Mathematical modelling of mass transfer in a multi-stage rotating disc contactor column

In this study, the development of an improved forward and inverse models for the mass transfer process in the Rotating Disc Contactor (RDC) column were carried out. The existing mass transfer model with constant boundary condition does not accurately represent the mass transfer process. Thus, a time-varying boundary condition was formulated and consequently the new fractional approach to equilibrium was derived. This derivation initiated the formulation of the modified quadratic driving force, called Time-dependent Quadratic Driving Force (TQDF). Based on this formulation, a Mass Transfer of A Single Drop (MTASD) Algorithm was designed, followed by a more realistic Mass Transfer of Multiple Drops (MTMD) Algorithm which was later refined to become another algorithm named the Mass Transfer Steady State (MTSS) Algorithm. The improved forward models, consisting of a system of multivariate equations, successfully calculate the amount of mass transfer from the continuous phase to the dispersed phase and was validated by the simulation results. The multivariate system is further simplified as the Multiple Input Multiple Output (MIMO) system of a functional from a space of functions to a plane. This system serves as the basis for the inverse models of the mass transfer process in which fuzzy approach was used in solving the problems. In particular, two dimensional fuzzy number concept and the pyramidal membership functions were adopted along with the use of a triangular plane as the induced output parameter. A series of algorithms in solving the inverse problem were then developed corresponding to the forward models. This eventually brought the study to the implementation of the Inverse Single Drop Multistage (ISDMS)-2D Fuzzy Algorithm on the Mass Transfer of Multiple Drops in Multistage System. This new modelling approach gives useful information and provides a faster tool for decision-makers in determining the optimal input parameter for mas

Inverse model to determine the optimal number of drops of RDC column using fuzzy approach

Inverse modeling is natural in many real world application including industrial chemical engineering problems. This paper describes the process of determines optimal input and output of number of drops in various stage of rotating disc contactor column using fuzzy model. An algorithm of the fuzzy model is developed to simulate the above process

Kitaran harga dalam industri ternakan.

This paper discuss price and production model concerning a livestock industri which gives rise to a system of felay differential equations, as proposed by Larson[8]. In this model it is assumed that the demand curve is liunera , a lag between planned and (and propotional to) realized production, and that the rate of change of breeding is propotional to the derivation of price from equilibrium. We prove that there exists sinusodial solutions, which shows that exists price cycle in livestock industries, as conjectured by Larson. The sinusodial solutions can be obtained by using the method of step

Analysis of tumor growth and immune system interaction model

Immune system plays a vital role in controlling the tumor growth. Therefore, this paper proposes a new mathematical model that describes tumor-immune interaction, focusing on the role of natural killer (NK) cell and CD8+ T cell. The tumor population is subdivided into two different phases, namely interphase and mitosis. This model used Ordinary Differential Equations (ODEs) and the functions involved in the model represents tumor-immune growth, responses and interaction between the cells. The stability and analysis of the model are carried out. From the analysis, it shown that the stability curve limits tumor growth region. The curve from the model lie below the curve of the model with single immune response (CD8+ T cell). This result concluded that the proposed model with involvement of NK cell suppression will lower the tumor growth region

Mathematical analysis of plankton population dynamics

Harmful algal blooms (HABs) event that causes enormous economic loss and health effect raises concerns among environmentalists. In this paper, a mathematical model of interaction between nutrient, toxin-producing phytoplankton (TPP), non-toxic phytoplankton (NTP), zooplankton, and toxic chemicals is proposed to study on how the process of these HABs occurred. The model of interaction is represented by Ordinary Differential Equations (ODEs) and stability analysis of the model is conducted. Several conditions for the system to be stable around trivial and interior equilibrium point are obtained. From the analysis, it is observed that under nutrient limitation, the amounts of toxic chemicals secreted out by the TPP are increased. As a result, NTP population and zooplankton population are affected by the situation. If this situation is prolonged, this will result in the extinction of both populations. Overall, this study shows that TPP release more toxic chemicals when the nutrient is limited and gives a better understanding on the occurrence of HABs event

