Discrete Nonholonomic LL Systems on Lie Groups

This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two classical nonholonomic systems, the Suslov top and the Chaplygin sleigh. The preservation of the reduced energy by the discrete flow is observed and the discrete momentum conservation is discussed.Comment: 32 pages, 13 figure

Poisson structures for reduced non-holonomic systems

Borisov, Mamaev and Kilin have recently found certain Poisson structures with respect to which the reduced and rescaled systems of certain non-holonomic problems, involving rolling bodies without slipping, become Hamiltonian, the Hamiltonian function being the reduced energy. We study further the algebraic origin of these Poisson structures, showing that they are of rank two and therefore the mentioned rescaling is not necessary. We show that they are determined, up to a non-vanishing factor function, by the existence of a system of first-order differential equations providing two integrals of motion. We generalize the form of that Poisson structures and extend their domain of definition. We apply the theory to the rolling disk, the Routh's sphere, the ball rolling on a surface of revolution, and its special case of a ball rolling inside a cylinder.Comment: 22 page

Nanoscale phase separation in La0.7Ca0.3MnO3La_{0.7}Ca_{0.3}MnO_3 films: evidence for the texture driven optical anisotropy

The IR optical absorption (0.1-1.5 eV) in the $La_{0.7}Ca_{0.3}MnO_3$ films on LAO substrate exhibits the drastic temperature evolution of the spectral weight evidencing the insulator to metal transition. Single crystal films were found to reveal strong linear dichroism with anomalous spectral oscillations and fairly weak temperature dependence. Starting from the concept of phase separation, we develop the effective medium model to account for these effects. The optical anisotropy of the films is attributed to the texturization of the ellipsoidal inclusions of the quasimetal phase caused by a mismatch of the film and substrate and the twin texture of the latter.Comment: 6 pages, 5 Encapsulated PostScript figures, uses RevTeX

The David procedure after the Ross operation: case series

Pulmonary autograft in the aortic position provides high survival rate and quality of life for patients, low incidence of valve-related complications, and excellent hemodynamic characteristics both in the early and long-term period. However, in some patients in the long-term period, pulmonary autograft may dilate, which in turn is one of the reasons for reoperations. In patients who require surgery for annuloaortic ectasia with aortic valve (AV) regurgitation or aortic root aneurysm (or both) with normal AV leaflets, David procedure is considered.Aim. To analyze results of David procedure after a prior Ross operation.Material and methods. From April 2009 to December 2020, 212 Ross operations were performed on patients 18 years of age and older. The median age of the operated patients was 34 (27-45) years. In the long-term period, 10 (4,7%) patients required a second AV operation and 7 (3,3%) of them required another intervention on the ascending aorta due to aortic dilatation. Four out of 10 patients underwent David procedure. The follow-up period for patients after David procedure ranged from 2 to 84 months.Results. The age of patients ranged from 23 to 45 years. Three patients had hypertension. The follow-up period from Ross's operation to David's one was 26 to 140 months. All patients had enlarged aortic annulus from 27 to 30 mm. The duration of myocardial ischemia ranged from 87 to 142 minutes, while the duration of artificial circulation — from 119 to 165 minutes. The graft diameter was 30 mm in two patients and 32 mm in the remaining ones. The length of stay in intensive care unit ranged from 16 to 23 hours. In the early postoperative period, no one had following postoperative complications: acute renal failure requiring hemodialysis, perioperative myocardial injury, stroke, sternal infection, respiratory failure requiring mechanical ventilation for ≥24 hours, resternotomy for bleeding and tamponade. In addition, there were no in hospital deaths. All patients had no aortic regurgitation at the time of discharge. All patients are alive and there were no reoperations. In one patient, in the long-term period, there was a mild aortic regurgitation, while in three patients — there is no regurgitation.Conclusion. The presented case series show that David procedure can be performed safely and effectively in a significant number of patients requiring a second autograft surgery due to neosinus dilatation. In the medium term, the David procedure has shown good outcomes in these patients with 100% survival and no aortic regurgitation and reoperation

