Search results for: Population model

Authors: Rusliza Ahmad, Harun Budin

Abstract:

This paper studies the effect of time delay on stability of mutualism population model with limited resources for both species. First, the stability of the model without time delay is analyzed. The model is then improved by considering a time delay in the mechanism of the growth rate of the population. We analyze the effect of time delay on the stability of the stable equilibrium point. Result showed that the time delay can induce instability of the stable equilibrium point, bifurcation and stability switches.

Keywords: Bifurcation, Delay margin, Mutualism population model, Time delay

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1984

Authors: Changjin Xu, Peiluan Li

Abstract:

In this paper, a nonlinear delay population model is investigated. Choosing the delay as a bifurcation parameter, we demonstrate that Hopf bifurcation will occur when the delay exceeds a critical value. Global existence of bifurcating periodic solutions is established. Numerical simulations supporting the theoretical findings are included.

Keywords: Population model, Stability, Hopf bifurcation, Delay, Global Hopf bifurcation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1754

Authors: T. K. Sriram, Joydip Dhar

Abstract:

Models based on stage structure have found varied applications in population models. This paper proposes a stage structured model to study the trends in the computer and video game playing population of US. The game paying population is divided into three compartments based on their age group. After simulating the mathematical model, a forecast of the number of game players in each stage as well as an approximation of the average age of game players in future has been made.

Keywords: Age structure, Forecasting, Mathematical modeling, Stage structure.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1902

Authors: Zhouhong Li

Abstract:

In this paper, by applying Mawhin-s continuation theorem of coincidence degree theory, we study the existence of almost periodic solutions for neural multi-delay logarithmic population model and obtain one sufficient condition for the existence of positive almost periodic solution for the above equation. An example is employed to illustrate our result.

Keywords: Almost periodic solution, Multi-delay, Logarithmic population model, Coincidence degree.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1437

Authors: Xiaoyan Dou, Yongkun Li

Abstract:

In this paper, we consider a food-limited population model with delay and feedback control. By applying the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained.

Keywords: Almost periodic solution, food-limited population, feedback control, permanence.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1961

Authors: Rujira Kongnuy

Abstract:

Leptospirosis is recognized as an important zoonosis in tropical regions well as an important animal disease with substantial loss in production. In this study, the model for the transmission of the Leptospirosis disease to human population are discussed. Model is described the vector population dynamics and the Leptospirosis transmission to the human population are discussed. Local analysis of equilibria are given. We confirm the results by using numerical results.

Keywords: Eigenvalues, Leptospirosis, Local Stability, Numerical Result

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1307

Authors: Nuraini Yusoff, Harun Budin, Salemah Ismail

Abstract:

A climate dependent model is proposed to simulate the population of Aedes aegypti mosquito. In developing the model, average temperature of Shah Alam, Malaysia was used to determine the development rate of each stage of the life cycle of mosquito. Rainfall dependent function was proposed to simulate the hatching rate of the eggs under several assumptions. The proposed transition matrix was obtained and used to simulate the population of eggs, larvae, pupae and adults mosquito. It was found that the peak of mosquito abundance comes during a relatively dry period following a heavy rainfall. In addition, lag time between the peaks of mosquito abundance and dengue fever cases in Shah Alam was estimated.

Keywords: simulation, Aedes aegypti, Lefkovitch matrix, rainfall dependent model, Shah Alam

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2488

Authors: C. E. Madubueze, S. C. Madubueze, S. Ajama

Abstract:

Cholera is a disease that is predominately common in developing countries due to poor sanitation and overcrowding population. In this paper, a deterministic model for the dynamics of cholera is developed and control measures such as health educational message, therapeutic treatment, and vaccination are incorporated in the model. The effective reproduction number is computed in terms of the model parameters. The existence and stability of the equilibrium states, disease free and endemic equilibrium states are established and showed to be locally and globally asymptotically stable when R0 < 1 and R0 > 1 respectively. The existence of backward bifurcation of the model is investigated. Furthermore, numerical simulation of the model developed is carried out to show the impact of the control measures and the result indicates that combined control measures will help to reduce the spread of cholera in the population.

Keywords: Backward bifurcation, cholera, equilibrium, dynamics, stability.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2751

Authors: W. Triampo, D. Baowan, I.M. Tang, N. Nuttavut, J. Wong-Ekkabut, G. Doungchawee

Abstract:

In this work, we consider a deterministic model for the transmission of leptospirosis which is currently spreading in the Thai population. The SIR model which incorporates the features of this disease is applied to the epidemiological data in Thailand. It is seen that the numerical solutions of the SIR equations are in good agreement with real empirical data. Further improvements are discussed.

