Korteweg-De Vries Equation for Non-Linear Ion-Acoustic Waves in a Plasma with Negative Ions

The theoretical analysis, based on the perturbation technique, of ion-acoustic waves in the vicinity of a Korteweg-de Vries (K-dV) equation derived in a plasma with some negative ions has been made. The investigation shows that the negative ions in plasma with isothermal electrons introduced a critical concentration at which the ion-acoustic wave plays an important role of wave-breaking and forming a precursor while the plasma with non-isothermal electrons has no such singular behaviour of the wave. These two distinct features of ion waves lead to an overall different approach of present study of ion-waves. A distinct feature of non-uniform transition from the nonisothermal case to isothermal case has been shown. Few particular plasma models have been chosen to show the characteristics behaviour of the ion-waves existing in different cases

Korteweg-de Vries equation for the propagation of fast ion-acoustic waves in multi-dimensions

Abstract is not available.

Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T2 *-weighted magnetic resonance imaging at 7T

PURPOSE To study the utility of fractional calculus in modeling gradient-recalled echo MRI signal decay in the normal human brain. METHODS We solved analytically the extended time-fractional Bloch equations resulting in five model parameters, namely, the amplitude, relaxation rate, order of the time-fractional derivative, frequency shift, and constant offset. Voxel-level temporal fitting of the MRI signal was performed using the classical monoexponential model, a previously developed anomalous relaxation model, and using our extended time-fractional relaxation model. Nine brain regions segmented from multiple echo gradient-recalled echo 7 Tesla MRI data acquired from five participants were then used to investigate the characteristics of the extended time-fractional model parameters. RESULTS We found that the extended time-fractional model is able to fit the experimental data with smaller mean squared error than the classical monoexponential relaxation model and the anomalous relaxation model, which do not account for frequency shift. CONCLUSIONS We were able to fit multiple echo time MRI data with high accuracy using the developed model. Parameters of the model likely capture information on microstructural and susceptibility-induced changes in the human brain.

Constitutive equation for elevated temperature flow behavior of plain carbon steels using dimensional analysis

Dimensional analysis using π-theorem is applied to the variables associated with plastic deformation. The dimensionless groups thus obtained are then related and rewritten to obtain the constitutive equation. The constants in the constitutive equation are obtained using published flow stress data for carbon steels. The validity of the constitutive equation is tested for steels with up to 1.54 wt%C at temperatures: 850–1200 °C and strain rates: 6 × 10−6–2 × 10−2 s−1. The calculated flow stress agrees favorably with experimental data.

Dynamics of Barrierless and Activated Chemical Reactions in a Dispersive Medium within the Fractional Diffusion Equation Approach

Barrierless chemical reactions have often been modeled as a Brownian motion on a one-dimensional harmonic potential energy surface with a position-dependent reaction sink or window located near the minimum of the surface. This simple (but highly successful) description leads to a nonexponential survival probability only at small to intermediate times but exponential decay in the long-time limit. However, in several reactive events involving proteins and glasses, the reactions are found to exhibit a strongly nonexponential (power law) decay kinetics even in the long time. In order to address such reactions, here, we introduce a model of barrierless chemical reaction where the motion along the reaction coordinate sustains dispersive diffusion. A complete analytical solution of the model can be obtained only in the frequency domain, but an asymptotic solution is obtained in the limit of long time. In this case, the asymptotic long-time decay of the survival probability is a power law of the Mittag−Leffler functional form. When the barrier height is increased, the decay of the survival probability still remains nonexponential, in contrast to the ordinary Brownian motion case where the rate is given by the Smoluchowski limit of the well-known Kramers' expression. Interestingly, the reaction under dispersive diffusion is shown to exhibit strong dependence on the initial state of the system, thus predicting a strong dependence on the excitation wavelength for photoisomerization reactions in a dispersive medium. The theory also predicts a fractional viscosity dependence of the rate, which is often observed in the reactions occurring in complex environments.

Development of an efficiency equation for solar evaporator- collectors

Considering the growing energy needs and concern for environmental degradation, clean and inexhaustible energy sources, e.g solar energy are receiving greater attention for various applications. The use of solar energy systems for low temperature applications reduces the burden on conventional fossil fuels and has little or no harmful effects on the environment. The performance of a solar system depends to a great extent on the collector used for the conversion of solar radiant energy to thermal energy. A solar evaporatorcollector (SEC) is basically an unglazed flat plate collector where refrigerant, like R134a, is used as the working fluid. As the operating temperature of SEC is very low, it collects energy both from solar irradiation and ambient energy leading to a much higher efficiency than the conventional collectors. The capability of SEC to utilize ambient energy also enables the system to operate at night. Therefore it is not appropriate to use for the evaluation of performance of SEC by conventional efficiency equation where ambient energy and condensation is not considered as energy input in addition to irradiation. In the National University of Singapore, several Solar Assisted Heat Pump (SAHP) systems were built for the evaluation of performance under the metrological condition of Singapore for thermal applications of desalination and SEC was the main component to harness renewable energy. In this paper, the design and performance of SEC are explored. Furthermore, an attempt is made to develop an efficiency equation for SEC and maximum efficiency attained 98% under the meteorological condition of Singapore.

