Search results for: Sierpinski gasket

Authors: Abhilash Sahu, Amit Priyadarshi

Abstract:

In this paper, we will discuss the existence of weak solutions of the Kirchhoff type boundary value problem on the Sierpinski gasket. Where S denotes the Sierpinski gasket in R² and S₀ is the intrinsic boundary of the Sierpinski gasket. M: R → R is a positive function and h: S × R → R is a suitable function which is a part of our main equation. ∆p denotes the p-Laplacian, where p > 1. First of all, we will define a weak solution for our problem and then we will show the existence of at least two solutions for the above problem under suitable conditions. There is no well-known concept of a generalized derivative of a function on a fractal domain. Recently, the notion of differential operators such as the Laplacian and the p-Laplacian on fractal domains has been defined. We recall the result first then we will address the above problem. In view of literature, Laplacian and p-Laplacian equations are studied extensively on regular domains (open connected domains) in contrast to fractal domains. In fractal domains, people have studied Laplacian equations more than p-Laplacian probably because in that case, the corresponding function space is reflexive and many minimax theorems which work for regular domains is applicable there which is not the case for the p-Laplacian. This motivates us to study equations involving p-Laplacian on the Sierpinski gasket. Problems on fractal domains lead to nonlinear models such as reaction-diffusion equations on fractals, problems on elastic fractal media and fluid flow through fractal regions etc. We have studied the above p-Laplacian equations on the Sierpinski gasket using fibering map technique on the Nehari manifold. Many authors have studied the Laplacian and p-Laplacian equations on regular domains using this Nehari manifold technique. In general Euler functional associated with such a problem is Frechet or Gateaux differentiable. So, a critical point becomes a solution to the problem. Also, the function space they consider is reflexive and hence we can extract a weakly convergent subsequence from a bounded sequence. But in our case neither the Euler functional is differentiable nor the function space is known to be reflexive. Overcoming these issues we are still able to prove the existence of at least two solutions of the given equation.

Keywords: Euler functional, p-Laplacian, p-energy, Sierpinski gasket, weak solution

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Authors: Shigeyuki Haruyama, I Made Gatot Karohika, Akinori Sato, Didik Nurhadiyanto, Ken Kaminishi

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Contact width and contact stress are important design parameters for optimizing corrugated metal gasket performance based on elastic and plastic contact stress. In this study, we used a three-layer metal gasket with Al, Cu, Ni as the outer layer, respectively. A finite element method was employed to develop simulation solution. The gasket model was simulated by using two simulation stages which are forming and tightening simulation. The simulation result shows that aluminum with tangent modulus, Ehal = Eal/150 has the highest slope for contact width. The slope of contact width for plastic mode gasket was higher than the elastic mode gasket.

Keywords: contact width, contact stress, layer, metal gasket, corrugated, simulation

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Authors: I Made Gatot Karohika, Shigeyuki Haruyama, Ken Kaminishi

Abstract:

In this study, we proposed a three-layer metal gasket with Al, Cu, and SUS304 as the material, respectively. A finite element method was employed to develop simulation solution and design of experiment (DOE). Taguchi method was used to analysis the effect of each parameter design and predicts optimal design of new 25A-size three layer corrugated metal gasket. The L18 orthogonal array of Taguchi method was applied to design experiment matrix for eight factors with three levels. Based on elastic mode and plastic mode, optimum design gasket is gasket with core metal SUS304, surface layer aluminum, p1 = 4.5 mm, p2 = 4.5 mm, p3 = 4 mm, Tg = 1.2 mm, R = 3.5 mm, h = 0.4 mm and Ts = 0.3 mm.

Keywords: contact width, contact stress, layer, metal gasket, corrugated, simulation

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Authors: I. Made Gatot Karohika, Shigeyuki Haruyama, Ken Kaminishi, Oke Oktavianty, Didik Nurhadiyanto

Abstract:

Contact width and contact stress are important parameters related to the leakage behavior of corrugated metal gasket. In this study, contact width and contact stress of three-layer corrugated metal gasket are investigated due to the modulus of elasticity and thickness of surface layer for 2 type gasket (0-MPa and 400-MPa mode). A finite element method was employed to develop simulation solution to analysis the effect of each parameter. The result indicated that lowering the modulus of elasticity ratio of surface layer will result in better contact width but the average contact stresses are smaller. When the modulus of elasticity ratio is held constant with thickness ratio increase, its contact width has an increscent trend otherwise the average contact stress has decreased trend.

