Search results for: Nanoparticle Stabilization

Authors: Mu-Jen Young, Cheng-Yen Wu, Wen-Yuan Hsieh

Abstract:

Iron oxide nanoparticle was synthesized by reactive-precipitation method followed by high speed centrifuge and phase transfer in order to stabilized nanoparticles in the solvent. Particle size of SPIO was 8.2 nm by SEM, and the hydraulic radius was 17.5 nm by dynamic light scattering method. Coercivity and saturated magnetism were determined by VSM (vibrating sample magnetometer), coercivity of nanoparticle was lower than 10 Hc, and the saturated magnetism was higher than 65 emu/g. Stabilized SPIO was then transferred to aqueous phase by reacted with excess amount of poly (ethylene glycol) (PEG) silane. After filtration and dialysis, the SPIO T2 contrast agent was ready to use. The hydraulic radius of final product was about 70~100 nm, the relaxation rates R2 (1/T2) measured by magnetic resonance imaging (MRI) was larger than 200(sec-1).

Keywords: Contrast Agent, Iron Oxide Nanoparticle, Magnetic Resonance Imaging, Nanoparticle Stabilization

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Authors: Herbert Ugrinowitsch, Suziane Peixoto dos Santos-Naves, Michele Viviene Carbinatto, Rodolfo NovellinoBenda, Go Tani

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An experiment was conducted to examine the effect of the level of performance stabilization on the human adaptability to perceptual-motor perturbation in a complex coincident timing task. Three levels of performance stabilization were established operationally: pre-stabilization, stabilization, and super-stabilization groups. Each group practiced the task until reached its level of stabilization in a constant sequence of movements and under a constant time constraint before exposure to perturbation. The results clearly showed that performance stabilization is a pre-condition for adaptation. Moreover, variability before reaching stabilization is harmful to adaptation and persistent variability after stabilization is beneficial. Moreover, the behavior of variability is specific to each measure.

Keywords: Adaptation, motor skill, perturbation, stabilization.

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Authors: Xiu Liu, Shouming Zhong, Xiuyong Ding

Abstract:

This paper focuses on the quadratic stabilization problem for a class of uncertain impulsive switched systems. The uncertainty is assumed to be norm-bounded and enters both the state and the input matrices. Based on the Lyapunov methods, some results on robust stabilization and quadratic stabilization for the impulsive switched system are obtained. A stabilizing state feedback control law realizing the robust stabilization of the closed-loop system is constructed.

Keywords: Impulsive systems, switched systems, quadratic stabilization, robust stabilization.

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Authors: R. Eslami Farsani, S. Raissi, A. Shokuhfar, A. Sedghi

Abstract:

In this investigation, types of commercial and special polyacrylonitrile (PAN) fibers contain sodium 2-methyl-2- acrylamidopropane sulfonate (SAMPS) and itaconic acid (IA) comonomers were studied by fourier transform infrared (FT-IR) spectroscopy. The study of FT-IR spectra of PAN fibers samples with different comonomers shows that during stabilization of PAN fibers, the peaks related to C≡N bonds and CH2 are reduced sharply. These reductions are related to cyclization of nitrile groups and stabilization procedure. This reduction in PAN fibers contain IA comonomer is very intense in comparison with PAN fibers contain SAMPS comonomer. This fact indicates the cycling and stabilization for sample contain IA comonomer have been conducted more completely. Therefore the carbon fibers produced from this material have higher tensile strength due to suitable stabilization.

Keywords: PAN Fibers, Stabilization, Carbon Fibers, FT-IR.

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Authors: Myung-Gon Yoon, Jung-Ho Moon, Tae Kwon Ha

Abstract:

This paper studies a robust stabilization problem of a single agent in a multi-agent consensus system composed of identical agents, when the network topology of the system is completely unknown. It is shown that the transfer function of an agent in a consensus system can be described as a multiplicative perturbation of the isolated agent transfer function in frequency domain. From an existing robust stabilization result, we present sufficient conditions for a robust stabilization of an agent against unknown network topology.

Keywords: Multi-agent System, Robust Stabilization, Transfer Function.

