Search results for: mathematical equations

Authors: Hamed Khani Arani, Mohammad Shariyat, Armaghan Mohammadian

Abstract:

In the present study, the free vibration of magnetostrictive nano-plate (MsNP) resting on the Pasternak foundation is investigated. Firstly, the modified couple stress (MCS) and nonlocal elasticity theories are compared together and taken into account to consider the small scale effects; in this paper not only two theories are analyzed but also it improves the MCS theory is more accurate than nonlocal elasticity theory in such problems. A feedback control system is utilized to investigate the effects of a magnetic field. First-order shear deformation theory (FSDT), Hamilton’s principle and energy method are utilized in order to drive the equations of motion and these equations are solved by differential quadrature method (DQM) for simply supported boundary conditions. The MsNP undergoes in-plane forces in x and y directions. In this regard, the dimensionless frequency is plotted to study the effects of small scale parameter, magnetic field, aspect ratio, thickness ratio and compression and tension loads. Results indicate that these parameters play a key role on the natural frequency. According to the above results, MsNP can be used in the communications equipment, smart control vibration of nanostructure especially in sensor and actuators such as wireless linear micro motor and smart nano valves in injectors.

Keywords: feedback control system, magnetostrictive nano-plate, modified couple stress theory, nonlocal elasticity theory, vibration analysis

Procedia PDF Downloads 135

Authors: Davide Gotti, Milan Prodanovic, Sergio Pinilla, David Muñoz-Torrero

Abstract:

Since its proposal, the Doyle-Fuller-Newman (DFN) lithium-ion battery model has gained popularity in the electrochemical field. In fact, this model provides the user with theoretical support for designing the lithium-ion battery parameters, such as the material particle or the diffusion coefficient adjustment direction. However, the model is mathematically complex as it is composed of several partial differential equations (PDEs) such as Fick’s law of diffusion, the MacInnes and Ohm’s equations, among other phenomena. Thus, to efficiently use the model in a time-domain simulation environment, the selection of the discretization technique is of a pivotal importance. There are several numerical methods available in the literature that can be used to carry out this task. In this study, a comparison between the explicit Euler, Crank-Nicolson, and Chebyshev discretization methods is proposed. These three methods are compared in terms of accuracy, stability, and computational times. Firstly, the explicit Euler discretization technique is analyzed. This method is straightforward to implement and is computationally fast. In this work, the accuracy of the method and its stability properties are shown for the electrolyte diffusion partial differential equation. Subsequently, the Crank-Nicolson method is considered. It represents a combination of the implicit and explicit Euler methods that has the advantage of being of the second order in time and is intrinsically stable, thus overcoming the disadvantages of the simpler Euler explicit method. As shown in the full paper, the Crank-Nicolson method provides accurate results when applied to the DFN model. Its stability does not depend on the integration time step, thus it is feasible for both short- and long-term tests. This last remark is particularly important as this discretization technique would allow the user to implement parameter estimation and optimization techniques such as system or genetic parameter identification methods using this model. Finally, the Chebyshev discretization technique is implemented in the DFN model. This discretization method features swift convergence properties and, as other spectral methods used to solve differential equations, achieves the same accuracy with a smaller number of discretization nodes. However, as shown in the literature, these methods are not suitable for handling sharp gradients, which are common during the first instants of the charge and discharge phases of the battery. The numerical results obtained and presented in this study aim to provide the guidelines on how to select the adequate discretization technique for the DFN model according to the type of application to be performed, highlighting the pros and cons of the three methods. Specifically, the non-eligibility of the simple Euler method for longterm tests will be presented. Afterwards, the Crank-Nicolson and the Chebyshev discretization methods will be compared in terms of accuracy and computational times under a wide range of battery operating scenarios. These include both long-term simulations for aging tests, and short- and mid-term battery charge/discharge cycles, typically relevant in battery applications like grid primary frequency and inertia control and electrical vehicle breaking and acceleration.

