Sine Wave Model Research Articles

New Fourier-series-based analytical solution to the conduction–convection equation to calculate soil temperature, determine soil thermal properties, or estimate water flux

Temperature is an important physical variable of soil. Heat transfer in soils predominantly occurs due to conduction and convection. In this paper, we present a new analytical solution, based upon the Fourier series boundary conditions for soil surface temperature, in which the separation of variables for the heat conduction–convection equation was established. Data that had been collected from the Qinghai-Xizang (Tibet) Plateau (QXP) were used to calculate the thermal diffusivity and the liquid water flux density using different methods. The results of the soil thermal diffusivity using 5cm as the upper boundary for the soil depth were used to calculate the soil temperature using both the single sine wave conduction and conduction–convection model and the Fourier series conduction–convection model. These results were then compared with the values for the temperature of the field soil measured at a depth of 10cm. The average standard error of the estimate (SEE), the normalized standard error (NSEE) and Bias were 0.16°C, 2.70% and 0.11°C for the Fourier series conduction–convection method. The results indicate that the Fourier series model provides a better estimate of observed field temperatures than the sine wave model. This method provides a useful tool for determining soil thermal parameters, simulating soil temperature and the parameterization of land surface processes for modeling permafrost changes under global warming conditions.

Plasmodium knowlesi gene expression differs in ex vivo compared to in vitro blood-stage cultures.

BackgroundPlasmodium knowlesi is one of five Plasmodium species known to cause malaria in humans and can result in severe illness and death. While a zoonosis in humans, this simian malaria parasite species infects macaque monkeys and serves as an experimental model for in vivo, ex vivo and in vitro studies. It has underpinned malaria discoveries relating to host-pathogen interactions, the immune response and immune evasion strategies. This study investigated differences in P. knowlesi gene expression in samples from ex vivo and in vitro cultures.MethodsGene expression profiles were generated using microarrays to compare the stage-specific transcripts detected for a clone of P. knowlesi propagated in the blood of a rhesus macaque host and then grown in an ex-vivo culture, and the same clone adapted to long-term in vitro culture. Parasite samples covering one blood-stage cycle were analysed at four-hour intervals. cDNA was generated and hybridized to an oligoarray representing the P. knowlesi genome. Two replicate experiments were developed from in vitro cultures. Expression values were filtered, normalized, and analysed using R and Perl language and applied to a sine wave model to determine changes in equilibrium and amplitude. Differentially expressed genes from ex vivo and in vitro time points were detected using limma R/Bioconductor and gene set enrichment analysis (GSEA).ResultsMajor differences were noted between the ex vivo and in vitro time courses in overall gene expression and the length of the cycle (25.5 hours ex vivo; 33.5 hours in vitro). GSEA of genes up-regulated ex vivo showed an enrichment of various genes including SICAvar, ribosomal- associated and histone acetylation pathway genes. In contrast, certain genes involved in metabolism and cell growth, such as porphobilinogen deaminase and tyrosine phosphatase, and one SICAvar gene, were significantly up-regulated in vitro.ConclusionsThis study demonstrates how gene expression in P. knowlesi blood-stage parasites can differ dramatically depending on whether the parasites are grown in vivo, with only one cycle of development ex vivo, or as an adapted isolate in long-term in vitro culture. These data bring emphasis to the importance of studying the parasite, its biology and disease manifestations in the context of the host.Electronic supplementary materialThe online version of this article (doi:10.1186/s12936-015-0612-8) contains supplementary material, which is available to authorized users.

Investigating the influence of surface deviations in double walled carbon nanotube based nanomechanical sensors

