Search results for: Thermal expansion error of grating scale

Authors: G. Vinitha, A. Ramalingam

Abstract:

In view of a possible application in optical data storage devices, diffraction grating efficiency of an organic dye, Acid Fuchsin doped in PMMA matrix was studied under excitation with CW diode pumped Nd: YAG laser at 532 nm. The open aperture Zscan of dye doped polymer displayed saturable absorption and the closed aperture Z-scan of the samples exhibited negative nonlinearity. The diffraction efficiency of the grating is the ratio of the intensity of the first order diffracted power to the incident read beam power. The dye doped polymer films were found to be good media for recording. It is observed that the formation of gratings strongly depend on the concentration of dye in the polymer film, the intensity ratios of the writing beams and the angle between the writing beams. It has been found that efficient writing can be made at an angle of 20o and when the intensity ratio of the writing beams is unity.

Keywords: Diffraction efficiency, Nonlinear Optical material, saturable absorption, Surface-relief-gratings.

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Authors: Anjali Verma, Ram Jiwari, Jitender Kumar

Abstract:

This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.

Keywords: Shallow water wave equation, Exact solutions, (G'/G) expansion method.

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Authors: A. Soria-Salinas, M.-P. Zorzano, J. Martín-Torres, J. Sánchez-García-Casarrubios, J.-L. Pérez-Díaz, A. Vakkada-Ramachandran

Abstract:

The current state-of-the-art methods of mass gauging of Electric Propulsion (EP) propellants in microgravity conditions rely on external measurements that are taken at the surface of the tank. The tanks are operated under a constant thermal duty cycle to store the propellant within a pre-defined temperature and pressure range. We demonstrate using computational fluid dynamics (CFD) simulations that the heat-transfer within the pressurized propellant generates temperature and density anisotropies. This challenges the standard mass gauging methods that rely on the use of time changing skin-temperatures and pressures. We observe that the domes of the tanks are prone to be overheated, and that a long time after the heaters of the thermal cycle are switched off, the system reaches a quasi-equilibrium state with a more uniform density. We propose a new gauging method, which we call the Improved PVT method, based on universal physics and thermodynamics principles, existing TRL-9 technology and telemetry data. This method only uses as inputs the temperature and pressure readings of sensors externally attached to the tank. These sensors can operate during the nominal thermal duty cycle. The improved PVT method shows little sensitivity to the pressure sensor drifts which are critical towards the end-of-life of the missions, as well as little sensitivity to systematic temperature errors. The retrieval method has been validated experimentally with CO₂ in gas and fluid state in a chamber that operates up to 82 bar within a nominal thermal cycle of 38 °C to 42 °C. The mass gauging error is shown to be lower than 1% the mass at the beginning of life, assuming an initial tank load at 100 bar. In particular, for a pressure of about 70 bar, just below the critical pressure of CO₂, the error of the mass gauging in gas phase goes down to 0.1% and for 77 bar, just above the critical point, the error of the mass gauging of the liquid phase is 0.6% of initial tank load. This gauging method improves by a factor of 8 the accuracy of the standard PVT retrievals using look-up tables with tabulated data from the National Institute of Standards and Technology.

Keywords: Electric propulsion, mass gauging, propellant, PVT, xenon.

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Authors: S. Jalilzadeh, A. Kimiyaghalam, A. Ashouri

Abstract:

This paper presents a mathematical model and a methodology to analyze the losses in transmission expansion planning (TEP) under uncertainty in demand. The methodology is based on discrete particle swarm optimization (DPSO). DPSO is a useful and powerful stochastic evolutionary algorithm to solve the large-scale, discrete and nonlinear optimization problems like TEP. The effectiveness of the proposed idea is tested on an actual transmission network of the Azerbaijan regional electric company, Iran. The simulation results show that considering the losses even for transmission expansion planning of a network with low load growth is caused that operational costs decreases considerably and the network satisfies the requirement of delivering electric power more reliable to load centers.

Keywords: DPSO, TEP, Uncertainty

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Authors: Hadi Taghvafard

Abstract:

We present a new quadrature rule based on the spline interpolation along with the error analysis. Moreover, some error estimates for the reminder when the integrand is either a Lipschitzian function, a function of bounded variation or a function whose derivative belongs to Lp are given. We also give some examples to show that, practically, the spline rule is better than the trapezoidal rule.

