Solid propellant rocket motor internal ballistics performance variation analysis, phase 3

Results of research aimed at improving the predictability of off nominal internal ballistics performance of solid propellant rocket motors (SRMs) including thrust imbalance between two SRMs firing in parallel are reported. The potential effects of nozzle throat erosion on internal ballistic performance were studied and a propellant burning rate low postulated. The propellant burning rate model when coupled with the grain deformation model permits an excellent match between theoretical results and test data for the Titan IIIC, TU455.02, and the first Space Shuttle SRM (DM-1). Analysis of star grain deformation using an experimental model and a finite element model shows the star grain deformation effects for the Space Shuttle to be small in comparison to those of the circular perforated grain. An alternative technique was developed for predicting thrust imbalance without recourse to the Monte Carlo computer program. A scaling relationship used to relate theoretical results to test results may be applied to the alternative technique of predicting thrust imbalance or to the Monte Carlo evaluation. Extended investigation into the effect of strain rate on propellant burning rate leads to the conclusion that the thermoelastic effect is generally negligible for both steadily increasing pressure loads and oscillatory loads

Evolution Model for Epidemic Diseases Based on the Kaplan-Meier Curve Determination

[EN] We show a simple model of the dynamics of a viral process based, on the determination of the Kaplan-Meier curvePof the virus. Together with the function of the newly infected individualsI, this model allows us to predict the evolution of the resulting epidemic process in terms of the numberEof the death patients plus individuals who have overcome the disease. Our model has as a starting point the representation ofEas the convolution ofIandP. It allows introducing information about latent patients-patients who have already been cured but are still potentially infectious, and re-infected individuals. We also provide three methods for the estimation ofPusing real data, all of them based on the minimization of the quadratic error: the exact solution using the associated Lagrangian function and Karush-Kuhn-Tucker conditions, a Monte Carlo computational scheme acting on the total set of local minima, and a genetic algorithm for the approximation of the global minima. Although the calculation of the exact solutions of all the linear systems provided by the use of the Lagrangian naturally gives the best optimization result, the huge number of such systems that appear when the time variable increases makes it necessary to use numerical methods. We have chosen the genetic algorithms. Indeed, we show that the results obtained in this way provide good solutions for the model.This research was funded by Ministerio de Ciencia, Innovacion y Universidades: MTM2016-77054-C2-1-P and Generalitat Valenciana: Catedra de Transparencia y Gestion de Datos (U.P.V.). The authors would like to thank the referees for their valuable comments which helped to improve the manuscript. The author gratefully acknowledge the support of Cátedra de Transparencia y Gestión de Datos, Universitat Politècnica de València y Generalitat Valenciana, Spain. The last author gratefully acknowledges the support of the Ministerio de Ciencia, Innovación y Universidades (Spain) and FEDER under grant MTM2016-77054-C2-1-P.Calabuig, JM.; García-Raffi, LM.; García-Valiente, A.; Sánchez Pérez, EA. (2020). Evolution Model for Epidemic Diseases Based on the Kaplan-Meier Curve Determination. Mathematics. 