This manuscript investigates the influence of surface deviations, i.e. curvature in double walled carbon nanotube based nano sensors. A number of papers have been published regarding the sensing characteristics of carbon nanotubes particularly single walled carbon nanotubes. The effect of waviness or curvature has been considered and modeled in single walled carbon nanotubes when used as mass or other types of sensors but very little information is available regarding the deviations in double walled carbon nanotubes and the use of such tubes as sensors. It has been found from the experimental images that double walled carbon nanotubes are not straight and that they have a significant amount of surface deviation associated with them. It is also observed that CNTs do not possess the same wavy thickness throughout their length. Hence a constant curvature or radius model may give uniform thickness in terms of curvature throughout the length which may lead to some what inaccurate results. To model the actual curvature ratio a half sine wave model has been selected which better represents the non-uniform thickness. In this paper resonant frequency of double walled carbon nanotubes (DWCNT) with deviations along it is axis and different boundary conditions namely cantilever and bridged have been investigated. The nonlinear equations of motion of the double-walled carbon nanotubes are derived by using Euler beam theory and Hamilton principle, with considering the nonlinear van der Waals forces. The sensitivity of the apparently deviated double walled carbon nanotubes, different masses (attached to the end of outer tube tip on DWCNT and center outer tube tip of the bridged DWCNT) and different lengths has been explored and presented. The dynamic response of sensors has been explained using orbit plot. The system is seen to be exhibiting an onset of periodic and quasi periodic behavior with the change in the surface deviations. The presented results clearly suggest that change in the stiffness associated with the backed out modulus leads to a frequency shift which is considered as a measure of change in mass. The results obtained have been validated with the published experimental literature as well as shell model and are found in good agreement.

Prediction of daily global solar radiation by day of the year in four cities located in the sunny regions of Iran

In this study, by using long-term global solar radiation data, 6day of the year based empirical models were tested for prediction of daily global solar radiation in four Iranian cities of Bandarabass, Isfahan, Kerman and Tabass. The statistical non-linear regression technique was utilized to establish the models then their accuracy evaluated using the statistical indicators of mean absolute percentage error, mean absolute bias error, root mean square error and coefficient of determination. In Bandarabass, Kerman and Tabass, the hybrid sine and cosine wave model and in Isfahan the 4th order polynomial model provided the highest accuracy. To assess the performance of the models in different days of the year a further statistical analysis was performed using the relative percentage error. The number of days falling in its acceptable interval of −10% to 10% for the best models in Bandarabass, Isfahan, Kerman, and Tabass were 346, 322, 334 and 328, respectively. Making comparison with the predictions of some existing monthly averaged models stated the superiority of the newly established day of the year based models. Hence, they can be utilized swimmingly to estimate daily insolation in the corresponding cities and a vast similar climate region around them.

Two accurate phase-difference estimators for dual-channel sine-wave model

Two algorithms for estimating the phase-difference between two real sinusoids with common frequency in the presence of white noise are proposed. The first estimator utilizes the maximum likelihood criterion to find the phase of each channel output in a separable manner, and the phase-shift estimate is then given by their difference. The algorithm extension to unknown frequency and/or noise powers is also studied. On the other hand, the development of the second method is based on the linear prediction approach with a properly chosen sampling frequency. Furthermore, variance expressions for the two estimators are derived. Computer simulations are included to corroborate the theoretical calculations and to contrast the performance of the proposed schemes with several existing phase-difference estimators as well as Cramer-Rao lower bound.

IEEE-STD-1057 Three Parameter Sine Wave Fit for SNR Estimation: Performance Analysis and Alternative Estimators

This paper considers the three-parameter-fit sine wave model. Under a Gaussian noise assumption, it is known that the three-parameter fit given in IEEE Standards 1057 and 1241 coincides with the method of maximum likelihood (ML), which is known for its favorable properties in large samples. Under coherent sampling assumption, the Cramer–Rao Bound of an unbiased estimator (UE) of the signal-to-noise ratio (SNR) is derived followed by an exact finite-sample analysis of the ML estimator of SNR derived from the three-parameter fit, revealing its nonsymmetric F-distribution. Exact expressions for the bias, variance, and the mean squared error (MSE) of the ML estimator are then derived, revealing that the ML estimator in finite samples is far from optimal in terms of precision and accuracy. With the ML estimator as a starting point, several alternative estimators are derived, which outperform the method of ML. In particular, a UE is derived, with lower variance compared with the ML for small sample size. In addition, estimators are derived based on constrained minimization of the MSE. The theoretical findings are illustrated by simulations, showing an excellent agreement between theory and practice. Simulations using quantized data are also used to show the performance of the derived estimators mimicking an analog-to-digital converter (ADC) testing scenario. Furthermore, the derived estimators are applied to coherently and noncoherently sampled measurement data from a 12-bit ADC and, for small number of samples, all are shown to outperform the original estimate, showing the practical relevance of the theoretical findings.