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Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

Abstract:

The discrete-time uncertain system with time delay is investigated for bounded input bounded output (BIBO). By constructing an augmented Lyapunov function, three different sufficient conditions are established for BIBO stabilization. These conditions are expressed in the form of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Two numerical examples are provided to demonstrate the effectiveness of the derived results.

Keywords: Robust BIBO stabilization, delay-dependent stabilization, discrete-time system, time delay.

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Authors: R. Ziaie Moayed, F. Allahyari

Abstract:

Soil stabilization has been widely used to improve soil strength and durability or to prevent erosion and dust generation. Generally to reduce problems of clayey soils in engineering work and to stabilize these soils additional materials are used. The most common materials are lime, fly ash and cement. Using this materials, although improve soil property , but in some cases due to financial problems and the need to use special equipment are limited .One of the best methods for stabilization clayey soils is neutralization the clay particles. For this purpose we can use ion exchange materials. Ion exchange solution like CBR plus can be used for soil stabilization. One of the most important things in using CBR plus is determination the amount of this solution for various soils with different properties. In this study a laboratory experiment is conduct to evaluate the ion exchange capacity of three soils with various plasticity index (PI) to determine amount or required CBR plus solution for soil stabilization.

Keywords: CBR plus, clayey soils, ion exchange, soil stabilization

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Authors: Ping He

Abstract:

This paper addresses the problem of the partial state feedback stabilization of a class of nonlinear systems. In order to stabilization this class systems, the especial place of this paper is to reverse designing the state feedback control law from the method of judging system stability with the center manifold theory. First of all, the center manifold theory is applied to discuss the stabilization sufficient condition and design the stabilizing state control laws for a class of nonlinear. Secondly, the problem of partial stabilization for a class of plane nonlinear system is discuss using the lyapunov second method and the center manifold theory. Thirdly, we investigate specially the problem of the stabilization for a class of homogenous plane nonlinear systems, a class of nonlinear with dual-zero eigenvalues and a class of nonlinear with zero-center using the method of lyapunov function with homogenous derivative, specifically. At the end of this paper, some examples and simulation results are given show that the approach of this paper to this class of nonlinear system is effective and convenient.

Keywords: Partial stabilization, Nonlinear critical systems, Centermanifold theory, Lyapunov function, System reduction.

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Authors: Zixin Liu

Abstract:

The problem of robust stability and robust stabilization for a class of discrete-time uncertain systems with time delay is investigated. Based on Tchebychev inequality, by constructing a new augmented Lyapunov function, some improved sufficient conditions ensuring exponential stability and stabilization are established. These conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Compared with some previous results derived in the literature, the new obtained criteria have less conservatism. Two numerical examples are provided to demonstrate the improvement and effectiveness of the proposed method.

Keywords: Robust stabilization, robust stability, discrete-time system, time delay.

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Authors: Riku Hayashida, Tomoaki Hashimoto

Abstract:

This paper provides a robust stabilization method for rotational motion of underwater robots against parameter uncertainties. Underwater robots are expected to be used for various work assignments. The large variety of applications of underwater robots motivates researchers to develop control systems and technologies for underwater robots. Several control methods have been proposed so far for the stabilization of nominal system model of underwater robots with no parameter uncertainty. Parameter uncertainties are considered to be obstacles in implementation of the such nominal control methods for underwater robots. The objective of this study is to establish a robust stabilization method for rotational motion of underwater robots against parameter uncertainties. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: Robust control, stabilization method, underwater robot, parameter uncertainty.

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Authors: Kreangkri Ratchagit

Abstract:

This paper is concerned with exponential stability and stabilization of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton-s formula, a switching rule for the exponential stability and stabilization of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability and stabilization of the systems are first established in terms of LMIs. Numerical examples are included to illustrate the effectiveness of the results.

Keywords: Switching design, exponential stability and stabilization, switched linear systems, interval delay, Lyapunov function, linear matrix inequalities.

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Authors: Ping He, Heng-You Lan, Gong-Quan Tan

Abstract:

The multidelays linear control systems described by difference differential equations are often studied in modern control theory. In this paper, the delay-independent stabilization algebraic criteria and the theorem of delay-independent stabilization for linear systems with multiple time-delays are established by using the Lyapunov functional and the Riccati algebra matrix equation in the matrix theory. An illustrative example and the simulation result, show that the approach to linear systems with multiple time-delays is effective.

