Search results for: Jeremy J. Schmidt
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 43

Search results for: Jeremy J. Schmidt

43 Enhanced Gram-Schmidt Process for Improving the Stability in Signal and Image Processing

Authors: Mario Mastriani, Marcelo Naiouf

Abstract:

The Gram-Schmidt Process (GSP) is used to convert a non-orthogonal basis (a set of linearly independent vectors) into an orthonormal basis (a set of orthogonal, unit-length vectors). The process consists of taking each vector and then subtracting the elements in common with the previous vectors. This paper introduces an Enhanced version of the Gram-Schmidt Process (EGSP) with inverse, which is useful for signal and image processing applications.

Keywords: Digital filters, digital signal and image processing, Gram-Schmidt Process, orthonormalization.

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42 The Ethics of Instream Flows: Science and Policy in Southern Alberta, Canada

Authors: Jeremy J. Schmidt

Abstract:

Securing instream flows for aquatic ecosystems is critical for sustainable water management and the promotion of human and environmental health. Using a case study from the semiarid region of southern Alberta (Canada) this paper considers how the determination of instream flow standards requires judgments with respect to: (1) The relationship between instream flow indicators and assessments of overall environmental health; (2) The indicators used to determine adequate instream flows, and; (3) The assumptions underlying efforts to model instream flows given data constraints. It argues that judgments in each of these areas have an inherently ethical component because instream flows have direct effects on the water(s) available to meet obligations to humans and non-humans. The conclusion expands from the case study to generic issues regarding instream flows, the growing water ethics literature and prospects for linking science to policy.

Keywords: ethics, instream flows, policy, science, watermanagement

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41 Theoretical Appraisal of Satisfactory Decisions: Uncertainty, Evolutionary Ideas and Beliefs, and Satisfactory Time Use

Authors: Okay Gunes

Abstract:

Unsatisfactory experiences due to an information shortage regarding the future pay-offs of actual choices, yield satisficing decision-making. This research will examine, for the first time in the literature, the motivation behind suboptimal decisions due to uncertainty by subjecting Adam Smith’s and Jeremy Bentham’s assumptions about the nature of the actions that lead to satisficing behavior, in order to clarify the theoretical background of a “consumption-based satisfactory time” concept. The contribution of this paper with respect to the existing literature is threefold: firstly, it is showed in this paper that Adam Smith’s uncertainty is related to the problem of the constancy of ideas and not related directly to beliefs. Secondly, possessions, as in Jeremy Bentham’s oeuvre, are assumed to be just as pleasing, as protecting and improving the actual or expected quality of life, so long as they reduce any displeasure due to the undesired outcomes of uncertainty. Finally, each consumption decision incurs its own satisfactory time period, owed to not feeling hungry, being healthy, not having transportation…etc. This reveals that the level of satisfaction is indeed a behavioral phenomenon where its value would depend on the simultaneous satisfaction derived from all activities.

Keywords: Decision-making, idea and belief, satisficing, uncertainty.

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40 Non-Local Behavior of a Mixed-Mode Crack in a Functionally Graded Piezoelectric Medium

Authors: Nidhal Jamia, Sami El-Borgi

Abstract:

In this paper, the problem of a mixed-Mode crack embedded in an infinite medium made of a functionally graded piezoelectric material (FGPM) with crack surfaces subjected to electro-mechanical loadings is investigated. Eringen’s non-local theory of elasticity is adopted to formulate the governing electro-elastic equations. The properties of the piezoelectric material are assumed to vary exponentially along a perpendicular plane to the crack. Using Fourier transform, three integral equations are obtained in which the unknown variables are the jumps of mechanical displacements and electric potentials across the crack surfaces. To solve the integral equations, the unknowns are directly expanded as a series of Jacobi polynomials, and the resulting equations solved using the Schmidt method. In contrast to the classical solutions based on the local theory, it is found that no mechanical stress and electric displacement singularities are present at the crack tips when nonlocal theory is employed to investigate the problem. A direct benefit is the ability to use the calculated maximum stress as a fracture criterion. The primary objective of this study is to investigate the effects of crack length, material gradient parameter describing FGPMs, and lattice parameter on the mechanical stress and electric displacement field near crack tips.

Keywords: Functionally graded piezoelectric material, mixed-mode crack, non-local theory, Schmidt method.

