Search results for: symplectic geometry

Authors: Yong-Nam Kwon

Abstract:

In the present study, we have designed the hydro-mechanical forming in which AZ31 sheet was drawn to a kind of preform step following gas blow forming for accurate geometry. In order to judge a formability enhancement of AZ31 sheet, model geometry came from a practical automotive part which had quite depth with complicated curvatures, which was proven that a single sheet forming could not gave a successful part. Experimentally, we succeeded to make the model part with accurate dimension. The optimum forming conditions for respective forming steps were considered most important technical features of this hydro-mechanical and would be discussed in details. Also, the effort to avoid detrimental abnormal grain growth was given and discussed for a practical application.

Keywords: hydro-mechanical forming, AZ31, abnormal grain growth, model geometry

Procedia PDF Downloads 490

Authors: Mrinal Kanti Bhowmik, Kakali Das Jr., Barin Kumar De, Debotosh Bhattacharjee

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Breast cancer is the most common cancer and a leading cause of death for women in the 35 to 55 age group. Early detection of breast cancer can decrease the mortality rate of breast cancer. Mammography is considered as a ‘Gold Standard’ for breast cancer detection and a very popular modality, presently used for breast cancer screening and detection. The screening of digital mammograms often leads to over diagnosis and a consequence to unnecessary traumatic & painful biopsies. For that reason recent studies involving the use of thermal imaging as a screening technique have generated a growing interest especially in cases where the mammography is limited, as in young patients who have dense breast tissue. Tumor is a significant sign of breast cancer in both mammography and thermography. The tumors are complex in structure and they also exhibit a different statistical and textural features compared to the breast background tissue. Fractal geometry is a geometry which is used to describe this type of complex structure as per their main characteristic, where traditional Euclidean geometry fails. Over the last few years, fractal geometrics have been applied mostly in many medical image (1D, 2D, or 3D) analysis applications. In breast cancer detection using digital mammogram images, also it plays a significant role. Fractal is also used in thermography for early detection of the masses using the thermal texture. This paper presents an overview of the recent aspects and initiatives of fractals in breast cancer detection in both mammography and thermography. The scope of fractal geometry in automatic breast cancer detection using digital mammogram and thermogram images are analysed, which forms a foundation for further study on application of fractal geometry in medical imaging for improving the efficiency of automatic detection.

Keywords: fractal, tumor, thermography, mammography

Procedia PDF Downloads 353

Authors: Laurentiu Moruz, Jens Kitzhofer, Mircea Dinulescu

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The paper aims to extend the knowledge about jet behavior and jet interaction between five plane unventilated jets with large aspect ratio (AR). The distance between the single plane jets is two times the channel height. The experimental investigation applies 2D Particle Image Velocimetry (PIV) and static pressure measurements. Our study focuses on the influence of two different outlet nozzle geometries (triangular shape with 2 x 7.5° and blunt geometry) with respect to variation of Reynolds number from 5500 - 12000. It is shown that the outlet geometry has a major influence on the jet formation in terms of uniformity of velocity profiles downstream of the sudden expansion. Furthermore, we describe characteristic regions like converging region, merging region and combined region. The triangular outlet geometry generates most uniform velocity distributions in comparison to a blunt outlet nozzle geometry. The blunt outlet geometry shows an unstable behavior where the jets tend to attach to one side of the walls (ceiling) generating a large recirculation region on the opposite side. Static pressure measurements confirm the observation and indicate that the recirculation region is connected to larger pressure drop.