Keywords: Linear system, Delay-independent stabilization, Lyapunovfunctional, Riccati algebra matrix equation.

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Authors: R. Eslami Farsani, A. Shokuhfar, A. Sedghi

Abstract:

Carbon fibers are fabricated from different materials, such as special polyacrylonitrile (PAN) fibers, rayon fibers and pitch. Among these three groups of materials, PAN fibers are the most widely used precursor for the manufacture of carbon fibers. The process of fabrication carbon fibers from special PAN fibers includes two steps; oxidative stabilization at low temperature and carbonization at high temperatures in an inert atmosphere. Due to the high price of raw materials (special PAN fibers), carbon fibers are still expensive. In the present work the main goal is making carbon fibers from low price commercial PAN fibers with modified chemical compositions. The results show that in case of conducting completes stabilization process, it is possible to produce carbon fibers with desirable tensile strength from this type of PAN fibers. To this matter, thermal characteristics of commercial PAN fibers were investigated and based upon the obtained results, with some changes in conventional procedure of stabilization in terms of temperature and time variables; the desirable conditions of complete stabilization is achieved.

Keywords: Modified Commercial PAN Fibers, Stabilization, Carbonization, Carbon Fibers.

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Authors: Sanghoon Park, Ki-Jin Kim, Kwang-Ho Ahn

Abstract:

This paper discusses the undesirable charge transfer by the parasitic capacitances of the input transistors in a voltage sense amplifier. Due to its intrinsic rail-to-rail voltage transition, the input sides are inevitably disturbed. It can possible disturb the stabilities of the reference voltage levels. Moreover, it becomes serious in multi-channel systems by altering them for other channels, and so degrades the linearity of the systems. In order to alleviate the internal node voltage transition, the internal node stabilization technique is proposed by utilizing an additional biasing circuit. It achieves 47% and 43% improvements for node stabilization and input referred disturbance, respectively.

Keywords: Voltage sense amplifier, voltage transition, node stabilization, and biasing circuits.

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Authors: M. Ghasemi-Varnamkhasti, S. H. Yoosefian, A. Mohammad-Razdari

Abstract:

This study investigated the effects of Ag nanoparticle polyethylene film and active modified atmosphere on the postharvest quality of tomatoes stored at 6 ºC. The atmosphere composition used in the packaging was 7% O₂ + 7% CO₂ + 86% N₂, and synthetic air (control). The variables measured were weight loss, firmness, color and respiration rate over 21 days. The results showed that the combination of Ag nanoparticle polyethylene film and modified atmosphere could extend the shelf life of tomatoes to 21 days and could influence the postharvest quality of tomatoes. Also, existence of Ag nanoparticles caused preventing from increasing weight loss, a*, b*, Chroma, Hue angle and reducing firmness and L*. As well as, tomatoes at Ag nanoparticle polyethylene films had lower respiration rate than Polyethylene and paper bags to 13.27% and 23.50%, respectively. The combination of Ag nanoparticle polyethylene film and active modified atmosphere was effective with regard to delaying maturity during the storage period, and preserving the quality of tomatoes.

Keywords: Ag nanoparticles, modified atmosphere, polyethylene film, tomato.

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Authors: Sanghoon Park, Ki-Jin Kim, Kwang-Ho Ahn

Abstract:

This paper discusses the undesirable charge transfer through the parasitic capacitances of the input transistors in a multi-inputs voltage sense amplifier. Its intrinsic rail-to-rail voltage transitions at the output nodes inevitably disturb the input sides through the capacitive coupling between the outputs and inputs. Then, it can possible degrade the stabilities of the reference voltage levels. Moreover, it becomes more serious in multi-channel systems by altering them for other channels, and so degrades the linearity of the overall systems. In order to alleviate the internal node voltage transition, the internal node stabilization techniques are proposed. It achieves 45% and 40% improvements for node stabilization and input referred disturbance, respectively.

Keywords: Voltage sense amplifier, multi-inputs, voltage transition, node stabilization, and biasing circuits.

