High-resolution GNSS-tracked drifter for studying surface dispersion in shallow water

The use of GNSS tracked Lagrangian drifters allows more realistic quantification of fluid motion and dispersion coefficients than Eulerian techniques because such drifters are analogues of particles that are relevant to flow field characterisation and pollutant dispersion. Using the fast growing Real Time Kinematic (RTK) positioning technique derived from Global Satellite Navigation Systems (GNSS), drifters are developed for high frequency (10 Hz) sampling with position estimates to centimetre accuracy. The drifters are designed with small size and less direct wind drag to follow the sub-surface flow which characterizes dispersion in shallow waters. An analysis of position error from stationary observation indicates that the drifter can efficiently resolve motion up to 1 Hz. The result of the field deployments of the drifter in conjunction with acoustic Eulerian devices shows higher estimate of the drifter streamwise velocities. Single particle statistical analysis of field deployments in a shallow estuarine zone yielded dispersion coefficients estimate comparable to those of dye tracer studies. The drifters capture the tidal elevation during field studies in a tidal estuary.

Wide-band spectral power fluctuations characterize the response of simulated cortical networks to increasing stimulus intensity

The hippocampus is an anatomically distinct region of the medial temporal lobe that plays a critical role in the formation of declarative memories. Here we show that a computer simulation of simple compartmental cells organized with basic hippocampal connectivity is capable of producing stimulus intensity sensitive wide-band fluctuations of spectral power similar to that seen in real EEG. While previous computational models have been designed to assess the viability of the putative mechanisms of memory storage and retrieval, they have generally been too abstract to allow comparison with empirical data. Furthermore, while the anatomical connectivity and organization of the hippocampus is well defined, many questions regarding the mechanisms that mediate large-scale synaptic integration remain unanswered. For this reason we focus less on the specifics of changing synaptic weights and more on the population dynamics. Spectral power in four distinct frequency bands were derived from simulated field potentials of the computational model and found to depend on the intensity of a random input. The majority of power occurred in the lowest frequency band (3-6 Hz) and was greatest to the lowest intensity stimulus condition (1% maximal stimulus). In contrast, higher frequency bands ranging from 7-45 Hz show an increase in power directly related with an increase in stimulus intensity. This trend continues up to a stimulus level of 15% to 20% of the maximal input, above which power falls dramatically. These results suggest that the relative power of intrinsic network oscillations are dependent upon the level of activation and that above threshold levels all frequencies are damped, perhaps due to over activation of inhibitory interneurons.

A Crank--Nicolson ADI spectral method for a two-dimensional riesz space fractional nonlinear reaction-diffusion equation

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank--Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived method is stable and convergent of order $2$ in time. An optimal error estimate in space is also obtained by introducing a new orthogonal projector. The present method is extended to solve the fractional FitzHugh--Nagumo model. Numerical results are provided to verify the theoretical analysis.

A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation

The fractional Fokker-Planck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the non-local property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations. In this paper, a space-time spectral method is presented for the numerical solution of the time fractional Fokker-Planck initial-boundary value problem. The proposed method employs the Jacobi polynomials for the temporal discretization and Fourier-like basis functions for the spatial discretization. Due to the diagonalizable trait of the Fourier-like basis functions, this leads to a reduced representation of the inner product in the Galerkin analysis. We prove that the time fractional Fokker-Planck equation attains the same approximation order as the time fractional diffusion equation developed in [23] by using the present method. That indicates an exponential decay may be achieved if the exact solution is sufficiently smooth. Finally, some numerical results are given to demonstrate the high order accuracy and efficiency of the new numerical scheme. The results show that the errors of the numerical solutions obtained by the space-time spectral method decay exponentially.

Performance dispersion for evidence-based classification of stationary throwers

Background There is a need for better understanding of the dispersion of classification-related variable to develop an evidence-based classification of athletes with a disability participating in stationary throwing events. Objectives The purposes of this study are (A) to describe tools designed to comprehend and represent the dispersion of the performance between successive classes, and (B) to present this dispersion for the elite male and female stationary shot-putters who participated in Beijing 2008 Paralympic Games. Study design Retrospective study Methods This study analysed a total of 479 attempts performed by 114 male and female stationary shot-putters in three F30s (F32-F34) and six F50s (F52-F58) classes during the course of eight events during Beijing 2008 Paralympic Games. Results The average differences of best performance were 1.46±0.46 m for males between F54 and F58 classes as well as 1.06±1.18 m for females between F55 and F58 classes. The results demonstrated a linear relationship between best performance and classification while revealing two male Gold Medallists in F33 and F52 classes were outliers. Conclusions This study confirms the benefits of the comparative matrices, performance continuum and dispersion plots to comprehend classification-related variables. The work presented here represents a stepping stone into biomechanical analyses of stationary throwers, particularly on the eve of the London 2012 Paralympic Games where new evidences could be gathered.