Keywords: Leptospirosis, SIR Model, Deterministic model, Thailand.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1989

Authors: V. Nikkhah Rashidabad, M. Manteghian, M. Masoumi, S. Mousavian

Abstract:

In this research, the changes in bubbles diameter and  number that may occur due to the change in heat flux of pure water  during pool boiling process. For this purpose, test equipment was  designed and developed to collect test data. The bubbles were graded  using Caliper Screen software. To calculate the growth and  nucleation rates of bubbles under different fluxes, population balance  model was employed. The results show that the increase in heat flux  from q=20 kw/m2 to q= 102 kw/m2 raised the growth and nucleation  rates of bubbles.

 

Keywords: Heat flux, bubble growth, bubble nucleation, population balance model.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2468

Authors: Kejun Zhuang, Zhaohui Wen

Abstract:

This paper deals with a delayed single population model on time scales. With the assistance of coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained. Furthermore, the better estimations for bounds of periodic solutions are established.

Keywords: Coincidence degree, continuation theorem, periodic solutions, time scales

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1349

Authors: H. C. Chinwenyi, H. D. Ibrahim, J. O. Adekunle

Abstract:

The incubation period is defined as the time from infection with a microorganism to development of symptoms. In this research, two disease models: one with incubation period and another without incubation period were studied. The study involves the use of a  mathematical model with a single incubation period. The test for the existence and stability of the disease free and the endemic equilibrium states for both models were carried out. The fourth order Runge-Kutta method was used to solve both models numerically. Finally, a computer program in MATLAB was developed to run the numerical experiments. From the results, we are able to show that the endemic equilibrium state of the model with incubation period is locally asymptotically stable whereas the endemic equilibrium state of the model without incubation period is unstable under certain conditions on the given model parameters. It was also established that the disease free equilibrium states of the model with and without incubation period are locally asymptotically stable. Furthermore, results from numerical experiments using empirical data obtained from Nigeria Centre for Disease Control (NCDC) showed that the overall population of the infected people for the model with incubation period is higher than that without incubation period. We also established from the results obtained that as the transmission rate from susceptible to infected population increases, the peak values of the infected population for the model with incubation period decrease and are always less than those for the model without incubation period.

Keywords: Asymptotic stability, incubation period, Routh-Hurwitz criterion, Runge Kutta method.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 688

Authors: Puntani Pongsumpun, I-Ming Tang

Abstract:

The most Malaria cases are occur along Thai-Mynmar border. Mathematical model for the transmission of Plasmodium falciparum and Plasmodium vivax malaria in a mixed population of Thais and migrant Burmese living along the Thai-Myanmar Border is studied. The population is separated into two groups, Thai and Burmese. Each population is divided into susceptible, infected, dormant and recovered subclasses. The loss of immunity by individuals in the infected class causes them to move back into the susceptible class. The person who is infected with Plasmodium vivax and is a member of the dormant class can relapse back into the infected class. A standard dynamical method is used to analyze the behaviors of the model. Two stable equilibrium states, a disease-free state and an epidemic state, are found to be possible in each population. A disease-free equilibrium state in the Thai population occurs when there are no infected Burmese entering the community. When infected Burmese enter the Thai community, an epidemic state can occur. It is found that the disease-free state is stable when the threshold number is less than one. The epidemic state is stable when a second threshold number is greater than one. Numerical simulations are used to confirm the results of our model.

Keywords: Basic reproduction number, Burmese, local stability, Plasmodium Vivax malaria.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1868

Authors: Khawla Ben Abderrahim

Abstract:

In order to define a new model of Tunisian foot sizes and for building the most comfortable shoes, Tunisian industrialists must be able to offer for their customers products able to put on and adjust the majority of the target population concerned. Moreover, the use of models of shoes, mainly from others country, causes a mismatch between the foot and comfort of the Tunisian shoes. But every foot is unique; these models become uncomfortable for the Tunisian foot. We have a set of measures produced from a 3D scan of the feet of a diverse population (women, men ...) and we try to analyze this data to define a model of foot specific to the Tunisian footwear design. In this paper we propose tow new approaches to modeling a new foot sizes model. We used, indeed, the neural networks, and specially the Kohonen network. Next, we combine neural networks with the concept of half-foot size to improve the models already found. Finally, it was necessary to compare the results obtained by applying each approach and we decide what-s the best approach that give us the most model of foot improving more comfortable shoes.

