GPU accelerated investigation of a dual-frequency driven nonlinear oscillator

The bifurcation structure of a dual-frequency driven, second order nonlinear oscillator (Keller–Miksis equation) is investigated by exploiting the high computational resources of professional GPUs. The numerical scheme of the applied initial value problem solver was the explicit, adaptive Runge–Kutta–Cash–Karp method with embedded error estimation using solutions of order 4 and 5. The four dimensional parameter space (amplitudes and frequencies of the driving) is explored by means of several high resolution bi-parametric plots with the amplitudes as control parameters at fixed frequencies. The resolution of the control parameter plane is 500 × 500 with 10 initial conditions at each parameter pair (altogether 2.5 million initial value problems in each bi-parametric plot). The program code for one fine parameter scan runs approximately 50 times faster on a Tesla K20 GPU (Kepler architecture) than on an Intel i7-4790 4 core CPU even applying double precision floating point operations

Investigation of transition frequencies of two acoustically coupled bubbles using a direct numerical simulation technique

The theoretical results regarding the ``transition frequencies'' of two acoustically interacting bubbles have been verified numerically. The theory provided by Ida [Phys. Lett. A 297 (2002) 210] predicted the existence of three transition frequencies per bubble, each of which has the phase difference of $\pi /2$ between a bubble's pulsation and the external sound field, while previous theories predicted only two natural frequencies which cause such phase shifts. Namely, two of the three transition frequencies correspond to the natural frequencies, while the remaining does not. In a subsequent paper [M. Ida, Phys. Rev. E 67 (2003) 056617], it was shown theoretically that transition frequencies other than the natural frequencies may cause the sign reversal of the secondary Bjerknes force acting between pulsating bubbles. In the present study, we employ a direct numerical simulation technique that uses the compressible Navier-Stokes equations with a surface-tension term as the governing equations to investigate the transition frequencies of two coupled bubbles by observing their pulsation amplitudes and directions of translational motion, both of which change as the driving frequency changes. The numerical results reproduce the recent theoretical predictions, validating the existence of the transition frequencies not corresponding to the natural frequency.Comment: 18 pages, 8 figures, in pres

Dissection of QTL effects for root traits using a chromosome arm-specific mapping population in bread wheat

A high-resolution chromosome arm-specific mapping population was used in an attempt to locate/detect gene(s)/QTL for different root traits on the short arm of rye chromosome 1 (1RS) in bread wheat. This population consisted of induced homoeologous recombinants of 1RS with 1BS, each originating from a different crossover event and distinct from all other recombinants in the proportions of rye and wheat chromatin present. It provides a simple and powerful approach to detect even small QTL effects using fewer progeny. A promising empirical Bayes method was applied to estimate additive and epistatic effects for all possible marker pairs simultaneously in a single model. This method has an advantage for QTL analysis in minimizing the error variance and detecting interaction effects between loci with no main effect. A total of 15 QTL effects, 6 additive and 9 epistatic, were detected for different traits of root length and root weight in 1RS wheat. Epistatic interactions were further partitioned into inter-genomic (wheat and rye alleles) and intra-genomic (rye–rye or wheat–wheat alleles) interactions affecting various root traits. Four common regions were identified involving all the QTL for root traits. Two regions carried QTL for almost all the root traits and were responsible for all the epistatic interactions. Evidence for inter-genomic interactions is provided. Comparison of mean values supported the QTL detection

Cytotaxonomic studies on some Vicia L. species growing in the eastern Mediterranean and southern Aegean regions II.