Keywords: Doyle-Fuller-Newman battery model, partial differential equations, discretization, numerical methods

Procedia PDF Downloads 23

Authors: S. K. Ashiquer Rahman

Abstract:

The proper policy handling might not able to attain the target since some of recessions, e.g., pandemic-led crises, the variables shocks of the economics. At the level of this situation, the Central bank implements the monetary policy to choose increase the exogenous expenditure and level of money supply consecutively for booster level economic growth, whether the monetary policy is relatively more effective than fiscal policy in altering real output growth of a country or both stand for relatively effective in the direction of output growth of a country. The dispute with reference to the relationship between the monetary policy and fiscal policy is centered on the inflationary penalty of the shortfall financing by the fiscal authority. The latest variables socks of economics as well as the pandemic-led crises, central banks around the world predicted just about a general dilemma in relation to increase rates to face the or decrease rates to sustain the economic movement. Whether the prices hang about fundamentally unaffected, the aggregate demand has also been hold a significantly negative attitude by the outbreak COVID-19 pandemic. To empirically investigate the effects of economics shocks associated COVID-19 pandemic, the paper considers the effectiveness of the monetary policy and fiscal policy that linked to the adjustment mechanism of different economic variables. To examine the effects of economics shock associated COVID-19 pandemic towards the effectiveness of Monetary Policy and Fiscal Policy in the direction of output growth of a Country, this paper uses the Simultaneous equations model under the estimation of Two-Stage Least Squares (2SLS) and Ordinary Least Squares (OLS) Method.

Keywords: IS-LM framework, pandemic. Economics variables shocks, simultaneous equations model, output growth

Procedia PDF Downloads 95

Authors: Anuruddha Jayasuriya, Thanakorn Pheeraphan

Abstract:

In this paper, a review of different mathematical models which can be used as prediction tools to assess the time to crack reinforced concrete (RC) due to corrosion is investigated. This investigation leads to an experimental study to validate a selected prediction model. Most of these mathematical models depend upon the mechanical behaviors, chemical behaviors, electrochemical behaviors or geometric aspects of the RC members during a corrosion process. The experimental program is designed to verify the accuracy of a well-selected mathematical model from a rigorous literature study. Fundamentally, the experimental program exemplifies both one-dimensional chloride diffusion using RC squared slab elements of 500 mm by 500 mm and two-dimensional chloride diffusion using RC squared column elements of 225 mm by 225 mm by 500 mm. Each set consists of three water-to-cement ratios (w/c); 0.4, 0.5, 0.6 and two cover depths; 25 mm and 50 mm. 12 mm bars are used for column elements and 16 mm bars are used for slab elements. All the samples are subjected to accelerated chloride corrosion in a chloride bath of 5% (w/w) sodium chloride (NaCl) solution. Based on a pre-screening of different models, it is clear that the well-selected mathematical model had included mechanical properties, chemical and electrochemical properties, nature of corrosion whether it is accelerated or natural, and the amount of porous area that rust products can accommodate before exerting expansive pressure on the surrounding concrete. The experimental results have shown that the selected model for both one-dimensional and two-dimensional chloride diffusion had ±20% and ±10% respective accuracies compared to the experimental output. The half-cell potential readings are also used to see the corrosion probability, and experimental results have shown that the mass loss is proportional to the negative half-cell potential readings that are obtained. Additionally, a statistical analysis is carried out in order to determine the most influential factor that affects the time to corrode the reinforcement in the concrete due to chloride diffusion. The factors considered for this analysis are w/c, bar diameter, and cover depth. The analysis is accomplished by using Minitab statistical software, and it showed that cover depth is the significant effect on the time to crack the concrete from chloride induced corrosion than other factors considered. Thus, the time predictions can be illustrated through the selected mathematical model as it covers a wide range of factors affecting the corrosion process, and it can be used to predetermine the durability concern of RC structures that are vulnerable to chloride exposure. And eventually, it is further concluded that cover thickness plays a vital role in durability in terms of chloride diffusion.

