Peeling Bifurcations of Toroidal Chaotic Attractors

Chaotic attractors with toroidal topology (van der Pol attractor) have counterparts with symmetry that exhibit unfamiliar phenomena. We investigate double covers of toroidal attractors, discuss changes in their morphology under correlated peeling bifurcations, describe their topological structures and the changes undergone as a symmetry axis crosses the original attractor, and indicate how the symbol name of a trajectory in the original lifts to one in the cover. Covering orbits are described using a powerful synthesis of kneading theory with refinements of the circle map. These methods are applied to a simple version of the van der Pol oscillator.Comment: 7 pages, 14 figures, accepted to Physical Review

Need for a regional wind survey

Accurate measurements for the purpose of estimating wind energies are proposed in those regions of the USA where the greatest potentials exists. Preliminary wind characteristic calculations from weather station data are provided for the Southern Great Plains region; wind energies from 153 to 212 kW-hr/(ft squared-per year) for 1970 to 1972 are determined. It is concluded that a wind energy survey based on data compiled from weather service stations is feasible for determining the energy potential of a windpowered integrated energy network

Connections of the Mesencephalic Locomotor Region (MLR) in the Cat

The cat entopeduncular nucleus (EN), which is the main output of the basal ganglia, is known to project to the mesencephalic tegmentum. We have been able to elicit antidromic responses in single EN neurons from the region of the mesencephalic locomotor region (MLR), then transect (precollicular-postmamillary) the brainstem and elicit rhythmic movements of the limbs by stimulation of the same site in the same animal. Injections of the fluorescent dye 2,4 diamidino phenylindole 2 HCL (DAPI) into this area induces retrograde labeling of cell bodies in EN and motor cortex. Injections of a tritiated amino acid (leucine) into the motor cortex induce terminal labeling in the area of the MLR. These studies describe convergent projections from EN and motor cortex to the MLR. These connections may be involved in the sequencing and ordering of voluntary movements in which locomotion is necessary

Reminiscence of John Muir by Gilmore, E.E.