8(8):1-25. https://doi.org/10.3390/math8081260S12588Ai, T., Yang, Z., Hou, H., Zhan, C., Chen, C., Lv, W., … Xia, L. (2020). Correlation of Chest CT and RT-PCR Testing for Coronavirus Disease 2019 (COVID-19) in China: A Report of 1014 Cases. Radiology, 296(2), E32-E40. doi:10.1148/radiol.2020200642Chen, D., Xu, W., Lei, Z., Huang, Z., Liu, J., Gao, Z., & Peng, L. (2020). Recurrence of positive SARS-CoV-2 RNA in COVID-19: A case report. International Journal of Infectious Diseases, 93, 297-299. doi:10.1016/j.ijid.2020.03.003Kaplan, E. L., & Meier, P. (1958). Nonparametric Estimation from Incomplete Observations. Journal of the American Statistical Association, 53(282), 457-481. doi:10.1080/01621459.1958.10501452Kenah, E. (2010). Contact intervals, survival analysis of epidemic data, and estimation of R0. Biostatistics, 12(3), 548-566. doi:10.1093/biostatistics/kxq068Kenah, E. (2012). Non-parametric survival analysis of infectious disease data. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 75(2), 277-303. doi:10.1111/j.1467-9868.2012.01042.xOgłuszka, M., Orzechowska, M., Jędroszka, D., Witas, P., & Bednarek, A. K. (2019). Evaluate Cutpoints: Adaptable continuous data distribution system for determining survival in Kaplan-Meier estimator. Computer Methods and Programs in Biomedicine, 177, 133-139. doi:10.1016/j.cmpb.2019.05.023Hethcote, H. W. (2000). The Mathematics of Infectious Diseases. SIAM Review, 42(4), 599-653. doi:10.1137/s0036144500371907Silal, S. P., Little, F., Barnes, K. I., & White, L. J. (2016). Sensitivity to model structure: a comparison of compartmental models in epidemiology. Health Systems, 5(3), 178-191. doi:10.1057/hs.2015.2Kamvar, Z. N., Cai, J., Pulliam, J. R. C., Schumacher, J., & Jombart, T. (2019). Epidemic curves made easy using the R package incidence. F1000Research, 8, 139. doi:10.12688/f1000research.18002.1Lectures on Mathematical Modelling of Biological Systemshttp://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.465.8665&rep=rep1&type=pdfKeeling, M. J., & Danon, L. (2009). Mathematical modelling of infectious diseases. British Medical Bulletin, 92(1), 33-42. doi:10.1093/bmb/ldp038Brown, G. D., Oleson, J. J., & Porter, A. T. (2015). An empirically adjusted approach to reproductive number estimation for stochastic compartmental models: A case study of two Ebola outbreaks. Biometrics, 72(2), 335-343. doi:10.1111/biom.12432Huppert, A., & Katriel, G. (2013). Mathematical modelling and prediction in infectious disease epidemiology. Clinical Microbiology and Infection, 19(11), 999-1005. doi:10.1111/1469-0691.12308Paul, M. (2013). Foreseeing the future in infectious diseases: can we? Clinical Microbiology and Infection, 19(11), 991-992. doi:10.1111/1469-0691.12300Roosa, K., Lee, Y., Luo, R., Kirpich, A., Rothenberg, R., Hyman, J. M., … Chowell, G. (2020). Short-term Forecasts of the COVID-19 Epidemic in Guangdong and Zhejiang, China: February 13–23, 2020. Journal of Clinical Medicine, 9(2), 596. doi:10.3390/jcm9020596Package ‘GA’-CRAN-R Projecthttps://luca-scr.github.io/GA/Scrucca, L. (2013). GA: A Package for Genetic Algorithms inR. Journal of Statistical Software, 53(4). doi:10.18637/jss.v053.i0

The Landau Collision Integral in the Particle Basis in the PETSc Library

The Landau collision integral is often considered the gold standard in the context of kinetic plasma simulation due to its conservative properties, despite challenges involved in its discretization. The primary challenge when implementing an efficient computation of this operator is conserving physical properties of the continuum equation when the system is discretized. Recent work has achieved continuum discretizations using the method of Finite Elements which maintain conservation of mass, momentum, and energy, but which lacks monotonic entropy production. More recently, a particle discretization has been introduced which conserves mass, momentum, and energy, but maintains the benefit of monotonic entropy production necessary for the metriplecticity of the system. We present here an implementation of the particle basis Landau collision integral in the Portable Extensible Toolkit for Scientific Computing in 2 and 3V for the construction of a full geometry solver with a novel approach to computation of the entropy functional gradients. Verification of the operator is achieved with thermal equilibration and isotropization tests. All examples are available, open source, in the PETSc repository for reproduction