Lorenz-63 Model as a Metaphor for Transient Complexity in Climate

Dynamical systems like the one described by the three-variable Lorenz-63 model may serve as metaphors for complex natural systems such as climate systems. When these systems are perturbed by external forcing factors, they tend to relax back to their equilibrium conditions after the forcing has shut off. Here we investigate the behavior of such transients in the Lorenz-63 model by studying its trajectories initialized far away from the asymptotic attractor. Counterintuitively, these transient trajectories exhibit complex routes and, in particular, the sensitivity to initial conditions is akin to that of the asymptotic behavior on the attractor. Thus, similar extreme events may lead to widely different variations before the perturbed system returns back to its statistical equilibrium.     

Empirical Mode Decomposition-Derived Entropy Features Are Beneficial to Distinguish Elderly People with a Falling History on a Force Plate Signal

Fall risk prediction is an important issue for the elderly. A center of pressure signal, derived from a force plate, is useful for the estimation of body calibration. However, it is still difficult to distinguish elderly people’s fall history by using a force plate signal. In this study, older adults with and without a history of falls were recruited to stand still for 60 s on a force plate. Forces in the x, y and z directions (Fx, Fy, and Fz) and center of pressure in the anteroposterior (COPx) and mediolateral directions (COPy) were derived. There were 49 subjects in the non-fall group, with an average age of 71.67 (standard derivation: 6.56). There were also 27 subjects in the fall group, with an average age of 70.66 (standard derivation: 6.38). Five signal series—forces in x, y, z (Fx, Fy, Fz), COPX, and COPy directions—were used. These five signals were further decomposed with empirical mode decomposition (EMD) with seven intrinsic mode functions. Time domain features (mean, standard derivation and coefficient of variations) and entropy features (approximate entropy and sample entropy) of the original signals and EMD-derived signals were extracted. Results showed that features extracted from the raw COP data did not differ significantly between the fall and non-fall groups. There were 10 features extracted using EMD, with significant differences observed among fall and non-fall groups. These included four features from COPx and two features from COPy, Fx and Fz.     

On the Possibility of Chaos in a Generalized Model of Three Interacting Sectors

In this study we extend a model, proposed by Dendrinos, which describes dynamics of change of influence in a social system containing a public sector and a private sector. The novelty is that we reconfigure the system and consider a system consisting of a public sector, a private sector, and a non-governmental organizations (NGO) sector. The additional sector changes the model’s system of equations with an additional equation, and additional interactions must be taken into account. We show that for selected values of the parameters of the model’s system of equations, chaos of Shilnikov kind can exist. We illustrate the arising of the corresponding chaotic attractor and discuss the obtained results from the point of view of interaction between the three sectors.     

Complexity of Body Movements during Sleep in Children with Autism Spectrum Disorder

Recently, measuring the complexity of body movements during sleep has been proven as an objective biomarker of various psychiatric disorders. Although sleep problems are common in children with autism spectrum disorder (ASD) and might exacerbate ASD symptoms, their objectivity as a biomarker remains to be established. Therefore, details of body movement complexity during sleep as estimated by actigraphy were investigated in typically developing (TD) children and in children with ASD. Several complexity analyses were applied to raw and thresholded data of actigraphy from 17 TD children and 17 children with ASD. Determinism, irregularity and unpredictability, and long-range temporal correlation were examined respectively using the false nearest neighbor (FNN) algorithm, information-theoretic analyses, and detrended fluctuation analysis (DFA). Although the FNN algorithm did not reveal determinism in body movements, surrogate analyses identified the influence of nonlinear processes on the irregularity and long-range temporal correlation of body movements. Additionally, the irregularity and unpredictability of body movements measured by expanded sample entropy were significantly lower in ASD than in TD children up to two hours after sleep onset and at approximately six hours after sleep onset. This difference was found especially for the high-irregularity period. Through this study, we characterized details of the complexity of body movements during sleep and demonstrated the group difference of body movement complexity across TD children and children with ASD. Complexity analyses of body movements during sleep have provided valuable insights into sleep profiles. Body movement complexity might be useful as a biomarker for ASD.     

Kerr介质中J-C模型的色散近似耗散动力学

应用全量子论研究了含Kerr介质的Jaynes-Cummings模型在色散近似下系统和子系统的相干性丢失及纠缠特性,在输入场为相干场假设下计算了线性熵.结果表明,原子相干性丢失与Kerr效应无关,场和原子-场系统的相干性丢失因Kerr介质的存在而增强,原子与场之间的纠缠因Kerr效应而受到压制,场的相干性时间演化规律在定性和定量两方面都受到腔耗的影响.Kerr介质对场线性熵的作用要通过腔耗才能展现出来.     

Self-consistency of a Modification Method Based on Membrane Model with Minimal Length Considered

By adopting a result from generalized uncertainty principles (GUP), we modify the inner bound of the membrane model to a physical fixed value and get the cut-offs naturally rather than by hand, which are both in brickwall model and membrane model, and the semi-classical quantization condition could always be valid as well. We also calculate the entropies of Schwarzschild-de Sitter black hole and find the GUP we choose qualitatively shows that the requirement of mass in this method is the same as the natural requirement of the Schwarzschild-de Sitter black hole, which means the method might be self-consistent.     

