Microscopic Model of Cuprate Superconductivity

We present a model for cuprate superconductivity based on the identification of an experimentally detected "local superconductor" as a charge 2 fermion pairing in a circular, stationary density wave. This wave acts like a highly correlated local "boson" satisfying a modified Cooper problem with additional correlation stabilization relative to the separate right- and left-handed density waves composing it. This local "boson" could be formed in a two-bound roton-like manner; it has Fermion statistics. Delocalized superconductive pairing (superconductivity) is achieved by a Feshbach resonance of two unpaired holes (electrons) resonating with a virtual energy level of the bound pair state of the local "boson" as described by the Boson-Fermion-Gossamer (BFG) model. The spin-charge order interaction offers an explanation for the overall shape of the superconducting dome as well a microscopic basis for the cuprate superconducting transition temperatures. An explanation of the correlation of superconducting transition temperature with experimental inelastic neutron and electron Raman scattering is proposed, based on the energy of the virtual bound pair. These and other modifications discussed suggest a microscopic explanation for the entire cuprate superconductivity dome shape.Comment: 27 pages, 7 figures, presented at the 50th Sanibel Symposiu

Nonlinear Evolution of Instabilities Between Dust and Sound Waves

We study the non-linear evolution of the acoustic 'Resonant Drag Instability' (RDI) using numerical simulations. The acoustic RDI is excited in a dust-gas mixture when dust grains stream through gas, interacting with sound waves to cause a linear instability. We study this process in a periodic box by accelerating neutral dust with an external driving force. The instability grows as predicted by linear theory, eventually breaking into turbulence and saturating. As in linear theory, the non-linear behavior is characterized by three regimes - high, intermediate, and low wavenumbers - the boundary between which is determined by the dust-gas coupling strength and the dust-to-gas mass ratio. The high and intermediate wavenumber regimes behave similarly to one another, with large dust-to-gas ratio fluctuations while the gas remains largely incompressible. The saturated state is highly anisotropic: dust is concentrated in filaments, jets, or plumes along the direction of acceleration, with turbulent vortex-like structures rapidly forming and dissipating in the perpendicular directions. The low-wavenumber regime exhibits large fluctuations in gas and dust density, but the dust and gas remain more strongly coupled in coherent 'fronts' perpendicular to the acceleration. These behaviors are qualitatively different from those of dust 'passively' driven by external hydrodynamic turbulence, with no back-reaction force from dust onto gas. The virulent nature of these instabilities has interesting implications for dust-driven winds in a variety of astrophysical systems, including around cool-stars, in dusty torii around active-galactic-nuclei, and in and around giant molecular clouds.Comment: 11 pages, 9 figure

Letter from R. Squire to John Muir, 1863 Dec 21

[4]One could hardly ask for a greater enjoyment, on New Years day, than a warm fire, and there did not seem to be much pleasure away from it, your friends here are well, and you have some very good ones, We do not have very good meetings, this winter, And our school I am afraid will not amount so much, The children like her very much as an associate, (their teacher I mean) Mr. & Mrs. [Teoffer?] wish to be remembered to you with much respect, & Mr & Mrs Hays also, The girls have obtained your drawing, and I am sorry that it is so much soiled, I hope it will reach you safely. We shall always be glad to hear from you, whenever you can spare time to write. Give my respects to your Mother, and friends, and believe us, ever sanly shine, R. SquirePS We shall want to know whether you get your drawing. Please write and let us know, We shall send it with the letter [2]God has dealt very kindly with us in these times which [illegible]ly weing the hearts of many. My husband had the great affliction to bury his son after a weeks illness at Vicksburg, He died just before the surrender, We all grieve at his early death His father takes it very hard, he was himself, soon after, taken sick, and sent up to Mound City hospital, where he wrote for me to come after him, thinking he should never recover, if he staid there. I went down about the middle of August, and succeeded in getting a furlough for 20 days, After the expiration of which he went into the hospital at Madison where he still remains. It seems cruel that they will not let him stay at home.00344[3]but they tell me military orders must be obey\u27d , His health is slowly improving, and he is allowed to visit home about once in three weeks, for the long space of 24 hours, (generous, is it not?) I was absent from home two weeks, and was ill for several weeks after my return, but have quite recover\u27d my health, O, these are times, which try the faith of every honest man and woman, My patriotism is all gone, I am sorry to say it, (and could hardly dare to, before my husband) I suppose it is wrong to feel as I do somet -mes, but cant help it. (two weeks later, New Years and Christmas have passed, and I hope you have enjoy\u27d them pleasantl

