the long range of the
Coulomb interactions impedes the development of a simple local picture. We
address this general problem by mapping the properties of a nonuniform system
with Coulomb interactions onto those of a simpler system with short ranged
intermolecular interactions in an effective external field that accounts for
the averaged effects of appropriately chosen long ranged and slowly varying
components of the Coulomb interactions. The remaining short ranged components
combine with the other molecular core interactions and strongly affect pair
correlations in dense or strongly coupled systems. We show that pair
correlation functions in the effective short ranged system closely resemble
those in the uniform primitive model of ionic solutions, and illustrate the
formation of ion pairs and clusters at low densities. The theory accurately
describes detailed features of the effective attraction between two equally
charged walls at strong coupling and intermediate separations of the walls. New
analytical results for the minimal coupling strength needed to get any
attraction and for the separation where the attractive force is a maximum are
presented.Comment: 8 pages, 5 figures. To be published in PNA
Temperature effect on space charge dynamics in XLPE insulation
This paper reports on space charge evolution in crosslinked polyethylene (XLPE) planar samples approximately 1.20 mm thick subjected to electric stress level of 30 kVdc/mm under four temperature 25 oC, 50 oC, 70 oC and 90 oC for 24 hours. Space charge profiles in both as-received and degassed samples were measured using the laser induced pressure pulse (LIPP) technique. The dc threshold stresses at which space charge initiates are greatly affected by testing temperatures. The results suggest that testing temperature has numerous effects on space charge dynamics such as enhancement of ionic dissociation of polar crosslinked by-products, charge injection, charge mobility and electrical conductivity. Space charge distributions of very different nature were seen at lower temperatures when comparing the results of as-received samples with degassed samples. However at higher temperature, the space charge distribution took the same form, although of lower concentration in degassed samples. Space charge distributions are dominated by positive charge when tested at high temperatures regardless of sample treatment and positive charge propagation enhances as testing temperature increases. This can be a major cause of concern as positive charge propagation has been reported to be related to insulation breakdown
The effect of degassing on morphology and space charge
It is believed that space charge buildup in cross-linked polyethylene (XLPE) insulation is the main cause for premature failure of underground power cables. The space charge activities in XLPE depend on many factors such as additives, material treatment, ambient temperature, insulator/electrode interface, etc. Degassing is one of the material treatment process commonly employ in cable manufacturing to improve insulation performance. In this paper, investigation on the effect of degassing period has on the morphology and space charge was carried out. Planar XLPE samples of the same composite were subjected to different degassing time. It is discovered that apart from removing volatile by-products, degassing also anneal XLPE material; changing the morphology as a result
Painlev\'e V and time dependent Jacobi polynomials
In this paper we study the simplest deformation on a sequence of orthogonal
polynomials, namely, replacing the original (or reference) weight
defined on an interval by It is a well-known fact that under
such a deformation the recurrence coefficients denoted as and
evolve in according to the Toda equations, giving rise to the
time dependent orthogonal polynomials, using Sogo's terminology. The resulting
"time-dependent" Jacobi polynomials satisfy a linear second order ode. We will
show that the coefficients of this ode are intimately related to a particular
Painlev\'e V. In addition, we show that the coefficient of of the
monic orthogonal polynomials associated with the "time-dependent" Jacobi
weight, satisfies, up to a translation in the Jimbo-Miwa -form of
the same while a recurrence coefficient is up to a
translation in and a linear fractional transformation
These results are found
from combining a pair of non-linear difference equations and a pair of Toda
equations. This will in turn allow us to show that a certain Fredholm
determinant related to a class of Toeplitz plus Hankel operators has a
connection to a Painlev\'e equation
Calibration of the Pulsed Electroacoustic Technique in the Presence of Trapped Charge
The influence of pulse voltage on the accuracy of charge density distribution in the pulsed electroacoustic technique (PEA) is discussed. It is shown that significant error can be introduced if a low dc voltage and high pulse voltage are used to calibrate charge density. However, our main focus in the present paper is to deal with one of the practical situations where space charge exists in the material prior to any measurements. The conventional calibration method can no longer be used to calibrate charge density due to the interference by the charge on the electrode induced by space charge. A method has been proposed which is based on two measurements. Firstly, the sample containing charge is measured without any applied voltage. The second measurement is carried out with a small external applied voltage. The applied voltage should be small enough so there is no disturbance of the existing charge in the sample. The difference of the two measurements can be used for calibration. An additional advantage of the proposed method avoids the influence of the pulse voltage on calibration and therefore gives a more accurate representation of space charge. The proposed method has been validated
- âŠ