Keywords: 2D particle image velocimetry, parallel jet interaction, pressure drop, sudden expansion

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Authors: Man Singh Meena

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Structural engineers are facing different kind of challenges due to innovative & bold ideas of architects who are trying to design every structure with uniqueness. In RCC frame structures different geometry of columns can be used in design and rectangular columns can be placed with different type orientation. The analysis is design of structures can also be carried out by different type of software available i.e., STAAD Pro, ETABS and TEKLA. In recent times high-rise building modeling & analysis is done by ETABS due to its certain features which are superior to other software. The case study in this paper mainly emphasizes on structural behavior of high rise building for different column shape configurations like Circular, Square, Rectangular and Rectangular with 90-degree Rotation and rectangular shape plan. In all these column shapes the areas of columns are kept same to study the effect on design of concrete area is same. Modelling of 20-storeys R.C.C. framed building is done on the ETABS software for analysis. Post analysis of the structure, maximum bending moments, shear forces and maximum longitudinal reinforcement are computed and compared for three different story structures to identify the effectiveness of geometry of column.

Keywords: high-rise building, column geometry, building modelling, ETABS analysis, building design, structural analysis, structural optimization

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Authors: Cheng-Chi Yu, Yu-Shiue Wang, Kei-Lin Kuo

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Active Independent Front Steering system is a steering system which can according to vehicle driving situation adjusts the relation of steering angle between inner wheel and outer wheel. In low-speed cornering, AIFS sets the steering angles of inner and outer wheel into Ackerman steering geometry to make vehicle has less cornering radius. Besides, AIFS changes the steering geometry to parallel or even anti-Ackerman steering geometry to keep vehicle stability in high-speed cornering. Therefore, based on the analysis of the vehicle steering behavior from different steering geometries, this study develops a new screw type of active independent front steering system to make vehicles best cornering performance at any speeds. The screw type of active independent front steering system keeps the pinion and separates the rack into main rack and second rack. Two racks connect by a screw. Extra screw rotated motion powered by assistant motor through coupler makes second rack move relative to main rack, which can adjust both steering ratio and steering geometry. First of all, this study distinguishes the steering geometry by using Ackerman percentage and utilizes the software of ADAMS/Car to construct diverse steering geometry models. The different steering geometries are compared at low-speed and high-speed cornering, and then control strategies of the active independent front steering systems could be formulated. Secondly, this study applies closed loop equation to analyze tire steering angles and carries out optimization calculations to make the steering geometry from traditional rack and pinion steering system near to Ackerman steering geometry. Steering characteristics of the optimum steering mechanism and motion characteristics of vehicle installed the steering mechanism are verified by ADAMS/Car models of front suspension and full vehicle respectively. By adding dual auxiliary rack and dual motor to the optimum steering mechanism, the active independent front steering system could be developed to achieve the functions of variable steering ratio and variable steering geometry. At last, this study uses ADAMS/Car and Matlab/Simulink to co-simulate the cornering motion of vehicles confirms the vehicle installed the Active Independent Front Steering (AIFS) system has better handling performance than that with Active Independent Steering (AFS) system or with Electric Power Steering (EPS) system. At low-speed cornering, the vehicles with AIFS system and with AFS system have better maneuverability, less cornering radius, than the traditional vehicle with EPS system because that AIFS and AFS systems both provide function of variable steering ratio. However, there is a slight penalty in the motor(s) power consumption. In addition, because of the capability of variable steering geometry, the vehicle with AIFS system has better high-speed cornering stability, trajectory keeping, and even less motor(s) power consumption than that with EPS system and also with AFS system.

Keywords: active front steering system, active independent front steering system, steering geometry, steering ratio

Procedia PDF Downloads 151

Authors: Paffrath Meinhard, Zhou Yayun, Guo Yiqing, Ertl Harald

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Winding geometry design is an important part of power transformer electrical design. Conventionally, the winding geometry is designed manually, which is a time-consuming job because it involves many iteration steps in order to meet all cost, manufacturing and electrical requirements. Here a method is presented which automatically generates the winding geometry for given user parameters and allows the user to interactively set and change parameters. To achieve this goal, the winding problem is transferred to a mixed integer nonlinear optimization problem. The relevant geometrical design parameters are defined as optimization variables. The cost and other requirements are modeled as constraints. For the solution, a stochastic ant colony optimization algorithm is applied. It is well-known, that an optimizer can get stuck in a local minimum. For the winding problem, we present efficient strategies to come out of local minima, furthermore a reduced variable search range helps to accelerate the solution process. Numerical examples show that the optimization result is delivered within seconds such that the user can interactively change the variable search area and constraints to improve the design.

