Bifurcation and dynamic response analysis of a rotating blade excited by upstream vortices

Acknowledgements The authors acknowledge the projects supported by the National Basic Research Program of China (973 Project)(No. 2015CB057405) and the National Natural Science Foundation of China (No. 11372082) and the State Scholarship Fund of CSC. DW thanks for the hospitality of the University of Aberdeen.

Existence of multiple attractors and the nature of bifurcations in a discontinuous logistic map

We present the analytical investigations on a logistic map with a discontinuity at the centre. An explanation for the bifurcation phenomenon in discontinuous systems is presented. We establish that whenever the elements of an n-cycle (n > 1) approach the discontinuities of the nth iterate of the map, a bifurcation other than the usual period-doubling one takes place. The periods of the cycles decrease in an arithmetic progression, as the control parameter is varied. The system also shows the presence of multiple attractors. Our results are verified by numerical experiments as well.

Self-organized defensive behavior in honeybees

We investigated the defensive behavior of honeybees under controlled experimental conditions. During an attack on two identical targets, the spatial distribution of stings varied as a function of the total number of stings, evincing the classic “pitchfork bifurcation” phenomenon of nonlinear dynamics. The experimental results support a model of defensive behavior based on a self-organizing mechanism. The model helps to explain several of the characteristic features of the honeybee defensive response: (i) the ability of the colony to localize and focus its attack, (ii) the strong variability between different hives in the intensity of attack, as well as (iii) the variability observed within the same hive, and (iv) the ability of the colony to amplify small differences between the targets.

HOPF BIFURCATION FROM LINES of EQUILIBRIA WITHOUT PARAMETERS IN MEMRISTOR OSCILLATORS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Bifurcation study for a vertical channel with constant flux and large aspect ratio

Using suitable coupled Navier-Stokes Equations for an incompressible Newtonian fluid we investigate the linear and non-linear steady state solutions for both a homogeneously and a laterally heated fluid with finite Prandtl Number (Pr=7) in the vertical orientation of the channel. Both models are studied within the Large Aspect Ratio narrow-gap and under constant flux conditions with the channel closed. We use direct numerics to identify the linear stability criterion in parametric terms as a function of Grashof Number (Gr) and streamwise infinitesimal perturbation wavenumber (making use of the generalised Squire’s Theorem). We find higher harmonic solutions at lower wavenumbers with a resonance of 1:3exist, for both of the heating models considered. We proceed to identify 2D secondary steady state solutions, which bifurcate from the laminar state. Our studies show that 2D solutions are found not to exist in certain regions of the pure manifold, where we find that 1:3 resonant mode 2D solutions exist, for low wavenumber perturbations. For the homogeneously heated fluid, we notice a jump phenomenon existing between the pure and resonant mode secondary solutions for very specific wavenumbers .We attempt to verify whether mixed mode solutions are present for this model by considering the laterally heated model with the same geometry. We find mixed mode solutions for the laterally heated model showing that a bridge exists between the pure and 1:3 resonant mode 2D solutions, of which some are stationary and some travelling. Further, we show that for the homogeneously heated fluid that the 2D solutions bifurcate in hopf bifurcations and there exists a manifold where the 2D solutions are stable to Eckhaus criterion, within this manifold we proceed to identify 3D tertiary solutions and find that the stability for said 3D bifurcations is not phase locked to the 2D state. For the homogeneously heated model we identify a closed loop within the neutral stability curve for higher perturbation wavenumubers and analyse the nature of the multiple 2D bifurcations around this loop for identical wavenumber and find that a temperature inversion occurs within this loop. We conclude that for a homogeneously heated fluid it is possible to have abrup ttransitions between the pure and resonant 2D solutions, and that for the laterally heated model there exist a transient bifurcation via mixed mode solutions.

Desquamation Is A Novel Phenomenon For Collective Prostate Epithelial Cell Deletion After Castration.

