The trajectory of a charged particle in the magnetic field of an infinite current carrying wire in the nonrelativistic limit

We have calculated in a closed form solution, in terms of modified Bessel function the first kind of order 0 and 1, for the motion of a positively charged particle in the magnetic field of an infinitely long, current-carrying wire in the nonrelativistic range. The orbits are not closed but exhibit a drift in the direction of the current with a speed that is independent of the launch angle. We found the drift velocity, drift displacement and the corresponding time, which we call the period. Keywords: Trajectory of a charged particle in magnetic field, Drift velocity, Drift displacement, Modified bessel functio

Universality in Kinetic Models of Circadian Rhythms in \u3cem\u3eArabidopsis thaliana\u3c/em\u3e

Biological evolution has endowed the plant Arabidopsis thaliana with genetically regulated circadian rhythms. A number of authors have published kinetic models for these oscillating chemical reactions based on a network of interacting genes. To investigate the hypothesis that the Arabidopsis circadian dynamical system is poised near a Hopf bifurcation like some other biological oscillators, we varied the kinetic parameters in the models and searched for bifurcations. Finding that each model does exhibit a supercritical Hopf bifurcation, we performed a weakly nonlinear analysis near the bifurcation points to derive the Stuart-Landau amplitude equation. To illustrate a common dynamical structure, we scaled the numerical solutions to the models with the asymptotic solutions to the Stuart-Landau equation to collapse the circadian oscillations onto two universal curves-one for amplitude, and one for frequency. However, some models are close to bifurcation while others are far, some models are post-bifurcation while others are pre-bifurcation, and kinetic parameters that lead to a bifurcation in some models do not lead to a bifurcation in others. Future kinetic modeling can make use of our analysis to ensure models are consistent with each other and with the dynamics of the Arabidopsis circadian rhythm

The Microvariable Activity of BL Lacertae

We report on seven nights of optical observation taken over a two-week period, and the resultant analysis of the intermediate-frequency peaked BL Lac object (IBL), BL Lac itself, at redshift z = 0.069. The microvariable behavior can be confirmed over the course of minutes for each night. A relativistic beaming model was used in our analysis, to infer changes to the line of sight angles for the motion of the different relativistic components. This model has very few free parameters. The light curves we generated show both high and moderate frequency cadence to the variable behavior of BL Lac itself, in addition to the well documented long-term variability.Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Statistical Analysis of the Microvariable AGN Source Mrk 501

We report on the optical observations and analysis of the high-energy peaked BL Lac object (HBL), Mrk 501, at redshift z = 0.033. We can confirm microvariable behavior over the course of minutes on several occasions per night. As an alternative to the commonly understood dynamical model of random variations in intensity of the AGN, we develop a relativistic beaming model with a minimum of free parameters, which allows us to infer changes in the line of sight angles for the motion of the different relativistic components. We hope our methods can be used in future studies of beamed emission in other active microvariable sources, similar to the one we explored

Analysis of the Ebola Outbreak in 2014 and 2018 in West Africa and Congo by Using Artificial Adaptive Systems

In this manuscript the Ebola outbreaks in 2014 and 2018 have been studied. On March 23, 2014, the World Health Organization announced the beginning of the Ebola outbreak in West Africa. The initial location was in a forested area in the south eastern portion of Guinea. We used three different methods to determine the origin of the outbreak. The first was a suite of artificial adaptive systems called Topological Weighted Centroid which located the outbreak origin at Longitude: −10.5337, Latitude: 8.1517. This area is 64 km from Guekedou, Guinea. We also used a Dynamic Naive Bayesian/Dynamic Networks Block Algorithm. The Bayesian algorithm shows the main source of the Ebola outbreak at Kissidougou. Both of these methods revealed the outbreak started in the forested area southeast of Guinea. The distance between Guekedou and Kissidougou is about 69 km. Furthermore, we used an artificial neural network (ANN) called Selfie to predict the outbreak diffusion. The Ebola outbreak in May 2018 in Democratic Republic of Congo was not as widespread as the outbreak in 2014. The outbreak was effecting the health zones of Bikoro and Iboko, and Wangata in Congo. We have used an ANN algorithm and predicted the origin of the outbreak at (Longitude: 18.3046, Latitude: −0.6865) in the Equator about 20 km at North-West of Bikoro

A New Algorithm for Identifying Possible Epidemic Sources with Application to the German Escherichia coli Outbreak

In this paper we describe a recently developed algorithm called Topological Weighted Centroid (TWC). TWC takes locations of an event of interest and analyzes the possible associated dynamics using the ideas of free energy and entropy. This novel mathematical tool has been applied to a real world example, the epidemic outbreak caused by Escherichia coli that occurred in Germany in 2011, to point out the real source of the outbreak. Other four examples of application to other epidemic spreads are described: Chikungunya fever of 2007 in Italy; Foot and mouth disease of 1967 in England; Cholera of 1854 in London; and the Russian influenza of 1889–1890 in Sweden. Comparisons have been made with other already published algorithms: Rossmo Algorithm, NES, LVM, Mexican Prob. The TWC results are significantly superior in comparison with other algorithms according to four independent indexes: distance from the peak, sensitivity, specificity and searching area. They are consistent with the idea that the spread of infectious disease is not random but follows a progression based on inherent, but as yet undiscovered, mathematical laws. The TWC method could provide an additional powerful tool for the investigation of the early stages of an epidemic and novel simulation methods for understanding the process through which a disease is spread

A New Algorithm for Identifying Possible Epidemic Sources with Application to the German Escherichia coli Outbreak

In this paper we describe a recently developed algorithm called Topological Weighted Centroid (TWC). TWC takes locations of an event of interest and analyzes the possible associated dynamics using the ideas of free energy and entropy. This novel mathematical tool has been applied to a real world example, the epidemic outbreak caused by Escherichia coli that occurred in Germany in 2011, to point out the real source of the outbreak. Other four examples of application to other epidemic spreads are described: Chikungunya fever of 2007 in Italy; Foot and mouth disease of 1967 in England; Cholera of 1854 in London; and the Russian influenza of 1889–1890 in Sweden. Comparisons have been made with other already published algorithms: Rossmo Algorithm, NES, LVM, Mexican Prob. The TWC results are significantly superior in comparison with other algorithms according to four independent indexes: distance from the peak, sensitivity, specificity and searching area. They are consistent with the idea that the spread of infectious disease is not random but follows a progression based on inherent, but as yet undiscovered, mathematical laws. The TWC method could provide an additional powerful tool for the investigation of the early stages of an epidemic and novel simulation methods for understanding the process through which a disease is spread