Two-Dimensional Superfluid Flows in Inhomogeneous Bose-Einstein Condensates

We report a novel algorithm of constructing linear and nonlinear potentials in the two-dimensional Gross-Pitaevskii equation subject to given boundary conditions, which allow for exact analytic solutions. The obtained solutions represent superfluid flows in inhomogeneous Bose-Einstein condensates. The method is based on the combination of the similarity reduction of the two-dimensional Gross-Pitaevskii equation to the one-dimensional nonlinear Schrodinger equation, the latter allowing for exact solutions, with the conformal mapping of the given domain, where the flow is considered, to a half-space. The stability of the obtained flows is addressed. A number of stable and physically relevant examples are described.Comment: 6 pages, 3 figures, Accepted for publication in Phys. Rev.

Computability and analysis: the legacy of Alan Turing

We discuss the legacy of Alan Turing and his impact on computability and analysis.Comment: 49 page

Modeling release and distribution of harmful substances in river

The development and analysis of a computational algorithm for mathematical models of the release and spread of harmful substances is an important area of research that can help mitigate the impact of pollution on the environment and human health. Mathematical models of the distribution of harmful substances in the river are useful for predicting the spread of pollutants and identifying potential environmental and public health risks. The computational algorithm for the problem of diffusion of harmful substances can help researchers and policymakers to understand the mechanisms of pollutant dispersion and identify effective strategies for mitigating the impact of pollution. The algorithm can simulate the release and spread of harmful substances in various scenarios, including accidental spills, industrial discharges, and natural disasters. The results of a computational experiment can provide valuable insights into the behavior of pollutants in different environmental conditions and help identify potential risks and areas of concern. By analyzing the results of a computational experiment, researchers can develop effective strategies for managing and mitigating the impact of pollution on the environment and public health

In Memory of Vladimir Gerdt

Center for Computational Methods in Applied Mathematics of RUDN, Professor V.P. Gerdt, whose passing was a great loss to the scientific center and the computer algebra community. The article provides biographical information about V.P. Gerdt, talks about his contribution to the development of computer algebra in Russia and the world. At the end there are the author’s personal memories of V.P. Gerdt.Настоящая статья - мемориальная, она посвящена памяти руководителя научного центра вычислительных методов в прикладной математике РУДН, профессора В.П. Гердта, чей уход стал невосполнимой потерей для научного центра и всего сообщества компьютерной алгебры. В статье приведены биографические сведения о В.П. Гердте, рассказано о его вкладе в развитие компьютерной алгебры в России и мире. В конце приведены личные воспоминания автора о В.П. Гердте

