Geometrical properties of local dynamics in Hamiltonian systems: the Generalized Alignment Index (GALI) method

We investigate the detailed dynamics of multidimensional Hamiltonian systems by studying the evolution of volume elements formed by unit deviation vectors about their orbits. The behavior of these volumes is strongly influenced by the regular or chaotic nature of the motion, the number of deviation vectors, their linear (in)dependence and the spectrum of Lyapunov exponents. The different time evolution of these volumes can be used to identify rapidly and efficiently the nature of the dynamics, leading to the introduction of quantities that clearly distinguish between chaotic behavior and quasiperiodic motion on $N$-dimensional tori. More specifically we introduce the Generalized Alignment Index of order $k$ (GALI$_k$) as the volume of a generalized parallelepiped, whose edges are $k$ initially linearly independent unit deviation vectors from the studied orbit whose magnitude is normalized to unity at every time step. The GALI$_k$ is a generalization of the Smaller Alignment Index (SALI) (GALI$_2$ $\propto$ SALI). However, GALI$_k$ provides significantly more detailed information on the local dynamics, allows for a faster and clearer distinction between order and chaos than SALI and works even in cases where the SALI method is inconclusive.Comment: 45 pages, 10 figures, accepted for publication in Physica

The electronic specific heat in the pairing pseudogap regime

When pairing correlations in a quasi two dimensional electron system induce a pseudogap in the single particle density of states, the specific heat must also contain a sizeable pair contribution. The theoretically calculated specific heat for such a system is compared to the experimental results of Loram and his collaborators for underdoped YBa_2Cu_3O_{6+x} and La_{2-x}Sr_{x}CuO_4 samples. The size and doping dependence of the extracted pseudogap energy scale for both materials is comparable to the values obtained from a variety of other experiments.Comment: 4 pages, 5 eps figure

Sensing of minute airflow motions near walls using pappus-type nature-inspired sensors

This work describes the development and use of pappus-like structures as sensitive sensors to detect minute air-flow motions. We made such sensors from pappi taken from nature-grown seed, whose filiform hairs' length-scale is suitable for the study of large-scale turbulent convection flows. The stem with the pappus on top is fixated on an elastic membrane on the wall and tilts under wind-load proportional to the velocity magnitude in direction of the wind, similar as the biological sensory hairs found in spiders, however herein the sensory hair has multiple filiform protrusions at the tip. As the sensor response is proportional to the drag on the tip and a low mass ensures a larger bandwidth, lightweight pappus structures similar as those found in nature with documented large drag are useful to improve the response of artificial sensors. The pappus of a Dandelion represents such a structure which has evolved to maximize wind-driven dispersion, therefore it is used herein as the head of our sensor. Because of its multiple hairs arranged radially around the stem it generates uniform drag for all wind directions. While still being permeable to the flow, the hundreds of individual hairs on the tip of the sensor head maximize the drag and minimize influence of pressure gradients or shear-induced lift forces on the sensor response as they occur in non-permeable protrusions. In addition, the flow disturbance by the sensor itself is limited. The optical recording of the head-motion allows continuously remote-distance monitoring of the flow fluctuations in direction and magnitude. Application is shown for the measurement of a reference flow under isothermal conditions to detect the early occurrence of instabilities

Addressing the sample size problem in behavioural operational research: simulating the newsvendor problem

Laboratory-based experimental studies with human participants are beneficial for testing hypotheses in behavioural operational research. However, such experiments are not without their problems. One specific problem is obtaining a sufficient sample size, not only in terms of the number of participants but also the time they are willing to devote to an experiment. In this paper, we explore how agent-based simulation (ABS) can be used to address the sample size problem and demonstrate the approach in the newsvendor setting. The decision-making strategies of a small sample of individual decision-makers are determined through laboratory experiments. The interactions of these suppliers and retailers are then simulated using an ABS to generate a large sample set of decisions. With only a small number of participants, we demonstrate that it is possible to produce similar results to previous experimental studies that involved much larger sample sizes. We conclude that ABS provides the potential to extend the scope of experimental research in behavioural operational research

