A family of Kurchatov-type methods and its stability

[EN] We present a parametric family of iterative methods with memory for solving of nonlinear problems including Kurchatov¿s scheme, preserving its second-order of convergence. By using the tools of multidimensional real dynamics, the stability of members of this family is analyzed on low-degree polynomials, showing some elements of this class more stable behavior than the original Kurchatov¿s method. The iteration is extended for multi-dimensional case. Computational efficiencies of proposed technique is discussed and compared with the existing methods. A couple of numerical examples are considered to test the performance of the new family of iterations.The authors thank to the anonymous referees for their valuable comments and for the suggestions that have improved the final version of the paper. This research was partially supported by Ministerio de Economia y Competitividad MTM2014-52016-C2-2-P and Generalitat Valenciana PROMETEO/2016/089.Cordero Barbero, A.; Soleymani, F.; Torregrosa Sánchez, JR.; Haghani, FK. (2017). A family of Kurchatov-type methods and its stability. Applied Mathematics and Computation. 294:264-279. https://doi.org/10.1016/j.amc.2016.09.021S26427929

Dynamical analysis of an iterative method with memory on a family of third-degree polynomials

Qualitative analysis of iterative methods with memory has been carried out a few years ago. Most of the papers published in this context analyze the behaviour of schemes on quadratic polynomials. In this paper, we accomplish a complete dynamical study of an iterative method with memory, the Kurchatov scheme, applied on a family of cubic polynomials. To reach this goal we transform the iterative scheme with memory into a discrete dynamical system defined on R2. We obtain a complete description of the dynamical planes for every value of parameter of the family considered. We also analyze the bifurcations that occur related with the number of fixed points. Finally, the dynamical results are summarized in a parameter line. As a conclusion, we obtain that this scheme is completely stable for cubic polynomials since the only attractors that appear for any value of the parameter, are the roots of the polynomial.This paper is supported by the MCIU grant PGC2018-095896-B-C22. The first and the last authors are also supported by University Jaume I grant UJI-B2019-18. Moreover, the authors would like to thank the anonymous reviewers for their comments and suggestions

COLLABORATING TO RUIN? US NATIONAL LABORATORIES AND THE IMPACT OF INTERNATIONAL RESEARCH PARTNERSHIPS

Following the Cold War, Russian and US research institutions forged new collaborative ties to take advantage of perceived complementarities in conducting scientific research as part of US nonproliferation initiatives. These ties appear to have been successful in the broader nonproliferation context as relatively few Russian nuclear scientists emigrated to perceived rogue states like Iran and North Korea in the years that immediately followed the dissolution of the Soviet Union. Early on, the research benefits of these ties appeared to be significant. Today, as the Russian science and technology cadre is going through a demographic transition and the Russian state is following a corporatist policy in rebuilding its scientific research and development base, the appropriable benefits associated with continuing these policies for US research partners are less obvious. This assessment is an attempt to gain an empirical understanding of the appropriable benefits from US-Russian research engagement apart from the nonproliferation context. As such, this study examines these collaborations using an alternative network analysis methodology with reference to a knowledge-based model of research and development generation. To assure tractability, the analysis focuses its attention on a subset of institutions that have been broadly ignored in studies of research collaboration — US national laboratories and their Russian counterparts. The resulting analysis challenges the conventional wisdom of the appropriable virtues of scientific collaboration. For the limited set of relationships examined in this study, this analysis suggests participation in international collaborations between the largest US national laboratories and their Russian counterparts can actually reduce individual researchers basic research productivity — clearly not a policy goal for a major national research and development establishment. To achieve better appropriability, this finding and its contextual factors are used to demarcate areas of inquiry where Russian-US engagement has an empirical track record of utility and should continue from areas where collaboration has had little success

A new design for a green calcium indicator with a smaller size and a reduced number of calcium-binding sites

Genetically encoded calcium indicators (GECIs) are mainly represented by two- or one-fluorophore-based sensors. One type of two-fluorophore-based sensor, carrying Opsanus troponin C (TnC) as the Ca2+-binding moiety, has two binding sites for calcium ions, providing a linear response to calcium ions. One-fluorophore-based sensors have four Ca2+-binding sites but are better suited for in vivo experiments. Herein, we describe a novel design for a one-fluorophore-based GECI with two Ca2+-binding sites. The engineered sensor, called NTnC, uses TnC as the Ca2+-binding moiety, inserted in the mNeonGreen fluorescent protein. Monomeric NTnC has higher brightness and pH-stability in vitro compared with the standard GECI GCaMP6s. In addition, NTnC shows an inverted fluorescence response to Ca2+. Using NTnC, we have visualized Ca2+ dynamics during spontaneous activity of neuronal cultures as confirmed by control NTnC and its mutant, in which the affinity to Ca2+ is eliminated. Using whole-cell patch clamp, we have demonstrated that NTnC dynamics in neurons are similar to those of GCaMP6s and allow robust detection of single action potentials. Finally, we have used NTnC to visualize Ca2+ neuronal activity in vivo in the V1 cortical area in awake and freely moving mice using two-photon microscopy or an nVista miniaturized microscope