Keywords: Morphology of the foot, foot size, half foot size, neural network, Kohonen network, model of foot size.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1558

Authors: Akiko Kondo, Akio Kondo

Abstract:

We are facing serious problems related to long-term depopulation and an aging society with a falling birth rate in Japan. In this situation, we are suffering from a shortfall in human resources as well as a shortage of workforce in rural regions. In addition, we are struggling with a protracted economic slump and excess concentration of population in the Tokyo Metropolitan area. It is an urgent national issue to consider how to live in this country and what kind of structure of society and administration policy is needed. It is necessary to clarify people’s desire for their way of living and social assistance to be provided. The aim of this study is to clarify the characteristics of regional issues and the degree of their seriousness in local municipalities of Japan. We conducted a questionnaire survey about regional agenda in all local municipalities in Japan. We obtained responses concerning the degree of seriousness of regional issues and degree of importance of policies. Based on the data gathered from the survey, it is apparent that many local municipalities are facing an aging population and declining population. We constructed a model to analyze factors for declining population. Using the model, it was clarified that a population’s age structure, job opportunities and income level affect the decline of population. In addition, we showed the way of the evaluation of state of local municipality.

Keywords: Evaluation, Local municipality, Regional analysis, Regional issue.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1863

Authors: Felicia Magpantay, Kenzu Abdella

Abstract:

A model of a system concerning one species of demersal (inshore) fish and one of pelagic (offshore) fish undergoing fishing restricted by marine protected areas is proposed in this paper. This setup was based on the FISH-BE model applied to the Tabina fishery in Zamboanga del Sur, Philippines. The components of the model equations have been adapted from widely-accepted mechanisms in population dynamics. The model employs Gompertz-s law of growth and interaction on each type of protected and unprotected subpopulation. Exchange coefficients between protected and unprotected areas were assumed to be proportional to the relative area of the entry region. Fishing harvests were assumed to be proportional to both the number of fishers and the number of unprotected fish. An extra term was included for the pelagic population to allow for the exchange between the unprotected area and the outside environment. The systems were found to be bounded for all parameter values. The equations for the steady state were unsolvable analytically but the existence and uniqueness of non-zero steady states can be proven. Plots also show that an MPA size yielding the maximum steady state of the unprotected population can be found. All steady states were found to be globally asymptotically stable for the entire range of parameter values.

Keywords: fisheries modelling, marine protected areas, sustainablefisheries, Gompertz Law

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1908

Authors: Sukaesi Marianti

Abstract:

This study aims to develop the Relational Mobility Scale for the Indonesian population and to investigate its psychometric properties. New items of the scale were created taking into account the Indonesian population which consists of two parallel forms (A and A’). This study uses 30 newly orchestrated items while keeping in mind the characteristics of the targeted population. The scale was administered to 433 public high school students in Malang, Indonesia. Construct validity of its factor structure was demonstrated using exploratory factor analysis and confirmatory factor analysis. The result exhibits that he model fits the data, and that the delayed alternate form method shows acceptable result. Results yielded that 21 items of the three-dimensional Relational Mobility Scale is suitable for measuring relational mobility in high school students of Indonesian population.

Keywords: Confirmatory factor analysis, exploratory factor analysis, delayed alternate form, Indonesian population, relational mobility scale.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1038

Authors: Christian P. Crisostomo, Chrysline Margus N. Piñol

Abstract:

A zero-field ferromagnetic Ising model is utilized to simulate the propagation of infection in a population that assumes a square lattice structure. The rate of infection increases with temperature. The disease spreads faster among individuals with low J values. Such effect, however, diminishes at higher temperatures.

Keywords: Epidemiology, Ising model, lattice models

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2045

Authors: Hidetoshi Konno, Akio Suzuki

Abstract:

The paper presented a transient population dynamics of phase singularities in 2D Beeler-Reuter model. Two stochastic modelings are examined: (i) the Master equation approach with the transition rate (i.e., λ(n, t) = λ(t)n and μ(n, t) = μ(t)n) and (ii) the nonlinear Langevin equation approach with a multiplicative noise. The exact general solution of the Master equation with arbitrary time-dependent transition rate is given. Then, the exact solution of the mean field equation for the nonlinear Langevin equation is also given. It is demonstrated that transient population dynamics is successfully identified by the generalized Logistic equation with fractional higher order nonlinear term. It is also demonstrated the necessity of introducing time-dependent transition rate in the master equation approach to incorporate the effect of nonlinearity.