Fractal Properties of Robust Strange Nonchaotic Attractors in Maps of Two or More Dimensions

We consider the existence of robust strange nonchaotic attractors (SNA's) in a simple class of quasiperiodically forced systems. Rigorous results are presented demonstrating that the resulting attractors are strange in the sense that their box-counting dimension is N+1 while their information dimension is N. We also show how these properties are manifested in numerical experiments.Comment: 9 pages, 14 figure

Observation of an Efimov spectrum in an atomic system

In 1970 V. Efimov predicted a puzzling quantum-mechanical effect that is still of great interest today. He found that three particles subjected to a resonant pairwise interaction can join into an infinite number of loosely bound states even though each particle pair cannot bind. Interestingly, the properties of these aggregates, such as the peculiar geometric scaling of their energy spectrum, are universal, i.e. independent of the microscopic details of their components. Despite an extensive search in many different physical systems, including atoms, molecules and nuclei, the characteristic spectrum of Efimov trimer states still eludes observation. Here we report on the discovery of two bound trimer states of potassium atoms very close to the Efimov scenario, which we reveal by studying three-particle collisions in an ultracold gas. Our observation provides the first evidence of an Efimov spectrum and allows a direct test of its scaling behaviour, shedding new light onto the physics of few-body systems.Comment: 10 pages, 3 figures, 1 tabl

Eliciting a predatory response in the eastern corn snake (Pantherophis guttatus) using live and inanimate sensory stimuli: implications for managing invasive populations

North America's Eastern corn snake (Pantherophis guttatus) has been introduced to several islands throughout the Caribbean and Australasia where it poses a significant threat to native wildlife. Invasive snake control programs often involve trapping with live bait, a practice that, as well as being costly and labour intensive, raises welfare and ethical concerns. This study assessed corn snake response to live and inanimate sensory stimuli in an attempt to inform possible future trapping of the species and the development of alternative trap lures. We exposed nine individuals to sensory cues in the form of odour, visual, vibration and combined stimuli and measured the response (rate of tongue-flick [RTF]). RTF was significantly higher in odour and combined cues treatments, and there was no significant difference in RTF between live and inanimate cues during odour treatments. Our findings suggest chemical cues are of primary importance in initiating predation and that an inanimate odour stimulus, absent of simultaneous visual and vibratory cues, is a potential low-cost alternative trap lure for the control of invasive corn snake populations

Modelling overdispersion with integer-valued moving average processes

A new first-order integer-valued moving average, INMA(1), model based on the negative binomial thinning operation defined by Risti´c et al. [21] is proposed and characterized. It is shown that this model has negative binomial (NB) marginal distribution when the innovations follow a NB distribution and therefore it can be used in situations where the data present overdispersion. Additionally, this model is extended to the bivariate context. The Generalized Method of Moments (GMM) is used to estimate the unknown parameters of the proposed models and the results of a simulation study that intends to investigate the performance of the method show that, in general, the estimates are consistent and symmetric. Finally, the proposed model is fitted to a real dataset and the quality of the adjustment is evaluated.publishe

Tomography of pairing symmetry from magnetotunneling spectroscopy -- a case study for quasi-1D organic superconductors

We propose that anisotropic $p$-, $d$-, or $f$-wave pairing symmetries can be distinguished from a tunneling spectroscopy in the presence of magnetic fields, which is exemplified here for a model organic superconductor ${(TMTSF)}_{2}X$. The shape of the Fermi surface (quasi-one-dimensional in this example) affects sensitively the pairing symmetry, which in turn affects the shape (U or V) of the gap along with the presence/absence of the zero-bias peak in the tunneling in a subtle manner. Yet, an application of a magnetic field enables us to identify the symmetry, which is interpreted as an effect of the Doppler shift in Andreev bound states.Comment: 4 papegs, 4 figure