Effective Mathematical Model Research Articles

Improving sexual health through partner notification: the LUSTRUM mixed-methods research Programme including RCT of accelerated partner therapy

Improving sexual health through partner notification: the LUSTRUM mixed-methods research Programme including RCT of accelerated partner therapy

Mathematical Modeling of Effect of Pumping Rate on Contaminant Transport in Riverbank Filtration System

Riverbank filtration (RBF) is a natural technology that is used for river water treatment. This research seeks to investigate the effect of pumping rate on the transport of colloids in RBF. However, this work considered Dissolved Organic Matter (DOM) as a nutrient for bacteria. The mathematical model consists of groundwater flow equation and colloids concentration equations. The equations were solved analytically using parameter expanding method and Eigen function expansion techniques. The results obtained are presented graphically and discussed. It was observed that increase in pumping rate value enhance both the hydraulic head and concentration of colloids which slightly reduces the quality of pumped water from RBF.
 Keywords: Riverbank filtration, analytical model, colloids, hydraulic head and pumping rat

Finite Delay Response Harmonic Filters

This paper proposes a theory of harmonic filters and their mathematical models, applicable to periodically time varying (PTV) systems perturbed by a large periodic signal. The harmonic filters are based on a series of finite time delay and weighted sum operations, which allow selection or rejection of an input fundamental tone and/or its harmonics in a periodic manner. The harmonic filters are essentially array processors and can be analogous to digital FIR filters. The paper discusses optimum ways of choosing filter coefficients, time delays, and weights for the harmonic rejections and selections, equivalent to lowpass filters and highpass filters, respectively. Mathematical models for effects of hardware mismatches, weight and delay mismatches, on the filtering performance are provided and verified through ADS behavioral statistical simulations. The theory can be applicable to design quasi-sinusoidal mixers for a quality spectral purity, or harmonic carrier modulators and demodulators for high frequency applications .

Mathematical modeling of seismic gravity effect of oil and gas reservoir in crystalline basement

A new seismic and gravitational method for the decompacted zones detection in crystalline basement, based on a multi-crack-cavernous pore (gas or oil saturated) model of crystalline reservoir is proposed. To estimate the capabilities of the proposed method mathematical modeling of effective elastic and acoustic properties of granite reservoir rocks with different pore space structure is realized. The algorithm and software for solving the problem of joint inversion of seismic and gravimetric data based on Born's approximation for the space-time Green's function with root mean square background velocity for the horizontally-layered medium has been developed and tested. It has been determined that the most reliable estimation of density and seismic velocity can be obtained by joint inversion. Convincingly is illustrated on an example of the Prykerch shelf model that the presence of decompacted oil or gas saturated zone in granite basement can be confidently identified based on results of seismic and precise gravity observations.

Controlling Profile Error for Spherical Surface Micro-Lens in Precision Grinding

As the consumer market in the optics, electronics and aerospace industries grows, the profile accuracy demand for ultra-precision flat, spherical and aspheric optical surface micro-lens increases. Previous studies have found that machine system accuracy, tool alignment error and tool radius measurement error impact greatly on the profile accuracy of the machined surface. In this paper, we developed a grinding system based on the ultra-precision diamond lathe, presented a unified mathematical model of effects of all the geometric errors to the shape error by using the multi-body system theory. Aiming at the main source of profile error, the practical mathematical model is derived, and their propagation coefficients to profile error are calculated. By means of simulation analysis and grinding experiments of spherical part of tugnsten carbide, we conclude that the radial tool alignment error is the main influencing factor for the profile error of spherical surface; while tool radius measurement error influence the radius of sphere only.

A mathematical model of effects on specific joints during practice of the Sun Salutation – A sequence of yoga postures

The 'Sun Salutation' consists of a sequence of ten yoga postures, each posture counteracting the preceding one producing a balance between flexion and extension, performed with synchronized breathing and aerobic activity. As this sequence is often performed and recommended by many yoga practitioners, there is a need for the development of a biomechanical model to support its reported clinical benefits. This requires a detailed knowledge of the nature of the forces and moments at the various joints involved. A simple mathematical model based on rigid body mechanics is developed for each of the Sun Salutation postures. Dynamic moments with high magnitudes and rates, applied with unusual distribution patterns, optimal for osteogenesis, are found to occur. Also, the joints are subjected to submaximal loadings thus ensuring that none of the joints are overstressed.

Mathematical modelling of effects of Irawan irrigation project water abstractions on the Murzuq aquifer systems in Libya

The Murzuq basin in southwest Libya contains some of the main aquifers providing water for meeting the various water demands in the country. In particular, the Murzuq basin serves a number of irrigation agricultural development projects, including the large-scale Irawan Agricultural project. However, despite its strategic significance for the overall water balance in the country, very limited studies have been undertaken on the Murzuq to determine the long term impacts of the extensive water abstractions taking place in the basin. The aim of this study was to develop and apply a modular finite-difference groundwater flow (MODFLOW) model of the Murzuq. Extensive validation of the model showed it to be capable of adequately reproducing historic water levels within the aquifer. The validated transient model was then used to assess the impacts of medium and long-term water abstractions at Irawan on the piezometric levels in the aquifer. The results show that, with current farming practices at Irawan, the piezometric surface in the centre of the field closest to the cluster of the pumping wells will stabilize in year 2033 at 470 m.a.s.l., representing a maximum drawdown of 30 m. Further significant depression may not occur unless agricultural practices change, such as through an increase in the area cultivated or change in crops grown.

Mathematical Models for Effects of Xenobiotics on Heme Biosynthesis Application to Lead

Mathematical Models for Effects of Xenobiotics on Heme Biosynthesis Application to Lead