Keywords: Transient population dynamics, Phase singularity, Birth-death process, Non-stationary Master equation, nonlinear Langevin equation, generalized Logistic equation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1602

Authors: Xu Du, Aparna S. Varde

Abstract:

In this research, we propose to conduct diagnostic and predictive analysis about the key factors and consequences of urban population relocation. To achieve this goal, urban simulation models extract the urban development trends as land use change patterns from a variety of data sources. The results are treated as part of urban big data with other information such as population change and economic conditions. Multiple data mining methods are deployed on this data to analyze nonlinear relationships between parameters. The result determines the driving force of population relocation with respect to urban sprawl and urban sustainability and their related parameters. This work sets the stage for developing a comprehensive urban simulation model for catering to specific questions by targeted users. It contributes towards achieving sustainability as a whole.

Keywords: Data Mining, Environmental Modeling, Sustainability, Urban Planning.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1784

Authors: Abdel Hamid Ajbar, Emad Ali

Abstract:

Saudi Arabia is an arid country which depends on costly desalination plants to satisfy the growing residential water demand. Prediction of water demand is usually a challenging task because the forecast model should consider variations in economic progress, climate conditions and population growth. The task is further complicated knowing that Mecca city is visited regularly by large numbers during specific months in the year due to religious occasions. In this paper, a neural networks model is proposed to handle the prediction of the monthly and yearly water demand for Mecca city, Saudi Arabia. The proposed model will be developed based on historic records of water production and estimated visitors- distribution. The driving variables for the model include annuallyvarying variables such as household income, household density, and city population, and monthly-varying variables such as expected number of visitors each month and maximum monthly temperature.

Keywords: Water demand forecast; Neural Networks model; water resources management; Saudi Arabia.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1816

Authors: Abu Qudeiri Jaber, Yamamoto Hidehiko Rizauddin Ramli

Abstract:

To create a solution for a specific problem in machine learning, the solution is constructed from the data or by use a search method. Genetic algorithms are a model of machine learning that can be used to find nearest optimal solution. While the great advantage of genetic algorithms is the fact that they find a solution through evolution, this is also the biggest disadvantage. Evolution is inductive, in nature life does not evolve towards a good solution but it evolves away from bad circumstances. This can cause a species to evolve into an evolutionary dead end. In order to reduce the effect of this disadvantage we propose a new a learning tool (criteria) which can be included into the genetic algorithms generations to compare the previous population and the current population and then decide whether is effective to continue with the previous population or the current population, the proposed learning tool is called as Keeping Efficient Population (KEP). We applied a GA based on KEP to the production line layout problem, as a result KEP keep the evaluation direction increases and stops any deviation in the evaluation.

Keywords: Genetic algorithms, Layout problem, Machinelearning, Production system.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1629

Authors: Ahmed H. Abdullah, Pavel Kroupa

Abstract:

Globular clusters (GC) are important objects for tracing the early evolution of a galaxy. We study the correlation between the cluster population and the global properties of the host galaxy. We found that the correlation between cluster population (NGC) and the baryonic mass (Mb) of the host galaxy are best described as 10 −5.6038Mb. In order to understand the origin of the U -shape relation between the GC specific frequency (SN) and Mb (caused by the high value of SN for dwarfs galaxies and giant ellipticals and a minimum SN for intermediate mass galaxies≈ 1010M), we derive a theoretical model for the specific frequency (SNth). The theoretical model for SNth is based on the slope of the power-law embedded cluster mass function (β) and different time scale (Δt) of the forming galaxy. Our results show a good agreement between the observation and the model at a certain β and Δt. The model seems able to reproduce higher value of SNth of β = 1.5 at the midst formation time scale.

Keywords: Galaxies, dwarf, globular cluster, specific frequency, formation time scale.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 801

Authors: P. Pongsumpun

Abstract:

Dengue virus is transmitted from person to person through the biting of infected Aedes Aegypti mosquitoes. DEN-1, DEN-2, DEN-3 and DEN-4 are four serotypes of this virus. Infection with one of these four serotypes apparently produces permanent immunity to it, but only temporary cross immunity to the others. The length of time during incubation of dengue virus in human and mosquito are considered in this study. The dengue patients are classified into infected and infectious classes. The infectious human can transmit dengue virus to susceptible mosquitoes but infected human can not. The transmission model of this disease is formulated. The human population is divided into susceptible, infected, infectious and recovered classes. The mosquito population is separated into susceptible, infected and infectious classes. Only infectious mosquitoes can transmit dengue virus to the susceptible human. We analyze this model by using dynamical analysis method. The threshold condition is discussed to reduce the outbreak of this disease.

