Novel symplectic integrators for the Klein-Gordon equation with space- and time-dependent mass

[EN] We consider the numerical time-integration of the non-stationary Klein-Gordon equation with position- and time-dependent mass. A novel class of time-averaged symplectic splitting methods involving double commutators is analyzed and 4th- and 6th-order integrators are obtained. In contrast with standard splitting methods (that contain negative coefficients if the order is higher than two), additional commutators are incorporated into the schemes considered here. As a result, we can circumvent this order barrier and construct high order integrators with positive coefficients and a much reduced number of stages, thus improving considerably their efficiency. The performance of the new schemes is tested on several examples.This work has been funded by Ministerio de Economia, Industria y Competitividad (Spain) through project MTM2016-77660-P (AEI/FEDER, UE). Kopylov has also been partly supported by grant GRISOLIA/2015/A/137 from the Generalitat Valenciana.Bader, P.; Blanes Zamora, S.; Casas, F.; Kopylov, N. (2019). Novel symplectic integrators for the Klein-Gordon equation with space- and time-dependent mass. Journal of Computational and Applied Mathematics. 350:130-138. https://doi.org/10.1016/j.cam.2018.10.011S13013835

Symplectic propagators for the Kepler problem with time-dependent mass

[EN] New numerical integrators specifically designed for solving the two-body gravitational problem with a time-varying mass are presented. They can be seen as a generalization of commutator-free quasi-Magnus exponential integrators and are based on the compositions of symplectic flows. As a consequence, in their implementation they use the mapping that solves the autonomous problem with averaged masses at intermediate stages. Methods up to order eight are constructed and shown to be more efficient than other symplectic schemes on numerical examples.This work has been funded by Ministerio de Economia, Industria y Competitividad (Spain) through project MTM2016-77660-P (AEI/FEDER, UE). Kopylov has also been partly supported by Grant GRISOLIA/2015/A/137 from the Generalitat Valenciana.Bader, P.; Blanes Zamora, S.; Casas, F.; Kopylov, N. (2019). Symplectic propagators for the Kepler problem with time-dependent mass. Celestial Mechanics and Dynamical Astronomy. 131(6):1-19. https://doi.org/10.1007/s10569-019-9903-7S1191316Abraham, R., Marsden, J.: Foundations of Mechanics, 2nd edn. Addison-Wesley, Reading (1978)Adams, F., Anderson, K., Bloch, A.: Evolution of planetary systems with time-dependent stellar mass-loss. Month. Not. R. Astronom. Soc. 432, 438–454 (2013)Alvermann, A., Fehske, H.: High-order commutator-free exponential time-propagation of driven quantum systems. J. Comput. Phys. 230, 5930–5956 (2011)Arnold, V.: Mathematical Methods of Classical Mechanics, 2nd edn. Springer, Berlin (1989)Blanes, S.: Time-average on the numerical integration of non-autonomous differential equations. SIAM J. Numer. Anal. 56, 2513–2536 (2018)Blanes, S., Casas, F.: A Concise Introduction to Geometric Numerical Integration. CRC Press, Boca Raton (2016)Blanes, S., Casas, F., Ros, J.: Processing symplectic methods for near-integrable Hamiltonian systems. Celest. Mech. Dyn. Astron. 77, 17–35 (2000)Blanes, S., Casas, F., Oteo, J., Ros, J.: The Magnus expansion and some of its applications. Phys. Rep. 470, 151–238 (2009)Blanes, S., Casas, F., Thalhammer, M.: High-order commutator-free quasi-Magnus exponential integrators for non-autonomous linear evolution equations. Comput. Phys. Commun. 220, 243–262 (2017)Blanes, S., Casas, F., Thalhammer, M.: Convergence analysis of high-order commutator-free quasi Magnus exponential integrators for nonautonomous linear evolution equations of parabolic type. IMA J. Numer. Anal. 38, 743–778 (2018)Danby, J.: Fundamentals of Celestial Mechanics. Willmann-Bell, Richmond (1988)El-Saftawy, M., El-Salam, F.A.: Second-order theory for the two-body problem with varying mass including periastron effect. Nonlinear Dyn. 88, 1723–1732 (2017)Farrés, A., Laskar, J., Blanes, S., Casas, F., Makazaga, J., Murua, A.: High precision symplectic integrators for the solar system. Celest. Mech. Dyn. Astron. 116, 141–174 (2013)Hadjidemetriou, J.: Secular variation of mass and the evolution of binary systems. In: Kopal, Z. (ed.) Advances in Astronomy and Astrophysics, vol. 5, pp. 131–188. Academic Press, New York (1967)Hairer, E., Nørsett, S., Wanner, G.: Solving Ordinary Differential Equations I, Nonstiff Problems, Second revised edn. Springer, Berlin (1993)Hairer, E., Lubich, C., Wanner, G.: Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations, Second edn. Springer, Berlin (2006)Laskar, J.: Analytical framework in Poincaré variables for the motion of the solar system. In: Roy, A. (ed.) Predictability, Stability and Chaos in $$N$$-Body Dynamical Systems, NATO ASI, pp. 93–114. Plenum Press, New York (1991)Laskar, J., Robutel, P.: High order symplectic integrators for perturbed Hamiltonian systems. Celest. Mech. Dyn. Astron. 80, 39–62 (2001)Li, L.S.: Secular influence of the evolution of orbits of near-Earth asteroids induced by temporary variation of G and solar mass-loss. Month. Not. R. Astron. Soc. 431, 2971–2974 (2013)McLachlan, R.: On the numerical integration of ODE’s by symmetric composition methods. SIAM J. Sci. Comput. 16, 151–168 (1995)McLachlan, R., Quispel, R.: Splitting methods. Acta Numer. 11, 341–434 (2002)Oteo, J.A., Ros, J.: The Magnus expansion for classical Hamiltonian systems. J. Phys. A: Math. Gen. 24, 5751–5762 (1991)Rahoma, W.: Investigating exoplanet orbital evolution around binary star systems. J. Astron. Space Sci. 33, 257–264 (2016)Rahoma, W., El-Salam, F.A., Ahmed, M.: Analytical treatment of the two-body problem with slowly varying mass. J. Astrophys. Astron. 30, 187–205 (2009)Sanz-Serna, J., Calvo, M.: Numerical Hamiltonian Problems. Chapman & Hall, London (1994)Veras, D., Hadjidemetriou, J., Tout, C.: An exoplanet’s response to anisotropic stellar mass loss during birth and death. Month. Not. R. Astron. Soc. 435, 2416–2430 (2013)Wisdom, J., Holman, M.: Symplectic maps for the N-body problem. Astron. J. 102, 1528–1538 (1991