The mechanism underlying castration-induced prostate regression, which is a classical physiological concept translated into the therapeutic treatment of advanced prostate cancer, involves epithelial cell apoptosis. In searching for events and mechanisms contributing to prostate regression in response to androgen modulation, we have frequently observed the collective deletion of epithelial cells. This work was undertaken to characterize this phenomenon hereafter named desquamation and to verify its presence after 17β-estradiol (E2) administration. Electron microscopy revealed that the desquamating cells had preserved cell-cell junctions and collapsed nuclear contents. The TUNEL reaction was negative for these cells, which were also negative for cleaved caspases-8, -9, -3 and nuclear apoptosis-inducing factor. Detailed analyses revealed that the condensed chromatin was first affected detaching from the nuclear lamina, which was observable after lamin A immunohistochemistry, suggesting the lack of lamin A degradation. A search in animals treated with supraphysiological E2 employed as an alternative anti-androgen treatment revealed no desquamation. The combined treatment (Cas + E2 group) caused changes particular to each treatment, including desquamation. In conclusion, desquamation appeared as a novel phenomenon contributing to collective prostate epithelial cell deletion, distinct from the classical castration-induced apoptosis and particular to the androgen deprivation resulting from surgical castration, and should be considered as part of the mechanisms promoting organ regression.

Genetic Aspects Of Athletic Performance: The African Runners Phenomenon.

The current dominance of African runners in long-distance running is an intriguing phenomenon that highlights the close relationship between genetics and physical performance. Many factors in the interesting interaction between genotype and phenotype (eg, high cardiorespiratory fitness, higher hemoglobin concentration, good metabolic efficiency, muscle fiber composition, enzyme profile, diet, altitude training, and psychological aspects) have been proposed in the attempt to explain the extraordinary success of these runners. Increasing evidence shows that genetics may be a determining factor in physical and athletic performance. But, could this also be true for African long-distance runners? Based on this question, this brief review proposed the role of genetic factors (mitochondrial deoxyribonucleic acid, the Y chromosome, and the angiotensin-converting enzyme and the alpha-actinin-3 genes) in the amazing athletic performance observed in African runners, especially the Kenyans and Ethiopians, despite their environmental constraints.

The beneficial effects of exercise in rodents are preserved after detraining: a phenomenon unrelated to GLUT4 expression

Background: Although exercise training has well-known cardiorespiratory and metabolic benefits, low compliance with exercise training programs is a fact, and the harmful effects of physical detraining regarding these adaptations usually go unnoticed. We investigated the effects of exercise detraining on blood pressure, insulin sensitivity, and GLUT4 expression in spontaneously hypertensive rats (SHR) and normotensive Wistar Kyoto rats (WKY). Methods: Studied animals were randomized into sedentary, trained (treadmill running/5 days a week, 60 min/day for 10 weeks), 1 week of detraining, and 2 weeks of detraining. Blood pressure (tail-cuff system), insulin sensitivity (kITT), and GLUT4 (Western blot) in heart, gastrocnemius and white fat tissue were measured. Results: Exercise training reduced blood pressure (19%), improved insulin sensitivity (24%), and increased GLUT4 in the heart (+34%); gastrocnemius (+36%) and fat (+22%) in SHR. In WKY no change in either blood pressure or insulin sensitivity were observed, but there was an increase in GLUT4 in the heart (+25%), gastrocnemius (+45%) and fat (+36%) induced by training. Both periods of detraining did not induce any change in neither blood pressure nor insulin sensitivity in SHR and WKY. One-week detraining reduced GLUT4 in SHR (heart: -28%; fat: -23%) and WKY (heart: -19%; fat: -22%); GLUT4 in the gastrocnemius was reduced after a 2-week detraining (SHR: -35%; WKY: -25%). There was a positive correlation between GLUT4 (gastrocnemius) and the maximal velocity in the exercise test (r = 0.60, p = 0.004). Conclusions: The study findings show that in detraining, despite reversion of the enhanced GLUT4 expression, cardiorespiratory and metabolic beneficial effects of exercise are preserved.

