Abstract: Modeling transfer phenomena in several chemical
engineering operations leads to the resolution of partial differential
equations systems. According to the complexity of the operations
mechanisms, the equations present a nonlinear form and analytical
solution became difficult, we have then to use numerical methods
which are based on approximations in order to transform a
differential system to an algebraic one.Finite element method is one
of numerical methods which can be used to obtain an accurate
solution in many complex cases of chemical engineering.The packed
columns find a large application like contactor for liquid-liquid
systems such solvent extraction. In the literature, the modeling of this
type of equipment received less attention in comparison with the
plate columns.A mathematical bidimensionnal model with radial and
axial dispersion, simulating packed tower extraction behavior was
developed and a partial differential equation was solved using the
finite element method by adopting the Galerkine model. We
developed a Mathcad program, which can be used for a similar
equations and concentration profiles are obtained along the column.
The influence of radial dispersion was prooved and it can-t be
neglected, the results were compared with experimental concentration
at the top of the column in the extraction system:
acetone/toluene/water.
Abstract: The use of electronic sensors in the electronics
industry has become increasingly popular over the past few years,
and it has become a high competition product. The frequency
adjustment process is regarded as one of the most important process
in the electronic sensor manufacturing process. Due to inaccuracies
in the frequency adjustment process, up to 80% waste can be caused
due to rework processes; therefore, this study aims to provide a
preliminary understanding of the role of parameters used in the
frequency adjustment process, and also make suggestions in order to
further improve performance. Four parameters are considered in this
study: air pressure, dispensing time, vacuum force, and the distance
between the needle tip and the product. A full factorial design for
experiment 2k was considered to determine those parameters that
significantly affect the accuracy of the frequency adjustment process,
where a deviation in the frequency after adjustment and the target
frequency is expected to be 0 kHz. The experiment was conducted on
two levels, using two replications and with five center-points added.
In total, 37 experiments were carried out. The results reveal that air
pressure and dispensing time significantly affect the frequency
adjustment process. The mathematical relationship between these
two parameters was formulated, and the optimal parameters for air
pressure and dispensing time were found to be 0.45 MPa and 458 ms,
respectively. The optimal parameters were examined by carrying out
a confirmation experiment in which an average deviation of 0.082
kHz was achieved.
Abstract: This paper is described one of the intelligent control method in Autonomous systems, which is called fuzzy control to correct the three wheel omnidirectional robot movement while it make mistake to catch the target. Fuzzy logic is especially advantageous for problems that can not be easily represented by mathematical modeling because data is either unavailable, incomplete or the process is too complex. Such systems can be easily up grated by adding new rules to improve performance or add new features. In many cases , fuzzy control can be used to improve existing traditional controller systems by adding an extra layer of intelligence to the current control method. The fuzzy controller designed here is more accurate and flexible than the traditional controllers. The project is done at MRL middle size soccer robot team.
Abstract: Surface roughness (Ra) is one of the most important requirements in machining process. In order to obtain better surface roughness, the proper setting of cutting parameters is crucial before the process take place. This research presents the development of mathematical model for surface roughness prediction before milling process in order to evaluate the fitness of machining parameters; spindle speed, feed rate and depth of cut. 84 samples were run in this study by using FANUC CNC Milling α-Τ14ιE. Those samples were randomly divided into two data sets- the training sets (m=60) and testing sets(m=24). ANOVA analysis showed that at least one of the population regression coefficients was not zero. Multiple Regression Method was used to determine the correlation between a criterion variable and a combination of predictor variables. It was established that the surface roughness is most influenced by the feed rate. By using Multiple Regression Method equation, the average percentage deviation of the testing set was 9.8% and 9.7% for training data set. This showed that the statistical model could predict the surface roughness with about 90.2% accuracy of the testing data set and 90.3% accuracy of the training data set.