An Analytical Solution to the One‐Dimensional Heat Conduction–Convection Equation in Soil

Soil heat transfer occurs by conduction and convection. Soil temperatures below infiltrating water can provide a signal for water flux. In earlier work, analysis of field measurements with a sine wave model indicated that convection heat transfer made significant contributions to the subsurface temperature oscillations. In this work, we used a Fourier series to describe soil surface temperature variations with time. The conduction and convection heat transfer equation with a multi‐sinusoidal wave boundary condition was solved analytically using a Fourier transformation. Soil temperature values calculated by the single sine wave model and by the Fourier series model were compared with field soil temperature values measured at depths of 0.1 and 0.3 m below an infiltrating ponded surface. The Fourier series model provided better estimates of observed field temperatures than the sine wave model. The new model provides a general way to describe soil temperature under an infiltrating water source.

Large dam reservoirs are probably long‐period oscillators of fish diversity

Long-term fish population time series obtained annually in a backwater (upstream) and a tailwater (downstream) site of the large lowland Jeziorsko Reservoir, Poland, were analysed and compared to detect impoundment influence on the fluctuation of fish population density and on the fluctuation of a fish diversity measure. The partial-rate correlation function (PRCF) of all constantly occurring fish species displayed negative first-order feedback of past density on present density, both upstream and downstream. Weak and irregular cyclic patterns were observed in the autocorrelation function (ACF) of populations of several species upstream and of two species downstream. Most fish species exhibited no significant concordant variations between the two sites, but there were no data supporting different regulation. Probably, different exogenous (environmental) factors control fishes at the two sites. The ACFs of the time series of the exponential of Shannon entropy (N(1) diversity measure) obtained at the Jeziorsko tailwater site, and in the main body of the smaller Římov Reservoir, Czech Republic, revealed strong fluctuation patterns. The fluctuation was well fitted by a sine-wave model of a 9 year period at the Římov, although it co-occurred with a positive linear trend. A sine-wave model also fitted well with the trend at the Jeziorsko tailwater site, where, however, only one 16·5 year period occurred; hence, it is indicative of cyclicity. The results indicate that dam reservoirs may be oscillators of fish diversity and that part of the literature controversy over the effect of a reservoir on fish populations may be due to a too short sampling period: it is shown that both increase and decrease in diversity may be observed on the basis of samples selected from one diversity time series obtained at the tailwater.

Comparison of Two Parametric Methods to Estimate Pesticide Mass Loads in California’s Central Valley1

Saleh, Dina K., David L. Lorenz, and Joseph L. Domagalski, 2010. Comparison of Two Parametric Methods to Estimate Pesticide Mass Loads in California’s Central Valley. Journal of the American Water Resources Association (JAWRA) 00(0):1-11. DOI: 10.1111/j.1752-1688.2010.00506.x Abstract: Mass loadings were calculated for four pesticides in two watersheds with different land uses in the Central Valley, California, by using two parametric models: (1) the Seasonal Wave model (SeaWave), in which a pulse signal is used to describe the annual cycle of pesticide occurrence in a stream, and (2) the Sine Wave model, in which first-order Fourier series sine and cosine terms are used to simulate seasonal mass loading patterns. The models were applied to data collected during water years 1997 through 2005. The pesticides modeled were carbaryl, diazinon, metolachlor, and molinate. Results from the two models show that the ability to capture seasonal variations in pesticide concentrations was affected by pesticide use patterns and the methods by which pesticides are transported to streams. Estimated seasonal loads compared well with results from previous studies for both models. Loads estimated by the two models did not differ significantly from each other, with the exceptions of carbaryl and molinate during the precipitation season, where loads were affected by application patterns and rainfall. However, in watersheds with variable and intermittent pesticide applications, the SeaWave model is more suitable for use on the basis of its robust capability of describing seasonal variation of pesticide concentrations.