E. E. Gilmore POSTMASTER Lennox, South Dakota Tyrone, N.M. September 24,1916. Mr William L. Bade, Berkeley, Calif. Kind Sir: Yours of the 14th instant has just reached me, having been forwarded to me from my former home at Lennox, S. Dak.,and I am more than willing to furnish any information that I can with regard to one of my former teachers, and especially one that was as interesting a character as John Muir. A short distance south of gadison,Wisconsin is a small station on the Northwestern Ry. called Oregon. About three miles due west of this station is a small lake called Lake Harriet covering about a quarter section of land. A few rods north of the north shore of this lake, and about a half mile west, is an intersection of section lines, sometimes called four corners , and known locally at the time to which I am about to refer as McKibbe\u27s Corners . A short distance east of these corners is a small creek running in a southeasterly direction find emptying into Lake Harriet at its western extremity; at the point where this creek crosses the road running east and west it is spanned by a small bridge. About five or six rods east of this bridge, and on the north side of the road, is where, in 1860 and 1861, stood an old log school-house, in which John Muir taught the young idees during the winter of 1860 and 1861, if my memory serves me right. It is hard to recall the exact dimensions of this building, but from memory, I should judge that it must have been in the neighborhood of thirty feet wide by forty feet long with long wooden benches arranged in two tiers on each side, the right hand side for the girls and the left for the boys; the back tier of benches was provided with a long desk fastened against the wall running the full length of the building, and this was used of course by the larger scholars, the smaller ones having to occupy the front tier of benches, letting their feet hang over . John Muir at that time was a student in the University at Madison Wisconsin, and through the solicitations of out school board, consented to occupy the position of teacher of our school for that winter, the first arid only school that he ever taught, so far as I can ascertain. With one or two exceptions, he gave excellent satisfaction to both patrons and scholars, and I have always counted that winter as one of the bright spots in my history. For the first couple of weeks he was obliged to judge of the time by using the sun as a guide as he had no watch, watches being hard to obtain at that time; becoming tired of trying to guess at the time during cloudy days, he took a couple of common wooden water-pails, and bored a hole in the bottom of one of them, fitting a small wooden plug with a hole in the center, at the lower part of which was fitted a silver dime with a very tiny hole in the center which was inserted in such a way that the hole in the dime corresponded to the hole in the plug; he then took a common wooden bottomed chair and removed the bottom placing the pail with the plug in, in the place of the chair bottom. He then fixed a graduating scale on the\u27inside of the side of the pail and filled it about half full of water, and placing the other pail on the floor under this one, let the water drip slowly out of one pail into the other, the lowering of the water on the scale giving him the exact time of day. In those days it was customary for school teachers to board round that is, they would board a week or two in one place and then board a week or two in another and so on until ever patron of the school would have a chance to board the teacher , which the most of the patrons considered as a high honor; this system took the teacher at times quite a distance from the school-house, and as he had to be there at eight o\u27clock in the morning in order to have the fire built and the room good and warm, it was at times quite an inconvenience to him. This being an extremely cold winter, and very heavy, deep snows, Mr. Muir became tired of being compelled to reach the school-house so early in the morning, so he constructed a clock,e very part of which was wood with the exception of the springs, wooden frame, wooden wheels, wooden pendulum, and even the ball on the end of the pendulum was wood and from this wooden clock, which he fastened to the wall on the inside of the front of the school-house, he had a common string running to the hearth of the stove and fastened in such a way that the clock would jerk the string at a certain time every school morning and start the fire going, which was all arranged the night before, of course, before he left the school-house. Many, and many is the morning that I have watched the smoke begin to curl up from the school-house chimney promptly at eight o\u27clock, as we lived only about a mile from the school-house. About once a week he would give lectures on philosophy with practical demonstrations in the evening which became very popular and people would attend them from miles around, as they were extremely interesting. At the back end of the school-house, just behind the teachers desk, was a twelve foot blackboard fastened to the wall. The evening of the last day of school he gave one of his lectures and upon entering the building we were all surprised to see that he had constructed a clock out of large wooden wheels and here was that blackboard, which he had removed from the wall, swinging backwards and forwards, AS A PENDULUM for that clock. He was a firm believer at that time in perpetual motion, and I distinctly recollect the arguments that him and my father used to have over that question, sometimes spending the whole evening with the pros and cons . At the close of the school he returned to the University and the following year I came to Iowa with father and mother and I had lost all track of Mr. Muir, and often wondered what had become of him. During the winter he succeeded in sketching a fine view of the old school-house, doing the work during recesses and noon hours. In December, 1908 I happened to read an article in one of the leading magazines which was signed John Muir . This aroused my curiosity and I wrote the publishers asking to give me Mr. Muirs\u27s address, which they kindly did, so I wrote him, calling his attention ao a few incidents that occurred during that winter, and I am enclosing his reply to me, and you can imagine with what pleasure I read this letter. I have recieved two or three letters from him since, in one of which he requested me to write him at least once a year, which I have done. The balance of his letters, I am sorry to say, I have been unable to preserve, as I have been moving around a great deal of late. Will you kindly return this as soon as you are through with it as I would not part with it for any price. Of all of the pupils that attended that school, I am sorry to say that there is not one whose address I can call, to mind; just simply scattered to the four winds. I have two of his works, Early Days In Wisconsin , and his trip to Alaska, and am about to send for his Among The Sierras , and would be pleased to get A Thousand Mile Walk to the Gulf , and in fact shall order it just as soon as I see notice of its publication; also I would be pleased to hear from you about what time I can look for your publication, to appear in order that I may procure that also, as I am intensely interested in everything appertaining to his life. Yours in sincerity, E.E. Gilmore

Alternative determinism principle for topological analysis of chaos

The topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits has proved a powerful method, however knot theory can only be applied to three-dimensional systems. Still, the core principles upon which this approach is built, determinism and continuity, apply in any dimension. We propose an alternative framework in which these principles are enforced on triangulated surfaces rather than curves and show that in dimension three our approach numerically predicts the correct topological entropies for periodic orbits of the horseshoe map.Comment: Accepted for publication as Rapid Communication in Physical Review

SAR processing on the MPP

The processing of synthetic aperture radar (SAR) signals using the massively parallel processor (MPP) is discussed. The fast Fourier transform convolution procedures employed in the algorithms are described. The MPP architecture comprises an array unit (ARU) which processes arrays of data; an array control unit which controls the operation of the ARU and performs scalar arithmetic; a program and data management unit which controls the flow of data; and a unique staging memory (SM) which buffers and permutes data. The ARU contains a 128 by 128 array of bit-serial processing elements (PE). Two-by-four surarrays of PE's are packaged in a custom VLSI HCMOS chip. The staging memory is a large multidimensional-access memory which buffers and permutes data flowing with the system. Efficient SAR processing is achieved via ARU communication paths and SM data manipulation. Real time processing capability can be realized via a multiple ARU, multiple SM configuration

On N=8 attractors

We derive and solve the black hole attractor conditions of N=8 supergravity by finding the critical points of the corresponding black hole potential. This is achieved by a simple generalization of the symplectic structure of the special geometry to all extended supergravities with $N>2$. There are two solutions for regular black holes, one for 1/8 BPS ones and one for the non-BPS. We discuss the solutions of the moduli at the horizon for BPS attractors using N=2 language. An interpretation of some of these results in N=2 STU black hole context helps to clarify the general features of the black hole attractors.Comment: 15 page

Letter from Elmer E. Gilmore to John Muir, 1910 Feb 8.

