Chaotic dynamics from coupled magnetic monodomain and Josephson current.

The ordinary (superconductor-insulator-superconductor) Josephson junction cannot exhibit chaos in the absence of an external ac drive, whereas in the superconductor-ferromagnet-superconductor Josephson junction, known as the φ_{0} junction, the magnetic layer effectively provides two extra degrees of freedom that can facilitate chaotic dynamics in the resulting four-dimensional autonomous system. In this work, we use the Landau-Lifshitz-Gilbert model for the magnetic moment of the ferromagnetic weak link, while the Josephson junction is described by the resistively capacitively shunted-junction model. We study the chaotic dynamics of the system for parameters surrounding the ferromagnetic resonance region, i.e., for which the Josephson frequency is reasonably close to the ferromagnetic frequency. We show that, due to the conservation of magnetic moment magnitude, two of the numerically computed full spectrum Lyapunov characteristic exponents are trivially zero. One-parameter bifurcation diagrams are used to investigate various transitions that occur between quasiperiodic, chaotic, and regular regions as the dc-bias current through the junction, I, is varied. We also compute two-dimensional bifurcation diagrams, which are similar to traditional isospike diagrams, to display the different periodicities and synchronization properties in the I-G parameter space, where G is the ratio between the Josephson energy and the magnetic anisotropy energy. We find that as I is reduced the onset of chaos occurs shortly before the transition to the superconducting state. This onset of chaos is signaled by a rapid rise in supercurrent (I_{S}⟶I) which corresponds, dynamically, to increasing anharmonicity in phase rotations of the junction.

Bifurcation structure and chaos in dynamics of nanomagnet coupled to Josephson junction.

Irregular easy axis reorientation features are observed in numerical simulations of the nanomagnet coupled to the Josephson junction. We study magnetization bifurcations and chaos that appear in this system due to the interplay of superconductivity and magnetism. The bifurcation structure of magnetization under the variation of Josephson to magnetic energy ratio as a control parameter demonstrates several precessional motions that are related to chaotic behavior and orbits with different periodicities in the ferromagnetic resonance region. The effect of an external periodic signal on the bifurcation structure is also investigated. The results demonstrate high-frequency modes of a periodic motion and a chaotic response near resonance. Far from the ferromagnetic resonance, we observe a quasiperiodic behavior. The obtained results explain the irregular reorientation of the easy axis and the transitions between different types of motion.

Chimera Patterns of Synchrony in a Frustrated Array of Hebb Synapses.

The union of the Kuramoto-Sakaguchi model and the Hebb dynamics reproduces the Lisman switch through a bistability in synchronized states. Here, we show that, within certain ranges of the frustration parameter, the chimera pattern can emerge, causing a different, time-evolving, distribution in the Hebbian synaptic strengths. We study the stability range of the chimera as a function of the frustration (phase-lag) parameter. Depending on the range of the frustration, two different types of chimeras can appear spontaneously, i.e., from randomized initial conditions. In the first type, the oscillators in the coherent region rotate, on average, slower than those in the incoherent region; while in the second type, the average rotational frequencies of the two regions are reversed, i.e., the coherent region runs, on average, faster than the incoherent region. We also show that non-stationary behavior at finite N can be controlled by adjusting the natural frequency of a single pacemaker oscillator. By slowly cycling the frequency of the pacemaker, we observe hysteresis in the system. Finally, we discuss how we can have a model for learning and memory.

Probability distribution for heat exchange in plastic deformation.

Fluctuation theorems allow one to obtain equilibrium information from nonequilibrium experiments. The probability distribution function of the relevant magnitude measured along the irreversible nonequilibrium trajectories is an essential ingredient of fluctuation theorems. In small systems, where fluctuations can be larger than average values, probability distribution functions often deviate from being Gaussian, showing long tails, mostly exponential, and usually strongly asymmetric. Recently, the probability distribution function of the van Hove correlation function of the relevant magnitude was calculated, instead of that of the magnitude itself. The resulting probability distribution function is highly symmetric, obscuring the application of fluctuation theorems. Here, the discussion is illustrated with the help of results for the heat exchanged during plastic deformation of aluminum nanowires, obtained from molecular dynamics calculations. We find that the probability distribution function for the heat exchanged is centrally Gaussian, with asymmetric exponential tails further out. By calculating the symmetry function we show that this distribution is consistent with fluctuation theorems relating the differences between two equilibrium states to an infinite number of nonequilibrium paths connecting those two states.