Keywords: ant colony optimization, mixed integer nonlinear programming, power transformer, winding design

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Authors: Tokuei Sako

Abstract:

Laser-induced current in a quasi-one-dimensional nanostructure has been studied by a model of a few electrons confined in a 1D electrostatic potential coupled to electrodes at both ends and subjected to a pulsed laser field. The time-propagation of the one- and two-electron wave packets has been calculated by integrating the time-dependent Schrödinger equation directly by the symplectic integrator method with uniform Fourier grid. The temporal behavior of the resultant light-induced current in the studied systems has been discussed with respect to the lifetime of the quasi-bound states formed when the static bias voltage is applied.

Keywords: pulsed laser field, nanowire, electron wave packet, quantum dots, time-dependent Schrödinger equation

Procedia PDF Downloads 325

Authors: R. K. Dubey

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Bianchi type cosmological models have been studied on the basis of Lyra’s geometry. Exact solution has been obtained by considering a time dependent displacement field for constant deceleration parameter and varying cosmological term of the universe. The physical behavior of the different models has been examined for different cases.

Keywords: Bianchi type-I cosmological model, variable gravitational coupling, cosmological constant term, Lyra's model

Procedia PDF Downloads 325

Authors: Ahmet Calik

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In present study, the effect of adherend geometry on the tensile strength of adhesively single lap aluminum structures joint, bonded was numerically studied using by three dimensional finite element model. Six joint model were investigated. Analyses were performed in ANSYS commercial software. The results shows that the adherends shape has the highest effect on peel and shear stresses.

Keywords: adhesive, adherend, single lap joints, finite element

Procedia PDF Downloads 264

Authors: Almostafa Abdelaziz, Liang Guozhu, Anwer Elsayed

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The determination of grain geometry is an important and critical step in the design of solid propellant rocket motor. In this study, the design process involved parametric geometry modeling in CAD, MATLAB coding of performance prediction and 2D star grain ignition experiment. The 2D star grain burnback achieved by creating new surface via each web increment and calculating geometrical properties at each step. The 2D star grain is further modified to burn as a tapered 3D star grain. Zero dimensional method used to calculate the internal ballistic performance. Experimental and theoretical results were compared in order to validate the performance prediction of the solid rocket motor. The results show that the usage of 3D grain geometry will decrease the pressure inside the combustion chamber and enhance the volumetric loading ratio.

Keywords: burnback analysis, rocket motor, star grain, three dimensional grains

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Authors: Anahita Aris

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Geometry always plays a key role in natural structures, which can be a source of inspiration for architects and urban designers to create spaces. By understanding formative principles in nature, a variety of options can be provided that lead to freedom of formation. The main purpose of this paper is to analyze the geometrical order found in pomegranate to find formative principles explaining its complex structure. The point is how spherical arils of pomegranate pressed together inside the fruit and filled the space as they expand in the growing process, which made a self-organized system leads to the formation of each of the arils are unique in size, topology and shape. The main challenge of this paper would be using advanced architectural modeling techniques to discover these principles.

Keywords: advanced modeling techniques, architectural modeling, computational design, the geometry of natural formation, geometrical analysis, the natural order of pomegranate, voronoi diagrams

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Authors: Oláh Gál Róbert, Veress Bágyi Ibolya

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The scientific public has relatively little knowledge about the Hungarian János Bolyai, one of the greatest thinkers of all times. Few people know that apart from being the founder of the non-Euclidean geometry he was also interested in sociology, philosophy, epistemology and linguistics. According to the renowned Hungarian psychoanalytic Imre Hermann, who lives in France, János Bolyai was mentally deranged. However, this is incorrect. The present article intends to prove that he was completely sane until the moment of his death.

