Time Scales

نویسنده

  • L. ESSEN
چکیده

The accuracy of the National Research Council 2.1 m cesium beam frequency standard has been re-evaluated using the two NRC hydrogen masers as stable comparison standards. At the time of re-evaluation, the various uncertainties gave rise to an error limit of :!:3.8 x 10-12, with a most probable value of :!:1.5 x 10-12 if they were assumed to be random. Mter application of all corrections, the agreement with several other cesium standards, as determined from monthly VLF comparisons during January to March, 1968, appears generally to be within the narrower limits of :!:1.5 x 10-12. this, and in the synthesizer settings, are used to calculate the corresponding changes in the apparent cesium resonant frequency as determined by the cesium standard. The frequency ix of the 5 MHz crystal oscillator locked to the cesium resonance can be expressed as follows : 9192632000 .fw = 9192631770 + ~iH + L~i, (1) where 9192632000 refers to the nominal frequency synthesized, 9192631770 Hz is the defined value of the cesium hyperfine transition frequency, L~i, represents the sum of systematic errors ~i" i = 1, ..., n, and ~iH is the O field correction. In the NRC standard, ~iH is determined from measurements of the (4, -4) +-* (4, -3) transition frequencies, 'Vk, k = 1, ...8, over eight adjacent sections of the drift space between the two oscillating field regions. Introduction With the completion of a pair of hydrogen masers at the National Research Council [1] it has become possible to re-evaluate the accuracy of the NRC 2.1 m cesium beam frequency standard. This standard, in operation since 1965 [2], has exhibited much closer agreement [3,4,5] with other cesium frequency standards than the original estimate of accuracy:!: 1.9 x 10-11, might indicate. This initial estimate was based on experimental comparisons with a stable crystal oscillator, and appears to have been influenced mainly by the limitation of frequency stability imposed by this crystal rather than that of the standard itself. Use of the hydrogen masers, which possess frequency stabilities over short periods far in excess of that of the cesium standard, has eliminated this primary source of frequency instability, and has appreciably improved the precision of estimating the accuracy of the cesium standard. is Method of Re-Evaluation The technique used has been to observe changes in the relative frequency of the hydrogen and cesium standards when certain modifications to the cesium standard alone are made. The output of the 5 MHz crystal locked to the cesium resonance is used to drive a multiplier and synthesizer system used to detect the maser signal. The beat frequency between these two signals at 1420 MHz is then monitored, and changes in 24 Metrologla ~ = 230-<5IH}:;<511 (4) I 9192632000 and any change in this offset, d (7~ due to changes in I.5fH, or in :L:l.5f" is

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

First order linear fuzzy dynamic equations on time scales

In this paper, we study the concept of generalized differentiability for fuzzy-valued functions on time scales. Usingthe derivative of the product of two functions, we provide solutions to first order linear fuzzy dynamic equations. Wepresent some examples to illustrate our results.

متن کامل

On the existence and uniqueness of solution of initial value problem for fractional order differential equations on time scales

n this paper, at first the  concept of Caputo fractionalderivative is generalized on time scales. Then the fractional orderdifferential equations are introduced on time scales. Finally,sufficient and necessary conditions are presented for the existenceand uniqueness of solution of initial valueproblem including fractional order differential equations.

متن کامل

Existence of positive solutions for a second-order p-Laplacian impulsive boundary value problem on time scales

In this paper, we investigate the existence of positive solutions for a second-order multipoint p-Laplacian impulsive boundary value problem on time scales. Using a new fixed point theorem in a cone, sufficient conditions for the existence of at least three positive solutions are established. An illustrative example is also presented.

متن کامل

Permanence and Uniformly Asymptotic Stability of Almost Periodic Positive Solutions for a Dynamic Commensalism Model on Time Scales

In this paper, we study dynamic commensalism model with nonmonotic functional response, density dependent birth rates on time scales and derive sufficient conditions for the permanence. We also establish the existence and uniform asymptotic stability of unique almost periodic positive solution of the model by using Lyapunov functional method.

متن کامل

Theory of hybrid differential equations on time scales

‎In this paper‎, ‎we develop the theory of hybrid differential‎ ‎equations on time scales‎. ‎An existence theorem for hybrid‎ ‎differential equations on time scales is given under Lipschitz ‎conditions‎. ‎Some fundamental fractional differential inequalities‎ ‎are also established which are utilized to prove the existence of‎ ‎extremal solutions‎. ‎Necessary tools are considered and the‎ ‎compa...

متن کامل

Stability Analysis of a Strongly Displacement Time-Delayed Duffing Oscillator Using Multiple Scales Homotopy Perturbation Method

In the present study, some perturbation methods are applied to Duffing equations having a displacement time-delayed variable to study the stability of such systems. Two approaches are considered to analyze Duffing oscillator having a strong delayed variable. The homotopy perturbation method is applied through the frequency analysis and nonlinear frequency is formulated as a function of all the ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005