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39 Efficient Supplies to Assembly Areas from Storage Stages

Authors: Matthias Schmidt, Steffen C. Eickemeyer, Prof. Peter Nyhuis

Abstract:

Guaranteeing the availability of the required parts at the scheduled time represents a key logistical challenge. This is especially important when several parts are required together. This article describes a tool that supports the positioning in the area of conflict between low stock costs and a high service level for a consumer.

Keywords: Systems Modeling, Manufacturing Systems, Simulation & Control, logistics and supply chain management

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38 Development of a Performance Measurement System for Forwarders

Authors: K. Schmidt, Z. Miodrag, C. Geiger

Abstract:

Performance Measurement is still a difficult task for forwarding companies. This is caused on the one hand by missing resources and on the other hand by missing tools. The research project “Management Information System for Logistics Service Providers" aims for closing the gap between needed and disposable solutions. Core of the project is the development

Keywords: Forwarder, Logistics, Management Information, Performance Measurement.

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37 Hybrid Knowledge Approach for Determining Health Care Provider Specialty from Patient Diagnoses

Authors: Erin Lynne Plettenberg, Jeremy Vickery

Abstract:

In an access-control situation, the role of a user determines whether a data request is appropriate. This paper combines vetted web mining and logic modeling to build a lightweight system for determining the role of a health care provider based only on their prior authorized requests. The model identifies provider roles with 100% recall from very little data. This shows the value of vetted web mining in AI systems, and suggests the impact of the ICD classification on medical practice.

Keywords: Ontology, logic modeling, electronic medical records, information extraction, vetted web mining.

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36 Development of Bicomponent Fibre to Combat Insects

Authors: M. Bischoff, F. Schmidt, J. Herrmann, J. Mattheß, G. Seide, T. Gries

Abstract:

Crop yields have not increased as dramatically as the demand for food. One method to counteract this is to use pesticides to keep away predators, e.g. several forms of insecticide are available to fight insects. These insecticides and pesticides are both controversial as their application and their residue in the food product can also harm humans. In this study an alternative method to combat insects is studied. A physical insect-killing effect of SiO2 particles is used. The particles are applied on fibres to avoid erosion in the fields, which would occur when applied separately. The development of such SiO2 functionalized PP fibres is shown.

Keywords: Agriculture, environment, insects, protection, silica, textile.

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35 From Hype to Ignorance – A Review of 30 Years of Lean Production

Authors: Stefan Schmidt

Abstract:

Lean production (or lean management respectively) gained popularity in several waves. The last three decades have been filled with numerous attempts to apply these concepts in companies. However, this has only been partially successful. The roots of lean production can be traced back to Toyota-s just-in-time production. This concept, which according to Womack-s, Jones- and Roos- research at MIT was employed by Japanese car manufacturers, became popular under its international names “lean production", “lean-manufacturing" and was termed “Schlanke Produktion" in Germany. This contribution shows a review about lean production in Germany over the last thirty years: development, trial & error and implementation as well.

Keywords: Application, JIT, lean production, review, trial and error.

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34 Dynamic Safety-Stock Calculation

Authors: Julian Becker, Wiebke Hartmann, Sebastian Bertsch, Johannes Nywlt, Matthias Schmidt

Abstract:

In order to ensure a high service level industrial enterprises have to maintain safety-stock that directly influences the economic efficiency at the same time. This paper analyses established mathematical methods to calculate safety-stock. Therefore, the performance measured in stock and service level is appraised and the limits of several methods are depicted. Afterwards, a new dynamic approach is presented to gain an extensive method to calculate safety-stock that also takes the knowledge of future volatility into account.

Keywords: Inventory dimensioning, material requirement planning, safety-stock calculation.

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33 Implementation of Meshless FEM for Engineering Applications

Authors: A. Seidl, Th. Schmidt

Abstract:

Meshless Finite Element Methods, namely element-free Galerkin and point-interpolation method were implemented and tested concerning their applicability to typical engineering problems like electrical fields and structural mechanics. A class-structure was developed which allows a consistent implementation of these methods together with classical FEM in a common framework. Strengths and weaknesses of the methods under investigation are discussed. As a result of this work joint usage of meshless methods together with classical Finite Elements are recommended.

Keywords: Finite Elements, meshless, element-free Galerkin, point-interpolation.