Strong electric fields induced on a sharp stellar boundary

Due to a first order phase transition, a compact star may have a discontinuous distribution of baryon as well as electric charge densities, as e.g. at the surface of a strange quark star. The induced separation of positive and negative charges may lead to generation of supercritical electric fields in the vicinity of such a discontinuity. We study this effect within a relativistic Thomas-Fermi approximation and demonstrate that the strength of the electric field depends strongly on the degree of sharpness of the surface. The influence of strong electric fields on the stability of compact stars is discussed. It is demonstrated that stable configurations appear only when the counter-pressure of degenerate fermions is taken into consideration.Comment: 13 pages, 2 figure

Complex Phase Behavior of The System of Particles with Smooth Potential with Repulsive Shoulder and Attractive Well

We report a detailed simulation study of the phase behavior of core softened system with attractive well. Different repulsive shoulder widthes and attractive well depthes are considered which allows to monitor the influence of repulsive and attractive forces on the phase diagram of the system. Thermodynamic anomalies in the systems are also studied. It is shown that the diffusion anomaly is stabilized by small attraction.Comment: 11 pages, 13 figure

A study of stainless steel as a material of construction for a molten salt reactor

The aim of this work was to investigate the corrosion of stainless steel within a molten salt, with the possibility that it could be used as a construction material within a molten salt fuelled nuclear reactor. Four different metal compositions were used; stainless steel 316L, stainless steel 304L, LDX2101 and iron, and these were tested in two different molten salts, LiCl-KCl-NaCl and KCl-NaCl at 600 and 750°C. Stainless steel 316L was tested for one day, one, three, four and six weeks. The samples were analysed using SEM/EDX and XRD. It was found that in general, a lithium containing spinel formed on the surface of the stainless steel, LiCrO2, with a large percentage coverage. As immersion time increased the bulk also showed signs of attack. The three week test showed the formation of five different corrosion products and analysis suggests they are a combination of numerous mixed oxides. The three week test was subsequently repeated and showed the formation of a lithium containing spinel as observed in the one week test. Further testing investigated the role of lithium in the formation of the protective layer, a LiCrO2 layer formed on stainless steel 316L in the presence of a ternary salt, whereas mixed oxides were generally observed in the binary salt. Again an anomalous result was obtained in the three week binary test, where a tabular crystal containing sodium iron and oxide was formed. Finally compositional changes were examined, and the subsequent effect they had on the corrosion layer. It was found that increasing the chromium content does not necessarily increase the surface coverage and it is likely that other elements aid in the formation of the protective layer. From the results obtained in this work it is possible that with extensive research a stainless steel, which has been specifically designed, could be utilised within a molten salt reactor

Summary of the CERN Workshop on Materials for Collimators and Beam Absorbers

The main focus of the workshop was on collimators and beam absorbers for (mainly) High Energy Hadron Accelerators, with the energy stored in the beams far above damage limit. The objective was to better understand the technological limits imposed by mechanisms related to beam impact on materials. The idea to organise this workshop came up during the High Intensity High Brightness Hadron Beams, ICFA-HB2006 in Japan [1]. The workshop was organised 3-5 September 2007 at CERN, with about 60 participants, including 20 from outside CERN. About 30 presentations were given [2]. The event was driven by the LHC challenge, with more than 360 MJoule stored in each proton beam. The entire beam or its fraction will interact with LHC collimators and beam absorbers, and with the LHC beam dump blocks. Collimators and beam absorbers are also of the interest for other labs and accelerators: - CERN: for the CNGS target, for SPS beam absorbers (extraction protection) and collimators for protecting the transfer line between SPS and LHC - GSI: SIS18 and SIS 100/200, Super-FRS target, HED experiments, Antiproton target, etc. - Fermilab: Tevatron and Main Injector collimation systems; neutrino production targets (MINOS, SNuMI, NOVA); antiproton production targets; pion production targets and beam absorbers for neutrino factories and muon colliders - ILC: positron production targets, beam absorbers and collimators for a beam delivery system

High Performance Multidimensional Iterative Processes for Solving Nonlinear Equations