Abstract: Cardiovascular diseases, principally atherosclerosis, are responsible for 30% of world deaths. Atherosclerosis is due to the formation of plaque. The fatty plaque may be at risk of rupture, leading typically to stroke and heart attack. The plaque is usually associated with a high degree of lumen reduction, called a stenosis.It is increasingly recognized that the initiation and progression of disease and the occurrence of clinical events is a complex interplay between the local biomechanical environment and the local vascular biology. The aim of this study is to investigate the flow behavior through a stenosed artery. A physical experiment was performed using an artery model and blood analogue fluid. An axisymmetric model constructed consists of contraction and expansion region that follow a mathematical form of cosine function. A 30% diameter reduction was used in this study. The flow field was measured using particle image velocimetry (PIV). Spherical particles with 20μm diameter were seeded in a water-glycerol-NaCl mixture. Steady flow Reynolds numbers are 250. The area of interest is the region after the stenosis where the flow separation occurs. The velocity field was measured and the velocity gradient was investigated. There was high particle concentration in the recirculation zone. High velocity gradient formed immediately after the stenosis throat created a lift force that enhanced particle migration to the flow separation area.
Abstract: There is a complex situation on the transport environment in the cities of the world. For the analysis and prevention of environmental problems an accurate calculation hazardous substances concentrations at each point of the investigated area is required. In the turbulent atmosphere of the city the wellknown methods of mathematical statistics for these tasks cannot be applied with a satisfactory level of accuracy. Therefore, to solve this class of problems apparatus of mathematical physics is more appropriate. In such models, because of the difficulty as a rule the influence of uneven land surface on streams of air masses in the turbulent atmosphere of the city are not taken into account. In this paper the influence of the surface roughness, which can be quite large, is mathematically shown. The analysis of this problem under certain conditions identified the possibility of areas appearing in the atmosphere with pressure tending to infinity, i.e. so-called "wall effect".
Abstract: Stochastic models of biological networks are well established in systems biology, where the computational treatment of such models is often focused on the solution of the so-called chemical master equation via stochastic simulation algorithms. In contrast to this, the development of storage-efficient model representations that are directly suitable for computer implementation has received significantly less attention. Instead, a model is usually described in terms of a stochastic process or a "higher-level paradigm" with graphical representation such as e.g. a stochastic Petri net. A serious problem then arises due to the exponential growth of the model-s state space which is in fact a main reason for the popularity of stochastic simulation since simulation suffers less from the state space explosion than non-simulative numerical solution techniques. In this paper we present transition class models for the representation of biological network models, a compact mathematical formalism that circumvents state space explosion. Transition class models can also serve as an interface between different higher level modeling paradigms, stochastic processes and the implementation coded in a programming language. Besides, the compact model representation provides the opportunity to apply non-simulative solution techniques thereby preserving the possible use of stochastic simulation. Illustrative examples of transition class representations are given for an enzyme-catalyzed substrate conversion and a part of the bacteriophage λ lysis/lysogeny pathway.
Abstract: A lot of Scientific and Engineering problems require the solution of large systems of linear equations of the form bAx in an effective manner. LU-Decomposition offers good choices for solving this problem. Our approach is to find the lower bound of processing elements needed for this purpose. Here is used the so called Omega calculus, as a computational method for solving problems via their corresponding Diophantine relation. From the corresponding algorithm is formed a system of linear diophantine equalities using the domain of computation which is given by the set of lattice points inside the polyhedron. Then is run the Mathematica program DiophantineGF.m. This program calculates the generating function from which is possible to find the number of solutions to the system of Diophantine equalities, which in fact gives the lower bound for the number of processors needed for the corresponding algorithm. There is given a mathematical explanation of the problem as well. Keywordsgenerating function, lattice points in polyhedron, lower bound of processor elements, system of Diophantine equationsand : calculus.
Abstract: This paper describes an experimental investigation of
the drying behavior and conditions of rosehip in a convective
cyclone-type dryer. Drying experiments were conducted at air inlet
temperatures of 50, 60 and 70 o C and air velocities of 0.5, 1 and 1.5
ms–1. The parametric values obtained from the experiments were
fitted to the Newton mathematical models. Consequently, the drying
model developed by Newton model showed good agreement with the
data obtained from the experiments. Concluding, it was obtained that;
(i) the temperature is the major effect on the drying process, (ii) air
velocity has low effect on the drying of rosehip, (iii) the C-vitamin is
observed to change according to the temperature, moisture, drying
time and flow types. The changing ratio is found to be in the range of
0.70-0.74.