Keywords: Transmission model, intrinsic incubation period, extrinsic incubation period, basic reproductive number, equilibriumstates, local stability.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2189

Authors: Pham Van Nha, Le Cam Binh

Abstract:

Particle swarm optimization (PSO) is a population-based stochastic optimization algorithm. PSO was inspired by the natural behavior of birds and fish in migration and foraging for food. PSO is considered as a multidisciplinary optimization model that can be applied in various optimization problems. PSO’s ideas are simple and easy to understand but PSO is only applied in simple model problems. We think that in order to expand the applicability of PSO in complex problems, PSO should be described more explicitly in the form of a mathematical model. In this paper, we represent PSO in a mathematical model and apply in the multivariate data classification. First, PSOs general mathematical model (MPSO) is analyzed as a universal optimization model. Then, Model of Optimal Centroids (MOC) is proposed for the multivariate data classification. Experiments were conducted on some benchmark data sets to prove the effectiveness of MOC compared with several proposed schemes.

Keywords: Analysis of optimization, artificial intelligence-based optimization, optimization for learning and data analysis, global optimization.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 914

Authors: Mahdi Sharifian, Mohammad Ali Fanaei

Abstract:

Saccharomyces cerevisiae (baker-s yeast) can exhibit sustained oscillations during the operation in a continuous bioreactor that adversely affects its stability and productivity. Because of heterogeneous nature of cell populations, the cell population balance models can be used to capture the dynamic behavior of such cultures. In this paper an unstructured, segregated model is used which is based on population balance equation(PBE) and then in order to simulation, the 4th order Rung-Kutta is used for time dimension and three methods, finite difference, orthogonal collocation on finite elements and Galerkin finite element are used for discretization of the cell mass domain. The results indicate that the orthogonal collocation on finite element not only is able to predict the oscillating behavior of the cell culture but also needs much little time for calculations. Therefore this method is preferred in comparison with other methods. In the next step two controllers, a globally linearizing control (GLC) and a conventional proportional-integral (PI) controller are designed for controlling the total cell mass per unit volume, and performances of these controllers are compared through simulation. The results show that although the PI controller has simpler structure, the GLC has better performance.

Keywords: Bioreactor, cell population balance, finite difference, orthogonal collocation on finite elements, Galerkin finite element, feedback linearization, PI controller.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1884

Authors: Cristina Schreiner, Romeo Ciobanu, Marius Pislaru

Abstract:

This paper aims to build a system based on fuzzy models that can be implemented in the assessment of ecological systems, to determine appropriate methods of action for reducing adverse effects on environmental and implicit the population. The model proposed provides new perspective for environmental assessment, and it can be used as a practical instrument for decision –making.

Keywords: Ecosystem model, Environmental security, Fuzzy logic, Sustainability of habitable regions.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1982

Authors: R. Kongnuy, P. Pongsumpun

Abstract:

We used mathematical model to study the transmission of dengue disease. The model is developed in which the human population is separated into two populations, pregnant and non-pregnant humans. The dynamical analysis method is used for analyzing this modified model. Two equilibrium states are found and the conditions for stability of theses two equilibrium states are established. Numerical results are shown for each equilibrium state. The basic reproduction numbers are found and they are compared by using numerical simulations.

Keywords: Basic reproductive number, dengue disease, equilibrium states, pregnancy.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1595

Authors: Z. Zhou, Q. Chen, S. Wu

Abstract:

Population diversification phenomena becomes quite common in villages located in China’s developed coastal area. Based on the analysis of the traditional rural society and its landscape characteristics, and in consideration of diversified landscape requirements due to the population diversification, with dual ideas of heritage and innovation, methods for rural landscape design were explored by taking Duxuao Village in Zhejiang Province of China as an example.

Keywords: Rural landscape, Population diversification, Landscape design.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2255

Authors: Emmanuel Agunloye, Asterios Gavriilidis, Luca Mazzei

Abstract:

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.

Keywords: Gold nanoparticles, Citrate method, Turkevich organizer theory, population balance modelling.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1003