Finite-size particles, advection, and chaos: A collective phenomenon of intermittent bursting

We consider finite-size particles colliding elastically, advected by a chaotic flow. The collisionless dynamics has a quasiperiodic attractor and particles are advected towards this attractor. We show in this work that the collisions have dramatic effects in the system's dynamics, giving rise to collective phenomena not found in the one-particle dynamics. In particular, the collisions induce a kind of instability, in which particles abruptly spread out from the vicinity of the attractor, reaching the neighborhood of a coexisting chaotic saddle, in an autoexcitable regime. This saddle, not present in the dynamics of a single particle, emerges due to the collective particle interaction. We argue that this phenomenon is general for advected, interacting particles in chaotic flows.

Unusual magneto-optical phenomenon reveals low energy spin dispersion in the spin-1 anisotropic Heisenberg antiferromagnetic chain system NiCl(2)-4SC(NH(2))(2)

Electron paramagnetic resonance measurements of NiCl(2)-4SC(NH(2))(2) reveal the low-energy spin dispersion, including a magnetic-field interval in which the two-magnon continuum is within k(B)T of the ground state, allowing a continuum of excitations over a range of k states, rather than only the k=0 single-magnon excitations. This produces a novel Y shape in the frequency-field EPR spectrum measured at T >= 1.5 K. Since the interchain coupling J(perpendicular to)< k(B)T, this shape can be reproduced by a single S=1 antiferromagnetic Heisenberg chain with a strong easy-plane single-ion anisotropy. Importantly, the combination of experiment and modeling we report herein demonstrates a powerful approach to probing spin dispersion in a wide range of interacting magnetic systems without the stringent sample requirements and complications associated with inelastic scattering experiments.

Periodic-orbit analysis and scaling laws of intermingled basins of attraction in an ecological dynamical system

Chaotic dynamical systems with two or more attractors lying on invariant subspaces may, provided certain mathematical conditions are fulfilled, exhibit intermingled basins of attraction: Each basin is riddled with holes belonging to basins of the other attractors. In order to investigate the occurrence of such phenomenon in dynamical systems of ecological interest (two-species competition with extinction) we have characterized quantitatively the intermingled basins using periodic-orbit theory and scaling laws. The latter results agree with a theoretical prediction from a stochastic model, and also with an exact result for the scaling exponent we derived for the specific class of models investigated. We discuss the consequences of the scaling laws in terms of the predictability of a final state (extinction of either species) in an ecological experiment.

Bifurcation in growth patterns for arrays of parallel Griffith, edge and sliding cracks

This paper presents the recent finding by Muhlhaus et al [1] that bifurcation of crack growth patterns exists for arrays of two-dimensional cracks. This bifurcation is a result of the nonlinear effect due to crack interaction, which is, in the present analysis, approximated by the dipole asymptotic or pseudo-traction method. The nonlinear parameter for the problem is the crack length/ spacing ratio lambda = a/h. For parallel and edge crack arrays under far field tension, uniform crack growth patterns (all cracks having same size) yield to nonuniform crack growth patterns (i.e. bifurcation) if lambda is larger than a critical value lambda(cr) (note that such bifurcation is not found for collinear crack arrays). For parallel and edge crack arrays respectively, the value of lambda(cr) decreases monotonically from (2/9)(1/2) and (2/15.096)(1/2) for arrays of 2 cracks, to (2/3)(1/2)/pi and (2/5.032)(1/2)/pi for infinite arrays of cracks. The critical parameter lambda(cr) is calculated numerically for arrays of up to 100 cracks, whilst discrete Fourier transform is used to obtain the exact solution of lambda(cr) for infinite crack arrays. For geomaterials, bifurcation can also occurs when array of sliding cracks are under compression.

