Phase transition in a healthy human heart rate

A healthy human heart rate displays complex fluctuations which share characteristics of physical systems in a critical state. We demonstrate that the human heart rate in healthy individuals undergoes a dramatic breakdown of criticality characteristics, reminiscent of continuous second order phase transitions. By studying the germane determinants, we show that the hallmark of criticality--highly correlated fluctuations--is observed only during usual daily activity, and a breakdown of these characteristics occurs in prolonged, strenuous exercise and sleep. This finding is the first reported discovery of the dynamical phase transition phenomenon in a biological control system and will be a key to understanding the heart rate control system in health and disease.     

Scaling Behaviour and Memory in Heart Rate of Healthy Human

We investigate a set of complex heart rate time series from healthy human in different behaviour states with the detrended fluctuation analysis and diffusion entropy （DE） method. It is proposed that the scaling properties are influenced by behaviour states. The memory detected by DE exhibits an approximately same pattern after a detrending procedure. Both of them demonstrate the long-range strong correlations in heart rate. These findings may be helpful to understand the underlying dynamical evolution process in the heart rate control system, as well as to model the cardiac dynamic process.     

Effect of kinesin velocity distribution on slow axonal transport

The goal of this paper is to investigate the effect that a distribution of kinesin motor velocities could have on cytoskeletal element (CE) concentration waves in slow axonal transport. Previous models of slow axonal transport based on the stop-and-go hypothesis (P. Jung, A. Brown, Modeling the slowing of neurofilament transport along the mouse sciatic nerve, Physical Biology 6 (2009) 046002) assumed that in the anterograde running state all CEs move with one and the same velocity as they are propelled by kinesin motors. This paper extends the aforementioned theoretical approach by allowing for a distribution of kinesin motor velocities; the distribution is described by a probability density function (PDF). For a two kinetic state model (that accounts for the pausing and running populations of CEs) an analytical solution describing the propagation of the CE concentration wave is derived. Published experimental data are used to obtain an analytical expression for the PDF characterizing the kinesin velocity distribution; this analytical expression is then utilized as an input for computations. It is demonstrated that accounting for the kinesin velocity distribution increases the rate of spreading of the CE concentration waves, which is a significant improvement in the two kinetic state model.     

Deviations from uniform power law scaling in nonstationary time series

A classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long-range correlations. Here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat-to-beat fluctuations in the human heart rate. We develop techniques based on the Fano factor and Allan factor functions, as well as on detrended fluctuation analysis, for quantifying deviations from uniform power-law scaling in nonstationary time series. By analyzing extremely long data sets of up to N = 10(5) beats for 11 healthy subjects, we find that the fluctuations in the heart rate scale approximately uniformly over several temporal orders of magnitude. By contrast, we find that in data sets of comparable length for 14 subjects with heart disease, the fluctuations grow erratically, indicating a loss of scaling stability.     

Probabilistic solution of nonlinear oscillators excited by combined Gaussian and Poisson white noises

The stationary probability density function (PDF) solution of the stochastic response of nonlinear oscillators is investigated in this paper. The external excitation is assumed to be a combination of Gaussian and Poisson white noises. The PDF solution is governed by the generalized Kolmogorov equation which is solved by the exponential-polynomial closure (EPC) method. In order to evaluate the effectiveness of the EPC method, different nonlinear oscillators are considered in numerical analysis. Nonlinearity exists either in displacement or in velocity for these nonlinear oscillators. The impulse arrival rate, mono-modal PDF and bi-modal PDF are also considered in this study. Compared to the PDF given by Monte Carlo simulation, the EPC method presents good agreement with the simulated result, which can also be observed in the tail region of the PDF solution.     

Detailed mapping of the local Ir4+ dimers through the metal-insulator transitions of CuIr2S4 thiospinel by X-ray atomic pair distribution function measurements

The evolution of the short-range structural signature of the Ir4+ dimer state in CuIr2S4 thiospinel has been studied across the metal-insulator phase transitions as the metallic state is induced by temperature, Cr doping, and x-ray fluence. An atomic pair distribution function (PDF) approach reveals that there are no local dimers that survive into the metallic phase when this is invoked by temperature and doping. The PDF shows Ir4+ dimers when they exist, regardless of whether or not they are long-range ordered. At 100 K, exposure to a 98 keV x-ray beam melts the long-range dimer order within a few seconds, though the local dimers remain intact. This shows that the metallic state accessed on warming and doping is qualitatively different from the state obtained under x-ray irradiation.     

Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series

The healthy heartbeat is traditionally thought to be regulated according to the classical principle of homeostasis whereby physiologic systems operate to reduce variability and achieve an equilibrium-like state [Physiol. Rev. 9, 399-431 (1929)]. However, recent studies [Phys. Rev. Lett. 70, 1343-1346 (1993); Fractals in Biology and Medicine (Birkhauser-Verlag, Basel, 1994), pp. 55-65] reveal that under normal conditions, beat-to-beat fluctuations in heart rate display the kind of long-range correlations typically exhibited by dynamical systems far from equilibrium [Phys. Rev. Lett. 59, 381-384 (1987)]. In contrast, heart rate time series from patients with severe congestive heart failure show a breakdown of this long-range correlation behavior. We describe a new method--detrended fluctuation analysis (DFA)--for quantifying this correlation property in non-stationary physiological time series. Application of this technique shows evidence for a crossover phenomenon associated with a change in short and long-range scaling exponents. This method may be of use in distinguishing healthy from pathologic data sets based on differences in these scaling properties.     

Steady-state probability density function in wave turbulence under large volume limit

We investigate the possibility for two-mode probability density function(PDF) to have a non-zero flux steady state solution.We take the large volume limit so that the space of modes becomes continuous.It is shown that in this limit all the steady-state two-or higher-mode PDFs are the product of one-mode PDFs.The flux of this steady-state solution turns out to be zero for any finite mode PDF.     

Ordinal pattern statistics for the assessment of heart rate variability

The recognition of all main features of a healthy heart rhythm (the so-called sinus rhythm) is still one of the biggest challenges in contemporary cardiology. Recently the interesting physiological phenomenon of heart rate asymmetry has been observed. This phenomenon is related to unbalanced contributions of heart rate decelerations and accelerations to heart rate variability. In this paper we apply methods based on the concept of ordinal pattern to the analysis of electrocardiograms (inter-peak intervals) of healthy subjects in the supine position. This way we observe new regularities of the heart rhythm related to the distribution of ordinal patterns of lengths 3 and 4.     

旋流燃烧NO生成的USM湍流反应模型

用统一二阶矩(USM)湍流反应模型对不同旋流数下甲烷-空气旋流燃烧NO生成进行了数值模拟,并和EBU-Arrhenius(E-A)燃烧模型对燃烧的模拟结果和简化PDF湍流反应模型对NO生成的模拟结果以及相应的实验结果进行对比。结果表明,USM模型显著地优于E-A模型和简化PDF模型。E-A模型不能合理地模拟有限反应动力学,而简化PDF模型用两个单变量PDF的乘积代替联合PDF,大大地低估了NO湍流反应率。USM模型预报结果和实验结果符合最好。     

基于双参数Weibull分布的视频编码率失真模型的研究

对视频序列离散余弦变换(DCT)系数统计分布进行了分析,提出了一种基于Weibull概率密度的视频DCT系数统计模型,该模型较Laplace概率密度与Cauchy概率密度更好地描述了视频序列的DCT特征.随后以该统计模型为基础,依据熵编码的理论分别给出了视频序列的速率-量化关系和失真-量化关系,并根据实际视频序列特性对其进行合理地简化近似,得到一种新的较为精确的视频序列率失真模型.经大量仿真实验证明,文中提出的基于Weibull分布的率失真模型对于Intra帧和Inter帧两种编码的真实视频序列率失真特性都具有较好的描述.     

Statistics of biophysical signal characteristics and state specificity of the human EEG

The arguments are given that local exponents obtained in multifractal analysis by two methods: wavelet transform modulus maxima (WTMM) and multifractal detrended fluctuation analysis (MDFA) allow to separate statistically hearts of healthy people and subjects suffering from reduced left ventricle systolic function (NYHA I–III class). Proposed indices of fractality suggest that a signal of human heart rate is a mixture of two processes: monofractal and multifractal ones.     

