Moments of the three-parameter Fermi distribution

2017 ◽  
Vol 32 (36) ◽  
pp. 1750195 ◽  
Author(s):  
L. Zhang ◽  
Y. Gao ◽  
H. Zheng ◽  
M. R. Huang ◽  
X. Liu
Keyword(s):  
General Expression ◽  
Numerical Results ◽  
Neutron Skin ◽  
Fermi Distribution ◽  
Density Radius ◽  
The Moment ◽  
Diffuseness Parameter

The moments [Formula: see text] of the spherical three-parameter Fermi distribution (3pF) are presented for [Formula: see text] to 8 as a function of the parameter [Formula: see text], the half-density radius [Formula: see text] and the diffuseness parameter [Formula: see text] through the introduced parameter [Formula: see text], which can be applied to study the neutron skin in neutron rich nuclei. The general expression of the moment can be written as the combination of integrals [Formula: see text] with [Formula: see text]. The errors of the analytic moments [Formula: see text] are estimated with the typical values of the parameters in 3pF compared with the numerical results.

The formation and evolution of a diffusive interface

1997 ◽  
Vol 331 ◽  
pp. 199-229 ◽  
Author(s):  
M. JEROEN MOLEMAKER ◽  
HENK A. DIJKSTRA
Keyword(s):  
Numerical Simulation ◽  
Mixed Layer ◽  
Numerical Results ◽  
Necessary Condition ◽  
Mixing Efficiency ◽  
Final Thickness ◽  
Formation And Evolution ◽  
Diffusive Interface ◽  
The Moment ◽  
Energy Balances

The formation and evolution of a diffusive interface in a stable salt-stratified layer cooled from above is studied in a two-dimensional geometry by direct numerical simulation. For a typical example with realistic parameters, the evolution of the flow is computed up to the moment where three layers can be distinguished. Focus is on the development of the first mixed layer. The convective velocity scaling as proposed by Hunt (1984) and previously proposed expressions for the interfacial heat flux (Huppert 1971; Fernando 1989a) are shown to correspond well with the results of the simulation. The evolution of the first layer can be well described by an entrainment relation based on a local balance between kinetic and potential energy with mixing efficiency γ. The new entrainment relation is shown to fit the numerical results well and an interpretation of γ in terms of the overall energy balances of the flow is given.Previously, two rival mechanisms have been proposed that determine the final thickness of the first layer (Turner 1968; Fernando 1987). One of the distinguishing features of both mechanisms is whether a transition in entrainment regime – as the first layer develops – is a necessary condition for the mixed layer to stop growing. Another is the presence of a buoyancy jump over the interface before substantial convection in the second layer occurs. From the numerical results, we find a significant buoyancy jump even before the thermal boundary layer ahead of the first layer becomes unstable. Moreover, the convective activity in the second layer is too small to be able to stop the growth of the first layer. We therefore favour the view proposed by Fernando (1987) that a transition in entrainment regime determines the thickness of the first layer. Following this, a new one-dimensional model of layer formation is proposed. Important expressions within this model are verified using the results of the numerical simulation. The model contains two constants which are determined from the numerical results. The results of the new model fit experimental results quite well and the parameter dependence of the thickness of the first layer is not sensitive to the values of the two constants.

Nuclear charge density radius parameter and the β decay between mirror nuclei

1993 ◽  
Vol 71 (3-4) ◽  
pp. 162-164
Author(s):  
Cihat Ozhasoglu ◽  
M. L. Rustgi
Keyword(s):  
Charge Density ◽  
Electron Scattering ◽  
Nuclear Charge ◽  
Coulomb Energy ◽  
Β Decay ◽  
Radius Parameter ◽  
Density Radius ◽  
Diffuseness Parameter ◽  
Two Parameter ◽  
Fermi Type

A two-parameter Fermi-type charge-density distribution is used to determine the Coulomb energy of a nucleus of a given charge Z. The expression is used to determine the nuclear charge-density-radius parameter, r1, and the diffuseness parameter, a, from the maximum kinetic energies in the β+-decay experiments. The deduced parameters r1 and a are compatible with the values obtained from the analyses of electron-scattering experiments.

scholarly journals XVIII. On the formulæ investigated by Dr. Brinkley for the general term in the deve­lopment of Lagrange’s expression for the summation of series and for successive integrations

1860 ◽  
Vol 150 ◽  
pp. 319-323
Keyword(s):  
General Expression ◽  
Finite Differences ◽  
Royal Society ◽  
General Term ◽  
Numerical Results ◽  
The Other ◽  
Exponential Functions ◽  
Summation Of Series ◽  
The One ◽  
Form Of Expression