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32 Mass Transfer Modeling in a Packed Bed of Palm Kernels under Supercritical Conditions

Authors: I. Norhuda, A. K. Mohd Omar

Abstract:

Studies on gas solid mass transfer using Supercritical fluid CO2 (SC-CO2) in a packed bed of palm kernels was investigated at operating conditions of temperature 50 °C and 70 °C and pressures ranges from 27.6 MPa, 34.5 MPa, 41.4 MPa and 48.3 MPa. The development of mass transfer models requires knowledge of three properties: the diffusion coefficient of the solute, the viscosity and density of the Supercritical fluids (SCF). Matematical model with respect to the dimensionless number of Sherwood (Sh), Schmidt (Sc) and Reynolds (Re) was developed. It was found that the model developed was found to be in good agreement with the experimental data within the system studied.

Keywords: Mass Transfer, Palm Kernel, Supercritical fluid.

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31 Comparative Finite Element Simulation of Nonlinear Vibrations and Sensor Output Voltage of Smart Piezolaminated Structures

Authors: Ruediger Schmidt, Thang Duy Vu

Abstract:

Two geometrically nonlinear plate theories, based either on first- or third-order transverse shear deformation theory are used for finite element modeling and simulation of the transient response of smart structures incorporating piezoelectric layers. In particular the time histories of nonlinear vibrations and sensor voltage output of a thin beam with a piezoelectric patch bonded to the surface due to an applied step force are studied.

Keywords: Nonlinear vibrations, piezoelectric patches, sensor voltage output, smart structures.

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30 Towards the Design of Gripper Independent of Substrate Surface Structures

Authors: Annika Schmidt, Ausama Hadi Ahmed, Carlo Menon

Abstract:

End effectors for robotic systems are becoming more and more advanced, resulting in a growing variety of gripping tasks. However, most grippers are application specific. This paper presents a gripper that interacts with an object’s surface rather than being dependent on a defined shape or size. For this purpose, ingressive and astrictive features are combined to achieve the desired gripping capabilities. The developed prototype is tested on a variety of surfaces with different hardness and roughness properties. The results show that the gripping mechanism works on all of the tested surfaces. The influence of the material properties on the amount of the supported load is also studied and the efficiency is discussed.

Keywords: Claw, dry adhesion, insects, material properties.

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29 Group Similarity Transformation of a Time Dependent Chemical Convective Process

Authors: M. M. Kassem, A. S. Rashed

Abstract:

The time dependent progress of a chemical reaction over a flat horizontal plate is here considered. The problem is solved through the group similarity transformation method which reduces the number of independent by one and leads to a set of nonlinear ordinary differential equation. The problem shows a singularity at the chemical reaction order n=1 and is analytically solved through the perturbation method. The behavior of the process is then numerically investigated for n≠1 and different Schmidt numbers. Graphical results for the velocity and concentration of chemicals based on the analytical and numerical solutions are presented and discussed.

Keywords: Time dependent, chemical convection, grouptransformation method, perturbation method.

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28 Direct Numerical Simulation of Oxygen Transfer at the Air-Water Interface in a Convective Flow Environment and Comparison to Experiments

Authors: B. Kubrak J. Wissink H. Herlina

Abstract:

Two-dimensional Direct Numerical Simulation (DNS) of high Schmidt number mass transfer in a convective flow environment (Rayleigh-B'enard) is carried out and results are compared to experimental data. A fourth-order accurate WENO-scheme has been used for scalar transport in order to aim for a high accuracy in areas of high concentration gradients. It was found that the typical spatial distance between downward plumes of cold high concentration water and the eddy size are in good agreement with experiments using a combined PIV-LIF technique for simultaneous and spatially synoptic measurements of 2D velocity and concentration fields.

Keywords: Air-Water Interface, DNS, Gas Transfer, LIF.

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27 EMOES: Eye Motion and Ocular Expression Simulator

Authors: Nicoletta Adamo-Villani, Gerardo Beni, Jeremy White

Abstract:

We introduce, a new interactive 3D simulation system of ocular motion and expressions suitable for: (1) character animation applications to game design, film production, HCI (Human Computer Interface), conversational animated agents, and virtual reality; (2) medical applications (ophthalmic neurological and muscular pathologies: research and education); and (3) real time simulation of unconscious cognitive and emotional responses (for use, e.g., in psychological research). The system is comprised of: (1) a physiologically accurate parameterized 3D model of the eyes, eyelids, and eyebrow regions; and (2) a prototype device for realtime control of eye motions and expressions, including unconsciously produced expressions, for application as in (1), (2), and (3) above. The 3D eye simulation system, created using state-of-the-art computer animation technology and 'optimized' for use with an interactive and web deliverable platform, is, to our knowledge, the most advanced/realistic available so far for applications to character animation and medical pedagogy.