Symplectic integrators for second-order linear non-autonomous equations

[EN] Two families of symplectic methods specially designed for second-order time-dependent linear systems are presented. Both are obtained from the Magnus expansion of the corresponding first-order equation, but otherwise they differ in significant aspects. The first family is addressed to problems with low to moderate dimension, whereas the second is more appropriate when the dimension is large, in particular when the system corresponds to a linear wave equation previously discretised in space. Several numerical experiments illustrate the main features of the new schemes. (C) 2017 Elsevier B.V. All rights reserved.Bader, Blanes, Casas and Kopylov acknowledge the Ministerio de Economia y Competitividad (Spain) for financial support through the coordinated project MTM2013-46553-C3-3-P. Additionally, Kopylov has been partly supported by fellowship GRISOLIA/2015/A/137 from the Generalitat Valenciana.Bader, P.; Blanes Zamora, S.; Casas, F.; Kopylov, N.; Ponsoda Miralles, E. (2018). Symplectic integrators for second-order linear non-autonomous equations. Journal of Computational and Applied Mathematics. 330:909-919. https://doi.org/10.1016/j.cam.2017.03.028S90991933

Cation binding to 15-TBA quadruplex DNA is a multiple-pathway cation-dependent process

A combination of explicit solvent molecular dynamics simulation (30 simulations reaching 4 µs in total), hybrid quantum mechanics/molecular mechanics approach and isothermal titration calorimetry was used to investigate the atomistic picture of ion binding to 15-mer thrombin-binding quadruplex DNA (G-DNA) aptamer. Binding of ions to G-DNA is complex multiple pathway process, which is strongly affected by the type of the cation. The individual ion-binding events are substantially modulated by the connecting loops of the aptamer, which play several roles. They stabilize the molecule during time periods when the bound ions are not present, they modulate the route of the ion into the stem and they also stabilize the internal ions by closing the gates through which the ions enter the quadruplex. Using our extensive simulations, we for the first time observed full spontaneous exchange of internal cation between quadruplex molecule and bulk solvent at atomistic resolution. The simulation suggests that expulsion of the internally bound ion is correlated with initial binding of the incoming ion. The incoming ion then readily replaces the bound ion while minimizing any destabilization of the solute molecule during the exchange

Personalized Medicine in Coronary Artery Disease: Where Are We in 2022?