Keywords: Imre Hermann, insane, János Bolyai, mathematics, non-Euclidean geometry, psyphoanalytic

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Authors: Lida Balilan, Dariush Sattarzadeh, Rana Koorepaz

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In the Ilkhanid era, the mystical school of Tabriz manifested itself as an art school in various aspects, including miniatures, architecture, urban planning and design, simultaneously with the expansion of the many sciences of its time. In this era, mysticism, both in form and in poetry and prose, as well as in works of art reached its peak. Mysticism, as an inner belief and thought, brought the audience to the artistic and aesthetical view using allegorical and symbolic expression of the religion and had a direct impact on the formation of the intellectual and cultural layers of the society. At the same time, Mystic school of Tabriz could create a symbolic and allegorical language to create magnificent works of architecture with the expansion of science in various fields and using various sciences such as mathematics, geometry, science of numbers and by Abjad letters. In this era, geometry is the middle link between mysticism and architecture and it is divided into two categories, including intellectual and sensory geometry and based on its function. Soltaniyeh dome is one of the prominent buildings of the Tabriz school with the shrine land use. In this article, information is collected using a historical-interpretive method and the results are analyzed using an analytical-comparative method. The results of the study suggest that the designers and builders of the Soltaniyeh dome have used shapes, colors, numbers, letters and words in the form of motifs, geometric patterns as well as lines and writings in levels and layers ranging from plans to decorations and arrays for architectural symbolization and encryption to express and transmit mystical ideas.

Keywords: geometry, Tabriz school, mystical thoughts, dome of Soltaniyeh

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Authors: Steven D. P Moore

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A novel method referred to asKýklos(Ky) dimensional geometry is proposed as an entity specific core geometric dimensional measurement system. Ky geometric measures can constructscaled multi-dimensionalmodels using regular and irregular sets in IRn. This entity specific-derived geometric measurement system shares similar fractal methods in which a ‘fractal transformation operator’ is applied to a set S to produce a union of N copies. The Kýklos’ inputs use 1D geometry as a core measure. One-dimensional inputs include the radius interval of a circle/sphere or the semiminor/semimajor axes intervals of an ellipse or spheroid. These geometric inputs have finite values that can be measured by SI distance units. The outputs for each interval are divided and subdivided 1D subcomponents with a union equal to the interval geometry/length. Setting a limit of subdivision iterations creates a finite value for each 1Dsubcomponent. The uniqueness of this method is captured by allowing the simplest 1D inputs to define entity specific subclass geometric core measurements that can also be used to derive length measures. Current methodologies for celestial based measurement of time, as defined within SI units, fits within this methodology, thus combining spatial and temporal features into geometric core measures. The novel Ky method discussed here offers geometric measures to construct scaled multi-dimensional structures, even models. Ky classes proposed for consideration include celestial even subatomic. The application of this offers incredible possibilities, for example, geometric architecture that can represent scaled celestial models that incorporates planets (spheroids) and celestial motion (elliptical orbits).

Keywords: Kyklos, geometry, measurement, celestial, dimension

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Authors: B. Prashantha, S. Anish

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The aim of the present study is to computationally evaluate the hemodynamic factors which affect the formation of atherosclerosis and plaque rupture in the human artery. An increase of atherosclerosis disease in the artery causes geometry changes, which results in hemodynamic changes such as flow separation, reattachment, and adhesion of new cells (chemotactic) in the artery. Hence, geometry plays an important role in the determining the nature of hemodynamic patterns. Influence of stenosis in the non-bifurcating artery, under pulsatile flow condition, has been studied on an idealized geometry. Analysis of flow through symmetric and asymmetric stenosis in the artery revealed the significance of oscillating shear index (OSI), flow separation, low WSS zones and secondary flow patterns on plaque formation. The observed characteristic of flow in the post-stenotic region highlight the importance of plaque eccentricity on the formation of secondary stenosis on the arterial wall.

