Stretched Exponentials - Revision history

Jess at 18:28, 17 September 2022

2022-09-17T18:28:05Z

WikiSysop at 20:04, 29 August 2022

2022-08-29T20:04:08Z

WikiSysop at 17:47, 29 August 2022

2022-08-29T17:47:24Z

WikiSysop: Created page with "In between exponential $\exp(-\lambda t)$ and gaussian $\exp[-(\sigma t)^2]$ relaxation (and indeed extending beyond either) is the much-abused empirical..."

2022-08-29T17:45:15Z

Created page with "In between exponential <math>\exp(-\lambda t)</math> and gaussian <math>\exp[-(\sigma t)^2]</math> relaxation (and indeed extending beyond either) is the much-abused empirical..."

New page

In between exponential <math>\exp(-\lambda t)</math> and gaussian <math>\exp[-(\sigma t)^2]</math> relaxation (and indeed extending beyond either) is the much-abused empirical "'''''stretched exponential'''''" function, <center><math>\exp[-(\Lambda t)^\beta]</math></center>
I don't much care for it. It will ''fit'' a wide variety of ZF-µSR relaxation functions, but what do the results ''mean''? What do they tell us about the physics? There are cases where "root exponential" relaxation functions (<math>\beta = 1/2</math>) suggest a rapidly fluctuating spin glass, but fit results with <math>\beta</math> all the way from 0.25 to 3 have been published without any hint of irony. Please don't resort to this.

@@ Line 5: / Line 5: @@
 I don't much care for it.  It will ''fit'' a wide variety of ZF-&micro;SR relaxation functions, but what do the results ''mean''?  What do they tell us about the physics?  There are cases where "root exponential" relaxation functions (<math>\beta = 1/2</math>) suggest a rapidly fluctuating spin glass, but fit results with <math>\beta</math> all the way from 0.25 to 3 have been published without any hint of irony.  Please don't resort to this.
 <center>
-[[Image:StrExp_color.png|600px|inline image (click to see full size)]]
+[[Image:StrExp_color.png|400px|inline image (click to see full size)]]
 {| width="80%"
 ! align="left" |

@@ Line 4: / Line 4: @@
 In between exponential <math>\exp(-\lambda t)</math> and gaussian <math>\exp[-(\sigma t)^2]</math> relaxation (and indeed extending beyond either) is the much-abused empirical "'''''stretched exponential'''''" function, <center><math>\exp[-(\Lambda t)^\beta]</math></center>
 I don't much care for it.  It will ''fit'' a wide variety of ZF-&micro;SR relaxation functions, but what do the results ''mean''?  What do they tell us about the physics?  There are cases where "root exponential" relaxation functions (<math>\beta = 1/2</math>) suggest a rapidly fluctuating spin glass, but fit results with <math>\beta</math> all the way from 0.25 to 3 have been published without any hint of irony.  Please don't resort to this.
+<center>
+[[Image:StrExp_color.png|600px|inline image (click to see full size)]]
+{| width="80%"
+! align="left" |
+<math>G(t) = \exp[-(\Lambda t)^\beta]</math> for <math>\Lambda = 1</math> and <math>\beta = 0.25, 0.5, 1, 2, 3</math>.  Only <math>\beta = 1, 2</math> and sometimes <math>0.5</math> have familiar physical meanings.
+|}

@@ Line 1: / Line 1: @@
+[[Relaxonomy]] --> here
+----
 In between exponential <math>\exp(-\lambda t)</math> and gaussian <math>\exp[-(\sigma t)^2]</math> relaxation (and indeed extending beyond either) is the much-abused empirical "'''''stretched exponential'''''" function, <center><math>\exp[-(\Lambda t)^\beta]</math></center>
 I don't much care for it.  It will ''fit'' a wide variety of ZF-&micro;SR relaxation functions, but what do the results ''mean''?  What do they tell us about the physics?  There are cases where "root exponential" relaxation functions (<math>\beta = 1/2</math>) suggest a rapidly fluctuating spin glass, but fit results with <math>\beta</math> all the way from 0.25 to 3 have been published without any hint of irony.  Please don't resort to this.

Stretched Exponentials - Revision history

Jess at 18:28, 17 September 2022

WikiSysop at 20:04, 29 August 2022

WikiSysop at 17:47, 29 August 2022

WikiSysop: Created page with "In between exponential \exp(-\lambda t) and gaussian \exp[-(\sigma t)^2] relaxation (and indeed extending beyond either) is the much-abused empirical..."

WikiSysop: Created page with "In between exponential $\exp(-\lambda t)$ and gaussian $\exp[-(\sigma t)^2]$ relaxation (and indeed extending beyond either) is the much-abused empirical..."