A Mathematical Investigation of the Turkevich Organizer Theory in the Citrate Method for the Synthesis of Gold Nanoparticles

Gold nanoparticles are commonly synthesized by reducing chloroauric acid with sodium citrate. This method, referred to as the citrate method, can produce spherical gold nanoparticles (NPs) in the size range 10-150 nm. Gold NPs of this size are useful in many applications. However, the NPs are usually polydisperse and irreproducible. A better understanding of the synthesis mechanisms is thus required. This work thoroughly investigated the only model that describes the synthesis. This model combines mass and population balance equations, describing the NPs synthesis through a sequence of chemical reactions. Chloroauric acid reacts with sodium citrate to form aurous chloride and dicarboxy acetone. The latter organizes aurous chloride in a nucleation step and concurrently degrades into acetone. The unconsumed precursor then grows the formed nuclei. However, depending on the pH, both the precursor and the reducing agent react differently thus affecting the synthesis. In this work, we investigated the model for different conditions of pH, temperature and initial reactant concentrations. To solve the model, we used Parsival, a commercial numerical code, whilst to test it, we considered various conditions studied experimentally by different researchers, for which results are available in the literature. The model poorly predicted the experimental data. We believe that this is because the model does not account for the acid-base properties of both chloroauric acid and sodium citrate.

A Comparison of Inverse Simulation-Based Fault Detection in a Simple Robotic Rover with a Traditional Model-Based Method

Robotic rovers which are designed to work in extra-terrestrial environments present a unique challenge in terms of the reliability and availability of systems throughout the mission. Should some fault occur, with the nearest human potentially millions of kilometres away, detection and identification of the fault must be performed solely by the robot and its subsystems. Faults in the system sensors are relatively straightforward to detect, through the residuals produced by comparison of the system output with that of a simple model. However, faults in the input, that is, the actuators of the system, are harder to detect. A step change in the input signal, caused potentially by the loss of an actuator, can propagate through the system, resulting in complex residuals in multiple outputs. These residuals can be difficult to isolate or distinguish from residuals caused by environmental disturbances. While a more complex fault detection method or additional sensors could be used to solve these issues, an alternative is presented here. Using inverse simulation (InvSim), the inputs and outputs of the mathematical model of the rover system are reversed. Thus, for a desired trajectory, the corresponding actuator inputs are obtained. A step fault near the input then manifests itself as a step change in the residual between the system inputs and the input trajectory obtained through inverse simulation. This approach avoids the need for additional hardware on a mass- and power-critical system such as the rover. The InvSim fault detection method is applied to a simple four-wheeled rover in simulation. Additive system faults and an external disturbance force and are applied to the vehicle in turn, such that the dynamic response and sensor output of the rover are impacted. Basic model-based fault detection is then employed to provide output residuals which may be analysed to provide information on the fault/disturbance. InvSim-based fault detection is then employed, similarly providing input residuals which provide further information on the fault/disturbance. The input residuals are shown to provide clearer information on the location and magnitude of an input fault than the output residuals. Additionally, they can allow faults to be more clearly discriminated from environmental disturbances.

Gas Condensing Unit with Inner Heat Exchanger

Gas condensing units with inner tubes heat exchangers represent third generation technology and differ from second generation heat and mass transfer units, which are fulfilled by passive filling material layer. The first one improves heat and mass transfer by increasing cooled contact surface of gas and condensate drops and film formed in inner tubes heat exchanger. This paper presents a selection of significant factors which influence the heat and mass transfer. Experimental planning is based on the research and analysis of main three independent variables; velocity of water and gas as well as density of spraying. Empirical mathematical models show that the coefficient of heat transfer is used as dependent parameter which depends on two independent variables; water and gas velocity. Empirical model is proved by the use of experimental data of two independent gas condensing units in Lithuania and Russia. Experimental data are processed by the use of heat transfer criteria-Kirpichov number. Results allow drawing the graphical nomogram for the calculation of heat and mass transfer conditions in the innovative and energy efficient gas cooling unit.