Keywords: Quadrature, Spline interpolation, Trapezoidal rule, Numericalintegration, Error analysis.

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Authors: M. Ali, K. Alam, E. Ohioma

Abstract:

This paper presents a numerical investigation on the behavior of fiber reinforced polymer composite tubes (FRP) under thermomechanical coupled loading using finite element software ABAQUS and a special add-on subroutine, CZone. Three cases were explored; pure mechanical loading, pure thermal loading, and coupled thermomechanical loading. The failure index (Tsai-Wu) under all three loading cases was assessed for all plies in the tube walls. The simulation results under pure mechanical loading showed that composite tube failed at a tensile load of 3.1 kN. However, with the superposition of thermal load on mechanical load on the composite tube, the failure index of the previously failed plies in tube walls reduced significantly causing the tube to fail at 6 kN. This showed 93% improvement in the load carrying capacity of the composite tube in present study. The increase in load carrying capacity was attributed to the stress effects of the coefficients of thermal expansion (CTE) on the laminate as well as the inter-lamina stresses induced due to the composite stack layup.

Keywords: Thermal, mechanical, composites, square tubes.

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Authors: Mihai Brânzei, Ioan Plotog, Ion Pencea

Abstract:

The Pads have unique values of thermophysical properties (THP) having important contribution over heat transfer into the PCB structure. Materials with high thermal diffusivity (TD) rapidly adjust their temperature to that of their surroundings, because the HT is quick in compare to their volumetric heat capacity (VHC). In the paper is presenting the diffusivity tests (ASTM E1461 flash method) for PCBs with different core materials. In the experiments, the multilayer structure of PCBA was taken into consideration, an equivalent property referring to each of experimental structure be practically measured. Concerning to entire structure, the THP emphasize the major contribution of substrate in establishing of reflow soldering process (RSP) heat transfer necessities. This conclusion offer practical solution for heat transfer time constant calculation as function of thickness and substrate material diffusivity with an acceptable error estimation.

Keywords: heat transfer time constant, packaging, reflowsoldering process, thermal diffusivity.

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Authors: Simon Brown

Abstract:

Glomerular filtration rate (GFR) is a measure of kidney function. It is usually estimated from serum concentrations of cystatin C or creatinine although there has been considerable debate in the literature about (i) the best equation to use and (ii) the variability in the correlation between the concentrations of creatinine and cystatin C. The equations for GFR can be written in a general form and from these I calculate the error of the GFR estimates associated with analyte measurement error. These show that the error of the GFR estimates is such that it is not possible to distinguish between the equations over much of the concentration range of either analyte. The general forms of the equations are also used to derive an expression for the concentration of cystatin C as a function of the concentration of creatinine. This equation shows that these analyte concentrations are not linearly related. Clinical reports of cystatin C and creatinine concentration are consistent with the expression derived.

Keywords: creatinine, cystatin C, error analysis, glomerularfiltration rate, measurement error.

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Authors: Phornpat Chewasoonthorn, Surat Kwanmuang

Abstract:

Indoor positioning technologies have been evolved rapidly. They augment the Global Positioning System (GPS) which requires line-of-sight to the sky to track the location of people or objects. In this study, we developed an error correction method for an indoor real-time location system (RTLS) based on an ultra-wideband (UWB) sensor from Decawave. Multiple stationary nodes (anchor) were installed throughout the workspace. The distance between stationary and moving nodes (tag) can be measured using a two-way-ranging (TWR) scheme. The result has shown that the uncorrected ranging error from the sensor system can be as large as 1 m. To reduce ranging error and thus increase positioning accuracy, we present an online correction algorithm using the Kalman filter. The results from experiments have shown that the system can reduce ranging error down to 5 cm.

Keywords: Indoor positioning, ultra-wideband, error correction, Kalman filter.