Keywords: contact width, contact stress, layer, metal gasket, corrugated, simulation

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Authors: Lingge Tan, Hongpeng Xu, Jieun Yang, Maarten Hornikx

Abstract:

Acoustic diffusers are important components in enhancing the quality of room acoustics. This paper provides a type of modular diffuser based on the Sierpinski Triangle of the plane and combines it with fractal theory to expand the effective frequency range. In numerical calculations and full-scale model experiments, the effect of fractal design elements on normal-incidence diffusion coefficients is examined. It is demonstrated the reasonable times of iteration of modules is three, and the coverage density is 58.4% in the design frequency from 125Hz to 4kHz.

Keywords: acoustic diffuser, fractal, Sierpinski-triangle, diffusion coefficient

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Authors: Wajdi Mohamed Ratemi

Abstract:

The very well-known stacked sets of numbers referred to as Pascal’s triangle present the coefficients of the binomial expansion of the form (x+y)n. This paper presents an approach (the Staircase Horizontal Vertical, SHV-method) to the generalization of planar Pascal’s triangle for polynomial expansion of the form (x+y+z+w+r+⋯)n. The presented generalization of Pascal’s triangle is different from other generalizations of Pascal’s triangles given in the literature. The coefficients of the generalized Pascal’s triangles, presented in this work, are generated by inspection, using embedded Pascal’s triangles. The coefficients of I-variables expansion are generated by horizontally laying out the Pascal’s elements of (I-1) variables expansion, in a staircase manner, and multiplying them with the relevant columns of vertically laid out classical Pascal’s elements, hence avoiding factorial calculations for generating the coefficients of the polynomial expansion. Furthermore, the classical Pascal’s triangle has some pattern built into it regarding its odd and even numbers. Such pattern is known as the Sierpinski’s triangle. In this study, a presentation of Sierpinski-like patterns of the generalized Pascal’s triangles is given. Applications related to those coefficients of the binomial expansion (Pascal’s triangle), or polynomial expansion (generalized Pascal’s triangles) can be in areas of combinatorics, and probabilities.

Keywords: pascal’s triangle, generalized pascal’s triangle, polynomial expansion, sierpinski’s triangle, combinatorics, probabilities

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Authors: I. Zahraoui, J. Terhzaz, A. Errkik, El. H. Abdelmounim, A. Tajmouati, L. Abdellaoui, N. Ababssi, M. Latrach

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This paper presents a novel design of a microstrip fractal antenna based on the use of Sierpinski triangle shape, it’s designed and simulated by using FR4 substrate in the operating frequency bands (GPS, WiMAX), the design is a fractal antenna with a modified ground structure. The proposed antenna is simulated and validated by using CST Microwave Studio Software, the simulated results presents good performances in term of radiation pattern and matching input impedance.

Keywords: dual-band antenna, fractal antenna, GPS band, modified ground structure, sierpinski triangle, WiMAX band

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Authors: Pemika Ketsuwan, Pitt Supaphol, Manit Nithitanakul

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A typical used of ethylene methyl acrylate (EMA) gasket is in the manufacture of optical lens, and often, they are deteriorated rapidly due to high temperature during the process. The objective of this project is to improve the thermal stability of the EMA copolymer gasket by preparing EMA with cellulose and silica composites. Hydroxy propyl methyl cellulose (HPMC) and Carboxy methyl cellulose (CMC) were used in preparing of EMA/cellulose composites and fumed silica (SiO2) was used in preparing EMA/silica composites with different amounts of filler (3, 5, 7, 10, 15 wt.%), using a twin screw extruder at 160 °C and the test specimens were prepared by the injection molding machine. The morphology and dispersion of fillers in the EMA matrix were investigated by field emission scanning electron microscopy (FESEM). The thermal stability of the composite was determined by thermal gravimetric analysis (TGA), and differential scanning calorimeter (DSC). Mechanical properties were evaluated by tensile testing. The developed composites were found to enhance thermal and mechanical properties when compared to that of the EMA copolymer alone.