The Impact of Physics Taught with Simulators and Texts in Brazilian High School: A Study in the Adult and Youth Education

The teaching of physics in Brazilian public schools emphasizes strongly the theoretical aspects of this science, showing its philosophical and mathematical basis, but neglecting its experimental character. Perhaps the lack of science laboratories explains this practice. In this work, we present a method of teaching physics using the computer. As alternatives to real experiments, we have the trials through simulators, many of which are free software available on the internet. In order to develop a study on the use of simulators in teaching, knowing the impossibility of simulations on all topics in a given subject, we combined these programs with phenomenological and/or experimental texts in order to mitigate this limitation. This study proposes the use of simulators and the debate using phenomenological/experimental texts on electrostatic theme in groups of the 3rd year of EJA (Adult and Youth Education) in order to verify the advantages of this methodology. Some benefits of the hybridization of the traditional method with the tools used were: Greater motivation of the students in learning, development of experimental notions, proactive socialization to learning, greater easiness to understand some concepts and the creation of collaborative activities that can reduce timidity of part of the students.

Performance of Derna Steam Power Plant at Varying Super-Heater Operating Conditions Based on Exergy

In the current study, energy and exergy analysis of a 65 MW steam power plant was carried out. This study investigated the effect of variations of overall conductance of the super heater on the performance of an existing steam power plant located in Derna, Libya. The performance of the power plant was estimated by a mathematical modelling which considers the off-design operating conditions of each component. A fully interactive computer program based on the mass, energy and exergy balance equations has been developed. The maximum exergy destruction has been found in the steam generation unit. A 50% reduction in the design value of overall conductance of the super heater has been achieved, which accordingly decreases the amount of the net electrical power that would be generated by at least 13 MW, as well as the overall plant exergy efficiency by at least 6.4%, and at the same time that would cause an increase of the total exergy destruction by at least 14 MW. The achieved results showed that the super heater design and operating conditions play an important role on the thermodynamics performance and the fuel utilization of the power plant. Moreover, these considerations are very useful in the process of the decision that should be taken at the occasions of deciding whether to replace or renovate the super heater of the power plant.

Heat and Mass Transfer of Triple Diffusive Convection in a Rotating Couple Stress Liquid Using Ginzburg-Landau Model

A nonlinear study of triple diffusive convection in a rotating couple stress liquid has been analysed. It is performed to study the effect of heat and mass transfer by deriving Ginzburg-Landau equation. Heat and mass transfer are quantified in terms of Nusselt number and Sherwood numbers, which are obtained as a function of thermal and solute Rayleigh numbers. The obtained Ginzburg-Landau equation is Bernoulli equation, and it has been elucidated numerically by using Mathematica. The effects of couple stress parameter, solute Rayleigh numbers, and Taylor number on the onset of convection and heat and mass transfer have been examined. It is found that the effects of couple stress parameter and Taylor number are to stabilize the system and to increase the heat and mass transfer.

Travel Time Model for Cylinder Type Parking System

In this paper, we mainly analyze an automated parking system where the storage and retrieval requests are performed by a tower crane. In this parking system, the S/R crane which is located at the middle of the bottom of the cylinder parking area can rotate in both clockwise and counterclockwise and three kinds of movements can be done simultaneously. We develop some mathematical travel time models for the single command cycle under the random storage assignment using the characteristics of this system. Finally, we compare these travel models with discrete case and it is shown that these travel models display a good satisfactory performance.

Mathematical Study for Traffic Flow and Traffic Density in Kigali Roads

This work investigates a mathematical study for traffic flow and traffic density in Kigali city roads and the data collected from the national police of Rwanda in 2012. While working on this topic, some mathematical models were used in order to analyze and compare traffic variables. This work has been carried out on Kigali roads specifically at roundabouts from Kigali Business Center (KBC) to Prince House as our study sites. In this project, we used some mathematical tools to analyze the data collected and to understand the relationship between traffic variables. We applied the Poisson distribution method to analyze and to know the number of accidents occurred in this section of the road which is from KBC to Prince House. The results show that the accidents that occurred in 2012 were at very high rates due to the fact that this section has a very narrow single lane on each side which leads to high congestion of vehicles, and consequently, accidents occur very frequently. Using the data of speeds and densities collected from this section of road, we found that the increment of the density results in a decrement of the speed of the vehicle. At the point where the density is equal to the jam density the speed becomes zero. The approach is promising in capturing sudden changes on flow patterns and is open to be utilized in a series of intelligent management strategies and especially in noncurrent congestion effect detection and control.