Computational planning tools in ophthalmology: Intrastromal corneal ring surgery

This thesis addresses the problem of the simulation of intrastromal corneal ring segment surgery for the reduction of myopia and astigmatism, as well as the stabilisation of keratoconus (KC). This disease causes high myopia, irregular astigmatism and reduction of the patient's visual acuity to the point of blindness. Therefore there are several techniques to try to stabilise it and, thus, prevent its progression. For mild keratoconus, it is enough to use special spectacles or lenses to try to correct it, but in more advanced cases it would be necessary to use refractive surgery to try to stop the progression of the disease. The most common ones to avoid the cornea transplant (PK) are the cross-linking and the additive surgery of intrastromal rings. The current planning tools are empirical, based on the nomograms of the ring manufactures, and rely on the experience of the surgeon. Unfortunately, deterministic tools able to estimate the postsurgical visual results of this treatment do not exist. Therefore, the aim of the current thesis is to establish a realistic numerical framework to simulate intrastromal ring surgeries and estimate the mechanical and optical postsurgical outcomes. There are different types of rings depending on their angle and cross-section. There are two large groups of rings: segments which have an angle of less than 360º and those that cover the entire circumference. In the first group we find rings of triangular section such as the Keraring (Mediaphacos, BeloHorizonte, Brazil) and the Ferrara (AJL Ophthalmic Ltd, Spain) and rings of hexagonal section like the Intacs (Additional Technology Inc.). In the second group we can find the MyoRing (Dioptex, GmbH.) whose cross-section is the combination of a parabola and a circumference and the Intacs SK whose section is oval. Due to the complexity of the simulation, since multiple variables are involved, such as the type of rings, the model of the corneal material, the contact conditions between them, etc., two methodologies arised which simulated the insertion of the rings. Both are based on generating a hole in the corneal stroma, introducing the ring and closing the hole with the ring inside, establishing contact until the simulation is completed. In the first of the methodologies the hole was generated by introducing a pressure, while the second was used to an auxiliary tool, such as balloon angioplasty to introduce endovascular stents, which is displaced generating enough hole to insert the rings. As with all numerical simulations, they were not exempt of limitations, although with the first of the methodologies only circular cross--section rings were simulated and in some configurations, there was pressure inside the hole, so it was decided to focus on the second. Nevertheless, interesting conclusions were obtained: the greatest correction was obtained by placing the rings with the largest section near the apex, and whether the ring is located near the epithelium, the stresses generated in the stroma can cause the ring to extrude. With the second methodology based on a displacement control, it was possible to simulate most of the cross-sections and very interesting studies were carried out that gave conclusive results. The most important were: i) the most influential parameter is the depth of insertion; ii) considering the physiological depth of the surgery, the greater optical change is provided by the diameter of the ring, and the fine adjusted is reached with the size of the implant cross--section, i.e the diameter of the implant and the size of the cross--section are the key on regulating the refractive correction; iii) the friction between ring and stroma is important to consider it because a prediction of 2 or 3 diopters could be lost; iv) whether the KC progression is stress-driven, only MyoRing can stop its progression; v) when the covered arc of the segments is more than 320º, axisymmetric model could be used instead of tridimensional model, saving computational time; vi) the anisotropy of the model does not play an important role because the rings are much stiffer than corneal tissue; vii) the implants cannot consider such as second limbus since they act as a dynamic pivot that moves along the circadian cycles of intraocular pressure (IOP); viii) preliminary nomograms is built which allow the estimation of the optical outputs according to the size and typology of the ring and optical zone of implantation.Additionally, a characterisation of ring material was carried out by means two complementary methods: uncertainty analysis and iFEM optimisation, concluding that the manufacturing process of the rings could be the cause of the alteration of the material between the raw PMMA and the ring already prepared for its insertion.<br /

Space programs summary no. 37-59, volume 3, for the period 1 August to 30 September, 1969. Supporting research and advanced development

Technical research and development work for NASA space progra

Aeronautical engineering: A continuing bibliography with indexes (supplement 225)

This bibliography lists 429 reports, articles, and other documents introduced into the NASA scientific and technical information system in March, 1988

Aeronautical Engineering: A special bibliography with indexes, supplement 64, December 1975

This bibliography lists 288 reports, articles, and other documents introduced into the NASA scientific and technical information system in November 1975

Sparsity Methods for Systems and Control

The method of sparsity has been attracting a lot of attention in the fields related not only to signal processing, machine learning, and statistics, but also systems and control. The method is known as compressed sensing, compressive sampling, sparse representation, or sparse modeling. More recently, the sparsity method has been applied to systems and control to design resource-aware control systems. This book gives a comprehensive guide to sparsity methods for systems and control, from standard sparsity methods in finite-dimensional vector spaces (Part I) to optimal control methods in infinite-dimensional function spaces (Part II). The primary objective of this book is to show how to use sparsity methods for several engineering problems. For this, the author provides MATLAB programs by which the reader can try sparsity methods for themselves. Readers will obtain a deep understanding of sparsity methods by running these MATLAB programs. Sparsity Methods for Systems and Control is suitable for graduate level university courses, though it should also be comprehendible to undergraduate students who have a basic knowledge of linear algebra and elementary calculus. Also, especially part II of the book should appeal to professional researchers and engineers who are interested in applying sparsity methods to systems and control