Computation of bifurcation boundaries for power systems: A new Delta-plane method

This paper is devoted to the problems of finding the load flow feasibility, saddle node, and Hopf bifurcation boundaries in the space of power system parameters. The first part contains a review of the existing relevant approaches including not-so-well-known contributions from Russia. The second part presents a new robust method for finding the power system load flow feasibility boundary on the plane defined by any three vectors of dependent variables (nodal voltages), called the Delta plane. The method exploits some quadratic and linear properties of the load now equations and state matrices written in rectangular coordinates. An advantage of the method is that it does not require an iterative solution of nonlinear equations (except the eigenvalue problem). In addition to benefits for visualization, the method is a useful tool for topological studies of power system multiple solution structures and stability domains. Although the power system application is developed, the method can be equally efficient for any quadratic algebraic problem.

Uncommon mechanism of egg incubation in the endemic Southern hermit crab Loxopagurus loxochelis: how is this phenomenon related to egg production?

The aim of the present work was to characterize the egg production of Loxopagurus loxochelis. A total of 71 ovigerous females were obtained, 28% of which were simultaneously incubating eggs at different developmental stages. This phenomenon can be the result of incomplete fertilization, or may represent a rapid gonadal cycle by this species in this area, which is, to our understanding, the best explanation of this phenomenon. Egg volume decreased 25.6% during the incubation period. The reproductive output based on dry and wet weight was 6.8 and 19.3%, respectively. Water was the prevailing component of the eggs, representing 86.0% of the total weight at initial stage, increasing to 95.1% at the final stage. Ash content increased at the same time as a decrease in the organic content occurred, indicating the consumption of yolk and absorption of salts from the water medium. In conclusion, we hypothesized that this population has the capacity to copulate and deposit another brood even before the release of the larvae from the previous one, intensifying the reproductive effort of these hermit crabs as a strategy of adaptation in a region considered the northern limit of the geographical distribution of this species.

Cutaneous vasculitis in systemic lupus erythematosus: association with anti-ribosomal P protein antibody and Raynaud phenomenon

Ninety-one consecutive systemic lupus erythematosus (SLE) patients (American College of Rheumatology criteria) with a history of cutaneous vasculitis were compared to 163 SLE controls without this clinical manifestation from July to December 2007 in order to determine the possible clinical and serological association of this manifestation. Data were obtained in an ongoing electronic database protocol and autoantibodies to anti-double-stranded DNA, anti-Sm, anti-RNP, anti-Ro/SS-A, anti-La/SS-B, and anticardiolipin and ribosomal P protein antibody (anti-P) were detected by standard techniques. Exclusion criteria were the presence of anti-phospholipid syndrome or antibodies, Sjogren syndrome, and a history of thrombosis. The mean age (38.5 +/- 11.5 vs. 37.8 +/- 11.6 years, p = 0.635), disease duration (12.5 +/- 7.8 vs. 11.8 +/- 7.9 years, p = 0.501), and frequency of white race (71.4% vs. 70.5%, p = 0.872) and female sex (96.8% vs. 93.7%, p = 0.272) were comparable in both groups. The vasculitis group had a higher frequency of malar rash (97.9% vs. 87.4%, p = 0.004), photosensitivity (91.4% vs. 81.6%, p = 0.030), and Raynaud phenomenon (RP; 27.7% vs. 7.5%, p < 0.001), whereas all other clinical manifestation including renal and central nervous system involvements were similar to the control group. Laboratorial data revealed that only anti-P (35.1% vs. 12.1%, p < 0.001) was more frequent in patients with vasculitis. In a multivariate logistic regression model, cutaneous vasculitis was associated to the presence of RP (OR = 3.70; 95% confidence interval [CI] = 1.73-8.00) and anti-P (OR = 3.42; 95% CI = 1.76-6.66). In summary, SLE cutaneous vasculitis characterizes a subgroup of patients with more RP and anti-P antibodies but not accompanied by a higher frequency of renal and central nervous system involvements.