原子与频率随时间变化场相互作用系统中场熵的演化

利用多光子Jaynes-Cummings模型,考虑场频率随时间以正弦函数形式作小量变化,在旋波近似下,研究了二能级原子通过多光子跃迁与单模辐射场相互作用系统中场熵的演化规律.利用数值计算方法给出场熵随时间的演化曲线.研究结果表明:场熵的演化受场频率随时间正弦函数形式变化的调制,场频率振荡的幅值u越大调制作用越强,在场频率振荡的幅值u大于一定值后,场熵将按场频率周期性的变化规律作周期性振荡.     

Thermodynamical Properties of Spin-3/2 Ising Model in a Longitudinal Random Field with Crystal Field

A theoretical study of a spin-3/2 Ising model in a longitudinal random field with crystal field is studiedby using of the effective-field theory with correlations. The phase diagrams and the behavior of the tricritical point areinvestigated numerically for the honeycomb lattice when the randorm field is bimodal. In particular, the specific heatand the internal energy are examined in detail for the system with a crystal-field constant in the critical region wherethe ground-state configuration may change from the spin-3/2 state to the spin-1/2 state. We find many interestingphenomena in the system.     

Thermodynamical Properties of Spin-3/2 Ising Model in a Longitudinal Random Field with Crystal Field

A theoretical study of a spin-3/2 Ising model in a longitudinal random field with crystal field is studied by using of the effective-field theory with correlations. The phase diagrams and the behavior of the tricritical point are investigated numerically for the honeycomb lattice when the random field is bimodal. In particular, the specific heat and the internal energy are examined in detail for the system with a crystal-field constant in the critical region where the ground-state configuration may change from the spin-3/2 state to the spin-1/2 state. We find many interesting phenomena in the system.     

Simulation of the Second Grade Fluid Model for Blood Flow through a Tapered Artery with a Stenosis

We analyze the blood flow through a tapered artery, assuming the blood to be a second order fluid model. The resulting nonlinear implicit system of partial differential equations is solved by the perturbation method. The expressions for shear stress, velocity, flow rate, wall shear stress and longitudinal impedance are obtained. The physical behavior of different parameters is also discussed, as are trapping phenomena.     

Fluid Model of a Sheath Formed in Front of an Electron Emitting Electrode Immersed in a Plasma with Two Electron Temperatures

The formation of a sheath in front of a negatively biased electrode (collector) that emits electrons is studied by a one‐dimensional fluid model. Electron and ion emission coefficients are introduced in the model. It is assumed that the electrode is immersed in a plasma that contains energetic electrons. The electron velocity distribution function is assumed to be a sum of two Maxwellian distributions with two different temperatures, while the ions and the emitted electrons are assumed to be monoenergetic. The condition for zero electric field at the collector is derived. Using this equation the dependence of electron and ion critical emission coefficients on various parameters ‐ like the ratio between the hot and cool electron density, the ratio between hot and cool electron temperature and the initial velocity of secondary electrons ‐ is calculated for a floating collector. A modification of the Bohm criterion due to the presence of hot and emitted electrons is also given. The transition between space charge limited and temperature limited electron emission for a current‐carrying collector is also analyzed. The critical potential, where this transition occurs, is calculated as a function of several parameters like the Richardson emission current, the ratio between the hot and cool electron density, the ratio between hot and cool electron temperature and the initial velocity of secondary electrons. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

分形复合油藏非牛顿幂律流体不稳定渗流的数学模型

对不稳定渗流的数学模型进行了推导并建立了分形复合油藏不稳定渗流模型.在无限大地层、有界定压、有界封闭三种外边界条件下分别求出了它们在Laplace空间的解析解.对于两区的特殊情况,分析了井底压力动态特征和参数影响,制作了典型曲线.非牛顿幂律流体的幂律指数,分形参数均对典型曲线产生较大的影响,呈现出与牛顿流体和均质油藏明显不同的特征.这对于非均质油藏非牛顿流体的不稳定试井分析和研究非线性渗流特征都是十分重要的.     

Characterization of fish schooling behavior with different numbers of Medaka (Oryzias latipes) and goldfish (Carassius auratus) using a Hidden Markov Model

Fish that swim in schools benefit from increased vigilance, and improved predator recognition and assessment. Fish school size varies according to species and environmental conditions. In this study, we present a Hidden Markov Model (HMM) that we use to characterize fish schooling behavior in different sized schools, and explore how school size affects schooling behavior. We recorded the schooling behavior of Medaka (Oryzias latipes) and goldfish (Carassius auratus  ) using different numbers of individual fish (10–40), in a circular aquarium. Eight to ten 3 s video clips were extracted from the recordings for each group size. Schooling behavior was characterized by three variables: linear speed, angular speed, and Pearson coefficient. The values of the variables were categorized into two events each for linear and angular speed (high and low), and three events for the Pearson coefficient (high, medium, and low). Schooling behavior was then described as a sequence of 12 events (2×2×3$2\times 2\times 3$), which was input to an HMM as data for training the model. Comparisons of model output with observations of actual schooling behavior demonstrated that the HMM was successful in characterizing fish schooling behavior. We briefly discuss possible applications of the HMM for recognition of fish species in a school, and for developing bio-monitoring systems to determine water quality.