Keywords: ethylene methyl acrylate, HPMC, Silica, Thermal stability

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Authors: Ashwini Shripatwar, Mayur Biyani, Nikhil Rao, Rajendra Bodake, Sachin Sane

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This paper documents the correlation of valve cover sealing, cracking, and warpage Finite Element Modelling with observations on engine test development. The valve cover is a component mounted on engine head with a gasket which provides sealing against oil which flows around camshaft, valves, rockers, and other overhead components. Material nonlinearity and contact nonlinearity characteristics are taken into consideration because the valve cover is made of a composite material having temperature dependent elastic-plastic properties and because the gasket load-deformation curve is also nonlinear. The leakage is observed between the valve cover and the engine head due to the insufficient contact pressure. The crack is observed on the valve cover due to force application at a region with insufficient stiffness and with elevated temperature. The valve cover shrinkage is observed during the disassembly process on hot exhaust side bolt holes after the engine has been running. In this paper, an analytical approach is developed to correlate a Finite Element Model with the observed failures and to address the design issues associated with the failure modes in question by making design changes in the model.

Keywords: cracking issue, gasket sealing analysis, nonlinearity of contact and material, valve cover

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Authors: Sanjeet Kumar Singh, Shanatanu Bhattacharaya

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Design of high- efficiency low, frequency (<1000Hz) soundproof window or wall absorber which is transparent to airflow is presented. Due to the massive rise in human population and modernization, environmental noise has significantly risen globally. Prolonged noise exposure can cause severe physiological and psychological symptoms like nausea, headaches, fatigue, and insomnia. There has been continuous growth in building construction and infrastructure like offices, bus stops, and airports due to urban population. Generally, a ventilated window is used for getting fresh air into the room, but at the same time, unwanted noise comes along. Researchers used traditional approaches like noise barrier mats in front of the window or designed the entire window using sound-absorbing materials. However, this solution is not aesthetically pleasing, and at the same time, it's heavy and not adequate for low-frequency noise shielding. To address this challenge, we design a transparent hexagonal panel based on Sierpiński fractal triangle, which is aesthetically pleasing, demonstrates normal incident sound absorption coefficient more than 0.96 around 700 Hz and transmission loss around 23 dB while maintaining e air circulation through triangular cutout. Next, we present a concept of fabrication of large acoustic panel for large-scale applications, which lead to suppressing the urban noise pollution.

Keywords: acoustic metamaterials, noise, functional materials, ventilated

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Authors: Sanjeet Kumar Singh, Shantanu Bhatacharya

Abstract:

Design of high-efficiency low, frequency (<1000Hz) soundproof window or wall absorber which is transparent to airflow is presented. Due to the massive rise in human population and modernization, environmental noise has significantly risen globally. Prolonged noise exposure can cause severe physiological and psychological symptoms like nausea, headaches, fatigue, and insomnia. There has been continuous growth in building construction and infrastructure like offices, bus stops, and airports due to the urban population. Generally, a ventilated window is used for getting fresh air into the room, but at the same time, unwanted noise comes along. Researchers used traditional approaches like noise barrier mats in front of the window or designed the entire window using sound-absorbing materials. However, this solution is not aesthetically pleasing, and at the same time, it's heavy and not adequate for low-frequency noise shielding. To address this challenge, we design a transparent hexagonal panel based on the Sierpiński fractal triangle, which is aesthetically pleasing and demonstrates a normal incident sound absorption coefficient of more than 0.96 around 700 Hz and transmission loss of around 23 dB while maintaining e air circulation through the triangular cutout. Next, we present a concept of fabrication of large acoustic panels for large-scale applications, which leads to suppressing urban noise pollution.