钝体后湍流预混燃烧的PDF模拟

本文采用PDF方法对矩形燃烧室内钝体后的湍流预混火焰进行了数值模拟。脉动速度-频率-标量联合的PDF输运方程用Monte Carlo方法求解,质量、动量和能量的平均值由基于无结构网格的有限体积法求解,压力通过状态方程获得。PDF方程中所需的平均密度、平均速度和压力由有限体积法提供,并将用Monte Carlo方法求出的雷诺应力、化学反应源项和比热比传递给有限体积法。本文对丙烷和空气燃烧的不同简化化学反应机理进行了研究,并与实验结果进行比较,获得满意的结果。     

Modeling of multicomponent-fuel drop-laden mixing layers having a multitude of species

A formulation representing multicomponent-fuel (MC-fuel) composition as a probability distribution function (PDF) depending on the molar mass is used to construct a model of a large number of MC-fuel drops evaporating in a gas flow, so as to assess the extent of fuel specificity on the vapor composition. The PDF is a combination of two Gamma PDFs, which was previously shown to duplicate the behavior of a fuel composed of many species during single drop evaporation. The conservation equations are Eulerian for the flow and Lagrangian for the physical drops, all of which are individually followed. The gas conservation equations for mass, momentum, species, and energy are complemented by differential conservation equations for the first four moments of the gas-composition PDF; all coupled to the perfect gas equation of state. Source terms in all conservation equations couple the gas phase to the drops. The drop conservation equations for mass, position, momentum, and energy are complemented by differential equations for four moments of the liquid-composition PDF. The simulations are performed for a three-dimensional mixing layer whose lower stream is initially laden with drops. Initial perturbations excite the layer to promote the double pairing of its four initial spanwise vortices to an ultimate vortex. The drop temperature is initially lower than that of the surrounding gas, initiating drop heating and evaporation. The results focus on both evolution and the state of the drops and gas when layers reach a momentum-thickness maximum past the double vortex pairing; particular emphasis is on the gas composition. Comparisons between simulations with n-decane, diesel, and three kerosenes show that at same initial Reynolds number and Stokes number distribution, a single-component fuel cannot represent MC fuels. Substantial differences among the MC-fuel vapor composition indicate that fuel specificity must be captured for the prediction of combustion.     

Multi-environment probability density function method for modelling turbulent combustion using realistic chemical kinetics

A computational fluid dynamics (CFD) tool for performing turbulent combustion simulations that require finite-rate chemistry is developed and tested by modelling a series of bluff-body stabilized flames that exhibit different levels of finite-rate chemistry effects ranging from near equilibrium to near global extinction. The new modelling tool is based on the multi-environment probability density function (MEPDF) methodology and combines the following: the direct quadrature method of moments (DQMOM); the interaction-by-exchange-with-the-mean (IEM) mixing model; and realistic combustion chemistry. Using DQMOM, the MEPDF model can be derived from the transport PDF equation by depicting the joint composition PDF as a weighted summation of a finite number of multi-dimensional Dirac delta functions in the composition space. The MEPDF method with multiple reactive scalars retains the unique property of the joint PDF method of treating chemical reactions exactly. However, unlike the joint PDF methods that typically must resort to particle-based Monte-Carlo solution schemes, the MEPDF equations (i.e. the transport equations of the weighted delta-peaks) can be solved by traditional Eulerian grid-based techniques. In the current study, a pseudo time-splitting scheme is adopted to solve the MEPDF equations; the reaction source terms are computed with a highly efficient and accurate in-situ adaptive tabulation (ISAT) algorithm. A 19-species reduced mechanism based on quasi-steady state assumptions is used in the simulations of the bluff-body flames. The modelling results are compared with the experimental data, including mixing, temperature, major species and important minor species such as CO and NO. Compared with simulations using a Monte-Carlo joint PDF method, the new approach shows comparable accuracy.     

Statistical physics and physiology: monofractal and multifractal approaches.

Even under healthy, basal conditions, physiologic systems show erratic fluctuations resembling those found in dynamical systems driven away from a single equilibrium state. Do such "nonequilibrium" fluctuations simply reflect the fact that physiologic systems are being constantly perturbed by external and intrinsic noise? Or, do these fluctuations actually, contain useful, "hidden" information about the underlying nonequilibrium control mechanisms? We report some recent attempts to understand the dynamics of complex physiologic fluctuations by adapting and extending concepts and methods developed very recently in statistical physics. Specifically, we focus on interbeat interval variability as an important quantity to help elucidate possibly non-homeostatic physiologic variability because (i) the heart rate is under direct neuroautonomic control, (ii) interbeat interval variability is readily measured by noninvasive means, and (iii) analysis of these heart rate dynamics may provide important practical diagnostic and prognostic information not obtainable with current approaches. The analytic tools we discuss may be used on a wider range of physiologic signals. We first review recent progress using two analysis methods--detrended fluctuation analysis and wavelets--sufficient for quantifying monofractual structures. We then describe recent work that quantifies multifractal features of interbeat interval series, and the discovery that the multifractal structure of healthy subjects is different than that of diseased subjects.     