Keywords: atherosclerotic plaque, oscillatory shear index, stenosis nature, wall shear stress

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Authors: Arkadiusz Mezyk, Wojciech Klein, Mariusz Pawlak, Jacek Gnilka

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The aortic heart valve stents should fulfill many criterions. These criteria have a strong impact on the geometrical shape of the stent. Usually, the final construction of stent is a result of many year experience and knowledge. Depending on patents claims, different stent shapes are produced by different companies. This causes difficulties for biomechanics engineers narrowing the domain of feasible solutions. The paper present optimization method for stent geometry defining by a specific analytical equation based on various mathematical functions. This formula was implemented as APDL script language in ANSYS finite element environment. For the purpose of simulation tests, a few parameters were separated from developed equation. The application of the genetic algorithms allows finding the best solution due to selected objective function. Obtained solution takes into account parameters such as radial force, compression ratio and coefficient of expansion on the transverse axial.

Keywords: aortic stent, optimization process, geometry, finite element method

Procedia PDF Downloads 254

Authors: A. El Hamdouni, J. Zbitou, A. Tajmouati, L. El Abdellaoui, A. Errkik, A. Tribak, M. Latrach

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This paper presents a novel fractal antenna structure proposed for UWB (Ultra – Wideband) applications. The frequency band 3.1-10.6 GHz released by FCC (Federal Communication Commission) as the commercial operation of UWB has been chosen as frequency range for this antenna based on coplanar waveguide (CPW) feed and circular shapes fulfilled according to fractal geometry. The proposed antenna is validated and designed by using an FR4 substrate with overall area of 34 x 43 mm2. The simulated results performed by CST-Microwave Studio and compared by ADS (Advanced Design System) show good matching input impedance with return loss less than -10 dB between 2.9 GHz and 11 GHz.

Keywords: Fractal antenna, Fractal Geometry, CPW Feed, UWB, FCC

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Authors: Reza Abbasi, Ahmad Hamidi Benam

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Shell structures have many geometrical variables that modify some of these parameters to improve the mechanical behavior of the shell. On the other hand, the behavior of such structures depends on their geometry rather than on mass. Optimization techniques are useful in finding the geometrical shape of shell structures to improve mechanical behavior, especially to prevent or reduce bending anchors. The overall objective of this research is to optimize the shape of concrete shells using the thickness and height parameters along the reference curve and the overall shape of this curve. To implement the proposed scheme, the geometry of the structure was formulated using nonlinear curves. Shell optimization was performed under equivalent static loading conditions using the modified bird community algorithm. The results of this optimization show that without disrupting the initial design and with slight changes in the shell geometry, the structural behavior is significantly improved.

Keywords: concrete shells, shape optimization, spinless curves, modified particle community algorithm

Procedia PDF Downloads 196

Authors: K. Geetha Ramesh, A. Ramachandraiah

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In an internal building space, daylight becomes a powerful source of illumination. The challenge therefore, is to develop means of utilizing both direct and diffuse natural light in buildings while maintaining and improving occupant's visual comfort, particularly at greater distances from the windows throwing daylight. The geometrical features of windows in a building have significant effect in providing daylight. The main goal of this research is to develop an innovative window geometry, which will effectively provide the daylight component adequately together with internal reflected component(IRC) and also the external reflected component(ERC), if any. This involves exploration of a light redirecting system using fractal geometry for windows, in order to penetrate and distribute daylight more uniformly to greater depths, minimizing heat gain and glare, and also to reduce building energy use substantially. Of late the creation of fractal geometrical window and the occurrence of daylight illuminance due to such windows is becoming an interesting study. The amount of daylight can change significantly based on the window geometry and sky conditions. This leads to the (i) exploration of various fractal patterns suitable for window designs, and (ii) quantification of the effect of chosen fractal window based on the relationship between the fractal pattern, size, orientation and glazing properties for optimizing daylighting. There are a lot of natural lighting applications able to predict the behaviour of a light in a room through a traditional opening - a regular window. The conventional prediction methodology involves the evaluation of the daylight factor, the internal reflected component and the external reflected component. Having evaluated the daylight illuminance level for a conventional window, the technical performance of a fractal window for an optimal daylighting is to be studied and compared with that of a regular window. The methodologies involved are highlighted in this paper.