Transport of Analytes under Mixed Electroosmotic and Pressure Driven Flow of Power Law Fluid

In this study, we have analyzed the transport of analytes under a two dimensional steady incompressible flow of power-law fluids through rectangular nanochannel. A mathematical model based on the Cauchy momentum-Nernst-Planck-Poisson equations is considered to study the combined effect of mixed electroosmotic (EO) and pressure driven (PD) flow. The coupled governing equations are solved numerically by finite volume method. We have studied extensively the effect of key parameters, e.g., flow behavior index, concentration of the electrolyte, surface potential, imposed pressure gradient and imposed electric field strength on the net average flow across the channel. In addition to study the effect of mixed EOF and PD on the analyte distribution across the channel, we consider a nonlinear model based on general convective-diffusion-electromigration equation. We have also presented the retention factor for various values of electrolyte concentration and flow behavior index.

Mathematical Modeling of Human Cardiovascular System: A Lumped Parameter Approach and Simulation

The purpose of this work is to develop a mathematical model of Human Cardiovascular System using lumped parameter method. The model is divided in three parts: Systemic Circulation, Pulmonary Circulation and the Heart. The established mathematical model has been simulated by MATLAB software. The innovation of this study is in describing the system based on the vessel diameters and simulating mathematical equations with active electrical elements. Terminology of human physical body and required physical data like vessel’s radius, thickness etc., which are required to calculate circuit parameters like resistance, inductance and capacitance, are proceeds from well-known medical books. The developed model is useful to understand the anatomic of human cardiovascular system and related syndromes. The model is deal with vessel’s pressure and blood flow at certain time.

Jointly Learning Python Programming and Analytic Geometry

The paper presents an original Python-based application that outlines the advantages of combining some elementary notions of mathematics with the study of a programming language. The application support refers to some of the first lessons of analytic geometry, meaning conics and quadrics and their reduction to a standard form, as well as some related notions. The chosen programming language is Python, not only for its closer to an everyday language syntax – and therefore, enhanced readability – but also for its highly reusable code, which is of utmost importance for a mathematician that is accustomed to exploit already known and used problems to solve new ones. The purpose of this paper is, on one hand, to support the idea that one of the most appropriate means to initiate one into programming is throughout mathematics, and reciprocal, one of the most facile and handy ways to assimilate some basic knowledge in the study of mathematics is to apply them in a personal project. On the other hand, besides being a mean of learning both programming and analytic geometry, the application subject to this paper is itself a useful tool for it can be seen as an independent original Python package for analytic geometry.

An Advanced Exponential Model for Seismic Isolators Having Hardening or Softening Behavior at Large Displacements

In this paper, an advanced Nonlinear Exponential Model (NEM), able to simulate the uniaxial dynamic behavior of seismic isolators having a continuously decreasing tangent stiffness with increasing displacement in the relatively large displacements range and a hardening or softening behavior at large displacements, is presented. The mathematical model is validated by comparing the experimental force-displacement hysteresis loops obtained during cyclic tests, conducted on a helical wire rope isolator and a recycled rubber-fiber reinforced bearing, with those predicted analytically. Good agreement between the experimental and simulated results shows that the proposed model can be an effective numerical tool to predict the force-displacement relationship of seismic isolation devices within the large displacements range. Compared to the widely used Bouc-Wen model, unable to simulate the response of seismic isolators at large displacements, the proposed one allows to avoid the numerical solution of a first order nonlinear ordinary differential equation for each time step of a nonlinear time history analysis, thus reducing the computation effort. Furthermore, the proposed model can simulate the smooth transition of the hysteresis loops from small to large displacements by adopting only one set of five parameters determined from the experimental hysteresis loops having the largest amplitude.