In the Transactions of the Royal Society for 1807, Dr. Brinkley has investigated the general value of the coefficient of any term in the development of the function( t / e t -1) n , and his result is remarkable for the mode of its expression in terms of the successive differences of the powers of zero, or of the numbers comprised in the general expression ∆ m 0 n . Since that time, in my paper published in the Transactions of the Society for 1815, “On the Development of Exponential Functions,” I have exhibited other, and much more simple as well as more easily calculable expressions for the same coefficient, by means of the same useful and valuable differences, and in that and other subsequent memoirs, have extended their application to a variety of interesting inquiries in the theory of differences and series. It is singular, however, that up to the present time it has never been shown that the formulæ of Dr. Brinkley, and my own, though affording in all cases coincident numerical results, are analytically reconcileable with each other; nor indeed is it at all easy to see either from the course of his investigation, which turns upon an intricate application of the combinatory analysis, or from the nature of the formula itself, how it is possible to pass from the one form of expression to the other so as to show their identity. This is what I now propose. Referring to my “Collection of Examples in the Calculus of Finite Differences,” will be found the following relation, which enables us to pass from the differences of any one power of zero, as 0 z , to those of any other, as 0 x + n , viz.— {log (1 + ∆) } n . f (∆)0 x = x ( x - 1) .... ( x - n +1). f (∆)0 x - n , or changing x into x + n , {log (1 + ∆)} n . f (∆)0 x + n = ( x +1)( x +2) .... ( x + n ). f (∆)0 x .

Vibration of a Fluid Conveying Pipe Carrying a Discrete Mass

1974 ◽  
Vol 96 (4) ◽  
pp. 268-272 ◽  
Author(s):  
T. T. Wu ◽  
P. P. Raju
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Flow Velocity ◽  
General Expression ◽  
Normal Modes ◽  
Critical Value ◽  
Numerical Results ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Discrete Mass

This paper presents a method to predict the dynamic response of a fluid conveying pipe carrying a discrete mass when the flow velocity is less than its critical value. A general expression for the normal modes of a vibrating pipe with various boundary conditions is newly derived herein. Also presented for a particular case are the numerical results of eigenfunctions and eigenvalues which can be used to calculate the dynamic response of a simply-supported pipe with an attached discrete mass at its mid-span.

The Impact of Moments Near Discontinuities in Structural-Acoustic Systems

2003 ◽  
Vol 125 (2) ◽  
pp. 137-144
Author(s):  
W. Steve Shepard,
Keyword(s):  
Infinite Plate ◽  
Acoustic Power ◽  
Numerical Results ◽  
Structural Discontinuity ◽  
Simple Supports ◽  
The Moment ◽  
The Impact ◽  
Rigid Baffle

The impact of a moment excitation on the vibrational and acoustical response of a fluid-loaded system containing a structural discontinuity is examined. The response metric of interest is the acoustic power radiated from a semi-infinite plate supported in a rigid baffle. The impact of a moment excitation located near a locally reacting distributed-mass discontinuity as well as near the simple supports is examined. Numerical results show that the addition of a moment component can have a dramatic impact on the radiated acoustic power. Both the magnitude and phase of the moment relative to the force can impact the radiated acoustic power.

scholarly journals Relativity effects in the rotation of the Earth and the motion of atmospheric masses

1986 ◽  
Vol 114 ◽  
pp. 289-292
Author(s):  
V. G. Shkodrov ◽  
V. G. Ivanova
Keyword(s):  
Angular Velocity ◽  
Observational Data ◽  
Atmospheric Pressure ◽  
Earth Rotation ◽  
Numerical Results ◽  
Moment Of Inertia ◽  
The Earth ◽  
Rotation Of The Earth ◽  
The Moment

On the basis of observational data on atmospheric pressure (1963–1967), the variation of the moment of inertia, and, with certain restrictions, the changes in the angular velocity of the Earth are obtained. The numerical results derived are compared to the relativity effects in Earth rotation. The comparison shows that both effects are equal in periods and very close in amplitudes.

scholarly journals Brazier Effect of Thin Angle-Section Beams under Bending

2018 ◽  
Vol 10 (9) ◽  
pp. 3047
Author(s):  
Zhiguang Zhou ◽  
Liuyun Xu ◽  
Chaoxin Sun ◽  
Songtao Xue
Keyword(s):  
Nonlinear Response ◽  
Beam Theory ◽  
Bending Moment ◽  
Numerical Results ◽  
Experimental Results ◽  
Angle Section ◽  
Thin Walled ◽  
The Moment ◽  
Good Agreement ◽  
Brazier Effect

Thin-walled section beams have Brazier effect to exhibit a nonlinear response to bending moments, which is a geometric nonlinearity problem and different from eigenvalue problem. This paper is aimed at investigating the Brazier effect in thin-walled angle-section beams subjected to pure bending about its weak axis. The derivation using energy method is presented to predict the maximum bending moment and section deformation. Both numerical analyses and experimental results were used to show the validity of the proposed formula. Numerical results show that the boundary condition can influence the results due to the end effect, and that the influence tends to be negligible when the length of angle beam goes up to 30 times as the length of beam side. When the collapse in experiments is governed by Brazier flattening, the moment vs. curvature curve deviates significantly from the linear beam theory, but coincides well with the proposed formula in consideration of the restraint due to limited span of experimental setup. It can be concluded that the proposed formula shows good agreement with numerical results and experimental results.

