翻訳と辞書 Words near each other ・ E-Ship 1 ・ E-Sir ・ E-site ・ E-skills UK ・ E-social science ・ E-society ・ E-speak ・ E-file.lu ・ E-FIT ・ E-flat ・ E-flat clarinet ・ E-flat major ・ E-flat minor ・ E-flux ・ E-flux publications ・ E-folding ・ E-Foundation for Cancer Research ・ E-function ・ E-G8 Forum ・ E-Genius ・ E-GIF ・ E-girls ・ E-GMS ・ E-Go ・ E-gold ・ E-Governance ・ E-governance in excise and taxation department in Punjab ・ E-Governance in the United States ・ E-Government ・ E-Government Act of 2002 Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク E-folding ： ウィキペディア英語版 E-folding In science, ''e''-folding is the time interval in which an exponentially growing quantity increases by a factor of ''e''; it is the base-''e'' analog of doubling time. This term is often used in many areas of science, such as in atmospheric chemistry, medicine and theoretical physics, especially when cosmic inflation is investigated. Physicists and chemists often talk about the ''e''-folding time scale that is determined by the proper time in which the length of a patch of space or spacetime increases by the factor ''e'' mentioned above. In finance the logarithmic return or continuously compounded return, also known as force of interest, is the reciprocal of the e-folding time. The term ''e''-folding time is also sometimes used similarly in the case of exponential decay, to refer to the timescale for a quantity to decrease to 1/''e'' of its previous value. The process of evolving to equilibrium is often characterized by a time scale called the e-folding time, τ. This time is used for processes which evolve exponentially toward a final state (equilibrium). In other words if we examine an observable, X, associated with a system, (temperature or density for example) then after a time, τ, the initial difference between the initial value of the observable and the equilibrium value, ΔXi, will have decreased to ΔXi /e where the number e ~ 2.71828. ==Example of Lifetime of as e-Folding Time== The concept of e-folding time may be used in the analysis of kinetics. Let us consider a chemical species A, which decays into another chemical species, B. We could depict this as an equation: $A\backslash rightarrow\; B$ Let us assume that this reaction follows first order kinetics, meaning that the conversion of A into B depends only on the concentration of A, and the rate constant which dictates the velocity at which this happens, k. We could write the following reaction to describe this first order kinetic process: $\backslash frac=-k()$ What this ordinary differential equation states is that a change (in this case the disappearance) of the concentration of A, d()/dt, is equal to the rate constant k multiplied by the concentration of A. Consider what the units of k would be. On the left hand side, we have a concentration divided by a unit of time. The units for k would need to allow for these to be replicated on the right hand side. For this reason, the units of k, here, would be 1/time. Because this is a linear, homogeneous and separable differential equation, we may separate the terms such that the equation becomes: $\backslash frac=-k\; dt$ We may then take the integral of this function, which results in the inclusion of the constant e. $\backslash int\_\}\; \backslash frac=\backslash int\_^-kdt$ $ln()\_-ln()\_=-kdt-k(0)$ $\backslash frac\}=-kt$ $e^\}\}=e^$ $\backslash frac\}=e^$ Where ()f and ()i are the final and initial concentrations of A. Upon comparing the ratio on the left hand side to the equation on the right hand side, we conclude that the ratio between the final and initial concentrations follows an exponential function, of which e is the base. ' As mentioned above, the units for k are inverse time. If we were to take the reciprocal of this, we would be left with units of time. For this reason, we often state that the lifetime of a species which undergoes first order decay is equal to the reciprocal of k. Consider, now, what would happen if we were to set the time, t, to the reciprocal of the rate constant, k such that t = 1/k. This would yield $\backslash frac\}=e^)\}=e^=\backslash frac\backslash approx\; 0.37$ This states that after one lifetime (1/k), the ratio of final to initial concentrations is equal to about 0.37. Stated another way, after one lifetime, we have $\backslash frac\}=37/100=37\backslash \%$ which means that we have lost (1-.37=.63) 63% of A, with only 37% left. With this, we now know that if we have 1 lifetime passed, we have gone through 1 "e-folding". What would 2 "e-foldings" look like? After two lifetimes, we would have t=1\k+1\k=2\k, which would result in $\backslash frac\}=e^)\}=e^=\backslash frac\backslash approx\; 0.14\; =\; 14\backslash \%$ which says that only about 14% of A remains. It is in this manner that e-folding lends us an easy way to describe the number of lifetimes which have passed. After 1 lifetime, we have 1/e remaining. After 2 lifetimes, we have 1/e2 remaining. One lifetime, therefore, is one e-folding time, which is the most descriptive way of stating the decay. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「E-folding」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.