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Authors: Byoung-Uk Nam, Hag-Seong Kim, Ho-Jung Lee, Dong-Hyun Kim

Abstract:

This paper focuses on systematic analysis and controller design of the two-inertia STABILIZATION system, considering the angular motion on a base body. This approach is essential to the stabilization system to aim at a target under three or six degrees of freedom base motion. Four controllers, such as conventional PDF(Pseudo-Derivative Feedback) controller with motor speed feedback, PDF controller with load speed feedback, modified PDF controller with motor-load speed feedback and feedforward controller added to modified PDF controller, are suggested to improve reference tracking and disturbance rejection performance. Characteristics and performance of each controller are analyzed and validated by simulation in the case of the modified PDF controller with and without a feedforward controller.

Keywords: Two-Inertia stabilization System, ITAE criterion, Speed Control.

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Authors: P. Gunnasegaran, M. Z. Abdullah, M. Z. Yusoff, Nur Irmawati

Abstract:

This study presents experimental and optimization of nanoparticle mass concentration and heat input based on the total thermal resistance (Rth) of loop heat pipe (LHP), employed for PCCPU cooling. In this study, silica nanoparticles (SiO2) in water with particle mass concentration ranged from 0% (pure water) to 1% is considered as the working fluid within the LHP. The experimental design and optimization is accomplished by the design of experimental tool, Response Surface Methodology (RSM). The results show that the nanoparticle mass concentration and the heat input have significant effect on the Rth of LHP. For a given heat input, the Rth is found to decrease with the increase of the nanoparticle mass concentration up to 0.5% and increased thereafter. It is also found that the Rth is decreased when the heat input is increased from 20W to 60W. The results are optimized with the objective of minimizing the Rth, using Design-Expert software, and the optimized nanoparticle mass concentration and heat input are 0.48% and 59.97W, respectively, the minimum thermal resistance being 2.66 (ºC/W).

Keywords: Loop heat pipe, nanofluid, optimization, thermal resistance.

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Authors: M. De la Sen, O. Barambones

Abstract:

This paper presents an indirect adaptive stabilization scheme for first-order continuous-time systems under saturated input which is described by a sigmoidal function. The singularities are avoided through a modification scheme for the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be non-singular and then the estimated plant model is controllable. The modification mechanism involves the use of a hysteresis switching function. An alternative hybrid scheme, whose estimated parameters are updated at sampling instants is also given to solve a similar adaptive stabilization problem. Such a scheme also uses hysteresis switching for modification of the parameter estimates so as to ensure the controllability of the estimated plant model.

Keywords: Hybrid dynamic systems, discrete systems, saturated input, control, stabilization.

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Authors: Ahmed O. Apampa, Yinusa A. Jimoh

Abstract:

The paper examines the mechanism of pozzolan-soil reactions, using a recent study on the chemical stabilization of a Class A-2-7 (3) lateritic soil, with corn cob ash (CCA) as case study. The objectives are to establish a nexus between cation exchange capacity of the soil, the alkaline forming compounds in CCA and percentage CCA addition to soil beyond which no more improvement in strength properties can be achieved; and to propose feasible chemical reactions to explain the chemical stabilization of the lateritic soil with CCA alone. The lateritic soil, as well as CCA of pozzolanic quality Class C were separately analysed for their metallic oxide composition using the X-Ray Fluorescence technique. The cation exchange capacity (CEC) of the soil and the CCA were computed theoretically using the percentage composition of the base cations Ca²⁺, Mg²⁺ K⁺ and Na²⁺ as 1.48 meq/100 g and 61.67 meq/100 g respectively, thus indicating a ratio of 0.024 or 2.4%. This figure, taken as the theoretical amount required to just fill up the exchangeable sites of the clay molecules, compares well with the laboratory observation of 1.5% for the optimum level of CCA addition to lateritic soil. The paper went on to present chemical reaction equations between the alkaline earth metals in the CCA and the silica in the lateritic soil to form silicates, thereby proposing an extension of the theory of mechanism of soil stabilization to cover chemical stabilization with pozzolanic ash only. The paper concluded by recommending further research on the molecular structure of soils stabilized with pozzolanic waste ash alone, with a view to confirming the chemical equations advanced in the study.