Mapping Displacement and Deformation of the Heart With Local Sine-Wave Modeling

The new SinMod method extracts motion from magnetic resonance imaging (MRI)-tagged (MRIT) image sequences. Image intensity in the environment of each pixel is modeled as a moving sine wavefront. Displacement is estimated at subpixel accuracy. Performance is compared with the harmonic-phase analysis (HARP) method, which is currently the most common method used to detect motion in MRIT images. SinMod can handle line tags, as well as speckle patterns. In artificial images (tag distance six pixels), SinMod detects displacements accurately (error < 0.02 pixels). Effects of noise are suppressed effectively. Sharp transitions in motion at the boundary of an object are smeared out over a width of 0.6 tag distance. For MRIT images of the heart, SinMod appears less sensitive to artifacts, especially later in the cardiac cycle when image quality deteriorates. For each pixel, the quality of the sine-wave model in describing local image intensity is quantified objectively. If local quality is low, artifacts are avoided by averaging motion over a larger environment. Summarizing, SinMod is just as fast as HARP, but it performs better with respect to accuracy of displacement detection, noise reduction, and avoidance of artifacts.

Optimal Lomb transform variant in HRV assessment

This study used to compare the performance of Lomb, fast Lomb and averaged Lomb on PSD estimates to examine the systematic differences for: 1) frequency and amplitudes distortions; 2) size of RR-interval series; 3) computational time. The PSD estimates realised using non-uniformly sampled RR-interval series are found to be within an error range of 1%, 3% and 40% for averaged Lomb, Lomb and fast Lomb transforms respectively, for sine wave model, while 30%, 60% and 80% when simulations were carried using IPFM model, with respect to FFT-based estimates of uniformly sampled data. The computational time for PSD using averaged Lomb transform is quite higher (over ten times in case of sine wave model and 100 times in case of IPFM model) to that of fast Lomb transform and lies in approximately same range, but slightly higher than that for Lomb transform.

Comparative Analysis of Three Algorithms for Two-Channel Common Frequency Sinewave Parameter Estimation: Ellipse Fit, Seven Parameter Sine Fit and Spectral Sinc Fit

Comparative Analysis of Three Algorithms for Two-Channel Common Frequency Sinewave Parameter Estimation: Ellipse Fit, Seven Parameter Sine Fit and Spectral Sinc FitIn this paper, a comparison analysis of three different algorithms for the estimation of sine signal parameters in two-channel common frequency situations is presented. The relevance of this situation is clearly understood in multiple applications where the algorithms have been applied. They include impedance measurements, eddy currents testing, laser anemometry and radio receiver testing for example. The three algorithms belong to different categories because they are based on different approaches. The ellipse fit algorithm is a parametric fit based on the XY plot of the samples of both signals. The seven parameter sine fit algorithm is a least-squares algorithm based on the time domain fitting of a single tone sinewave model to the acquired samples. The spectral sinc fit performs a fitting in the frequency domain of the exact model of an acquired sinewave on the acquired spectrum. Multiple simulation situations and real measurements are included in the comparison to demonstrate the weaknesses and strong points of each algorithm.

Computation formulas by FFT of the nonlinear orbital velocity in three-dimensional surface wave fields

Accurate representations of the surface potential and the orbital velocity of nonlinear water waves are obtained, given the spatial wave-elevation field and its time derivative along two-dimensional sections of the ocean surface. The effect of a horizontal current is accounted for. The method is three-dimensional. The kernel of an integral equation and its right-hand side, both nonlinear functions of the elevation, are obtained in series expansions, and expressed explicitly by Fourier transform (FFT). Calculations for a periodic sine-wave and non-periodic model directional irregular wave field over swaths (wave slope in the range ±0.3 in both cases) illustrate the formulas. The Gibbs phenomenon along the boundaries affects the very high-order contributions in the non-periodic case.

Parameter Estimation Employing a Dual-Channel Sine-Wave Model Under a Gaussian Assumption

The Cramer-Rao bound (CRB) is a lower bound on the error variance of any estimator. For a Gaussian scenario, the CRB is derived for a seven-parameter, dual-channel sine-wave model, which is a model relevant to applications such as impedance measurements and the estimation of particle size and velocity by laser anemometry. Four different parameterizations were considered: the common quadrature/in-phase and amplitude-phase models and two relative amplitude-phase models. The CRB indicated the achievable error variance of an unbiased estimator as a function of the signal-to-noise ratio (SNR), the number of samples, and noise power. A nonlinear least squares fit of the signal model to the collected data was employed. The problem at hand is separable and can be solved by a 1-D search followed by a linear least squares fit of the remaining parameters. The performance of the method was investigated with the aid of a simulation study, and the outcome was compared with that of the corresponding CRB and with a recently proposed seven-parameter fit. For high SNRs, the performance of the proposed method is close to optimal with an error variance close to the predictions made by the CRB.

