The point charge oscillator: Qualitative and analytical investigations

We determine the global phase portrait of a mathematical model describing the point charge oscillator. It shows that the family of closed orbits describing the point charge oscillations has two envelopes: an equilibrium point and a homoclinic orbit to an equilibrium point at infinity. We derive an expression for the growth rate of the primitive perod Τα of the oscillation with the amplitude α as α tends to infinity. Finally, we determine an exact relation between period and amplitude by means of the Jacobi elliptic function cn

The point charge oscillator: qualitative and analytical investigations

We study the mathematical model of the point charge oscillator which has been derived by A. Beléndez et al. [2]. First we determine the global phase portrait of this model in the Poincaré disk. It consists of a family of closed orbits surrounding the unique finite equilibrium point and of a continuum of homoclinic orbits to the unique equilibrium point at infinity. Next we derive analytic expressions for the relationship between period (frequency) and amplitude. Further, we prove that the period increases monotone with the amplitude and derive an expression for its growth rate as the amplitude tends to infinity. Finally, we determine a relation between period and amplitude by means of the complete elliptic integral of the first kind K(k) and of the Jacobi elliptic function cn

High-Order Energy Balance Method to Nonlinear Oscillators

Energy balance method (EBM) is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the first- and second-order approximation, respectively. The third-order approximation has an accuracy as high as 0.008%. Excellent agreement of the approximated frequencies and periodic solutions with the exact ones is demonstrated for several values of parameters of the oscillator

Elements of Ion Linear Accelerators, Calm in The Resonances, Other_Tales

The main part of this book, Elements of Linear Accelerators, outlines in Part 1 a framework for non-relativistic linear accelerator focusing and accelerating channel design, simulation, optimization and analysis where space charge is an important factor. Part 1 is the most important part of the book; grasping the framework is essential to fully understand and appreciate the elements within it, and the myriad application details of the following Parts. The treatment concentrates on all linacs, large or small, intended for high-intensity, very low beam loss, factory-type application. The Radio-Frequency-Quadrupole (RFQ) is especially developed as a representative and the most complicated linac form (from dc to bunched and accelerated beam), extending to practical design of long, high energy linacs, including space charge resonances and beam halo formation, and some challenges for future work. Also a practical method is presented for designing Alternating-Phase- Focused (APF) linacs with long sequences and high energy gain. Full open-source software is available. The following part, Calm in the Resonances and Other Tales, contains eyewitness accounts of nearly 60 years of participation in accelerator technology. (September 2023) The LINACS codes are released at no cost and, as always,with fully open-source coding. (p.2 & Ch 19.10)Comment: 652 pages. Some hundreds of figures - all images, there is no data in the figures. (September 2023) The LINACS codes are released at no cost and, as always,with fully open-source coding. (p.2 & Ch 19.10

Engineering Dynamics and Life Sciences

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Chemical Sensors (Modelling the Photophysics of Cation Detection by Organic Dyes)

La présence croissante de diverses substances dans notre environnement, conséquencedes activités anthropiques de ces dernières décennies, a entraîné un besoingrandissant et urgent de nouveaux matériaux et dispositifs dans la quête de senseurschimiques efficaces et fiables. D'énormes progrès technologiques ont permis de mettreà disposition toute une gamme d'outils techniques pour leur développement, enprenant en compte les exigences à respecter en terme de sélectivité ou de rapidité deréponse, entre autres. Dans ce contexte, les méthodes de chimie quantique permettentune compréhension fondamentale des processus en jeu dans la détection des espèceschimiques, et par extension, l'élaboration de manière rationnelle de nouveauxmatériaux sensibles. Certaines molécules organiques pouvant être largementfonctionnalisées, elles constituent un point de départ idéal en raison des importantesmodulations possibles de leurs propriétés par des modifications structuralesappropriées.Cette étude vise à développer de manière rationnelle des chromoionophores pour lacomplexation de cations par une approche combinant méthodes de chimiecomputationnelles et caractérisation par spectroscopie optique. Deux pointsprincipaux ont été traités à l'aide de la Théorie de la Fonctionnelle de la Densité(DFT) et son extension dépendante du temps (TD-DFT): d'une part les relationsstructure moléculaire-propriétés optiques de chromophores, d'autre part le phénomènede complexation. En particulier, la détection de l'ion Zn2+, démontrée de manièrethéorique et expérimentale, est finalement réalisée après intégration du senseurmoléculaire dans un dispositif à fibre optique.The increasing presence of various substances in our environment has brought abouta growing need for rapid emergence of new materials and devices in the quest forefficient and reliable chemical sensors. Massive technological progress have madeavailable an extensive range of technical tools to serve their development, accountingfor the requirements to be fulfilled (selectivity, quick response..). In this context,quantum chemistry methods provide a fundamental understanding of the processes atstake in the detection of chemical species and allow for rational design of sensingmaterials. Certain organic molecules can be extensively functionalised and thusconstitute an evident starting point owing to the tunability of their propertiesprovided by appropriate choice of structural modifications. The versatility of somechromophores associated to the selectivity offered by receptor units constitute theresearch playground for the development of ever better chemosensors.The present research aims at the rational development of chromoionophores for thecomplexation of cations, combining computational chemistry methods with basicspectroscopic characterisation. Using Density Functional Theory (DFT) and its timedependentextension (TD-DFT), two main aspects were treated, namely therelationship between molecular structure and optical properties of organicchromophores featuring valuable characteristics, and the complexation phenomenon.Photophysics of Zn2+ ion detection were more specifically studied, and recognitionwas demonstrated with both quantum-chemical calculations and experiments,accounting for the future integration of the chemical sensor in an optical fibre device.BORDEAUX1-Bib.electronique (335229901) / SudocSudocFranceF

Molecular dynamics simulations of liquid crystals and photoresponsive systems

Neisseria gonorrhoeae (Ngo) expressing the outer membrane protein OpaHSPG can adhere to and invade epithelial cells via binding to heparan sulphate proteoglycan (HSPG) receptors. In this study, we have investigated the role of syndecan-1 and syndecan-4, two members of the HSPG family, in the uptake of Ngo by epithelial cells. When overexpressed in HeLa cells, both syndecans co-localize with adherent Ngo on the host cell surface. This overexpression of syndecan-1 and syndecan-4 leads to a three- and sevenfold increase in Ngo invasion respectively. In contrast, transfection with the syndecan-1 and syndecan-4 mutant constructs lacking the intracellular domain results in an abrogation of the invasion process, characteristic of a dominant-negative mode of action. A concomitant loss of the capacity to mediate Ngo uptake was also observed with syndecan-4 mutant constructs carrying lesions in the dimerization motif necessary for the binding of protein kinase C (PKC) and phosphatidylinositol 4,5-bisphosphate (PIP2), and mutants that are deficient in a C-terminal EFYA amino acid motif responsible for binding to syntenin or CASK. We conclude that syndecan-1 and syndecan-4 can both mediate Ngo uptake into epithelial cells, and that their intracellular domains play a crucial role in this process, perhaps by mediating signal transduction or anchorage to the cytoskeleton