A conceptual framework for ranking the multiple intelligences of people with epilepsy

Intelligence of a person can be enhanced if the person focuses and practices regularly. ATIE©, a psychometric test, was developed based on the Multiple Intelligence (MI) theory of Howard Gardner to measure eight types of intelligence skills namely musical, kinesthetic, math-logic, spatial, verbal, interpersonal, intrapersonal and naturalist. The inverse model of ATIE , Fuzzy Inverse ATIE (FIA) was developed to get the best intelligence parameters that would be garnered to maximize the employment probability of people with epilepsy (PWE). In this paper, we present a conceptual framework of a model to rank the suggested intelligences obtained from FIA which are to be improved. This information is essential in order to improve the chances of PWE to be employed

Mathematical analysis for tumor growth model of ordinary differential equations

Special functions occur quite frequently in mathematical analysis and lend itself rather frequently in physical and engineering applications. Among the special functions, gamma function seemed to be widely used. The purpose of this thesis is to analyse the various properties of gamma function and use these properties and its definition to derive and tackle some integration problem which occur quite frequently in applications. It should be noted that if elementary techniques such as substitution and integration by parts were used to tackle most of the integration problems, then we will end up with frustration. Due to this, importance of gamma function cannot be denied

The notion of stability of a differential equation and delay differential equation model of HIV infection of CD4+ T-Cells

This research presents a deep insight to address the notion of stability of an epidemical model of the HIV infection of CD4+ T-Cells. Initially, the stability of an ordinary differential equation (ODE) model is studied. This is followed by studying a delay differential equation (DDE) model the HIV infection of CD4+ T-Cells. The available literature on the stability analysis of the ODE model and the DDE model of the CD4+ T-Cells shows that the stability of the models depends on the basic reproduction number “R0”. Accordingly, for the basic reproduction number R0 1, the models are globally stable. This research further studies the stability of the models and address the lower possible stability limits for the infection rate of CD4+ T-Cells with virus and the reproduction rate of infectious CD4+ T-Cells, respectively. Accordingly, the results shows that the lower possible limits for the infection rate of CD4+ T-Cells with virus are 0.0000027 mm-3 and 0.000066 mm-3 for the ODE and DDE models, respectively. Again, the lower stability limits for the reproduction rate of infectious CD4+ T-Cells with virus are 12 mm3day-1 and 273.4 mm3day-1 for the ODE and DDE models, respectively. The research minutely studies the stability of the models and gives a deep insight of the stability of the ODE and DDE models of the HIV infection of CD4+ T-Cells with virus

Ionizing radiation effects modelling in cells population with gold nanoparticles

Radiosensitizer such as gold nanoparticle is a promising agent to be used in radiotherapy to increase the number of cancer cell death. Gold nanoparticle increases the production of the secondary electron after being hit by primary radiation that will cause DNA damage. The gold nanoparticle can be targeted to specific cancer cells and therefore reduce damage to the healthy nearby cell. Thus, nanoparticles will elevate the efficacy of radiation treatment without delivering a high radiation dose that will damage the organ at risk. Therefore, this paper aimed to study the effects of radiosensitizer on radiation therapy. The study was done by incorporating the function of dose deposited by gold nanoparticles into the existing model of ionizing radiation effects. The model was mathematically described using Ordinary Differential Equations (ODEs). The simulation results were fitted to the Linear Quadratic (LQ) formulation to give the ratio for α/β. Next, the parameter estimation and sensitivity analysis of the model are carried out using experimental data of HeLa cell with the aid of the MATLAB programming. The estimated parameter values can explain the radiobiology process, which can support the result of the experimental design. The result showed that the sum-squared error (SSE) between simulation data and experimental data obtained is 0.015 which indicates an excellent fit to the experimental data. Thus, this model is in line with the experimental result. The model is able to explain the dynamics process of ionizing radiation effects with gold nanoparticles on the cell population

Homeomorphism between Sphere and Cube

In this paper, we present the construction of homeomorphism from unit sphere; S2 to unit cube; C3. On route, we produced an explicit mapping between the two topological spaces where proving by construction is mainly adopted in this wor