Influence of harvest residues and vegetation on microsite soil and air temperatures in a young conifer plantation

Soil temperature influences many processes in young forest stands including growth and phenology of trees, water uptake, and nutrient mineralization. Effects of harvest residue management and other site preparation techniques on soil and air temperatures have previously been reported at the treatment level, but there is little information on temperature patterns in the various microsites created by these treatments. This study examines the effects of bole-only harvesting with and without vegetation control (BO + VC; BO − VC) and total-tree harvesting plus removal of legacy woody debris with vegetation control (TTP + VC) on microsite temperature in a young Douglas-fir ( Pseudotsuga menziesii (Mirb.) Franco) plantation. Hourly soil temperatures were recorded at a 10-cm mineral soil depth for 5 years post-planting, and near-ground (25 cm) air temperatures were recorded for 1 year. In the TTP + VC treatment, mean soil temperature and diurnal range in soil temperature during the growing season differed by microsite surface condition in the following sequence: exposed mineral soil > intact forest floor > decaying wood over soil > shade of stumps. In the BO treatments, soil temperature differences among microsites were smaller, and only the stump-shade microsite differed significantly from the others. Near-ground air temperature did not differ by microsite. A sine-wave model showed that diurnal warming of soil beneath decaying wood occurred more slowly than for other microsites. Total annual soil degree-day accumulation was 25–37% greater in the TTP + VC treatment than in the BO + VC treatment; the greatest difference occurred in the year with the warmest spring air temperature. Vegetation control treatments had little effect on soil temperature in the BO harvest treatment. The reduced microsite variability and diurnal fluctuation in soil temperature in the BO harvest treatment may be beneficial where summer temperature extremes are a concern. Alternatively, the warmer spring and early summer soil temperatures of the TTP harvest treatment may be advantageous for early seedling development.

The Visual Scoring of Sleep in Adults

The 1968 Rechtschaffen and Kales (R & K) sleep scoring manual was published 15 years after REM sleep was discovered. Advances in the ensuing 28 years warranted a re-look at visual scoring of sleep stages. This paper describes the work of the AASM Visual Scoring Task Force, including methodology, a literature review and the rationale behind the new rules. Reliability studies of R & K scoring were reviewed; reliability was low for stage one and moderate for slow wave sleep. Evidence indicated that K complexes and slow waves are expressed maximal frontally, spindles centrally and alpha rhythm over the occipital region. Three derivations of EEG, two of electro-oculography, and one of chin EMG were recommended. Scoring by 30-second epochs was retained. New terminology for sleep stages was proposed. Attenuation of alpha rhythm was determined to be the most valid electrophysiological marker of sleep onset. Alternative measures were proposed for non-alpha generating subjects. K complexes associated with arousals were determined to be insufficient alone to define the new stage N2. No evidence was found to justify dividing slow wave sleep into two stages. No reasons were found to alter the current slow wave amplitude criteria at any age. The phenomena of REM sleep were defined. The rules for defining onset and termination of REM sleep periods were simplified. Movement time was eliminated and major body movements defined. Studies are needed to test the reliability of the new rules. Future advances in technology may require modification of these rules with time.