Keywords: daylighting, fractal geometry, fractal window, optimization

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Authors: Rizwan Rizwan

Abstract:

Secure Multiparty Computation is an emerging area of research within the cryptographic community, enabling secure collaboration among multiple parties while safeguarding their sensitive data. Secure Multiparty Computation has been extensively studied in the context of plane geometry, its application to complex solid geometry shapes remains relatively unexplored. This research paper aims to bridge this gap by proposing a solution for the secure multiparty computation of intersecting tetrahedra. We present an approach to calculate the volume of intersecting tetrahedra securely while preserving the privacy of the input data provided by each participating party. The proposed solution leverages accepted simulation paradigms to prove the privacy of the computation. We thoroughly analyze the computational and communication complexities of our approach, demonstrating that they closely align with the minimum theoretical complexity for the problems at hand. This optimal nature of our solution ensures efficient and secure collaborative geometric computations.

Keywords: cryptography, secure multiparty computation, solid geometry, protocol, simulation paradigm

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Authors: Pranjali Sharma, Swati Neogi

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Composite pressure vessels are low weight structures mainly used in a variety of applications such as automobiles, aeronautics and chemical engineering. Fiber reinforced polymer (FRP) composite materials offer the simplicity of design and use, high fuel storage capacity, rapid refueling capability, excellent shelf life, minimal infrastructure impact, high safety due to the inherent strength of the pressure vessel, and little to no development risk. Apart from these preliminary merits, the subsidized weight of composite vessels over metallic cylinders act as the biggest asset to the automotive industry, increasing the fuel efficiency. The result is a lightweight, flexible, non-explosive, and non-fragmenting pressure vessel that can be tailor-made to attune with specific applications. The winding pattern of the composite over-wrap is a primary focus while designing a pressure vessel. The critical stresses in the system depend on the thickness, angle and sequence of the composite layers. The composite over-wrap is wound over a plastic liner, whose geometry can be varied for the ease of winding. In the present study, we aim to optimize the FRP vessel geometry that provides an ease in winding and also aids in weight reduction for enhancing the vessel performance. Finite element analysis is used to study the effect of dome geometry, yielding a design with maximum value of burst pressure and least value of vessel weight. The stress and strain analysis of different dome ends along with the cylindrical portion is carried out in ANSYS 19.2. The failure is predicted using different failure theories like Tsai-Wu theory, Tsai-Hill theory and Maximum stress theory. Corresponding to a given winding sequence, the optimum dome geometry is determined for a fixed internal pressure to identify the theoretical value of burst pressure. Finally, this geometry is used to decrease the number of layers to reach the set value of safety in accordance with the available safety standards. This results in decrease in the weight of the composite over-wrap and manufacturing cost of the pressure vessel. An improvement in the overall weight performance of the pressure vessel gives higher fuel efficiency for its use in automobile applications.

Keywords: Compressed Gas Storage, Dome geometry, Theoretical Analysis, Type-4 Composite Pressure Vessel, Improvement in Vessel Weight Performance

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Authors: Gabriel I. Loaiza Ossa, Carlos A. Cadavid Moreno, Juan C. Arango Parra

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It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ= -1/2, as does the family of usual Gaussian distributions. In the present paper, firstly, we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ₁, θ₂; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the inverse q-Gaussian distribution family (q < 3) as the family obtained by replacing the usual exponential function with the Tsallis q-exponential function in the expression for the inverse Gaussian distribution and observe that it supports two possible geometries, the Fisher and the q-Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q-Fisher geometry of the inverse q-Gaussian distribution family, similar to the ones obtained in the case of the inverse Gaussian distribution family.