Simulation of Dynamic Behavior of Seismic Isolators Using a Parallel Elasto-Plastic Model

In this paper, a one-dimensional (1d) Parallel Elasto- Plastic Model (PEPM), able to simulate the uniaxial dynamic behavior of seismic isolators having a continuously decreasing tangent stiffness with increasing displacement, is presented. The parallel modeling concept is applied to discretize the continuously decreasing tangent stiffness function, thus allowing to simulate the dynamic behavior of seismic isolation bearings by putting linear elastic and nonlinear elastic-perfectly plastic elements in parallel. The mathematical model has been validated by comparing the experimental force-displacement hysteresis loops, obtained testing a helical wire rope isolator and a recycled rubber-fiber reinforced bearing, with those predicted numerically. Good agreement between the simulated and experimental results shows that the proposed model can be an effective numerical tool to predict the forcedisplacement relationship of seismic isolators within relatively large displacements. Compared to the widely used Bouc-Wen model, the proposed one allows to avoid the numerical solution of a first order ordinary nonlinear differential equation for each time step of a nonlinear time history analysis, thus reducing the computation effort, and requires the evaluation of only three model parameters from experimental tests, namely the initial tangent stiffness, the asymptotic tangent stiffness, and a parameter defining the transition from the initial to the asymptotic tangent stiffness.

Nonlinear Dynamic Analysis of Base-Isolated Structures Using a Partitioned Solution Approach and an Exponential Model

The solution of the nonlinear dynamic equilibrium equations of base-isolated structures adopting a conventional monolithic solution approach, i.e. an implicit single-step time integration method employed with an iteration procedure, and the use of existing nonlinear analytical models, such as differential equation models, to simulate the dynamic behavior of seismic isolators can require a significant computational effort. In order to reduce numerical computations, a partitioned solution method and a one dimensional nonlinear analytical model are presented in this paper. A partitioned solution approach can be easily applied to base-isolated structures in which the base isolation system is much more flexible than the superstructure. Thus, in this work, the explicit conditionally stable central difference method is used to evaluate the base isolation system nonlinear response and the implicit unconditionally stable Newmark’s constant average acceleration method is adopted to predict the superstructure linear response with the benefit in avoiding iterations in each time step of a nonlinear dynamic analysis. The proposed mathematical model is able to simulate the dynamic behavior of seismic isolators without requiring the solution of a nonlinear differential equation, as in the case of widely used differential equation model. The proposed mixed explicit-implicit time integration method and nonlinear exponential model are adopted to analyze a three dimensional seismically isolated structure with a lead rubber bearing system subjected to earthquake excitation. The numerical results show the good accuracy and the significant computational efficiency of the proposed solution approach and analytical model compared to the conventional solution method and mathematical model adopted in this work. Furthermore, the low stiffness value of the base isolation system with lead rubber bearings allows to have a critical time step considerably larger than the imposed ground acceleration time step, thus avoiding stability problems in the proposed mixed method.

Modelling for Temperature Non-Isothermal Continuous Stirred Tank Reactor Using Fuzzy Logic

Many types of controllers were applied on the continuous stirred tank reactor (CSTR) unit to control the temperature. In this research paper, Proportional-Integral-Derivative (PID) controller are compared with Fuzzy Logic controller for temperature control of CSTR. The control system for temperature non-isothermal of a CSTR will produce a stable response curve to its set point temperature. A mathematical model of a CSTR using the most general operating condition was developed through a set of differential equations into S-function using MATLAB. The reactor model and S-function are developed using m.file. After developing the S-function of CSTR model, User-Defined functions are used to link to SIMULINK file. Results that are obtained from simulation and temperature control were better when using Fuzzy logic control compared to PID control.

Element-Independent Implementation for Method of Lagrange Multipliers

Treatment for the non-matching interface is an important computational issue. To handle this problem, the method of Lagrange multipliers including classical and localized versions are the most popular technique. It essentially imposes the interface compatibility conditions by introducing Lagrange multipliers. However, the numerical system becomes unstable and inefficient due to the Lagrange multipliers. The interface element-independent formulation that does not include the Lagrange multipliers can be obtained by modifying the independent variables mathematically. Through this modification, more efficient and stable system can be achieved while involving equivalent accuracy comparing with the conventional method. A numerical example is conducted to verify the validity of the presented method.