Abstract: South Africa is facing a crisis with not being able to produce enough graduates in the scarce skills areas to sustain economic growth. The crisis is fuelled by a school system that does not produce enough potential students with Mathematics, Accounting and Science. Since the introduction of the new school curriculum in 2008, there is no longer an option to take pure maths on a standard grade level. Instead, only two mathematical subjects are offered: pure maths (which is on par with higher grade maths) and mathematical literacy. It is compulsory to take one or the other. As a result, lees student finishes Grade 12 with pure mathematics every year. This national problem needs urgent attention if South Africa is to make any headway in critical skills development as mathematics is a gateway to scarce skills professions. Higher education institutions initiated several initiatives in an attempt to address the above, including preparatory courses, bridging programmes and extended curricula with foundation provisions. In view of the above, and government policy directives to broaden access in the scarce skills areas to increase student throughput, foundation provision was introduced for Commerce and Information Technology programmes at the Vaal Triangle Campus (VTC) of North-West University (NWU) in 2010. Students enrolling for extended programmes do not comply with the minimum prerequisites for the normal programmes. The question then arises as to whether these programmes have the intended impact? This paper reports the results of a two year longitudinal study, tracking the first year academic achievement of the two cohorts of enrolments since 2010. The results provide valuable insight into the structuring of an extended programme and its potential impact.
Abstract: The medical studies often require different methods
for parameters selection, as a second step of processing, after the
database-s designing and filling with information. One common
task is the selection of fields that act as risk factors using wellknown
methods, in order to find the most relevant risk factors and
to establish a possible hierarchy between them. Different methods
are available in this purpose, one of the most known being the
binary logistic regression. We will present the mathematical
principles of this method and a practical example of using it in the
analysis of the influence of 10 different psychiatric diagnostics
over 4 different types of offences (in a database made from 289
psychiatric patients involved in different types of offences).
Finally, we will make some observations about the relation
between the risk factors hierarchy established through binary
logistic regression and the individual risks, as well as the results of
Chi-squared test. We will show that the hierarchy built using the
binary logistic regression doesn-t agree with the direct order of risk
factors, even if it was naturally to assume this hypothesis as being
always true.
Abstract: Anaerobic Digestion has become a promising
technology for biological transformation of organic fraction of the
municipal solid wastes (MSW). In order to represent the kinetic
behavior of such biological process and thereby to design a reactor
system, development of a mathematical model is essential.
Addressing this issue, a simplistic mathematical model has been
developed for anaerobic digestion of MSW in a continuous flow
reactor unit under homogeneous steady state condition. Upon
simulated hydrolysis, the kinetics of biomass growth and substrate
utilization rate are assumed to follow first order reaction kinetics.
Simulation of this model has been conducted by studying sensitivity
of various process variables. The model was simulated using typical
kinetic data of anaerobic digestion MSW and typical MSW
characteristics of Kolkata. The hydraulic retention time (HRT) and
solid retention time (SRT) time were mainly estimated by varying
different model parameters like efficiency of reactor, influent
substrate concentration and biomass concentration. Consequently,
design table and charts have also been prepared for ready use in the
actual plant operation.
Abstract: This paper presents parametric probability density
models for call holding times (CHTs) into emergency call center
based on the actual data collected for over a week in the public
Emergency Information Network (EIN) in Mongolia. When the set of
chosen candidates of Gamma distribution family is fitted to the call
holding time data, it is observed that the whole area in the CHT
empirical histogram is underestimated due to spikes of higher
probability and long tails of lower probability in the histogram.