Keywords: Cation exchange capacity, corn cob ash, lateritic soil, soil stabilization.

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Authors: A. Ghafouri, N. Pourmahmoud, I. Mirzaee

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In this numerical study, effects of using Al2O3-water nanofluid on the rate of heat transfer have been investigated. Physical model is a square enclosure with insulated top and bottom horizontal walls, while the vertical walls are kept at different constant temperatures. Two appropriate models are used to evaluate the viscosity and thermal conductivity of nanofluid. The governing stream-vorticity equations are solved using a second order central finite difference scheme, coupled to the conservation of mass and energy. The study has been carried out for the nanoparticle diameter 30, 60 and 90 nm and the solid volume fraction 0 to 0.04. Results are presented by average Nusselt number and normalized Nusselt number in different range of φ and D for mixed convection dominated regime. It is found that different heat transfer rate is predicted when the effect of nanoparticle diameter is taken into account.

Keywords: Nano-fluid, nanoparticle diameter, heat transfer enhancement, square enclosure, Nusselt number.

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Authors: Myung-Gon Yoon, Jung-Ho Moon, Tae Kwon Ha

Abstract:

This paper deals with a stabilization problem for multi-agent systems, when all agents in a multi-agent system receive the same broadcasting control signal and the controller can measure not each agent output but the sum of all agent outputs. It is analytically shown that when the sum of all agent outputs is bounded with a certain broadcasting controller for a given reference, each agent output is separately bounded: stabilization of the sum of agent outputs always results in the stability of every agent output. A numerical example is presented to illustrate our theoretic findings in this paper.

Keywords: Broadcasting Control, Multi-agent System, Transfer Function

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Authors: G. M. Ayininuola, O. S. Oladeji

Abstract:

The research investigated the use of nylon solution to enhance the California bearing ratio (CBR) of soil. Used nylon sachet of potable water were dissolved in four separate solvents namely acetone, toluene, ethyl glycol and dual purpose kerosene (DPK). It was discovered that DPK has the highest nylon solubility of 29g/ml at 91^oC. The nylon solution was used to stabilize poorly graded sandy soil. The result showed that at less or equal to 4% stabilization, the CBR value decreased from 25.3% to 15.85% and later appreciated to 67.78% at 16% stabilization. The initial decrease in CBR value of soil sample observed was as a result of inadequate nylon solution to coat soil particles for proper bonding.

Keywords: Nylon solution, Soil stabilization, Dual purpose kerosene, California bearing ratio.

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Authors: Behrooz Rezaie, Zahra Rahmani Cherati, Mohammad Reza Jahed Motlagh, Mohammad Farrokhi

Abstract:

In this paper, a fuzzy controller is designed for stabilization of the Lorenz chaotic equations. A simple Mamdani inference method is used for this purpose. This method is very simple and applicable for complex chaotic systems and it can be implemented easily. The stability of close loop system is investigated by the Lyapunov stabilization criterion. A Lyapunov function is introduced and the global stability is proven. Finally, the effectiveness of this method is illustrated by simulation results and it is shown that the performance of the system is improved.

Keywords: Chaotic system, Fuzzy control, Lorenz equation.

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Authors: Ziya Uddin

Abstract:

This paper deals with the theoretical and numerical investigation of magneto hydrodynamic boundary layer flow of a nanofluid past a wedge shaped wick in heat pipe used for the cooling of electronic components and different type of machines. To incorporate the effect of nanoparticle diameter, concentration of nanoparticles in the pure fluid, nanothermal layer formed around the nanoparticle and Brownian motion of nanoparticles etc., appropriate models are used for the effective thermal and physical properties of nanofluids. To model the rotation of nanoparticles inside the base fluid, microfluidics theory is used. In this investigation ethylene glycol (EG) based nanofluids, are taken into account. The non-linear equations governing the flow and heat transfer are solved by using a very effective particle swarm optimization technique along with Runge-Kutta method. The values of heat transfer coefficient are found for different parameters involved in the formulation viz. nanoparticle concentration, nanoparticle size, magnetic field and wedge angle etc. It is found that, the wedge angle, presence of magnetic field, nanoparticle size and nanoparticle concentration etc. have prominent effects on fluid flow and heat transfer characteristics for the considered configuration.