Modeling Ischemia-Induced Dyssynchronous Myocardial Contraction

Left ventricular (LV) contraction dyssynchrony is not easily quantified. We previously described a model for quantifying LV dyssynchrony that referenced regional amplitude and phase angles to global LV systole using esmolol-induced regional dyskinesis. We tested the hypothesis that our sine wave model and phase angle analysis of regional dyssynchrony in a canine model could also assess dyssynchrony of contraction during regional ischemia. Hence we compared intracoronary esmolol and matched regional ischemia in 10 anesthetized open-chest dogs. Regional and total LV volumes (conductance catheter), piezoelectric crystal shortening, and LV pressures were measured before, during, and after esmolol-induced apical dyskinesis and matched regional ischemia. We defined regional phase angle of contraction (alpha) as the relative distance, measured in degrees, that regional minimal volume differed from global end-systole. We also compared maximal stroke volume (SV), observed effective SV (that portion of regional SV contributing to total SV for each treatment), and calculated effective SV (total regional SV x cosine alpha). Dobutamine infusion increased homogeneity of regional alpha relative to baseline. Both esmolol and ischemia significantly delayed (P < 0.05) apical contraction as quantified by increased alpha (12.4 degrees +/- 28.1 degrees to 27.4 degrees +/- 30.4 degrees and 54.2 degrees +/- 32.6 degrees , respectively) (mean +/- sd) and decreased regional effective SV (4.7 +/- 2.5 mL to 3.6 +/- 2.2 mL and 4 +/- 2.5 mL, respectively) relative to baseline. Our study indicates that intracoronary esmolol and ischemia induced qualitatively similar mechanical effects on myocardial function and that a sine wave model to estimate regional effective SV is a sensitive method to detect and quantify regional dyssynchrony induced by ischemia. Potentially, phase angle and regional amplitude analyses may prove to be effective measures to identify and quantify the beneficial effects of resynchronization therapies on myocardial function.

ADC Characterization in Time Domain] Frequency Estimation to Linearize Time-Domain Analysis of A/D Converters

Time-domain analysis is a powerful tool for testing A/D converters (ADCs), particularly by incoherent sampling. This sampling is encountered for instance in real application and systems where the clock is generated by an on-board crystal oscillator. In the case of the sine-wave model for ADC output samples, fitting a sine-wave function to the data record is nonlinear with respect to the frequency. To overcome the convergence problem, the authors propose some alternative methods based on frequency estimation by means of fast Fourier transform and eigenanalysis of the autocorrelation matrix. This leads to a simple linear problem. The effectiveness of these methods is proven on both simulation and experimental results

Spatial and seasonal variability in elemental content, δ13C, and δ15N ofThalassia testudinum from South Florida and its implications for ecosystem studies

Elemental and isotopic composition of leaves of the seagrassThalassia testudinum was highly variable across the 10,000 km2 and 8 years of this study. The data reported herein expand the reported range in carbon:nitrogen (C:N) and carbon:phosphorus (C:P) ratios and δ13C and δ15N values reported for this species worldwide; 13.2–38.6 for C:N and 411–2,041 for C:P. The 981 determinations in this study generated a range of −13.5‰ to −5.2‰ for δ13C and −4.3‰ to 9.4‰ for δ15N. The elemental and isotope ratios displayed marked seasonality, and the seasonal patterns could be described with a simple sine wave model. C:N, C:P, δ13C, and δ15N values all had maxima in the summer and minima in the winter. Spatial patterns in the summer maxima of these quantities suggest there are large differences in the relative availability of N and P across the study area and that there are differences in the processing and the isotopic composition of C and N. This work calls into question the interpretation of studies about nutrient cycling and food webs in estuaries based on few samples collected at one time, since we document natural variability greater than the signal often used to imply changes in the structure or function of ecosystems. The data and patterns presented in this paper make it clear that there is no threshold δ15N value for marine plants that can be used as an unambiguous indicator of human sewage pollution without a thorough understanding of local temporal and spatial variability.

A Simple Method for Measuring Stiffness during Running

The spring-mass model, representing a runner as a point mass supported by a single linear leg spring, has been a widely used concept in studies on running and bouncing mechanics. However, the measurement of leg and vertical stiffness has previously required force platforms and high-speed kinematic measurement systems that are costly and difficult to handle in field conditions. We propose a new "sine-wave" method for measuring stiffness during running. Based on the modeling of the force-time curve by a sine function,this method allows leg and vertical stiffness to be estimated from just a few simple mechanical parameters: body mass, forward velocity, leg length, flight time, and contact time. We compared this method to force-platform-derived stiffness measurements for treadmill dynamometer and overground running conditions, at velocities ranging from 3.33 m.s-1 to maximal running velocity in both recreational and highly trained runners. Stiffness values calculated with the proposed method ranged from 0.67 % to 6.93 % less than the force platform method, and thus were judged to be acceptable. Furthermore, significant linear regressions (p < 0.01) close to the identity line were obtained between force platform and sine-wave model values of stiffness. Given the limits inherent in the use of the spring-mass model, it was concluded that this sine-wave method allows leg and stiffness estimates in running on the basis of a few mechanical parameters, and could be useful in further field measurements.