Keywords: 3D animation, HCI, medical simulation, ocularmotion and expression.

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26 3D Simulator of Ocular Motion and Expression

Authors: Nicoletta Adamo-Villani, Gerardo Beni, Jeremy White

Abstract:

We introduce a new interactive 3D simulator of ocular motion and expressions suitable for: (1) character animation applications to game design, film production, HCI (Human Computer Interface), conversational animated agents, and virtual reality; (2) medical applications (ophthalmic neurological and muscular pathologies: research and education); and (3) real time simulation of unconscious cognitive and emotional responses (for use, e.g., in psychological research). Using state-of-the-art computer animation technology we have modeled and rigged a physiologically accurate 3D model of the eyes, eyelids, and eyebrow regions and we have 'optimized' it for use with an interactive and web deliverable platform. In addition, we have realized a prototype device for realtime control of eye motions and expressions, including unconsciously produced expressions, for application as in (1), (2), and (3) above. The 3D simulator of eye motion and ocular expression is, to our knowledge, the most advanced/realistic available so far for applications in character animation and medical pedagogy.

Keywords: 3D animation, HCI, medical simulation, ocularmotion and expression.

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25 Optimization Based Obstacle Avoidance

Authors: R. Dariani, S. Schmidt, R. Kasper

Abstract:

Based on a non-linear single track model which describes the dynamics of vehicle, an optimal path planning strategy is developed. Real time optimization is used to generate reference control values to allow leading the vehicle alongside a calculated lane which is optimal for different objectives such as energy consumption, run time, safety or comfort characteristics. Strict mathematic formulation of the autonomous driving allows taking decision on undefined situation such as lane change or obstacle avoidance. Based on position of the vehicle, lane situation and obstacle position, the optimization problem is reformulated in real-time to avoid the obstacle and any car crash.

Keywords: Autonomous driving, Obstacle avoidance, Optimal control, Path planning.

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24 An Investigation on Ultrasonic Pulse Velocity of Hybrid Fiber Reinforced Concretes

Authors: Soner Guler, Demet Yavuz, Refik Burak Taymuş, Fuat Korkut

Abstract:

Because of the easy applying and not costing too much, ultrasonic pulse velocity (UPV) is one of the most used non-destructive techniques to determine concrete characteristics along with impact-echo, Schmidt rebound hammer (SRH) and pulse-echo. This article investigates the relationship between UPV and compressive strength of hybrid fiber reinforced concretes. Water/cement ratio (w/c) was kept at 0.4 for all concrete mixes. Compressive strength of concrete was targeted at 35 MPa. UPV testing and compressive strength tests were carried out at the curing age of 28 days. The UPV of concrete containing steel fibers has been found to be higher than plain concrete for all the testing groups. It is decided that there is not a certain relationship between fiber addition and strength.

Keywords: Ultrasonic pulse velocity, hybrid fiber, compressive strength, fiber.

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23 The System Architecture of the Open European Nephrology Science Centre

Authors: G. Lindemann, D. Schmidt, T. Schrader, M. Beil, T. Schaaf, H.-D. Burkhard

Abstract:

The amount and heterogeneity of data in biomedical research, notably in interdisciplinary research, requires new methods for the collection, presentation and analysis of information. Important data from laboratory experiments as well as patient trials are available but come out of distributed resources. The Charite Medical School in Berlin has established together with the German Research Foundation (DFG) a new information service center for kidney diseases and transplantation (Open European Nephrology Science Centre - OpEN.SC). The system is based on a service-oriented architecture (SOA) with main and auxiliary modules arranged in four layers. To improve the reuse and efficient arrangement of the services the functionalities are described as business processes using the standardised Business Process Execution Language (BPEL).