Lennox, S. Dak. February 8,1910Mr. John Muir,Martinez, California.Dear Sir:It has been so long since I recieved your kind, and welcome letter, nearly a year ago that I am almost ashamed to write, but office duties have crowded in so thick and fast that I have had but little time to attend to personal correspondence, but as I have a little time at present I shall answer yours first of all.Unless you are of a sensitive nature, like myself, you little realize the thrill of pleasure it gave me to hear, and know for a certainty that I had at last discovered the whereabouts of my old school-teacher whose peculiar scientific experiments left such a deep impression on our young minds that, I at least, have never been able to erase them even if I would; for instance, your weekly lectures on philosophy, your experiments with mice placed in jars containing hydrogen and nitrogen gases; your firing corks out of a funnel shaped receptacle which pleased Wesley Stevens so well that he wanted to keep you at it all night; your clock constructed out of a common water-pail; your other clock made out of wooden wheels hung on a burr-oak bush shaped in the shape of a scythe which hung on the wall of the old log school-house, and last but not least the clock which took the whole of the old black-board to serve it as a pendulum which hung in the back part of the school-house on the evening of the close of school; these and many other impressions come crowding into my mind whenever I think of that winter.Father died in the spring of 1888 and often spoke of the arguments which you and he used to have over the subject of perpetual motion. Do you remember about it?With regard to the scholars who attended the school that winter, I can furnish you but little information I am afraid, as we moved away from there to Iowa a short time afterwards and, while we kept track of a feww of them for a while, still there was so many changes going on that we finally lost track of them all, except our immediate relatives•My oldest sister is now living in Wadena, Minn., is married and her husband is County Treasurer of that county, of course she was(Over)04699 small at that time,still she can call to mind a great many of the incidents of that winter.About eight,or nine years ago I was back there to visit the old scenes,and although I had net seen the old homestead for forty years, I had no difficulty in recognizing all of the old places,but none of the old neighbors were left except Mr.Nangles people,but their children had grown up and I had difficulty in recognizing them.The old log school-house has long since been torn down,and a new frame one stands on the corner across the creek to the west of it.I had no difficulty,however,in recognizing the place where the old one stood,although it is overgrown with a thick growth of jack-oak underbrush.The house in which we lived when you were there has been torn down,and I was unable to find out what became of it.Just before leaving there,I happened to meet Mr. Aalgaard, one of our old neighbours,who lived two miles south of us,but he was unable to give me much information with regard to the old settlers as he said that it had been simply impossible to keep track of themj but he stated that the Fay,or Harper family as you possibly knew them,had all gone to the bad,except Lucius who was,at that time manager of the Wisconsin Democrat,and was living at Madison,Wis.but he died about two,or three years ago.I wrote to Mr.Aalgaard once,or twice after I came back but as he was pretty well along in years,I suppose that it was too much of an effort for him to answer,and I doubt very much whether or not he is living yet.I note that you are very much interested in the conservation of our public parks,and baauty spots,and I bid you a hearty God-speed in your noble work in this direction,as I have no sympathy for these land-grabbers who would sacrifice every beautiful place in our fair land for the sole purpose of enriching themselves.Well,just a word with regard to myself and I will close.I am a married man with a wife and three grown up children,two girls and a boy,and am,at present Postmaster at this place recieving a salary of $1200.per year. My eldest daughter filed on a claim in the western part of this state last fall and is going out to establish residence on it this spring.Wishing you the best of success in your noble work,I remain,Yours sincerely,Elmer E.Gilmore,P.M.0469

Further Evidence for a Merger Origin for the Thick Disk: Galactic Stars Along Lines-of-sight to Dwarf Spheroidal Galaxies

The history of the Milky Way Galaxy is written in the properties of its stellar populations. Here we analyse stars observed as part of surveys of local dwarf spheroidal galaxies, but which from their kinematics are highly probable to be non-members. The selection function -- designed to target metal-poor giants in the dwarf galaxies, at distances of ~100kpc -- includes F-M dwarfs in the Milky Way, at distances of up to several kpc. Thestars whose motions are analysed here lie in the cardinal directions of Galactic longitude l ~ 270 and l ~ 90, where the radial velocity is sensitive to the orbital rotational velocity. We demonstrate that the faint F/G stars contain a significant population with V_phi ~ 100km/s, similar to that found by a targeted, but limited in areal coverage, survey of thick-disk/halo stars by Gilmore, Wyse & Norris (2002). This value of mean orbital rotation does not match either the canonical thick disk or the stellar halo. We argue that this population, detected at both l ~ 270 and l ~ 90, has the expected properties of `satellite debris' in the thick-disk/halo interface, which we interpret as remnants of the merger that heated a pre-existing thin disk to form the thick disk.Comment: Accepted, Astrophysical Journal Letter