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Authors: M. N. Eshtiaghi, N. Yoswathana

Abstract:

The aim of this study was to extract sugar from sugarcane using high electric field pulse (HELP) as a non-thermal cell permeabilization method. The result of this study showed that it is possible to permeablize sugar cane cells using HELP at very short times (less than 10 sec.) and at room temperature. Increasing the field strength (from 0.5kV/cm to 2kV/cm) and pulse number (1 to 12) led to increasing the permeabilization of sugar cane cells. The energy consumption during HELP treatment of sugar cane (2.4 kJ/kg) was about 100 times less compared to thermal cell disintegration at 85 <=C (about 271.7 kJ/kg). In addition, it was possible to extract sugar cane at a moderate temperature (45 <=C) using HELP pretreatment. With combination of HELP pretreatment followed by thermal extraction at 75 <=C, extraction resulted in up to 3% more sugar (on the basis of total extractable sugar) compared to samples without HELP pretreatment.

Keywords: Cell permeabilization, High electric field pulses, Non-thermal processing, Sugar cane extraction.

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Authors: Chiharu Okuma, Naoki Yamamoto, Jun Murakami

Abstract:

As a method of expanding a higher-order tensor data to tensor products of vectors we have proposed the Third-order Orthogonal Tensor Product Expansion (3OTPE) that did similar expansion as Higher-Order Singular Value Decomposition (HOSVD). In this paper we provide a computation algorithm to improve our previous method, in which SVD is applied to the matrix that constituted by the contraction of original tensor data and one of the expansion vector obtained. The residual of the improved method is smaller than the previous method, truncating the expanding tensor products to the same number of terms. Moreover, the residual is smaller than HOSVD when applying to color image data. It is able to be confirmed that the computing time of improved method is the same as the previous method and considerably better than HOSVD.

Keywords: Singular value decomposition (SVD), higher-orderSVD (HOSVD), outer product expansion, power method.

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Authors: Azmi Zakaria, Reza Zamiri, Parisa Vaziri, Elias Saion, M. Shahril Husin

Abstract:

In this study we applied thermal lens (TL) technique to study the effect of size on thermal diffusivity of cadmium sulphide (CdS) nanofluid prepared by using γ-radiation method containing particles with different sizes. In TL experimental set up a diode laser of wavelength 514 nm and intensity stabilized He-Ne laser were used as the excitation source and the probe beam respectively, respectively. The experimental results showed that the thermal diffusivity value of CdS nanofluid increases when the of particle size increased.

Keywords: Thermal diffusivity, nanofluids, thermal lens

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Authors: M. S. Kang, D. H. Kim, J. S. Yoon, B. S. Park, J. K. Lee

Abstract:

Since straightness error of linear motor stage is hardly dependent upon machining accuracy and assembling accuracy, there is limit on maximum realizable accuracy. To cope with this limitation, this paper proposed a servo system to compensate straightness error of a linear motor stage. The servo system is mounted on the slider of the linear motor stage and moves in the direction of the straightness error so as to compensate the error. From position dependency and repeatability of the straightness error of the slider, a feedforward compensation control is applied to the platform servo control. In the consideration of required fine positioning accuracy, a platform driven by an electro-magnetic actuator is suggested and a sliding mode control was applied. The effectiveness of the sliding mode control was verified along with some experimental results.

Keywords: Linear Motor Stage, Straightness Error, Friction, Sliding Mode Control.

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Authors: Bin Su

Abstract:

Auckland has a temperate climate with comfortable warm, dry summers and mild, wet winters. An Auckland school normally does not need air conditioning for cooling during the summer and only needs heating during the winter. The Auckland school building thermal design should more focus on winter thermal performance and indoor thermal comfort for energy efficiency. This field study of testing indoor and outdoor air temperatures, relative humidity and indoor surface temperatures of three classrooms with different envelopes were carried out in the Avondale College during the winter months in 2013. According to the field study data, this study is to compare and evaluate winter thermal performance and indoor thermal conditions of school buildings with different envelopes.

Keywords: Building envelope, Building mass effect, Building thermal comfort, Building thermal performance, School building.

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Authors: M. Capocelli, A. Caputo, M. De Falco, D. Mazzei, V. Piemonte

Abstract:

This paper presents the experimental results and the related modeling of a thermal energy storage (TES) facility, ideated and realized by ENEA and realizing the thermocline with an innovative geometry. Firstly, the thermal energy exchange model of an equivalent shell & tube heat exchanger is described and tested to reproduce the performance of the spiral exchanger installed in the TES. Through the regression of the experimental data, a first-order thermocline model was also validated to provide an analytical function of the thermocline, useful for the performance evaluation and the comparison with other systems and implementation in simulations of integrated systems (e.g. power plants). The experimental data obtained from the plant start-up and the short-cut modeling of the system can be useful for the process analysis, for the scale-up of the thermal storage system and to investigate the feasibility of its implementation in actual case-studies.