Coronary artery disease (CAD) is the leading cause of morbidity and mortality in developed and in most developing countries [...

Computational Analysis of Haemodynamic Indices in Synthetic Atherosclerotic Coronary Netwroks

Haemodynamic indices are widely used in clinical practice when deciding on a particular type of treatment. Low quality of the computed tomography data and tachycardia complicate interpretation of the measured or simulated values. In this work, we present a novel approach for evaluating resistances in terminal coronary arteries. Using 14 measurements from 10 patients, we show that this algorithm retains the accuracy of 1D haemodynamic simulations in less detailed (truncated) geometric models of coronary networks. We also apply the variable systole fraction model to study the effect of elevated heart rate on the values of fractional flow reserve (FFR), coronary flow reserve (CFR) and instantaneous wave-free ratio (iFR). We conclude that tachycardia may produce both overestimation or underestimation of coronary stenosis significance

Remote electrocardiogram monitoring in cancer patients for detecting cardiotoxicity. Case report

Cardiotoxicity is the direct adverse effect of anticancer agents on the function or structure of the heart, occurring both during treatment and many years later. The manifestations of cardiotoxicity can be very different: heart failure, coronary heart disease, cardiomyopathy, myocarditis, pericarditis, and arrhythmias, including atrial fibrillation (AF). The incidence of AF in the cancer patient population during therapy is 20–30%. Current options of remote electrocardiogram monitoring ensure the timely detection and treatment of AF in cancer patients, including the administration of anticoagulants. The article presents a clinical case of a 59-year-old patient with squamous cell carcinoma of the lower third of the esophagus after the first course of the TPF polychemotherapy regimen (docetaxel, cisplatin, 5-fluorouracil) with AF detected using a single-channel electrocardiogram monitor in a smartphone case

DUOX1 Gene Missense Mutation Confers Susceptibility on Type 2 Amiodarone-Induced Thyrotoxicosis

Possible triggers and genetic markers involved in pathogenesis of amiodarone-induced thyrotoxicosis (AIT) or amiodarone-induced hypothyroidism (AIH) are currently unknown. This study aimed to analyze the association between polymorphisms in the genes involved in thyroid hormones biosynthesis and metabolism. Thirty-nine consecutive patients with confirmed type 2 amiodarone-induced thyrotoxicosis were enrolled; 39 patients on the same therapy for at least 6 months without thyroid pathology were included as a control group. A comparative study was carried out to determine the distribution and genotypes of polymorphic markers of the (Na)-iodide symporter (NIS) genes (rs7250346, C/G substitution), thyroid stimulating hormone receptor (TSHR) (rs1991517, C/G substitution), thyroid peroxidase (TPO) (rs 732609, A/C substitution), DUOX 1-1 (C/T substitution), DUOX 1-2 (G/T substitution), DUOX 1-3 (C/T substitution), glutathione peroxidase 3 (GPX3) (C/T substitution), glutathione peroxidase 4 (GPX4) (C/T substitution). Statistical analysis was performed using Prism (Version 9.0.0 (86)). This study showed that the risk of AIT2 is 3.18 times higher in the G/T of the DUOX1 gene carriers. This study is the first report of genetic markers associated with amiodarone-related adverse events conducted in humans. The obtained results indicate the necessity for a personalized approach to amiodarone administration

Pharmacodynamics of frigid zone plant Taxus cuspidata S. et Z. against skin melanin deposition, oxidation, inflammation and allergy

Taxus cuspidata S. et Z. is a precious species of frigid zone plant belonging to the Taxaceae family, which possesses anticancer, anti-inflammatory, hypoglycemic, and antibacterial pharmacological properties. While taxane extracted from Taxus chinensis has been reported to elicit antioxidant activities, whether Taxus cuspidata S. et Z. has skin-protective actions against injuries remained unknown. This study aims to explore the pharmacological effects of three Taxus extracts on skin melanin deposition, oxidation, inflammation, and allergy so as to provide new ideas for the prevention and treatment of various diseases related to skin damage