Keywords: accelerated corrosion, chloride diffusion, corrosion cracks, passivation layer, reinforcement corrosion

Procedia PDF Downloads 218

Authors: Berhane Tewelday Weldhiwot

Abstract:

This research investigates the pivotal role of modular forms in modern cryptographic systems, particularly focusing on their applications in secure communications and data integrity. Modular forms, which are complex analytic functions with rich arithmetic properties, have gained prominence due to their connections to number theory and algebraic geometry. This study begins by outlining the fundamental concepts of modular forms and their historical development, followed by a detailed examination of their applications in cryptographic protocols such as elliptic curve cryptography and zero-knowledge proofs. By employing techniques from analytic number theory, the research delves into how modular forms can enhance the efficiency and security of cryptographic algorithms. The findings suggest that leveraging modular forms not only improves computational performance but also fortifies security measures against emerging threats in digital communication. This work aims to contribute to the ongoing discourse on integrating advanced mathematical theories into practical applications, ultimately fostering innovation in cryptographic methodologies.

Keywords: modular forms, cryptography, elliptic curves, applications, mathematical theory

Procedia PDF Downloads 16

Authors: Y. S. Shen, B. H. Liao

Abstract:

This study aimed to develop the design equation of a laminar-falling-film-slurry (LFFS) type photoreactor for the treatment of organic wastewaters containing isopropyl alcohol (IPA) by VUV-based advanced oxidation processes (AOPs). The photoreactor design equations were established by combining with the chemical kinetics of the photocatalytic system, light absorption model within the photoreactor, and was used to predict the decomposition of IPA in aqueous solutions in the photoreactors of different geometries at various operating conditions (volumetric flow rate, oxidants, catalysts, solution pH values, UV light intensities, and initial concentration of pollutants) to verify its rationality and feasibility. By the treatment of the LFFS-VUV only process, it was found that the decomposition rates of IPA in aqueous solutions increased with the increase of volumetric flow rate, VUV light intensity, dosages of TiO2 and H2O2. The removal efficiencies of IPA by photooxidation processes were in the order: VUV/H2O2>VUV/TiO2/H2O2>VUV/TiO2>VUV only. In VUV, VUV/H2O2, VUV/TiO2/H2O2 processes, integrating with the reaction kinetic equations of IPA, the mass conservation equation and the linear light source model, the photoreactor design equation can reasonably to predict reaction behaviors of IPA at various operating conditions and to describe the concentration distribution profiles of IPA within photoreactors.The results of this research can be useful basis for the future application of the homogeneous and heterogeneous VUV-based advanced oxidation processes.

Keywords: isopropyl alcohol, photoreactor design, VUV, AOPs

Procedia PDF Downloads 377

Authors: Georgi Vendramin, Aurea Lúcia, Yamamoto, Carlos Itsuo, Souza Melegari, N. Samuel

Abstract:

This article describes the development of a model that uses a method where openings are represented by single glass and double glass. The model is based on a healthy balance equations purely theoretical and empirical data. Simplified equations are derived through a synthesis of the measured data obtained from meteorological stations. The implementation of the model in a design tool integrated buildings is discussed in this article, to better punctuate the requirements of comfort and energy efficiency in architecture and engineering. Sustainability, energy efficiency, and the integration of alternative energy systems and concepts are beginning to be incorporated into designs for new buildings and renovations to existing buildings. Few means have existed to effectively validate the potential performance benefits of the design concepts. It was used a method of degree-days for an assessment of the energy performance of a building showed that the design of the architectural design should always be considered the materials used and the size of the openings. The energy performance was obtained through the model, considering the location of the building Central Park Shopping Mall, in the city of Cascavel - PR. Obtained climatic data of these locations and in a second step, it was obtained the coefficient of total heat loss in the building pre-established so evaluating the thermal comfort and energy performance. This means that the more openings in buildings in Cascavel – PR, installed to the east side, they may be higher because the glass added to the geometry of architectural spaces will cause the environment conserve energy.

Keywords: sustainable design, energy modeling, design validation, degree-days methods

Procedia PDF Downloads 419

Authors: A. S. Gorobtsov, A. S. Polyanina, A. E. Andreev

Abstract:

The movement of points feet of the anthropomorphous robot in space occurs along some stable trajectory of a known form. A large number of modifications to the methods of control of biped robots indicate the fundamental complexity of the problem of stability of the program trajectory and, consequently, the stability of the control for the deviation for this trajectory. Existing gait generators use piecewise interpolation of program trajectories. This leads to jumps in the acceleration at the boundaries of sites. Another interpolation can be realized using differential equations with fractional derivatives. In work, the approach to synthesis of generators of program trajectories is considered. The resulting system of nonlinear differential equations describes a smooth trajectory of movement having rectilinear sites. The method is based on the theory of an asymptotic stability of invariant sets. The stability of such systems in the area of localization of oscillatory processes is investigated. The boundary of the area is a bounded closed surface. In the corresponding subspaces of the oscillatory circuits, the resulting stable limit cycles are curves having rectilinear sites. The solution of the problem is carried out by means of synthesis of a set of the continuous smooth controls with feedback. The necessary geometry of closed trajectories of movement is obtained due to the introduction of high-order nonlinearities in the control of stabilization systems. The offered method was used for the generation of trajectories of movement of point’s feet of the anthropomorphous robot. The synthesis of the robot's program movement was carried out by means of the inverse method.

Keywords: control, limits cycle, robot, stability

Procedia PDF Downloads 331

Authors: Leonardo Juan Ramírez López, Javier Oswaldo Rodriguez Velasquez

Abstract:

We have designed a Holter that measures the heart´s activity for over 24 hours, implemented a prediction methodology, and generate alarms as well as indicators to patients and treating physicians. Various diagnostic advances have been developed in clinical cardiology thanks to Holter implementation; however, their interpretation has largely been conditioned to clinical analysis and measurements adjusted to diverse population characteristics, thus turning it into a subjective examination. This, however, requires vast population studies to be validated that, in turn, have not achieved the ultimate goal: mortality prediction. Given this context, our Insight Research Group developed a mathematical methodology that assesses cardiac dynamics through entropy and probability, creating a numerical and geometrical attractor which allows quantifying the normalcy of chronic and acute disease as well as the evolution between such states, and our Tigum Research Group developed a holter device with 12 channels and advanced computer software. This has been shown in different contexts with 100% sensitivity and specificity results.

Keywords: attractor , cardiac, entropy, holter, mathematical , prediction

Procedia PDF Downloads 169

Authors: H. Asadi, H. Naderan Tahan

Abstract:

The aim of this paper is to investigate the effect of geometrical properties of helical fins in double pipe heat exchangers. On the other hand, the purpose of this project is to derive the hydraulic and thermal design tables and equations of double heat exchangers with helical fins. The numerical modeling is implemented to calculate the considered parameters. Design tables and correlated equations are generated by repeating the parametric numerical procedure for different fin geometries. Friction factor coefficient and Nusselt number are calculated for different amounts of Reynolds, fluid Prantle and fin twist angles for the range of laminar fluid flow in annular tube with helical fins. Results showed that friction factor coefficient and Nusselt number will be increased for higher Reynolds numbers and fins’ twist angles in general. These two parameters follow different patterns in response to Reynolds number increment. Thermal performance factor is defined to analyze these different patterns. Temperature and velocity contours are plotted against twist angle and number of fins to describe the changes in flow patterns in different geometries of twisted finned annulus. Finally twisted finned annulus friction factor coefficient, Nusselt Number and thermal performance factor are correlated by simulating the model in different design points.

Keywords: double pipe heat exchangers, heat exchanger performance, twisted fins, computational fluid dynamics

Procedia PDF Downloads 289

Authors: Krish Jhurani

Abstract:

The research paper presents an in-depth analysis of symmetry properties in linear algebraic systems under the operation of non-canonical scalar multiplication structures, specifically semirings, and near-rings. The objective is to unveil the profound alterations that occur in traditional linear algebraic structures when we replace conventional field multiplication with these non-canonical operations. In the methodology, we first establish the theoretical foundations of non-canonical scalar multiplication, followed by a meticulous investigation into the resulting symmetry properties, focusing on eigenvectors, eigenspaces, and invariant subspaces. The methodology involves a combination of rigorous mathematical proofs and derivations, supplemented by illustrative examples that exhibit these discovered symmetry properties in tangible mathematical scenarios. The core findings uncover unique symmetry attributes. For linear algebraic systems with semiring scalar multiplication, we reveal eigenvectors and eigenvalues. Systems operating under near-ring scalar multiplication disclose unique invariant subspaces. These discoveries drastically broaden the traditional landscape of symmetry properties in linear algebraic systems. With the application of these findings, potential practical implications span across various fields such as physics, coding theory, and cryptography. They could enhance error detection and correction codes, devise more secure cryptographic algorithms, and even influence theoretical physics. This expansion of applicability accentuates the significance of the presented research. The research paper thus contributes to the mathematical community by bringing forth perspectives on linear algebraic systems and their symmetry properties through the lens of non-canonical scalar multiplication, coupled with an exploration of practical applications.