Keywords: Thermocline, modelling, heat exchange, spiral, shell, tube.

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Authors: Jung-Ho Moon, Tae Kwon Ha

Abstract:

Continually increasing working temperature and growing need for greater efficiency and reliability of automotive exhaust require systematic investigation into the thermal fatigue properties especially of high temperature stainless steels. In this study, thermal fatigue properties of 300 series austenitic stainless steels have been evaluated in the temperature ranges of 200-800^oC and 200-900^oC. Systematic methods for control of temperatures within the predetermined range and measurement of load applied to specimens as a function of temperature during thermal cycles have been established. Thermal fatigue tests were conducted under fully constrained condition, where both ends of specimens were completely fixed. Load relaxation behavior at the temperatures of thermal cycle was closely related with the thermal fatigue property.

Keywords: Austenitic stainless steel, automotive exhaust, thermal fatigue, microstructure, load relaxation.

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Authors: Mohammad Taghi Darvishi, Samad Kheybari

Abstract:

In this paper, the dynamics of a system of two van der Pol oscillators with delayed position and velocity is studied. We provide an approximate solution for this system using parameterexpansion method. Also, we obtain approximate values for frequencies of the system. The parameter-expansion method is more efficient than the perturbation method for this system because the method is independent of perturbation parameter assumption.

Keywords: Parameter-expansion method, coupled van der pol oscillator, time-delay system.

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Authors: Juan P. Novoa, Mario A. Rios

Abstract:

This paper presents a transmission planning methodology that considers the conversion of HVAC transmission lines to HVDC as an alternative of expansion of power systems, as a consequence of restrictions for the construction of new lines. The transmission expansion planning problem formulates an optimization problem that minimizes the total cost that includes the investment cost to convert lines from HVAC to HVDC and possible required reinforcements of the power system prior to the conversion. The costs analysis assesses the impact of the conversion on the reliability because transmission lines are out of service during the conversion work. The presented methodology is applied to a test system considering a planning a horizon of 10 years.

Keywords: Cost optimization, energy non supplied, HVAC, HVDC, transmission expansion planning.

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Authors: Mazidah Tajjudin, Norhashim Mohd Arshad, Ramli Adnan

Abstract:

Fractional-order controller was proven to perform better than the integer-order controller. However, the absence of a pole at origin produced marginal error in fractional-order control system. This study demonstrated the enhancement of the fractionalorder PI over the integer-order PI in a steam temperature control. The fractional-order controller was cascaded with an error compensator comprised of a very small zero and a pole at origin to produce a zero steady-state error for the closed-loop system. Some modification on the error compensator was suggested for different order fractional integrator that can improve the overall phase margin.

Keywords: Fractional-order PI, Ziegler-Nichols tuning, Oustaloup's Recursive Approximation, steam temperature control.

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Authors: A. Badalyan, R. Hovsepyan, V. Mekhitaryan, P. Mantashyan, R. Drampyan

Abstract:

In this paper we report the technique of optical induction of 2 and 3-dimensional (2D and 3D) photonic lattices in photorefractive materials based on diffraction grating self replication -Talbot effect. 1D and 2D different rotational symmery diffraction masks with the periods of few tens micrometers and 532 nm cw laser beam were used in the experiments to form an intensity modulated light beam profile. A few hundred micrometric scale replications of mask generated intensity structures along the beam propagation axis were observed. Up to 20 high contrast replications were detected for 1D annular mask with 30

Keywords: Diffraction gratings, laser, photonic lattice, Talbot effect.