Keywords: Software development management, Business dataprocessing, Knowledge based systems in medicine

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22 Surface Modification by EUV laser Beam based on Capillary Discharge

Authors: O. Frolov, K. Kolacek, J. Schmidt, J. Straus, V. Prukner, A. Shukurov

Abstract:

Many applications require surface modification and micro-structuring of polymers. For these purposes is mainly used ultraviolet (UV) radiation from excimer lamps or excimer lasers. However, these sources have a decided disadvantage - degrading the polymer deep inside due to relatively big radiation penetration depth which may exceed 100 μm. In contrast, extreme ultraviolet (EUV) radiation is absorbed in a layer approximately 100 nm thick only. In this work, the radiation from a discharge-plasma EUV source (with wavelength 46.9 nm) based on a capillary discharge driver is focused with a spherical Si/Sc multilayer mirror for surface modification of PMMA sample or thin gold layer (thickness about 40 nm). It was found that the focused EUV laser beam is capable by one shot to ablate PMMA or layer of gold, even if the focus is significantly influenced by astigmatism.

Keywords: ablation, capillary discharge, EUV laser, surface modification

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21 Heat and Mass Transfer over an Unsteady Stretching Surface Embedded in a Porous Medium in the Presence of Variable Chemical Reaction

Authors: T. G. Emam

Abstract:

The effect of variable chemical reaction on heat and mass transfer characteristics over unsteady stretching surface embedded in a porus medium is studied. The governing time dependent boundary layer equations are transformed into ordinary differential equations containing chemical reaction parameter, unsteadiness parameter, Prandtl number and Schmidt number. These equations have been transformed into a system of first order differential equations. MATHEMATICA has been used to solve this system after obtaining the missed initial conditions. The velocity gradient, temperature, and concentration profiles are computed and discussed in details for various values of the different parameters.

Keywords: Heat and mass transfer, stretching surface, chemical reaction, porus medium.

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20 Quantum Enhanced Correlation Matrix Memories via States Orthogonalisation

Authors: Mario Mastriani, Marcelo Naiouf

Abstract:

This paper introduces a Quantum Correlation Matrix Memory (QCMM) and Enhanced QCMM (EQCMM), which are useful to work with quantum memories. A version of classical Gram-Schmidt orthogonalisation process in Dirac notation (called Quantum Orthogonalisation Process: QOP) is presented to convert a non-orthonormal quantum basis, i.e., a set of non-orthonormal quantum vectors (called qudits) to an orthonormal quantum basis, i.e., a set of orthonormal quantum qudits. This work shows that it is possible to improve the performance of QCMM thanks QOP algorithm. Besides, the EQCMM algorithm has a lot of additional fields of applications, e.g.: Steganography, as a replacement Hopfield Networks, Bilevel image processing, etc. Finally, it is important to mention that the EQCMM is an extremely easy to implement in any firmware.

Keywords: Quantum Algebra, correlation matrix memory, Dirac notation, orthogonalisation.

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19 Batch-Oriented Setting Time Optimisation in an Aerodynamic Feeding System

Authors: Jan Busch, Maurice Schmidt, Peter Nyhuis

Abstract:

The change of conditions for production companies in high-wage countries is characterized by the globalization of competition and the transition of a supplier´s to a buyer´s market. The companies need to face the challenges of reacting flexibly to these changes. Due to the significant and increasing degree of automation, assembly has become the most expensive production process. Regarding the reduction of production cost, assembly consequently offers a considerable rationalizing potential. Therefore, an aerodynamic feeding system has been developed at the Institute of Production Systems and Logistics (IFA), Leibniz Universitaet Hannover. This system has been enabled to adjust itself by using a genetic algorithm. The longer this genetic algorithm is executed the better is the feeding quality. In this paper, the relation between the system´s setting time and the feeding quality is observed and a function which enables the user to achieve the minimum of the total feeding time is presented.

Keywords: Aerodynamic feeding system, batch size, optimisation, setting time.

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18 An Integrated Planning Framework for Sustainable Tourism: Case Study of Tunisia

Authors: S. Halioui, I. Arikan, M. Schmidt

Abstract:

Tourism sector in Tunisia faces several problems that range from economic challenges to environmental degradation and social instability. These problems have been intensified because of the increased competition in the tourism market, the political instability, financial crises, and recently terrorism problems have aggravated the situation. As a consequence, a new framework that promotes sustainable tourism in the country and increases its competitiveness is urgently needed. Planning for sustainable tourism sector requires the integration of complex interactions between economic, social and environmental aspects. Sustainable tourism principles can be implemented with the help of Strategic Environmental Assessment (SEA) process, which ensures the full integration of economic, social and environmental considerations while planning for the tourism sector in Tunisia. Results of the paper have broad implications for policy makers and tourism professionals.