Keywords: acoustic metamaterials, ventilation, urban noise pollution, noise control

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Authors: K. Hiro, Y. Imai, T. Sasayama

Abstract:

Cavitation under static negative pressure is not revealed well. The Berthelot method to generate such negative pressure can be a means to study cavitation inception. In this study, metal Berthelot tubes built in observation windows are newly developed and are checked whether high static negative pressure is generated or not. Negative pressure in the tube with a pair of a corundum plate and an aluminum gasket increased with temperature cycles. The trend was similar to that as reported before.

Keywords: Berthelot method, cavitation, negative pressure, observation

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Authors: Grzegorz Sierpiński, Ireneusz Celiński, Marcin Staniek

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The article discusses multi modal mobility in contemporary societies as a main planning and organization issue in the functioning of administrative bodies, a problem which really exists in the space of contemporary cities in terms of shaping modern transport systems. The article presents classification of available resources and initiatives undertaken for developing multi modal mobility. Solutions can be divided into three groups of measures–physical measures in the form of changes of the transport network infrastructure, organizational ones (including transport policy) and information measures. The latter ones include in particular direct support for people travelling in the transport network by providing information about ways of using available means of transport. A special measure contributing to this end is a trip planner. The article compares several selected planners. It includes a short description of the Green Travelling Project, which aims at developing a planner supporting environmentally friendly solutions in terms of transport network operation. The article summarizes preliminary findings of the project.

Keywords: mobility, modal split, multimodal trip, multimodal platforms, sustainable transport

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Authors: Ketankumar Gandabhai Patel, Jalpit Balvantkumar Prajapati

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Plate type heat exchangers has many thin plates that are slightly apart and have very large surface areas and fluid flow passages that are good for heat transfer. This can be a more effective heat exchanger than the tube or shell heat exchanger due to advances in brazing and gasket technology that have made this plate exchanger more practical. Plate type heat exchangers are most widely used in food processing industries and dairy industries. Mostly fouling occurs in plate type heat exchanger due to deposits create an insulating layer over the surface of the heat exchanger, that decreases the heat transfer between fluids and increases the pressure drop. The pressure drop increases as a result of the narrowing of the flow area, which increases the gap velocity. Therefore, the thermal performance of the heat exchanger decreases with time, resulting in an undersized heat exchanger and causing the process efficiency to be reduced. Heat exchangers are often over sized by 70 to 80%, of which 30 % to 50% is assigned to fouling. The fouling can be reduced by varying some geometric parameters and flow parameters. Based on the study, a correlation will estimate for Nusselt number as a function of Reynolds number, Prandtl number and chevron angle.

Keywords: heat transfer coefficient, single phase flow, mass flow rate, pressure drop

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Authors: Yoftahe Nigussie

Abstract:

This report presents a final year project pertaining to the design of Fire tube boiler for the purpose of producing saturated steam. The objective of the project is to produce saturated steam for different purpose with a capacity of 2000kg/h at 12bar design pressure by performing a design of a higher performance fire tube boiler that considered the requirements of cost minimization and parameters improvement. This is mostly done in selection of appropriate material for component parts, construction materials and production methods in different steps of analysis. In the analysis process, most of the design parameters are obtained by iterating with related formulas like selection of diameter of tubes with overall heat transfer coefficient optimization, and the other selections are also as like considered. The number of passes is two because of the size and area of the tubes and shell. As the analysis express by using heavy oil fuel no6 with a higher heating value of 44000kJ/kg and lower heating value of 41300kJ/kg and the amount of fuel consumed 140.37kg/hr. and produce 1610kw of heat with efficiency of 85.25%. The flow of the fluid is a cross flow because of its own advantage and the arrangement of the tube in-side the shell is welded with the tube sheet, and the tube sheet is attached with the shell and the end by using a gasket and weld. The design of the shell, using European Standard code section, is as like pressure vessel by considering the weight, including content and the supplementary accessories such as lifting lugs, openings, ends, man hole and supports with detail and assembly drawing.

Keywords: steam generation, external treatment, internal treatment, steam velocity

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