Inertial effects in the dc+ac driven underdamped Frenkel-Kontorova model: Subharmonic steps, chaos, and hysteresis.

The effects of inertial terms on the dynamics of the dc+ac driven Frenkel-Kontorova model were examined. As the mass of particles was varied, the response of the system to the driving forces and appearance of the Shapiro steps were analyzed in detail. Unlike in the overdamped case, the increase of mass led to the appearance of the whole series of subharmonic steps in the staircase of the average velocity as a function of average driving force in any commensurate structure. At certain values of parameters, the subharmonic steps became separated by chaotic windows while the whole structure retained scaling similar to the original staircase. The mass of the particles also determined their sensitivity to the forces governing their dynamics. Depending on their mass, they were found to exhibit three types of dynamics, from dynamical mode-locking with chaotic windows, through to a typical dc response, to essentially a free-particle response. Examination of this dynamics in both the upforce and downforce directions showed that the system may not only exhibit hysteresis, but also that large Shapiro steps may appear in the downforce direction, even in cases for which no dynamical mode-locking occurred in the upforce direction.

Serum anti-Müllerian hormone dynamics in mares following immunocontraception with anti-zona pellucida or -GnRH vaccines.

Circulating anti-Müllerian hormone concentration (AMH) is positively correlated to the number of small growing follicles in the mare and may reflect ovarian function. Dynamics of AMH during immunocontraception have not previously been investigated. This study aimed to compare serum AMH in mares following treatment with native porcine zona pellucida (pZP), recombinant pZP3 and pZP4 (reZP) or gonadotrophin releasing hormone (GnRH) vaccines, and saline-treated controls. Stored sera collected during two previous studies examining ovarian activity in mares during zona pellucida (ZP) or GnRH immunocontraception were analysed for serum AMH. Data were compared among treatment groups using mixed-effects linear regression and one-way ANOVA with post hoc testing. Correlations between AMH and previously reported clinical variables were estimated using Spearman's rho. Mares immunized against GnRH showed variable but detectable AMH throughout successive breeding and non-breeding seasons that were not significantly different to unvaccinated control mares. Mares treated with pZP demonstrated marked, reversible suppression of AMH. Mares immunized using reZP showed an intermediate effect. In the ZP study, AMH was positively correlated to serum progesterone concentrations, mean ovarian volumes and antral follicle counts, whereas no correlations between AMH and serum progesterone concentrations, mean ovarian volumes, or the presence of one or more follicles ≥20 mm in diameter were detected in the GnRH study. In conclusion, marked suppression of AMH during pZP immunocontraception, but not during GnRH immunocontraception, suggested enhanced suppression of ovarian follicular development and, or follicular function during pZP immunocontraception. Serum AMH concentrations may provide a novel tool for the assessment of ovarian function during ZP-based immunocontraception.

Devil's staircase and the absence of chaos in the dc- and ac-driven overdamped Frenkel-Kontorova model.

The devil's staircase structure arising from the complete mode locking of an entirely nonchaotic system, the overdamped dc+ac driven Frenkel-Kontorova model with deformable substrate potential, was observed. Even though no chaos was found, a hierarchical ordering of the Shapiro steps was made possible through the use of a previously introduced continued fraction formula. The absence of chaos, deduced here from Lyapunov exponent analyses, can be attributed to the overdamped character and the Middleton no-passing rule. A comparative analysis of a one-dimensional stack of Josephson junctions confirmed the disappearance of chaos with increasing dissipation. Other common dynamic features were also identified through this comparison. A detailed analysis of the amplitude dependence of the Shapiro steps revealed that only for the case of a purely sinusoidal substrate potential did the relative sizes of the steps follow a Farey sequence. For nonsinusoidal (deformed) potentials, the symmetry of the Stern-Brocot tree, depicting all members of particular Farey sequence, was seen to be increasingly broken, with certain steps being more prominent and their relative sizes not following the Farey rule.

Structured chaos in a devil's staircase of the Josephson junction.