Keywords: base of changes, information geometry, inverse Gaussian distribution, inverse q-Gaussian distribution, statistical manifolds

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Authors: M.A.Bakry1, *, Aryn T. Shafeek1, +

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In this article, absolute Parallelism geometry is used to study the torsional gravitational field. And discovered the tetrad fields, torsion vector, and torsion scalar of Schwarzschild space. The new solution of the torsional gravitational field is a generalization of Schwarzschild in the context of general relativity. The results are applied to the planetary orbits.

Keywords: absolute parallelism geometry, tetrad fields, torsion vectors, torsion scalar

Procedia PDF Downloads 111

Authors: D. Baratian, A. Cavalli, D. van den Ende, F. Mugele

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The morphology of liquid bridges inside complex geometries is the subject of interest for many years. These efforts try to find stable liquid configuration considering the boundary condition and the physical properties of the system. On the other hand precise manipulation of droplets is highly significant in many microfluidic applications. The liquid configuration in a complex geometry can be switched by means of external stimuli. We show manipulation of droplets in a wedge structure. The profile and position of a drop in a wedge geometry has been calculated analytically assuming negligible contact angle hysteresis. The characteristic length of liquid bridge and its interfacial tension inside the surrounding medium along with the geometrical parameters of the system determine the morphology and equilibrium position of drop in the system. We use electrowetting to modify one the governing parameters to manipulate the droplet. Electrowetting provides the capability to have precise control on the drop position through tuning the voltage and consequently changing the contact angle. This technique is employed to tune drop displacement and control its position inside the wedge. Experiments demonstrate precise drop movement to its predefined position inside the wedge geometry. Experimental results show promising consistency as it is compared to our geometrical model predictions. For such a drop manipulation, appealing applications in microfluidics have been considered.

Keywords: liquid bridges, microfluidics, drop manipulation, wetting, electrowetting, capillarity

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Authors: Michaela Chovancova, Jakub Elcner

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Real bronchial tree is very complicated piping system. Analysis of flow and pressure losses in this system is very difficult. Due to the complex geometry and the very small size in the lower generations is examination by CFD possible only in the central part of bronchial tree. For specify the pressure losses of lower generations is necessary to provide a mathematical equation. Determination of mathematical formulas for calculating the pressure losses in the real lungs is due to its complexity and diversity lengthy and inefficient process. For these calculations is necessary the lungs to slightly simplify (same cross-section over the length of individual generation) or use one of the models of lungs. The simplification could cause deviations from real values. The article compares the values of pressure losses obtained from CFD simulation of air flow in the central part of the real bronchial tree with the values calculated in a slightly simplified real lungs by using a mathematical relationship derived from the Bernoulli equation and continuity equation. Then, evaluate the desirability of using this formula to determine the pressure loss across the bronchial tree.

Keywords: pressure gradient, airways resistance, real geometry of bronchial tree, breathing

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Authors: S. Srednyak

Abstract:

We study a class of functional partial differential equations(FPDEs). This class is suggested by Quantum Field Theory. We derive general properties of solutions to such equations. In particular, we demonstrate that they lead to systems of coupled integral equations with singular kernels. We show that solutions to such hierarchies can be sought among functions with regular singularities at a countable set of subvarieties of the physical space. We also develop a formal analogy of basic constructions of differential geometry on functional manifolds, as this is necessary for in depth study of FPDEs. We also consider the case of linear overdetermined systems of functional differential equations and show that it can be completely solved in terms of formal solutions of a functional equation that is a functional analogy of a system of determined algebraic equations. This development leads us to formally define the functional analogy of algebraic geometry, which we call functional algebraic geometry. We study basic properties of functional algebraic varieties. In particular, we investigate the case of a formally discrete set of solutions. We also define and study functional analogy of discriminants. In the case of fully determined systems such that the defining functionals have regular singularities, we demonstrate that formal solutions can be sought in the class of functions with regular singularities. This case provides a practical way to apply our results to physics problems.