Effect of carrier size on the dispersion of salmeterol xinafoate from interactive mixtures

The objective of this study was to determine the influence of lactose carrier size on drug dispersion of salmeterol xinafoate (SX) from interactive mixtures. SX dispersion was measured by using the fine particle fractions determined by a twin stage impinger attached to a Rotahaler1. The particle size of the lactose carrier in the SX interactive mixtures was varied using a range of commercial inhalation-grade lactoses. In addition, differing size fractions of individual lactose samples were achieved by dry sieving. The dispersion ofSXappeared to increase as the particle size of the lactose carrier decreased for the mixtures prepared from different particle size commercial samples of lactose and from different sieve fractions of the same lactose. Fine particles of lactose (<5 mm) associated with the lactose carrier were removed from the carrier surface by a wet decantation process to produce lactose samples with low but similar concentrations of fine lactose particles. The fine particle fractions of SX in mixtures prepared with the decanted lactose decreased significantly (analysis of variance, p<0.001) and the degree of dispersion became independent of the volume mean diameter of the carriers (analysis of variance, p<0.05). The dispersion behavior is therefore associated with the presence of fine adhered particles associated with the carriers and the inherent size of the carrier itself has little influence on dispersion.

Lactose surface modification by decantation: Are drug-fine lactose ratios the key to better dispersion of salmeterol xinafoate from lactose-interactive mixtures?

Purpose The role of fine lactose in the dispersion of salmeterol xinafoate (SX) from lactose mixtures was studied by modifying the fine lactose concentration on the surface of the lactose carriers using wet decantation. Methods Fine lactose was removed from lactose carriers by wet decantation using ethanol saturated with lactose. Particle sizing was achieved by laser diffraction. Fine particle fractions (FPFs) were determined by Twin Stage Impinger using a 2.5% SX mixture, and SX was analyzed by a validated high-performance liquid chromatography method. Adhesion forces between probes of SX and silica and the lactose surfaces were determined by atomic force microscopy. Results FPFs of SX were related to fine lactose concentration in the mixture for inhalation grade lactose samples. Reductions in FPF (2-4-fold) of Aeroflo 95 and 65 were observed after removing fine lactose by wet decantation; FPFs reverted to original values after addition of micronized lactose to decanted mixtures. FPFs of SX of sieved and decanted fractions of Aeroflo carriers were significantly different (p < 0.001). The relationship between FPF and fine lactose concentration was linear. Decanted lactose demonstrated surface modification through increased SX-lactose adhesion forces; however, any surface modification other than removal of fine lactose only slightly influenced FPF. Conclusions Fine lactose played a key and dominating role in controlling FPF. SX to fine lactose ratios influenced dispersion of SX with maximum dispersion occurring as the ratio approached unity.

Estimate of Lagrangian integral scales in shallow tidal water using high resolution GPS-tracked drifters

In estuaries and natural water channels, the estimate of velocity and dispersion coefficients is critical to the knowledge of scalar transport and mixing. This estimate is rarely available experimentally at sub-tidal time scale in shallow water channels where high frequency is required to capture its spatio-temporal variation. This study estimates Lagrangian integral scales and autocorrelation curves, which are key parameters for obtaining velocity fluctuations and dispersion coefficients, and their spatio-temporal variability from deployments of Lagrangian drifters sampled at 10 Hz for a 4-hour period. The power spectral densities of the velocities between 0.0001 and 0.8 Hz were well fitted with a slope of 5/3 predicted by Kolmogorov’s similarity hypothesis within the inertial subrange, and were similar to the Eulerian power spectral previously observed within the estuary. The result showed that large velocity fluctuations determine the magnitude of the integral time scale, TL. Overlapping of short segments improved the stability of the estimate of TL by taking advantage of the redundant data included in the autocorrelation function. The integral time scales were about 20 s and varied by up to a factor of 8. These results are essential inputs for spatial binning of velocities, Lagrangian stochastic modelling and single particle analysis of the tidal estuary.

Fourier spectral methods for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains ofRn. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.