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Authors: Arafat A. A. Shabaneh

Abstract:

Harsh environments require developed detection by an optical communication system to ensure a high level of security and safety. Fiber Bragg gratings (FBGs) are emerging sensing instruments that respond to variations in strain and temperature by varying wavelengths. In this study, a cascaded uniform FBG is designed as a strain sensor for 6 km length at 1550 nm wavelength with 30 °C temperature by analyzing dynamic strain and wavelength shifts. The FBG is placed in a small segment of an optical fiber that reflects light with a specific wavelength and passes on the remaining wavelengths. Consequently, periodic alteration occurs in the refractive index in the fiber core. The alteration in the modal index of the fiber is produced by strain effects on a Bragg wavelength. When the developed sensor is exposed to the strain (0.01) of the cascaded uniform FBG, the wavelength shifts by 0.0000144383 μm. The sensing accuracy of the developed sensor is 0.0012. Simulation results show the reliability and effectiveness of the strain monitoring sensor for remote sensing application.

Keywords: Remote sensing, cascaded fiber Bragg grating, strain sensor, wavelength shift.

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Authors: Irina Pyrlina

Abstract:

This article presents the results of a study conducted to identify operational risks for information systems (IS) with service-oriented architecture (SOA). Analysis of current approaches to risk and system error classifications revealed that the system error classes were never used for SOA risk estimation. Additionally system error classes are not normallyexperimentally supported with realenterprise error data. Through the study several categories of various existing error classifications systems are applied and three new error categories with sub-categories are identified. As a part of operational risks a new error classification scheme is proposed for SOA applications. It is based on errors of real information systems which are service providers for application with service-oriented architecture. The proposed classification approach has been used to classify SOA system errors for two different enterprises (oil and gas industry, metal and mining industry). In addition we have conducted a research to identify possible losses from operational risks.

Keywords: Enterprise architecture, Error classification, Oil&Gas and Metal&Mining industries, Operational risks, Serviceoriented architecture

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Authors: M. Abdou, M. K. Khalil

Abstract:

The heat pipe is a thermal device which allows efficient transport of thermal energy. The experimental work of this research was split into two phases; phase 1 is the development of the facilities, material and test rig preparation. Phase 2 is the actual experiments and measurements of the thermal control mockup inside the modified vacuum chamber (MVC). Due to limited funds, the development on the thermal control subsystem was delayed and the experimental facilities such as suitable thermal vacuum chamber with space standard specifications were not available from the beginning of the research and had to be procured over a period of time. In all, these delays extended the project by one and a half year. Thermal control subsystem needs a special facility and equipment to be tested. The available vacuum chamber is not suitable for the thermal tests. Consequently, the modification of the chamber was a must. A vacuum chamber has been modified to be used as a Thermal Vaccum Chamber (TVC). A MVC is a vacuum chamber modified by using a stainless mirror box with perfect reflectability and the infrared lamp connected with the voltage regulator to vary the lamp intensity as it will be illustrated through the paper.

Keywords: Heat pipe, thermal control, thermal vacuum chamber, satellite.

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Authors: Abdelghani Dendouga, Nour-Eddine Bouguechal, Souhil Kouda, Samir Barra

Abstract:

A behavioral model of a second order switchedcapacitor Sigma-Delta modulator is presented. The purpose of this work is the presentation of a behavioral model of a second order switched capacitor ΣΔ modulator considering (Error due to Clock Jitter, Thermal noise Amplifier Noise, Amplifier Slew-Rate, Non linearity of amplifiers, Gain error, Charge Injection, Clock Feedthrough, and Nonlinear on-resistance). A comparison between the use of MOS switches and the use transmission gate switches use is analyzed.

Keywords: Charge injection, clock feed through, Sigma Deltamodulators, Sigma Delta non-idealities, switched capacitor.

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Authors: Lingjiang Huang, Fangfang Liu

Abstract:

Vernacular building is considered as sustainable in energy consumption and environment and its thermal performance is more and more concerned by researchers. This paper investigates the thermal property of the vernacular building in Lhasa by theoretical analysis on the aspects of building form, envelope and materials etc. The values of thermal resistance and thermal capacity of the envelope are calculated and compared with the current China building code and modern building case. And it is concluded that Lhasa vernacular building meets the current China building code of thermal standards and have better performance in some aspects, which is achieved by various passive means with close response to local climate conditions.

Keywords: Climate, Vernacular Building, Thermal Property, Passive Means

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Authors: J. Zach, J. Hroudova, J. Brozovsky

Abstract:

Thermal insulation materials based on natural fibers represent a very promising area of materials based on natural easy renewable row sources. These materials may be in terms of the properties of most competing synthetic insulations, but show somewhat higher moisture sensitivity and thermal insulation properties are strongly influenced by the density and orientation of fibers. The paper described the problem of hygrothermal behavior of thermal insulation materials based on natural plant and animal fibers. This is especially the dependence of the thermal properties of these materials on the type of fiber, bulk density, temperature, moisture and the fiber orientation.