The phase dynamics of Josephson junctions (JJs) under external electromagnetic radiation is studied through numerical simulations. Current-voltage characteristics, Lyapunov exponents, and Poincaré sections are analyzed in detail. It is found that the subharmonic Shapiro steps at certain parameters are separated by structured chaotic windows. By performing a linear regression on the linear part of the data, a fractal dimension of D = 0.868 is obtained, with an uncertainty of ±0.012. The chaotic regions exhibit scaling similarity, and it is shown that the devil's staircase of the system can form a backbone that unifies and explains the highly correlated and structured chaotic behavior. These features suggest a system possessing multiple complete devil's staircases. The onset of chaos for subharmonic steps occurs through the Feigenbaum period doubling scenario. Universality in the sequence of periodic windows is also demonstrated. Finally, the influence of the radiation and JJ parameters on the structured chaos is investigated, and it is concluded that the structured chaos is a stable formation over a wide range of parameter values.

Reversibility of the effects of GnRH-vaccination used to suppress reproductive function in mares.

REASONS FOR PERFORMING STUDY: Active immunisation against gonadotrophin-releasing hormone (GnRH) provides a reversible method for control of oestrous behaviour and fertility in mares. Previous reports failed to demonstrate the interval to resumption of cyclic ovarian activity after GnRH-vaccination. HYPOTHESIS: Administration of the GnRH-vaccine Improvac in a large group of mares of various ages will result in effective, reliably reversible suppression of ovarian activity within a 2 year period. METHODS: The mares, subdivided into 3 age categories, were vaccinated twice (with a 35 day interval) using 400 µg Improvac and monitored via blood samples until Day 720 after initial vaccination for serum progesterone concentration determination by radioimmune assay and anti-GnRH antibody titre by enzyme immunoassay. Samples were collected until individuals resumed cyclic ovarian activity. RESULTS: All mares showed suppression of cyclic ovarian activity by clinical examination and serum progesterone concentration (SPC) ≤ 1 nmol/l by Day 70 and 92.2% resumed cyclic activity by SPC at Day 720 with a mean interval = 417.8 days (s.d. ± 23.9; range 232-488 days, median 344 days). A significant age effect (P = 0.028) on the interval, but not on GnRH-antibody titre response, was observed between the youngest (≤ 4 years) and oldest (≥ 11 years) categories. CONCLUSIONS: Immunising adult mares of all ages with Improvac resulted in a reversible suppression of cyclic ovarian activity in most mares. An age effect, with the youngest mares showing a longer interval to reversibility, was observed.

Mathematics at matriculation level as an indicator of success or failure in the 1st year of the Veterinary Nursing Diploma at the Faculty of Veterinary Science, University of Pretoria.

Mathematics at matriculation level (Grade 12) is one of the subjects required for admission to the Veterinary Nursing Diploma in the Faculty at Veterinary Science of the University of Pretoria. The present study shows that there is no statistically significant relationship between the grade of mathematics at matriculation level and the success or failure in the 1st year of study. There is, however, a statistical difference in the adjusted mark obtained for mathematics at matriculation level between the groups that passed and failed the 1st year of the veterinary nursing course. The results of this research are not consistent with other research which showed that secondary school mathematics results are not a significant factor in tertiary education. It is recommended that selection criteria for veterinary nurses should in future still include mathematics, but that cognisance should be taken of the mark obtained and students with higher marks (above 57%) given preference.

Luteolysis in early diestrous beagle bitches.

To induce luteolysis early in diestrus, 15 mated beagles were treated with 250 microg/kg prostaglandin F2alpha (PG), administered subcutaneously twice daily for 4 d, from Day 5 to Day 8 after the onset of cytological diestrus. They were divided into three groups of five bitches each: Group 1 received PG only. Group 2 received PG and 20 microg/kg/day bromocryptine orally. Group 3 received PG and 0.1 mg/kg/day dexamethasone intramuscularly. Fifteen untreated beagles served as controls. In each of the three treatment groups, four of the five bitches (80%) underwent complete luteolysis and did not whelp. The three bitches which did not undergo luteolysis whelped normally. All control bitches whelped normally. It was concluded that luteolysis is possible in bitches early in diestrus and the inclusion of bromocryptine or dexamethasone did not appear to influence luteolysis.