Keywords: eigenspaces, eigenvectors, invariant subspaces, near-rings, non-canonical scalar multiplication, semirings, symmetry properties

Procedia PDF Downloads 123

Authors: Shahbaz G. Hassan

Abstract:

Water quality models are very important to predict the changes in surface water quality for environmental management. The aim of this paper is to give an overview of the water qualities, and to provide directions for selecting models in specific situation. Water quality models include one kind of model based on a mechanistic approach, while other models simulate water quality without considering a mechanism. Mechanistic models can be widely applied and have capabilities for long-time simulation, with highly complexity. Therefore, more spaces are provided to explain the principle and application experience of mechanistic models. Mechanism models have certain assumptions on rivers, lakes and estuaries, which limits the application range of the model, this paper introduces the principles and applications of water quality model based on the above three scenarios. On the other hand, mechanistic models are more easily to compute, and with no limit to the geographical conditions, but they cannot be used with confidence to simulate long term changes. This paper divides the empirical models into two broad categories according to the difference of mathematical algorithm, models based on artificial intelligence and models based on statistical methods.

Keywords: empirical models, mathematical, statistical, water quality

Procedia PDF Downloads 264

Authors: Noury Bakrim

Abstract:

Formalization is indeed a foundational Mathematical Linguistics as demonstrated by the pioneering works. While dialoguing with this frame, we nonetheless propone, in our approach of language as a real object, a mathematical linguistics/biosemiotics defined as a dialectical synthesis between induction and computational deduction. Therefore, relying on the parametric interaction of cycles, rules, and features giving way to a sub-hypothetic biological point of view, we first hypothesize a factorial equation as an explanatory principle within Category Mathematics of the Ergobrain: our computation proposal of Universal Grammar rules per cycle or a scalar determination (multiplying right/left columns of the determinant matrix and right/left columns of the logarithmic matrix) of the transformable matrix for rule addition/deletion and cycles within representational mapping/cycle heredity basing on the factorial example, being the logarithmic exponent or power of rule deletion/addition. It enables us to propone an extension of minimalist merge/label notions to a Language Merge (as a computing principle) within cycle recursion relying on combinatorial mapping of rules hierarchies on external Entax of the Event Sequence. Therefore, to define combinatorial maps as language merge of features and combinatorial hierarchical restrictions (governing, commanding, and other rules), we secondly hypothesize from our results feature/hierarchy exponentiation on graph representation deriving from Gromov's Symbolic Dynamics where combinatorial vertices from Fe are set to combinatorial vertices of Hie and edges from Fe to Hie such as for all combinatorial group, there are restriction maps representing different derivational levels that are subgraphs: the intersection on I defines pullbacks and deletion rules (under restriction maps) then under disjunction edges H such that for the combinatorial map P belonging to Hie exponentiation by intersection there are pullbacks and projections that are equal to restriction maps RM₁ and RM₂. The model will draw on experimental biomathematics as well as structural frames with focus on Amazigh and English (cases from phonology/micro-semantics, Syntax) shift from Structure to event (especially Amazigh formant principle resolving its morphological heterogeneity).

Keywords: rule/cycle addition/deletion, bio-mathematical methodology, general merge calculation, feature exponentiation, combinatorial maps, event sequence

Procedia PDF Downloads 127

Authors: Carolina Payares-Asprino

Abstract:

Dual-phase duplex stainless steel comprised of ferrite and austenite has shown high strength and corrosion resistance in many aggressive environments. Joining duplex alloys is challenging due to several embrittling precipitates and metallurgical changes during the welding process. The welding parameters strongly influence the quality of a weld joint. Therefore, it is necessary to quantify the weld bead’s integral properties as a function of welding parameters, especially when part of the weld bead is removed through a machining process due to aesthetic reasons or to couple the elements in the in-service structure. The present study uses the existing stress-strain model to predict the stress-strain curves for duplex stainless-steel welds under different welding conditions. Having mathematical expressions that predict the shape of the stress-strain curve is advantageous since it reduces the experimental work in obtaining the tensile test. In analysis and design, such stress-strain modeling simplifies the time of operations by being integrated into calculation tools, such as the finite element program codes. The elastic zone and the plastic zone of the curve can be defined by specific parameters, generating expressions that simulate the curve with great precision. There are empirical equations that describe the stress-strain curves. However, they only refer to the stress-strain curve for the stainless steel, but not when the material is under the welding process. It is a significant contribution to the applications of duplex stainless steel welds. For this study, a 3x3 matrix with a low, medium, and high level for each of the welding parameters were applied, giving a total of 27 weld bead plates. Two tensile specimens were manufactured from each welded plate, resulting in 54 tensile specimens for testing. When evaluating the four models used to predict the stress-strain curve in the welded specimens, only one model (Rasmussen) presented a good correlation in predicting the strain stress curve.

Keywords: duplex stainless steels, modeling, stress-stress curve, tensile test, welding

Procedia PDF Downloads 167

Authors: S. J. Matlan, M. Mukhlisin, M. R. Taha

Abstract:

Characterization of the engineering behavior of unsaturated soil is dependent on the soil-water characteristic curve (SWCC), a graphical representation of the relationship between water content or degree of saturation and soil suction. A reasonable description of the SWCC is thus important for the accurate prediction of unsaturated soil parameters. The measurement procedures for determining the SWCC, however, are difficult, expensive, and time-consuming. During the past few decades, researchers have laid a major focus on developing empirical equations for predicting the SWCC, with a large number of empirical models suggested. One of the most crucial questions is how precisely existing equations can represent the SWCC. As different models have different ranges of capability, it is essential to evaluate the precision of the SWCC models used for each particular soil type for better SWCC estimation. It is expected that better estimation of SWCC would be achieved via a thorough statistical analysis of its distribution within a particular soil class. With this in view, a statistical analysis was conducted in order to evaluate the reliability of the SWCC prediction models against laboratory measurement. Optimization techniques were used to obtain the best-fit of the model parameters in four forms of SWCC equation, using laboratory data for relatively coarse-textured (i.e., sandy) soil. The four most prominent SWCCs were evaluated and computed for each sample. The result shows that the Brooks and Corey model is the most consistent in describing the SWCC for sand soil type. The Brooks and Corey model prediction also exhibit compatibility with samples ranging from low to high soil water content in which subjected to the samples that evaluated in this study.

Keywords: soil-water characteristic curve (SWCC), statistical analysis, unsaturated soil, geotechnical engineering

Procedia PDF Downloads 338

Authors: Pakhapoom Sarapat, James M. Hill, Duangkamon Baowan

Abstract:

Carbon nanotori provide several properties such as high tensile strength and heat resistance. They are promised to be ideal structures for encapsulation, and their encapsulation ability can be determined by the interaction energy between the carbon nanotori and the encapsulated nanostructures. Such interaction energy is evaluated using Lennard-Jones potential and continuum approximation. Here, four problems relating to toroidal molecules are determined in order to find the most stable configuration. Firstly, the interaction energy between a carbon nanotorus and an atom is examined. The second problem relates to the energy of a fullerene encapsulated inside a carbon nanotorus. Next, the interaction energy between two symmetrically situated and parallel nanotori is considered. Finally, the classical mechanics is applied to model the interaction energy between the toroidal structure of cyclodextrin and the spherical DNA molecules. These mathematical models might be exploited to study a number of promising devices for future developments in bio and nanotechnology.