The Pandolf load carriage equation is a poor predictor of metabolic rate while wearing explosive ordnance disposal protective clothing

This investigation aimed to quantify metabolic rate when wearing an explosive ordnance disposal (EOD) ensemble (~33kg) during standing and locomotion; and determine whether the Pandolf load carriage equation accurately predicts metabolic rate when wearing an EOD ensemble during standing and locomotion. Ten males completed 8 trials with metabolic rate measured through indirect calorimetry. Walking in EOD at 2.5, 4.0 and 5.5km·h−1 was significantly (p < 0.05) greater than matched trials without the EOD ensemble by 49% (127W), 65% (213W) and 78% (345W), respectively. Mean bias (95% limits of agreement) between predicted and measured metabolism during standing, 2.5, 4 and 5.5km·h−1 were 47W (19 to 75W); −111W (−172 to −49W); −122W (−189 to −54W) and −158W (−245 to −72W), respectively. The Pandolf equation significantly underestimated measured metabolic rate during locomotion. These findings have practical implications for EOD technicians during training and operation and should be considered when developing maximum workload duration models and work-rest schedules.

Forecasting day-ahead electricity load using a multiple equation time series approach

The quality of short-term electricity load forecasting is crucial to the operation and trading activities of market participants in an electricity market. In this paper, it is shown that a multiple equation time-series model, which is estimated by repeated application of ordinary least squares, has the potential to match or even outperform more complex nonlinear and nonparametric forecasting models. The key ingredient of the success of this simple model is the effective use of lagged information by allowing for interaction between seasonal patterns and intra-day dependencies. Although the model is built using data for the Queensland region of Australia, the method is completely generic and applicable to any load forecasting problem. The model’s forecasting ability is assessed by means of the mean absolute percentage error (MAPE). For day-ahead forecast, the MAPE returned by the model over a period of 11 years is an impressive 1.36%. The forecast accuracy of the model is compared with a number of benchmarks including three popular alternatives and one industrial standard reported by the Australia Energy Market Operator (AEMO). The performance of the model developed in this paper is superior to all benchmarks and outperforms the AEMO forecasts by about a third in terms of the MAPE criterion.

Benedict-Webb-Rubin equation of state constants for N2O4 ⇄ 2NO2,NO,and O2

Benedict-Webb-Rubin equation of state constants for NO, O2, and the equilibrium mixture N2O4 ⇄ 2NO2 are reported.

A generalized equation for diffusion in liquids

The association parameter in the diffuswn equaiior, dye fo Wiike one Chong has been interpreted in deferminable properties, thus permitting easily the calculation of the same for unknown systems. The proposed eqyotion a!se holds goods for water as soiute in organic solvenfs. The over-all percentage error remains the sarrse as that of the original equation.

Extended self-similarity works for the Burgers equation and why

Extended self-similarity (ESS), a procedure that remarkably extends the range of scaling for structure functions in Navier-Stokes turbulence and thus allows improved determination of intermittency exponents, has never been fully explained. We show that ESS applies to Burgers turbulence at high Reynolds numbers and we give the theoretical explanation of the numerically observed improved scaling at both the IR and UV end, in total a gain of about three quarters of a decade: there is a reduction of subdominant contributions to scaling when going from the standard structure function representation to the ESS representation. We conjecture that a similar situation holds for three-dimensional incompressible turbulence and suggest ways of capturing subdominant contributions to scaling.

Electron energy equation for an atomic radiating plasma

The electron-energy equation for an atomic radiating plasma is considered in this work. Using the atomic model of Bates, Kingston and McWhirter, the radiation loss-term valid for all optical thicknesses is obtained. A study of the energy gained by electrons in inelastic collisions shows that the radiation loss term can be neglected only for rapidly-decaying or fast-growing plasmas. Emission from optically thin plasmas is considered next and an exact expression is given for the total radiation loss in a recombination continuum. A derivation of the Kramers-Unsöld approximation is presented and the error involved in estimating the total emitted recombination radiation by this approximation is shown to be small.

Approximation of solutions to fractional integral equation

In this paper we shall study a fractional integral equation in an arbitrary Banach space X. We used the analytic semigroups theory of linear operators and the fixed point method to establish the existence and uniqueness of solutions of the given problem. We also prove the existence of global solution. The existence and convergence of the Faedo–Galerkin solution to the given problem is also proved in a separable Hilbert space with some additional assumptions on the operator A. Finally we give an example to illustrate the applications of the abstract results.

Asymtotic solution of the Frieman and Book equation for the pair-correlation function

Using Thomé's procedure, the asymptotic solutions of the Frieman and Book equation for the two-particle correlation in a plasma have been obtained in a complete form. The solution is interpreted in terms of the Lorentz distance. The exact expressions for the internal energy and pressure are evaluated and they are found to be a generalization of the result obtained earlier by others.

Computationally efficient optical tomographic reconstructions through waveletizing the normalized quadratic perturbation equation - art. no.61640R

In this paper, we present a wavelet - based approach to solve the non-linear perturbation equation encountered in optical tomography. A particularly suitable data gathering geometry is used to gather a data set consisting of differential changes in intensity owing to the presence of the inhomogeneous regions. With this scheme, the unknown image, the data, as well as the weight matrix are all represented by wavelet expansions, thus yielding the representation of the original non - linear perturbation equation in the wavelet domain. The advantage in use of the non-linear perturbation equation is that there is no need to recompute the derivatives during the entire reconstruction process. Once the derivatives are computed, they are transformed into the wavelet domain. The purpose of going to the wavelet domain, is that, it has an inherent localization and de-noising property. The use of approximation coefficients, without the detail coefficients, is ideally suited for diffuse optical tomographic reconstructions, as the diffusion equation removes most of the high frequency information and the reconstruction appears low-pass filtered. We demonstrate through numerical simulations, that through solving merely the approximation coefficients one can reconstruct an image which has the same information content as the reconstruction from a non-waveletized procedure. In addition we demonstrate a better noise tolerance and much reduced computation time for reconstructions from this approach.