FeCuNi金属玻璃中第二峰分裂的结构起源

基于分子动力学模拟, 采用双体分布函数(PDF) 、 最大标准团簇(LSC) 、 拓扑密堆团簇(TCP LSC) 和三维可视化技术等微观结构表征方法, 研究了1012K/s 冷速下六种不同组分的 Fe70Cu(30 -x ) Nix (x =0、5 、10、15 、20、30)金属玻璃中的偏PDF 特征以及 Ni 含量对 TCP LSCs 的影响. 研究结果表明:FeCuNi 金属玻璃中的ICO LSCs 不是PDF 第二峰分裂的主要结构起源, 而 TCP LSCs 可以相当完美地解释第二峰的分裂特征. Ni 含量对 TCP LSCs 微观结构产生微妙且复杂的影响. 拓扑不变性是 TCP LSCs 的基本特征.     

Computations of turbulent lean premixed combustion using conditional moment closure

Conditional Moment Closure (CMC) is a suitable method for predicting scalars such as carbon monoxide with slow chemical time scales in turbulent combustion. Although this method has been successfully applied to non-premixed combustion, its application to lean premixed combustion is rare. In this study the CMC method is used to compute piloted lean premixed combustion in a distributed combustion regime. The conditional scalar dissipation rate of the conditioning scalar, the progress variable, is closed using an algebraic model and turbulence is modelled using the standard k–? model. The conditional mean reaction rate is closed using a first order CMC closure with the GRI-3.0 chemical mechanism to represent the chemical kinetics of methane oxidation. The PDF of the progress variable is obtained using a presumed shape with the Beta function. The computed results are compared with the experimental measurements and earlier computations using the transported PDF approach. The results show reasonable agreement with the experimental measurements and are consistent with the transported PDF computations. When the compounded effects of shear-turbulence and flame are strong, second order closures may be required for the CMC.     

Photon time-interval statistics applied to the analysis of laser heterodyne signal with photon counter

In this paper, we report a mathematical derivation of probability density function (PDF) of time-interval between two successive photoelectrons of the laser heterodyne signal, and give a confirmation of the theoretical result by both numerical simulation and an experiment. The PDF curve of the beat signal displays a series of fluctuations, the period and amplitude of which are respectively determined by the beat frequency and the mixing efficiency. The beat frequency is derived from the frequency of fluctuations accordingly when the PDF curve is measured. This frequency measurement method still works while the traditional Fast Fourier Transform (FFT) algorithm hardly derives the correct peak value of the beat frequency in the condition that we detect 80 MHz beat signal with 8 Mcps (counts per-second) photons count rate, and this indicates an advantage of the PDF method.     

Zone-adaptive modeling of turbulent flames with multiple chemical mechanisms

A novel zone-adaptive modeling method (AdaCM) with multiple chemical mechanisms is proposed for turbulent flames to achieve high-fidelity, yet computationally efficient, predictions. Specifically, a computational economical species transport model, e.g., the well-mixed model, via finite volume algorithm is employed with a simple mechanism as the base model for the whole computational domain, while the advanced transported probability density function (TPDF) method via Lagrangian particle tracking is employed with a detailed mechanism only for spatial regions with intense turbulence-chemistry interaction (TCI), denoted as the “PDF regions”. The PDF regions are dynamically identified based on local flow and flame characteristics and may evolve with time. A two-way particle/finite volume submodel coupling is formulated to ensure the composition consistency between submodels in the PDF regions and impose the correct interface conditions for composition and mass flow rate on the boundary of the PDF regions. With regard to transformation between different species representations in the mechanisms, a species reconstruction/reduction approach based on constrained chemical equilibrium is proposed to ensure element conservation and an adequate specification of unrepresented species at the model interface. The proposed adaptive modeling method has been applied to the well-known Sandia Flame D, in which the well-mixed combustion model with a 6-species, two-step global mechanism is employed as a base model and the high-fidelity TPDF with a 25-species skeletal mechanism is employed for regions with intense TCI. Results demonstrate the consistency in PDF regions between submodels with two distinct mechanisms. The predictions from the adaptive modeling are almost identical to those of TPDF and agree well with experimental measurements, illustrating the preservation of prediction accuracy in the adaptive method. In addition, the total number of computational particles in AdaCM for Flame D is only 18% of that for the stand-alone TPDF, and the recorded computational speedup is about 2.8.