Keywords: carbon nanotori, continuum approximation, interaction energy, Lennard-Jones potential, nanotechnology

Procedia PDF Downloads 148

Authors: Desmond Agbolade Ademola

Abstract:

This work aimed to introduce a theory, called Guided Energy Theory of a particle that answered questions that arise from quantum foundation, quantum mechanics theory, and interpretation such as: what is nature of wavefunction? Is mathematical formalism of wavefunction correct? Does wavefunction collapse during measurement? Do quantum physical entanglement and many world interpretations really exist? In addition, is there uncertainty in the physical reality of our nature as being concluded in the Quantum theory? We have been able to show by the fundamental analysis presented in this work that the way quantum mechanics theory, and interpretation describes nature is not correlated with physical reality. Because, we discovered amongst others that, (1) Guided energy theory of a particle fundamentally provides complete physical observable series of quantized measurement of a particle momentum, force, energy e.t.c. in a given distance and time.In contrast, quantum mechanics wavefunction describes that nature has inherited probabilistic and indeterministic physical quantities, resulting in unobservable physical quantities that lead to many worldinterpretation.(2) Guided energy theory of a particle fundamentally predicts that it is mathematically possible to determine precise quantized measurementof position and momentum of a particle simultaneously. Because, there is no uncertainty in nature; nature however naturally guides itself against uncertainty. Contrary to the conclusion in quantum mechanics theory that, it is mathematically impossible to determine the position and the momentum of a particle simultaneously. Furthermore, we have been able to show by this theory that, it is mathematically possible to determine quantized measurement of force acting on a particle simultaneously, which is not possible on the premise of quantum mechanics theory. (3) It is evidently shown by our theory that, guided energy does not collapse, only describes the lopsided nature of a particle behavior in motion. This pretty offers us insight on gradual process of engagement - convergence and disengagement – divergence of guided energy holders which further highlight the picture how wave – like behavior return to particle-like behavior and how particle – like behavior return to wave – like behavior respectively. This further proves that the particles’ behavior in motion is oscillatory in nature. The mathematical formalism of Guided energy theory shows that nature is certainty whereas the mathematical formalism of Quantum mechanics theory shows that nature is absolutely probabilistics. In addition, the nature of wavefunction is the guided energy of the wave. In conclusion, the fundamental mathematical formalism of Quantum mechanics theory is wrong.

Keywords: momentum, physical entanglement, wavefunction, uncertainty

Procedia PDF Downloads 295

Authors: Jiangxia Han, Liang Xue, Keda Chen

Abstract:

Despite the significant progress over the last decades in reservoir simulation using numerical discretization, meshing is complex. Moreover, the high degree of freedom of the space-time flow field makes the solution process very time-consuming. Therefore, we present Physics-Informed Convolutional Neural Networks(PICNN) as a hybrid scientific theory and data method for reservoir modeling. Besides labeled data, the model is driven by the scientific theories of the underlying problem, such as governing equations, boundary conditions, and initial conditions. PICNN integrates governing equations and boundary conditions into the network architecture in the form of a customized convolution kernel. The loss function is composed of data matching, initial conditions, and other measurable prior knowledge. By customizing the convolution kernel and minimizing the loss function, the neural network parameters not only fit the data but also honor the governing equation. The PICNN provides a methodology to model and history-match flow and transport problems in porous media. Numerical results demonstrate that the proposed PICNN can provide an accurate physical solution from a limited dataset. We show how this method can be applied in the context of a forward simulation for continuous problems. Furthermore, several complex scenarios are tested, including the existence of data noise, different work schedules, and different good patterns.

Keywords: convolutional neural networks, deep learning, flow and transport in porous media, physics-informed neural networks, reservoir simulation

Procedia PDF Downloads 143

Authors: Khin Fai Chen, Jee-Hou Ho, Eng Hwa Yap

Abstract:

An acoustic micro-energy harvester (AMEH) is developed to convert wasted acoustical energy into useful electrical energy. AMEH is mathematically modeled using lumped element modelling (LEM) and Euler-Bernoulli beam (EBB) modelling. An experiment is designed to validate the mathematical model and assess the feasibility of AMEH. Comparison of theoretical and experimental data on critical parameter value such as Mm, Cms, dm and Ceb showed the variances are within 1% to 6%, which is reasonably acceptable. Hence, AMEH mathematical model is validated. Then, AMEH undergoes bandwidth tuning for performance optimization for further experimental work. The AMEH successfully produces 0.9 V⁄(m⁄s^2) and 1.79 μW⁄(m^2⁄s^4) at 60Hz and 400kΩ resistive load which only show variances about 7% compared to theoretical data. By integrating a capacitive load of 200µF, the discharge cycle time of AMEH is 1.8s and the usable energy bandwidth is available as low as 0.25g. At 1g and 60Hz resonance frequency, the averaged power output is about 2.2mW which fulfilled a range of wireless sensors and communication peripherals power requirements. Finally, the design for AMEH is assessed, validated and deemed as a feasible design.