Fractional diffusion models of cardiac electrical propagation: Role of structural heterogeneity in dispersion of repolarization

Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread is key to advancing our interpretation of dispersion of repolarization. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a means of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, analysed against in vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies relevant characteristics of cardiac electrical propagation at tissue level. These include conduction effects on action potential (AP) morphology, the shortening of AP duration along the activation pathway and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media.

Numerical analysis of a new space-time variable fractional order advection-dispersion equation

Many physical processes appear to exhibit fractional order behavior that may vary with time and/or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider a new space–time variable fractional order advection–dispersion equation on a finite domain. The equation is obtained from the standard advection–dispersion equation by replacing the first-order time derivative by Coimbra’s variable fractional derivative of order α(x)∈(0,1]α(x)∈(0,1], and the first-order and second-order space derivatives by the Riemann–Liouville derivatives of order γ(x,t)∈(0,1]γ(x,t)∈(0,1] and β(x,t)∈(1,2]β(x,t)∈(1,2], respectively. We propose an implicit Euler approximation for the equation and investigate the stability and convergence of the approximation. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

Development of multi-rotor localised surveillance using multi-spectral sensors for plant biosecurity

This report describes a proof of concept for multi-rotor localised surveillance using a multi-spectral sensor for plant biosecurity applications. A literature review was conducted on previous applications using airborne multispectral imaging for plant biosecurity purposes. A ready built platform was purchased and modified in order to fit and provide suitable clearance for a Tetracam Mini-MCA multispectral camera. The appropriate risk management documents were developed allowing the platform and the multi-spectral camera to be tested extensively. However, due to technical difficulties with the platform the Mini- MCA was not mounted to the platform. Once a suitable platform is developed, future extensions can be conducted into the suitability of the Mini-MCA for airborne surveillance of Australian crops.

On the order of the fractional Laplacian in determining the spatio-temporal evolution of a space-fractional model of cardiac electrophysiology

Space-fractional operators have been used with success in a variety of practical applications to describe transport processes in media characterised by spatial connectivity properties and high structural heterogeneity altering the classical laws of diffusion. This study provides a systematic investigation of the spatio-temporal effects of a space-fractional model in cardiac electrophysiology. We consider a simplified model of electrical pulse propagation through cardiac tissue, namely the monodomain formulation of the Beeler-Reuter cell model on insulated tissue fibres, and obtain a space-fractional modification of the model by using the spectral definition of the one-dimensional continuous fractional Laplacian. The spectral decomposition of the fractional operator allows us to develop an efficient numerical method for the space-fractional problem. Particular attention is paid to the role played by the fractional operator in determining the solution behaviour and to the identification of crucial differences between the non-fractional and the fractional cases. We find a positive linear dependence of the depolarization peak height and a power law decay of notch and dome peak amplitudes for decreasing orders of the fractional operator. Furthermore, we establish a quadratic relationship in conduction velocity, and quantify the increasingly wider action potential foot and more pronounced dispersion of action potential duration, as the fractional order is decreased. A discussion of the physiological interpretation of the presented findings is made.

Spectral analysis of pair-correlation bandwidth: Application to cell biology images

Images from cell biology experiments often indicate the presence of cell clustering, which can provide insight into the mechanisms driving the collective cell behaviour. Pair-correlation functions provide quantitative information about the presence, or absence, of clustering in a spatial distribution of cells. This is because the pair-correlation function describes the ratio of the abundance of pairs of cells, separated by a particular distance, relative to a randomly distributed reference population. Pair-correlation functions are often presented as a kernel density estimate where the frequency of pairs of objects are grouped using a particular bandwidth (or bin width), Δ>0. The choice of bandwidth has a dramatic impact: choosing Δ too large produces a pair-correlation function that contains insufficient information, whereas choosing Δ too small produces a pair-correlation signal dominated by fluctuations. Presently, there is little guidance available regarding how to make an objective choice of Δ. We present a new technique to choose Δ by analysing the power spectrum of the discrete Fourier transform of the pair-correlation function. Using synthetic simulation data, we confirm that our approach allows us to objectively choose Δ such that the appropriately binned pair-correlation function captures known features in uniform and clustered synthetic images. We also apply our technique to images from two different cell biology assays. The first assay corresponds to an approximately uniform distribution of cells, while the second assay involves a time series of images of a cell population which forms aggregates over time. The appropriately binned pair-correlation function allows us to make quantitative inferences about the average aggregate size, as well as quantifying how the average aggregate size changes with time.