Therefore, we provide the Gaussian parametric model of a mixture of
lognormal distributions with explicit analytical expressions for the
modeling of CHTs of PSNs. Finally, we show that the CHTs for
PSNs are fitted reasonably by a mixture of lognormal distributions
via the simulation of expectation maximization algorithm. This result
is significant as it expresses a useful mathematical tool in an explicit
manner of a mixture of lognormal distributions.
Abstract: Based on a global kinetics of direct dimethyl ether (DME) synthesis process from syngas, a steady-state one-dimensional mathematical model for the bubble column slurry reactor (BCSR) has been established. It was built on the assumption of plug flow of gas phase, sedimentation-dispersion model of catalyst grains and isothermal chamber regardless of reaction heats and rates for the design of an industrial scale bubble column slurry reactor. The simulation results indicate that higher pressure and lower temperature were favorable to the increase of CO conversion, DME selectivity, products yield and the height of slurry bed, which has a coincidence with the characteristic of DME synthesis reaction system, and that the height of slurry bed is lessen with the increasing of operation temperature in the range of 220-260℃. CO conversion, the optimal operation conditions in BCSR were proposed.
Abstract: The subcellular organelles called oil bodies (OBs) are lipid-filled quasi-spherical droplets produced from the endoplasmic reticulum (ER) and then released into the cytoplasm during seed development. It is believed that an OB grows by coalescence with other OBs and that its stability depends on the composition of oleosins, major proteins inserted in the hemi membrane that covers OBs. In this study, we measured the OB-volume distribution from different genotypes of A. thaliana after 7, 8, 9, 10 and 11 days of seed development. In order to test the hypothesis of OBs dynamics, we developed a simple mathematical model using non-linear differential equations inspired from the theory of coagulation. The model describes the evolution of OB-volume distribution during the first steps of seed development by taking into consideration the production of OBs, the increase of triacylglycerol volume to be stored, and the growth by coalescence of OBs. Fitted parameters values show an increase in the OB production and coalescence rates in A. thaliana oleosin mutants compared to wild type.
Abstract: This paper is concerned with the permanence and extinction problem of enterprises cluster constituted by m satellite enterprises and a dominant enterprise. We present the model involving impulsive effect based on ecology theory, which effectively describe the competition and cooperation of enterprises cluster in real economic environment. Applying comparison theorem of impulsive differential equation, we establish sufficient conditions which ultimately affect the fate of enterprises: permanence, extinction, and co-existence. Finally, we present numerical examples to explain the economical significance of mathematical results.
Abstract: In this paper, the authors take a look at advantages of
multiphase induction motors comparing them with three phase ones
and present the applications where six-phase induction motors are
used. They elaborate the mathematical model of six-phase induction
motor with two similar stator three phase winding, shifted by 30
degrees in space and three phase winding in rotor, in synchronous
reference frame for soft starting and scalar control. The authors
simulate and discuss results of speed and torque starting transients.
Abstract: The use of the oncologic index ISTER allows for a more effective planning of the radiotherapic facilities in the hospitals. Any change in the radiotherapy treatment, due to unexpected stops, may be adapted by recalculating the doses to the new treatment duration while keeping the optimal prognosis. The results obtained in a simulation model on millions of patients allow the definition of optimal success probability algorithms.
Abstract: Mathematical, graphical and intuitive models are often
constructed in the development process of computational systems.
The Unified Modeling Language (UML) is one of the most popular
modeling languages used by practicing software engineers. This
paper critically examines UML models and suggests an augmented
use case view with the addition of new constructs for modeling
software. It also shows how a use case diagram can be enhanced. The
improved modeling constructs are presented with examples for
clarifying important design and implementation issues.
Abstract: This paper presents modeling and simulation of Grid Connected Photovoltaic (PV) system by using improved mathematical model. The model is used to study different parameter variations and effects on the PV array including operating temperature and solar irradiation level. In this paper stepped P&O algorithm is proposed for MPPT control. This algorithm will identify the suitable duty ratio in which the DC-DC converter should be operated to maximize the power output. Photo voltaic array with proposed stepped P&O-MPPT controller can operate in the maximum power point for the whole range of solar data (irradiance and temperature).