<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">
Hi Piet,<div><br class="webkit-block-placeholder"></div><div>I am just reading your new paper on analytical solutions of</div><div>loop profiles, which overlaps and complements my new paper</div><div>on analytical approximations of loop dynamics. Here a few</div><div>overlapping aspects:</div><div><br class="webkit-block-placeholder"></div><div>(1) In Eq.(28) you show that the RTV scaling law survives in</div><div>your analytical solution, which fully agrees with my finding </div><div>(Eq.81-82 in my paper), even for different non-uniform </div><div>heating functions. For the constant of proportionality, I find</div><div>also slightly different values for different heating functions</div><div>(Eq.82), basically scaling with the Mach number of the upflows.</div><div><br class="webkit-block-placeholder"></div><div>(2) Also the second scaling law (your Eq.31) is reproduced</div><div>in my paper in an equivalent way (Eq. 20 in my paper), with</div><div>slightly different values for the constant for non-uniform heating.</div><div><br class="webkit-block-placeholder"></div><div>(3) The expression for the loop top temperature (your Eq.35)</div><div>is also reproduced in Eq.23 in my paper. <br><div><div><br></div><div>(4) Your analytical solutions for the temperature profiles</div><div>(Fig.3 in your paper) are nearly identical to the approximations</div><div>I derive in my paper (Fig.2), for uniform as well as non-uniform</div><div>heating.</div><div><br class="webkit-block-placeholder"></div><div>So, all the overlapping parts in your and my paper seems to</div><div>agree quite well, although my approach is based on some</div><div>approximations (such as neglecting the radiative loss during</div><div>the heating phase). On the other side, my approach is</div><div>complementary in the sense that it gives also an approximation</div><div>for the density profile n(s), as well as for the time evolution</div><div>of temperature T(s,t) and density n(s,t) during the heating</div><div>and cooling phase. So, both papers provide some analytical</div><div>tools in a complementary way, which might be useful for</div><div>quick forward-modeling of loops observed with Hinode and/or</div><div>STEREO.</div><div><br class="webkit-block-placeholder"></div><div>Congrats, again, to your very useful analytical study.</div><div>Cheers,</div><div><br class="webkit-block-placeholder"></div><div>Markus</div><div><br class="webkit-block-placeholder"></div></div><div> <span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 14px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><span class="Apple-style-span" style="border-collapse: separate; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; -webkit-text-decorations-in-effect: none; text-indent: 0px; -webkit-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><span class="Apple-style-span" style="border-collapse: separate; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; -webkit-text-decorations-in-effect: none; text-indent: 0px; -webkit-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><span class="Apple-style-span" style="border-collapse: separate; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; -webkit-text-decorations-in-effect: none; text-indent: 0px; -webkit-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><div>____________________________________________</div><div>Dr. Markus J. Aschwanden</div><div>Solar & Astrophysics Laboratory</div><div>Lockheed Martin Advanced Techology Center</div><div>Org. ADBS, Bldg. 252</div><div>3251 Hanover St., Palo Alto, CA 94304, USA</div><div>Phone: 650-424-4001, FAX: 650-424-3994</div><div>URL: <a href="http://www.lmsal.com/~aschwand/">http://www.lmsal.com/~aschwand/</a></div><div>e-mail: <a href="mailto:aschwanden@lmsal.com">aschwanden@lmsal.com</a></div><div>_______________________________________</div><br class="Apple-interchange-newline"></span></span></span></span><br class="Apple-interchange-newline"> </div><br></div></body></html>