Keywords: Sustainable tourism, strategic environmental assessment, tourism planning, policy.

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17 Performance Evaluation of an Aboveground LNG Storage Tank Cover using Nondestructive and Destructive Tests

Authors: Sungnam Hong, Sun-Kyu Park, Jieun Jeong, Jinwoong Choi

Abstract:

In this study, a new procedure for inspecting damages on LNG storage tanks was proposed with the use of structural diagnostic techniques: i.e., nondestructive inspection techniques such as macrography, the hammer sounding test, the Schmidt hammer test, and the ultrasonic pulse velocity test, and destructive inspection techniques such as the compressive strength test, the chloride penetration test, and the carbonation test. From the analysis of all the test results, it was concluded that the LNG storage tank cover was in good condition. Such results were also compared with the Korean concrete standard specifications and design values. In addition, the remaining life of the LNG storage tank was estimated by using existing models. Based on the results, an LNG storage tank cover performance evaluation procedure was suggested.

Keywords: Destructive test, LNG storage tank, Nondestructive test, Performance evaluation procedure, Remaining life.

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16 Rating Charts of R-22 Alternatives Flow through Adiabatic Capillary Tubes

Authors: E. Elgendy, J. Schmidt

Abstract:

Drop-in of R-22 alternatives in refrigeration and air conditioning systems requires a redesign of system components to improve system performance and reliability with the alternative refrigerants. The present paper aims at design adiabatic capillary tubes for R-22 alternatives such as R-417A, R-422D and R-438A. A theoretical model has been developed and validated with the available experimental data from literature for R-22 over a wide range of both operating and geometrical parameters. Predicted lengths of adiabatic capillary tube are compared with the lengths of the capillary tube needed under similar experimental conditions and majority of predictions are found to be within 4.4% of the experimental data. Hence, the model has been applied for R-417A, R- 422D and R-438A and capillary tube selection charts and correlations have been computed. Finally a comparison between the selected refrigerants and R-22 has been introduced and the results showed that R-438A is the closest one to R-22.

Keywords: Adiabatic flow, Capillary tube, R-22 alternatives, Rating charts, Modelling.

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15 Compressive Strength Evaluation of Underwater Concrete Structures Integrating the Combination of Rebound Hardness and Ultrasonic Pulse Velocity Methods with Artificial Neural Networks

Authors: Seunghee Park, Junkyeong Kim, Eun-Seok Shin, Sang-Hun Han

Abstract:

In this study, two kinds of nondestructive evaluation  (NDE) techniques (rebound hardness and ultrasonic pulse velocity  methods) are investigated for the effective maintenance of underwater  concrete structures. A new methodology to estimate the underwater  concrete strengths more effectively, named “artificial neural network  (ANN) – based concrete strength estimation with the combination of  rebound hardness and ultrasonic pulse velocity methods” is proposed  and verified throughout a series of experimental works.

 

Keywords: Underwater Concrete, Rebound Hardness, Schmidt hammer, Ultrasonic Pulse Velocity, Ultrasonic Sensor, Artificial Neural Networks, ANN.

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14 A Semi-Implicit Phase Field Model for Droplet Evolution

Authors: M. H. Kazemi, D. Salac

Abstract:

A semi-implicit phase field method for droplet evolution is proposed. Using the phase field Cahn-Hilliard equation, we are able to track the interface in multiphase flow. The idea of a semi-implicit finite difference scheme is reviewed and employed to solve two nonlinear equations, including the Navier-Stokes and the Cahn-Hilliard equations. The use of a semi-implicit method allows us to have larger time steps compared to explicit schemes. The governing equations are coupled and then solved by a GMRES solver (generalized minimal residual method) using modified Gram-Schmidt orthogonalization. To show the validity of the method, we apply the method to the simulation of a rising droplet, a leaky dielectric drop and the coalescence of drops. The numerical solutions to the phase field model match well with existing solutions over a defined range of variables.

Keywords: Coalescence, leaky dielectric, numerical method, phase field, rising droplet, semi-implicit method.

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