In this study, some natural Vicia L. species growing naturally in eastern Mediterranean and southern Aegean Regions have been investigated morphological and cytotaxonomic point of view. Morphology, chromosome number and morphometries of the 9 taxa belonging to the Vicia L. genus including Vicia peregrina, V. lutea var. hirta, V. anatolica, V. hybrida, V. grandiflora var. grandiflora, V. grandiflora var. dissecta, V. cuspidata, V. sativa subsp. sativa, V. sativa subsp. nigra var. segatalis have been studied by using karyological and numerical taxonomic techniques. Data obtained chromosome measurements were analysed by using cluster analysis. The chromosome number of studied Vicia species have been found as 2n = 10, 12 and 14. The member of Vicia section, related taxa were compared with respect to their chromosomal and morphological characteristics. Some karyological relationships among the studied Vicia taxa were discussed with help of taxonomic history and evolutionary data

Is the astronomical forcing a reliable and unique pacemaker for climate? A conceptual model study

There is evidence that ice age cycles are paced by astronomical forcing, suggesting some kind of synchronisation phenomenon. Here, we identify the type of such synchronisation and explore systematically its uniqueness and robustness using a simple paleoclimate model akin to the van der Pol relaxation oscillator and dynamical system theory. As the insolation is quite a complex quasiperiodic signal involving different frequencies, the traditional concepts used to define synchronisation to periodic forcing are no longer applicable. Instead, we explore a different concept of generalised synchronisation in terms of (coexisting) synchronised solutions for the forced system, their basins of attraction and instabilities. We propose a clustering technique to compute the number of synchronised solutions, each of which corresponds to a different paleoclimate history. In this way, we uncover multistable synchronisation (reminiscent of phase- or frequency-locking to individual periodic components of astronomical forcing) at low forcing strength, and monostable or unique synchronisation at stronger forcing. In the multistable regime, different initial conditions may lead to different paleoclimate histories. To study their robustness, we analyse Lyapunov exponents that quantify the rate of convergence towards each synchronised solution (local stability), and basins of attraction that indicate critical levels of external perturbations (global stability). We find that even though synchronised solutions are stable on a long term, there exist short episodes of desynchronisation where nearby climate trajectories diverge temporarily (for about 50 kyr). (...)Comment: 22 pages, 18 figure

Modeling Brain Resonance Phenomena Using a Neural Mass Model

Stimulation with rhythmic light flicker (photic driving) plays an important role in the diagnosis of schizophrenia, mood disorder, migraine, and epilepsy. In particular, the adjustment of spontaneous brain rhythms to the stimulus frequency (entrainment) is used to assess the functional flexibility of the brain. We aim to gain deeper understanding of the mechanisms underlying this technique and to predict the effects of stimulus frequency and intensity. For this purpose, a modified Jansen and Rit neural mass model (NMM) of a cortical circuit is used. This mean field model has been designed to strike a balance between mathematical simplicity and biological plausibility. We reproduced the entrainment phenomenon observed in EEG during a photic driving experiment. More generally, we demonstrate that such a single area model can already yield very complex dynamics, including chaos, for biologically plausible parameter ranges. We chart the entire parameter space by means of characteristic Lyapunov spectra and Kaplan-Yorke dimension as well as time series and power spectra. Rhythmic and chaotic brain states were found virtually next to each other, such that small parameter changes can give rise to switching from one to another. Strikingly, this characteristic pattern of unpredictability generated by the model was matched to the experimental data with reasonable accuracy. These findings confirm that the NMM is a useful model of brain dynamics during photic driving. In this context, it can be used to study the mechanisms of, for example, perception and epileptic seizure generation. In particular, it enabled us to make predictions regarding the stimulus amplitude in further experiments for improving the entrainment effect

Feedforward attractor targeting for non-linear oscillators using a dual-frequency driving technique

A feedforward control technique is presented to steer a harmonically driven, non-linear system between attractors in the frequency-amplitude parameter plane of the excitation. The basis of the technique is the temporary addition of a second harmonic component to the driving. To illustrate this approach, it is applied to the Keller-Miksis equation describing the radial dynamics of a single spherical gas bubble placed in an infinite domain of liquid. This model is a second-order, non-linear ordinary differential equation, a non-linear oscillator. With a proper selection of the frequency ratio of the temporary dual-frequency driving and with the appropriate tuning of the excitation amplitudes, the trajectory of the system can be smoothly transformed between specific attractors; for instance, between period-3 and period-5 orbits. The transformation possibilities are discussed and summarized for attractors originating from the subharmonic resonances and the equilibrium state (absence of external driving) of the system