Keywords: Thermal insulating materials, hemp fibers, sheep wool fibers, thermal conductivity, moisture.

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Authors: Nuha Omran Abokhdair, Azizah Bt Abdul Manaf

Abstract:

Reversible watermarking is a special branch of image watermarking, that is able to recover the original image after extracting the watermark from the image. In this paper, an adaptive prediction-based reversible watermarking scheme is presented, in order to increase the payload capacity of MRI medical images. The scheme divides the image into two parts, Region of Interest (ROI) and Region of Non-Interest (RONI). Two bits are embedded in each embeddable pixel of RONI and one bit is embedded in each embeddable pixel of ROI. The experimental results demonstrate that the proposed scheme is able to achieve high embedding capacity. This is mainly caused by two reasons. First, the pixels that were excluded from data embedding due to overflow/underflow are used for data embedding. Second, large location map that need to be added to watermark data as overhead is eliminated and thus lower data embedding capacity is prevented. Moreover, the scheme provides good visual quality to the watermarked image.

Keywords: Medical image watermarking, reversible watermarking, Difference Expansion, Prediction-Error Expansion.

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Authors: R. Resmi, M. R. Baiju

Abstract:

The thermal damping of a dynamic vibrating micromirror is an important factor affecting the design of MEMS based actuator systems. In the development process of new micromirror systems, assessing the extent of energy loss due to thermal damping accurately and predicting the performance of the system is very essential. In this paper, the depth of the thermal penetration layer at different eigenfrequencies and the temperature variation distributions surrounding a vibrating micromirror is analyzed. The thermal penetration depth corresponds to the thermal boundary layer in which energy is lost which is a measure of the thermal damping is found out. The energy is mainly dissipated in the thermal boundary layer and thickness of the layer is an important parameter. The detailed thermoacoustics is used to model the air domain surrounding the micromirror. The thickness of the boundary layer, temperature variations and thermal power dissipation are analyzed for a Si based torsional mode micromirror. It is found that thermal penetration depth decreases with eigenfrequency and hence operating the micromirror at higher frequencies is essential for reducing thermal damping. The temperature variations and thermal power dissipations at different eigenfrequencies are also analyzed. Both frequency-response and eigenfrequency analyses are done using COMSOL Multiphysics software.

Keywords: Eigen frequency analysis, micromirrors, thermal damping, thermoacoustic interactions.

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Authors: H. Shayeghi, M. Mahdavi, A. Kazemi

Abstract:

Transmission network expansion planning (TNEP) is a basic part of power system planning that determines where, when and how many new transmission lines should be added to the network. Up till now, various methods have been presented to solve the static transmission network expansion planning (STNEP) problem. But in all of these methods, transmission expansion planning considering network adequacy restriction has not been investigated. Thus, in this paper, STNEP problem is being studied considering network adequacy restriction using discrete particle swarm optimization (DPSO) algorithm. The goal of this paper is obtaining a configuration for network expansion with lowest expansion cost and a specific adequacy. The proposed idea has been tested on the Garvers network and compared with the decimal codification genetic algorithm (DCGA). The results show that the network will possess maximum efficiency economically. Also, it is shown that precision and convergence speed of the proposed DPSO based method for the solution of the STNEP problem is more than DCGA approach.

Keywords: DPSO algorithm, Adequacy restriction, STNEP.

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Authors: Bang-Shiuh Chen, Lien-Wen Chen

Abstract:

We have devised a thermal carpet cloak theoretically and implemented in silicon using layered metamaterial. The layered metamaterial is composed of single crystalline silicon and its phononic crystal. The design is based on a coordinate transformation. We demonstrate the result with numerical simulation. Great cloaking performance is achieved as a thermal insulator is well hidden under the thermal carpet cloak. We also show that the thermal carpet cloak can even the temperature on irregular surface. Using thermal carpet cloak to manipulate the heat conduction is effective because of its low complexity.

Keywords: Metamaterial, heat conduction, cloaking, phononic crystal.

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