Electoral Mathematics and Asymmetrical Treatment to Political Parties: The Mexican Case

The Mexican Chamber of Deputies is composed of 500 representatives: 300 of them elected by relative majority and another 200 ones elected through proportional representation in five electoral clusters (constituencies) with 40 representatives each. In this mixed-member electoral system, the seats distribution of proportional representation is not independent of the election by relative majority, as it attempts to correct representation imbalances produced in single-member districts. This two-fold structure has been maintained in the successive electoral reforms carried out along the last three decades (eight from 1986 to 2014). In all of them, the election process of 200 seats becomes complex: Formulas in the Law are difficult to understand and to be interpreted. This paper analyzes the Mexican electoral system after the electoral reform of 2014, which was applied for the first time in 2015. The research focuses on contradictions and issues of applicability, in particular situations where seats allocation is affected by ambiguity in the law and where asymmetrical treatment of political parties arises. Due to these facts, a proposal of electoral reform will be presented. It is intended to be simpler, clearer, and more enduring than the current system. Furthermore, this model is more suitable for producing electoral outcomes free of contradictions and paradoxes. This approach would allow a fair treatment of political parties and as a result an improved opportunity to exercise democracy.

Problem Solving in Chilean Higher Education: Figurations Prior in Interpretations of Cartesian Graphs

A Cartesian graph, as a mathematical object, becomes a tool for configuration of change. Its best comprehension is done through everyday life problem-solving associated with its representation. Despite this, the current educational framework favors general graphs, without consideration of their argumentation. Students are required to find the mathematical function without associating it to the development of graphical language. This research describes the use made by students of configurations made prior to Cartesian graphs with regards to an everyday life problem related to a time and distance variation phenomenon. The theoretical framework describes the function conditions of study and their modeling. This is a qualitative, descriptive study involving six undergraduate case studies that were carried out during the first term in 2016 at University of Los Lagos. The research problem concerned the graphic modeling of a real person’s movement phenomenon, and two levels of analysis were identified. The first level aims to identify local and global graph interpretations; a second level describes the iconicity and referentiality degree of an image. According to the results, students were able to draw no figures before the Cartesian graph, highlighting the need for students to represent the context and the movement of which causes the phenomenon change. From this, they managed Cartesian graphs representing changes in position, therefore, achieved an overall view of the graph. However, the local view only indicates specific events in the problem situation, using graphic and verbal expressions to represent movement. This view does not enable us to identify what happens on the graph when the movement characteristics change based on possible paths in the person’s walking speed.

Contaminant Transport Modeling Due to Thermal Diffusion Effects with the Effect of Biodegradation

The heat and mass transfer characteristics of contaminants in groundwater subjected to a biodegradation reaction is analyzed by taking into account the thermal diffusion (Soret) effects. This phenomenon is modulated mathematically by a system of partial differential equations which govern the motion of fluid (groundwater) and solid (contaminants) particles. The numerical results are presented graphically for different values of the parameters entering into the problem on the velocity profiles of fluid, contaminants, temperature and concentration profile.

Friction Calculation and Simulation of Column Electric Power Steering System

This study presents a procedure for friction calculation of column electric power steering (C-EPS) system which affects handling and comfort in driving. The friction losses estimation is obtained from experimental tests and mathematical calculation. Parts in C-EPS mainly involved in friction losses are bearings and worm gear. In the theoretical approach, the gear geometry and Hertz law were employed to measure the normal load and the sliding velocity and contact areas from the worm gears driving conditions. The viscous friction generated in the worm gear was obtained with a theoretical approach and the result was applied to model the friction in the steering system. Finally, by viscous friction coefficient and Coulomb friction coefficient, values of friction in worm gear were calculated. According to the Bearing Company and the characteristics of each bearing, the friction torques due to load and due to speed were calculated. A MATLAB Simulink model for calculating the friction in bearings and worm gear in C-EPS were done and the total friction value was estimated.