Keywords: functional equations, quantum field theory, holomorphic functions, Yang Mills mass gap problem, quantum chaos

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Authors: H. Loumi-Fergane, A. Belaidi

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The problem of symmetries in field theory has been analyzed using geometric frameworks, such as the multisymplectic models by using in particular the multivector field formalism. In this paper, we expand the vector fields associated to infinitesimal symmetries which give rise to invariant quantities as Noether currents for classical field theories and relativistic mechanic using the multisymplectic geometry where the Poincaré-Cartan form has thus been greatly simplified using the Second Order Partial Differential Equation (SOPDE) for multi-vector fields verifying Euler equations. These symmetries have been classified naturally according to the construction of the fiber bundle used.  In this work, unlike other works using the analytical method, our geometric model has allowed us firstly to distinguish the angular moments of the gauge field obtained during different transformations while these moments are gathered in a single expression and are obtained during a rotation in the Minkowsky space. Secondly, no conditions are imposed on the Lagrangian of the mechanics with respect to its dependence in time and in qⁱ, the currents obtained naturally from the transformations are respectively the energy and the momentum of the system.

Keywords: conservation laws, field theories, multisymplectic geometry, relativistic mechanics

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Authors: Milan Paudel, Fook Fah Yap, Anil K. Bastola

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The difficulties in riding small wheel bicycles and their lesser stability have been perceived for a long time. Although small wheel bicycles are designed using the similar approach and guidelines that have worked well for big wheel bicycles, the performance of the big wheelers and the smaller wheelers are markedly different. Since both the big wheelers and small wheelers have same fundamental geometry, most blame the small wheel for this discrepancy in the performance. This paper reviews existing guidelines for bicycle design, especially the front steering geometry for the bicycle, and provides a systematic and quantitative analysis of different wheel sized bicycles. A validated mathematical model has been used as a tool to assess the dynamic performance of the bicycles in term of their self-stability. The results obtained were found to corroborate the subjective perception of cyclists for small wheel bicycles. The current approach for small wheel bicycle design requires higher speed to be self-stable. However, it was found that increasing the headtube angle and selecting a proper trail could improve the dynamic performance of small wheel bicycles. A range of parameters for front steering geometry has been identified for small wheel bicycles that have comparable stability as big wheel bicycles. Interestingly, most of the identified geometries are found to be beyond the ISO recommended range and seem to counter the current approach of small wheel bicycle design. Therefore, it was successfully shown that the guidelines for big wheelers do not translate directly to small wheelers, but careful selection of the front geometry could make small wheel bicycles as stable as big wheel bicycles.

Keywords: big wheel bicycle, design approach, ISO requirements, small wheel bicycle, stability and performance

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Authors: D. S. Nagesh, G. L. Datta

Abstract:

In the field of welding, various studies had been made by some of the previous investigators to predict as well as optimize weld bead geometric descriptors. Modeling of weld bead shape is important for predicting the quality of welds. In most of the cases, design of experiments technique to postulate multiple linear regression equations have been used. Nowadays, Genetic Algorithm (GA) an intelligent information treatment system with the characteristics of treating complex relationships as seen in welding processes used as a tool for inverse mapping/optimization of the process is attempted.

Keywords: smaw, genetic algorithm, bead geometry, optimization/inverse mapping

Procedia PDF Downloads 421

Authors: D. S. Nagesh, G. L. Datta

Abstract:

In the field of welding, various studies had been made by some of the previous investigators to predict as well as optimize weld bead geometric descriptors. Modeling of weld bead shape is important for predicting the quality of welds. In most of the cases design of experiments technique to postulate multiple linear regression equations have been used. Nowadays Genetic Algorithm (GA) an intelligent information treatment system with the characteristics of treating complex relationships as seen in welding processes used as a tool for inverse mapping/optimization of the process is attempted.

Keywords: SMAW, genetic algorithm, bead geometry, optimization/inverse mapping

Procedia PDF Downloads 388