On the existence of infinitely many closed geodesics on orbifolds of revolution

Using the theory of geodesics on surfaces of revolution, we introduce the period function. We use this as our main tool in showing that any two-dimensional orbifold of revolution homeomorphic to S^2 must contain an infinite number of geometrically distinct closed geodesics. Since any such orbifold of revolution can be regarded as a topological two-sphere with metric singularities, we will have extended Bangert's theorem on the existence of infinitely many closed geodesics on any smooth Riemannian two-sphere. In addition, we give an example of a two-sphere cone-manifold of revolution which possesses a single closed geodesic, thus showing that Bangert's result does not hold in the wider class of closed surfaces with cone manifold structures.Comment: 21 pages, 4 figures; for a PDF version see http://www.calpoly.edu/~jborzell/Publications/publications.htm

Letter from Mrs. R. Squire to John Muir, 1862 Apr 14

[4] kindness you have shown me this from your naughty [hapil?] Alice [M.?] Squire00291[1] Oregon April 19th 1862 Mr. Muir it is always pleasant to be remembered by those for whom we entertain kind feelings, Therefore when I received your Grattitude so beautifully expressed, my heart was filled with a mixture of gladness & regret, Glad if indeed there existed any cause for Grattitude, Regret that there was so little, We appretiate your kindness & example, & hope when you come among us again, you will meet with a pleasant & hearty welcome, I hope you had a god time at Home, with your Mother & friends, Now I suppose you are gathering 7 laying up stores of useful knowledge for future use, 625 [2] I hope you will be successful & realize all your hopes, And I do not think you will quite forget your first school & the old Log School house, We shall ever remember you kindly & with pleasure, Yours very sincerely, Mrs R. Squire Good morning Mr Muir [How?] do you do all well I hope and enjoying yourself with your studdies I am glad that you went home and I hope you had a good visit We are well and was quite glad to hear from you I thank you very much for that nice gift of paints to Alice and my self as we were not here then to do so I like the book that you gave me One school commences the first of May I have written these few lines to let you know that I have not forgotten you nor your kindness, and I hope that I shall not forget the good instructions you have given[3] me I will now say good by. your wayward pupil Lucy Webster Good morning [dear teacher?] I hope you are well as I am C[illegible]ss & Smith is a going to teach our school this summer I hope we shall have as good a school as we had last winter. Do you have any one to [play?] [illegible] you up there to school I guess you dont. I hope you wont have to stand on the floor this summer. I am glad you went home and seen your Father and Mother and your little sisters. I thank you for that candie you have me I mean to keep it as long as you did I thank you for that box of paints you gave Lucy and myself. I like that book you gave me very much and the tin [tumble?] you gave me I drink out of every morning. I am sorry I was not here when you went away. I dont think I shall ever forget the good you have [taught?] me and th

Letter from Lucy Webster, R. Squire, W.F. Webster, and Alice M. Squire to John Muir, 1864 Jan 25

[2] Dear friend Muir I am now seated to write you a few lines to let you know that I am well and hope these few lines will find you the same There have been a great many men enlisting and there is a great many more to go to war. I wish this war would soon end but I fear it will be a long time before [illegible] rebellion is Crushed. Mr Muir I thank you a thousand times for [thoes?] images alltho they never entered our house. W. F. Webster[3] Dear Mr Muir I will write a few lines to you now the rest got through. I thank you very much for those presents. Those imagyes got broke the boys was playing ball and [they?] threw it through the window and hit them and broke them all to pieces but we got the bell Eddys Gilberts folks have moved down to Green County so he does not come to school this winter. A lady from Bellvile teaches our school. We have [99?] scholars. Weston and Charley came here to school this winter their Father has enlisted. I got that picture from Mrs. Heebys but it does not look much as it did for it was clean then but it is dirty now and looks real bad. They are having a singing school down to Storytown this winter Alice M SquireMr John Muir, 00347 [4]I shall have to explain the reason for delaying to send this letter or you will think we were very negligent, I have a Niece attending school at the University, and she said she would see the janitor and get him to bring those things you left, to her room, And she took your letter, lest she might forget, And if we could not remember your address, and did not get your letter again, until yesterday. Mr Squire has gone back to his Reg\u27t. and we feel very sad about it. I went up Saturday, expecting to see him but they had sent him away two days before, His Regiment are at Natehes. R Squire[1] January 11th 1864Dear friend Muir We received your kind letter and was very glad to hear from you and to know that you was enjoying yourself among your friends. we are all well at present we are going to school but do not have a very good one this winter we have a female teacher. Gilbert McKeeby is teaching up to the white school house this winter [Nett?] goes up there to school, Mr [illegible] people are as well as usual Willie as mischievous as ever. Sophia Mc Keeby is teaching down to Story town. Mr Smoles people I believe are all well Henerette and Jacob come here to school they had the great affliction to loose a son who came home sick from the army, Mrs Harper has returned from the east they are all well. I think of no more to write at present. write soon good by. [Long?] Webster64