The High Resolution Scanning Transmission Electron Microscope

1974 ◽  
Vol 32 ◽  
pp. 316-317
Author(s):  
A. V. Crewe
Keyword(s):  
Electron Microscope ◽  
High Resolution ◽  
High Vacuum ◽  
Scanning Transmission Electron Microscope ◽  
Ultra High Vacuum ◽  
Resolving Power ◽  
Imaging Characteristics ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
The Moment

The high resolution STEM is now a fact of life. I think that we have, in the last few years, demonstrated that this instrument is capable of the same resolving power as a CEM but is sufficiently different in its imaging characteristics to offer some real advantages.It seems possible to prove in a quite general way that only a field emission source can give adequate intensity for the highest resolution^ and at the moment this means operating at ultra high vacuum levels. Our experience, however, is that neither the source nor the vacuum are difficult to manage and indeed are simpler than many other systems and substantially trouble-free.

Pinocytotic-Like Forms of Mitochondria From Rat Anterior Pituitary

1968 ◽  
Vol 26 ◽  
pp. 146-147
Author(s):  
Burton B. Silver
Keyword(s):  
Electron Micrographs ◽  
Conformational Changes ◽  
Anterior Pituitary ◽  
Dynamic State ◽  
Surrounding Cell ◽  
The Matrix ◽  
The Moment ◽  
Cell Medium ◽  
Sectioned Tissue ◽  
State Of Activity

Sectioned tissue rarely indicates evidence of what is probably a highly dynamic state of activity in mitochondria which have been reported to undergo a variety of movements such as streaming, divisions and coalescence. Recently, mitochondria from the rat anterior pituitary have been fixed in a variety of configurations which suggest that conformational changes were occurring at the moment of fixation. Pinocytotic-like vacuoles which may be taking in or expelling materials from the surrounding cell medium, appear to be forming in some of the mitochondria. In some cases, pores extend into the matrix of the mitochondria. In other forms, the remains of what seems to be pinched off vacuoles are evident in the mitochondrial interior. Dense materials, resembling secretory droplets, appear at the junction of the pores and the cytoplasm. The droplets are similar to the secretory materials commonly identified in electron micrographs of the anterior pituitary.

Advances in Stem Instrumentation for Biology

1990 ◽  
Vol 48 (1) ◽  
pp. 362-363
Author(s):  
J. S. Wall
Keyword(s):  
Scanning Transmission Electron Microscope ◽  
Carbon Films ◽  
Specimen Preparation ◽  
Material Deposition ◽  
Active User ◽  
Percent Improvement ◽  
Scanning Transmission ◽  
The Moment ◽  
Film Substrate ◽  
High Level

The forte of the Scanning transmission Electron Microscope (STEM) is high resolution imaging with high contrast on thin specimens, as demonstrated by visualization of single heavy atoms. of equal importance for biology is the efficient utilization of all available signals, permitting low dose imaging of unstained single molecules such as DNA.Our work at Brookhaven has concentrated on: 1) design and construction of instruments optimized for a narrow range of biological applications and 2) use of such instruments in a very active user/collaborator program. Therefore our program is highly interactive with a strong emphasis on producing results which are interpretable with a high level of confidence.The major challenge we face at the moment is specimen preparation. The resolution of the STEM is better than 2.5 A, but measurements of resolution vs. dose level off at a resolution of 20 A at a dose of 10 el/A2 on a well-behaved biological specimen such as TMV (tobacco mosaic virus). To track down this problem we are examining all aspects of specimen preparation: purification of biological material, deposition on the thin film substrate, washing, fast freezing and freeze drying. As we attempt to improve our equipment/technique, we use image analysis of TMV internal controls included in all STEM samples as a monitor sensitive enough to detect even a few percent improvement. For delicate specimens, carbon films can be very harsh-leading to disruption of the sample. Therefore we are developing conducting polymer films as alternative substrates, as described elsewhere in these Proceedings. For specimen preparation studies, we have identified (from our user/collaborator program ) a variety of “canary” specimens, each uniquely sensitive to one particular aspect of sample preparation, so we can attempt to separate the variables involved.

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