Discrete Nonholonomic Lagrangian Systems on Lie Groupoids

This paper studies the construction of geometric integrators for nonholonomic systems. We derive the nonholonomic discrete Euler-Lagrange equations in a setting which permits to deduce geometric integrators for continuous nonholonomic systems (reduced or not). The formalism is given in terms of Lie groupoids, specifying a discrete Lagrangian and a constraint submanifold on it. Additionally, it is necessary to fix a vector subbundle of the Lie algebroid associated to the Lie groupoid. We also discuss the existence of nonholonomic evolution operators in terms of the discrete nonholonomic Legendre transformations and in terms of adequate decompositions of the prolongation of the Lie groupoid. The characterization of the reversibility of the evolution operator and the discrete nonholonomic momentum equation are also considered. Finally, we illustrate with several classical examples the wide range of application of the theory (the discrete nonholonomic constrained particle, the Suslov system, the Chaplygin sleigh, the Veselova system, the rolling ball on a rotating table and the two wheeled planar mobile robot).Comment: 45 page

Phoenix: A CubeSat Mission to Study the Impact of Urban Heat Islands Within the U.S.

Phoenix is a student-led CubeSat mission, developed at Arizona State University (ASU), to study the effects of Urban Heat Islands in several U.S. cities through infrared remote sensing and educate students on space mission design. The spacecraft is designed using commercial off-the-shelf components (COTS) and several custom support boards developed by the student team. As such, the student team was responsible for the design, test, and validation of the spacecraft to demonstrate the capability of using COTS hardware to conduct high-fidelity science. This paper details the mission’s concept of operations, as well as the spacecraft and ground system design that was developed to complete the mission objective. In addition, it details the mission’s current status now that Phoenix has entered the operations phase, along with resources which have proved beneficial to the team while working with the spacecraft in orbit

The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation

We consider the motion of a planar rigid body in a potential flow with circulation and subject to a certain nonholonomic constraint. This model is related to the design of underwater vehicles. The equations of motion admit a reduction to a 2-dimensional nonlinear system, which is integrated explicitly. We show that the reduced system comprises both asymptotic and periodic dynamics separated by a critical value of the energy, and give a complete classification of types of the motion. Then we describe the whole variety of the trajectories of the body on the plane.Comment: 25 pages, 7 figures. This article uses some introductory material from arXiv:1109.321

Pulmonary homograft dysfunction after Ross procedure in adults: a single center experience

The Ross procedure was first proposed by Donald Ross in 1967. Numerous studies show excellent long-term outcomes of the Ross operation. One of its disadvantages is the intervention on two valves due to pulmonary homograft dysfunction.Aim.  To study long-term outcomes of pulmonary homograft use after Ross operation (cumulative incidence of pulmonary homograft dysfunction, freedom from reoperation on pulmonary homograft, long-term survival, predictors of pulmonary homograft dysfunction) using data from one Russian center.Material  and  methods. A retrospective study included patients aged 18 years and older with aortic valve disease who underwent Ross procedure from April 2009 to December 2020 by a single surgeon. The age of the patients was 35 (26-44) years (men, 159 (75%)). Infective endocarditis as a cause of aortic valve pathology was diagnosed in 55 (26%) patients. Bicuspid aortic valve was diagnosed in 131 (62%) patients. The median follow-up period was 79 (26,5102,7) months.Results. Combined interventions were performed in 40 cases (18,9%). The modified Ross procedure was used in 54 (25,5%) cases (intra-aortic — 29, using Dacron tube graft — 25). Inhospital mortality was 0,5%. The 5- and 10-year allcause survival rates were 98,5% and 95,4%, while the 10-year cumulative pulmonary valve reoperation rate and pulmonary homograft dysfunction was 4,6% and 35,2%, respectively. The only factor affecting pulmonary homograft dysfunction was patient age ≤30 years (odds ratio =0,2 with 95% confidence interval: 0,06-0,7; p=0,02).Conclusion. Fresh pulmonary homografts have a low incidence of dysfunction and reintervention after Ross procedure. Young age is the only independent risk factor for pulmonary homograft dysfunction