Keywords: Heat transfer, Heat pipe, numerical modeling, nanofluid applications, particle swarm optimization, wedge shaped wick.

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Authors: I. Davies, O. L. C. Haas

Abstract:

In this paper, the problem of stability and stabilization for neutral delay-differential systems with infinite delay is investigated. Using Lyapunov method, new delay-independent sufficient condition for the stability of neutral systems with infinite delay is obtained in terms of linear matrix inequality (LMI). Memory-less state feedback controllers are then designed for the stabilization of the system using the feasible solution of the resulting LMI, which are easily solved using any optimization algorithms. Numerical examples are given to illustrate the results of the proposed methods.

Keywords: Infinite delays, Lyapunov method, linear matrix inequality, neutral systems, stability.

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Authors: Imana Shahrin Tania, Mohammad Ali

Abstract:

The present study reports the synthesis, characterization and application of nano-sized zinc-oxide (ZnO) particles on a cotton fabric surface. The aim of the investigations is to impart the antimicrobial activity on textile cloth. Nanoparticle is synthesized by wet chemical method from zinc sulphate and sodium hydroxide. SEM (scanning electron micrograph) images are taken to demonstrate the surface morphology of nanoparticles. XRD analysis is done to determine the crystal size of the nanoparticle. With the conformation of nanoformation, the cotton woven fabric is treated with ZnO nanoparticle by mechanical thermo-fixation (pad-dry-cure) technique. To increase the wash durability of nano treated fabric, an acrylic binder is used as a fixing agent. The treated fabric shows up to 90% bacterial reduction for S. aureus (Staphylococcus aureus) and 87% for E. coli (Escherichia coli) which is appreciable for bacteria protective clothing.

Keywords: Nanoparticle, zinc oxide, cotton fabric, antibacterial activity, binder.

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Authors: Kolay, P.K., Sii, H. Y., Taib, S.N.L.

Abstract:

This paper presents the stabilization potential of Class F pond ash (PA) from a coal fired thermal power station on tropical peat soil. Peat or highly organic soils are well known for their high compressibility, natural moisture content, low shear strength and long-term settlement. This study investigates the effect of different amount (i.e., 5, 10, 15 and 20%) of PA on peat soil, collected from Sarawak, Malaysia, mainly compaction and unconfined compressive strength (UCS) properties. The amounts of PA added to the peat soil sample as percentage of the dry peat soil mass. With the increase in PA content, the maximum dry density (MDD) of peat soil increases, while the optimum moisture content (OMC) decreases. The UCS value of the peat soils increases significantly with the increase of PA content and also with curing periods. This improvement on compressive strength of tropical peat soils indicates that PA has the potential to be used as a stabilizer for tropical peat soil. Also, the use of PA in soil stabilization helps in reducing the pond volume and achieving environment friendly as well as a sustainable development of natural resources.

Keywords: Compaction, Peat soil, Pond ash, Stabilization.

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Authors: Chikara Egami, Kazuhiro Kuwahara

Abstract:

Polarization-interferometric nonlinear confocal microscopy is proposed for measuring a nano-sized particle with optical anisotropy. The anisotropy in the particle was spectroscopically imaged through a three-dimensional distribution of third-order nonlinear dielectric polarization photoinduced.

Keywords: nanoparticle, optical storage, microscope

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Authors: E. Mat Tokit, Yusoff M. Z, Mohammed H.

Abstract:

Numerical investigation on the generality of nanoparticle velocity equation had been done on the previous published work. The three dimensional governing equations (continuity, momentum and energy) were solved using finite volume method (FVM). Parametric study of thermal performance between pure water-cooled and nanofluid-cooled are evaluated for volume fraction in the range of 1% to 4%, and nanofluid type of gamma-Al₂O₃ at Reynolds number range of 67.41 to 286.77. The nanofluid is modeled using single and two phase approach. Three different existing Brownian motion velocities are applied in comparing the generality of the equation for a wide parametric condition. Deviation in between the Brownian motion velocity is identified to be due to the different means of mean free path and constant value used in diffusion equation.

Keywords: Brownian nanoparticle velocity, heat transfer enhancement, nanofluid, two phase model.

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