[ES] En gran cantidad de problemas de la matemática aplicada, existe la necesidad de resolver ecuaciones y sistemas no lineales, dado que numerosos problemas, finalmente, se reducen a estos. Conforme aumenta la dificultad de los sistemas, la obtención de la solución analítica se vuelve más compleja. Además, con el aumento de las herramientas computacionales, las dimensiones de los problemas a resolver han crecido de manera exponencial, por lo que se vuelve más necesario obtener una aproximación a la solución de manera sencilla y que no requiera mucho tiempo y coste computacional. Esta es una de las razones por las que los métodos iterativos han aumentado su importancia en los últimos años, ya que se han diseñado multitud de procesos con el fin de que converjan rápidamente a la solución y, de esta forma, poder resolver problemas que con las herramientas clásicas resultaría más costoso. La presente Tesis Doctoral, se centra en estudiar y diseñar numerosos métodos iterativos que mejoren a los esquemas clásicos en cuanto a su orden de convergencia, accesibilidad, cantidad de soluciones que obtienen o aplicabilidad a problemas con características especiales, como la no diferenciabilidad o la multiplicidad de las raíces. Entre los procesos que se estudian en esta memoria, se pueden encontrar desde una familia de métodos multipaso óptimos para la resolución de ecuaciones, hasta una familia paramétrica libre de derivadas de esquemas con función peso a la que se introduce memoria para la resolución de sistemas no lineales. Se destacan otros métodos en esta memoria como esquemas iterativos que obtienen raíces con diversas multiplicidades para ecuaciones y procesos que aproximan raíces de forma simultánea, tanto para ecuaciones como para sistemas, y, tanto para raíces simples como para múltiples. Además, parte de esta memoria se centra en cómo realizar el análisis dinámico para métodos iterativos con memoria que resuelven sistemas de ecuaciones no lineales, a la par que se realiza dicho estudio para diversos esquemas iterativos conocidos. Este análisis dinámico permite visualizar y analizar los posibles comportamientos de los procesos iterativos en función de las aproximaciones iniciales. Los resultados anteriormente descritos forman parte de esta Tesis Doctoral para la obtención del título de Doctora en Matemáticas.[CA] En gran quantitat de problemes de la matemàtica aplicada, existeix la necessitat de resoldre equacions i sistemes no lineals, atés que nombrosos problemes, finalment, es redueixen a aquests. Conforme augmenta la dificultat dels sistemes, l'obtenció de la solució analítica es torna més complexa. A més, amb l'augment de les eines computacionals, les dimensions dels problemes a resoldre han crescut de manera exponencial, per la qual cosa es torna més necessari obtindre una aproximació a la solució de manera senzilla i que no requerisca molt temps i cost computacional. Aquesta és una de les raons per les quals els mètodes iteratius han augmentat la seua importància en els últims anys, ja que s'han dissenyat multitud de processos amb la finalitat que convergisquen ràpidament a la solució i, d'aquesta manera, poder resoldre problemes que amb les eines clàssiques resultaria més costós. La present Tesi Doctoral, es centra en estudiar i dissenyar nombrosos mètodes iteratius que milloren als esquemes clàssics en quant al seu ordre de convergència, accessibilitat, quantitat de solucions que obtenen o aplicabilitat a problemes amb característiques especials, com la no diferenciabilitat o la multiplicitat de les arrels. Entre els processos que s'estudien en aquesta memòria, es poden trobar des d'una família de mètodes multipas òptims per a la resolució d'equacions, fins a una família paramètrica lliure de derivades de esquemes amb funció pes a la que s'introdueix memòria per a la resolució de sistemes no lineals. Es destanquen altres mètodes en aquesta memòria com esquemes iteratius que obtenen arrels amb diverses multiplicitats per a equacions i processos que aproximen arrels de manera simultània, tant per a equacions com per a sistemes, i, tant per a arrels simples com per a múltiples. A més, part d'aquesta memòria es centra en com realitzar l'anàlisi dinàmic per a mètodes iteratius amb memòria que resolen sistemes d'equacions no lineals, al mateix temps que es realitza aquest estudi per a diversos esquemes iteratius coneguts. Aquest anàlisi dinàmic permet visualitzar i analitzar els possibles comportaments dels mètodes iteratius en funció de les aproximacions inicials. Els resultats anteriorment descrits formen part d'aquesta Tesi Doctoral per a l'obtenció del títol de Doctora en Matemàtiques.[EN] In a large number of problems in applied mathematics, there is a need to solve nonlinear equations and systems, since many problems eventually are reduced to these. As the difficulty of the systems increases, obtaining the analytical solution becomes more complex. Furthermore, with the growth of computational tools, the dimensions of the problems to be solved have increased exponentially, making it more essential to obtain an approximation to the solution in a simple way that does not require significant time and computational cost. That is one of the reasons why iterative methods have increased their importance in recent years, as a multitude of schemes have been designed to converge rapidly to the solution and, in this way, to be able to solve problems that would be more arduous to solve using classical tools. This Doctoral Thesis focuses on the study and design of numerous iterative methods that improve classical schemes in terms of their order of convergence, accessibility, number of solutions obtained or applicability to problems with special characteristics, such as non-differentiability or multiplicity of roots. The procedures studied in this report range from a family of optimal multi-step methods for solving equations, to a parametric derivative-free family of weight function schemes, to which memory is introduced for solving nonlinear systems. Additional procedures are described in this report such as iterative schemes that obtain roots with different multiplicities for equations and methods that approximate roots simultaneously for equations as well as for systems, and for simple as well as for multiples roots. In addition, part of this report focuses on how to perform the dynamical analysis for iterative schemes with memory that solve systems of nonlinear equations, as well as this study is carried out for different known iterative procedures. This dynamical analysis allows us to visualise and analyse the possible behaviours of the iterative methods depending on the initial approximations. The results described above form part of this Doctoral Thesis to obtain the title of Doctor in Mathematics.Triguero Navarro, P. (2023). High Performance Multidimensional Iterative Processes for Solving Nonlinear Equations [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/19426