Keywords: piezoelectric, acoustic, energy harvester

Procedia PDF Downloads 282

Authors: Thawtar Htun, Kim N. Irvine, Ranjna Jindal

Abstract:

This study aimed at modelling the wastewater collection system in Cha-Am Municipality using PCSWMM to investigate the quantity of combined sewage delivered to the aeration lagoon treatment system (ALTS). Cha-Am is a small sea resort town in Petchaburi Province located about 175 km southwest of Bangkok and is facing increasing development so it is important to understand current system performance and plan for future build out. PCSWMM was calibrated using observed ALTS inflow data for the period 15 June to 20 July 2015. The model was validated using observed ALTS inflow data for the periods 19 July to 20 October 2015 and 1 October to 31 December 2015, respectively. The 1:1 lines between modeled and observed peak flow and event volume for the calibration events qualitatively showed good correspondence. The r2 values between modeled and observed peak flow (99%) and event volume (89%) also were strong.

Keywords: combined sewer system, mathematical modelling, PCSWMM, wastewater collection system

Procedia PDF Downloads 213

Authors: Rabih Ghostine, Craig Kapfer, Viswanathan Kannan, Ibrahim Hoteit

Abstract:

Urban flooding resulting from a sudden release of water due to dam-break or excessive rainfall is a serious threatening environment hazard, which causes loss of human life and large economic losses. Anticipating floods before they occur could minimize human and economic losses through the implementation of appropriate protection, provision, and rescue plans. This work reports on the numerical modelling of flash flood propagation in urban areas after an excessive rainfall event or dam-break. A two-dimensional (2D) depth-averaged shallow water model is used with a refined unstructured grid of triangles for representing the urban area topography. The 2D shallow water equations are solved using a second-order well-balanced discontinuous Galerkin scheme. Theoretical test case and three flood events are described to demonstrate the potential benefits of the scheme: (i) wetting and drying in a parabolic basin (ii) flash flood over a physical model of the urbanized Toce River valley in Italy; (iii) wave propagation on the Reyran river valley in consequence of the Malpasset dam-break in 1959 (France); and (iv) dam-break flood in October 1982 at the town of Sumacarcel (Spain). The capability of the scheme is also verified against alternative models. Computational results compare well with recorded data and show that the scheme is at least as efficient as comparable second-order finite volume schemes, with notable efficiency speedup due to parallelization.

Keywords: dam-break, discontinuous Galerkin scheme, flood modeling, shallow water equations

Procedia PDF Downloads 175

Authors: N. Santatriniaina, J. Deseure, T. Q. Nguyen, H. Fontaine, C. Beitia, L. Rakotomanana

Abstract:

Nowadays, with the increasing of the wafer's size and the decreasing of critical size of integrated circuit manufacturing in modern high-tech, microelectronics industry needs a maximum attention to challenge the contamination control. The move to 300 mm is accompanied by the use of Front Opening Unified Pods for wafer and his storage. In these pods an airborne cross contamination may occur between wafers and the pods. A predictive approach using modeling and computational methods is very powerful method to understand and qualify the AMCs cross contamination processes. This work investigates the required numerical tools which are employed in order to study the AMCs cross-contamination transfer phenomena between wafers and FOUPs. Numerical optimization and finite element formulation in transient analysis were established. Analytical solution of one dimensional problem was developed and the calibration process of physical constants was performed. The least square distance between the model (analytical 1D solution) and the experimental data are minimized. The behavior of the AMCs intransient analysis was determined. The model framework preserves the classical forms of the diffusion and convection-diffusion equations and yields to consistent form of the Fick's law. The adsorption process and the surface roughness effect were also traduced as a boundary condition using the switch condition Dirichlet to Neumann and the interface condition. The methodology is applied, first using the optimization methods with analytical solution to define physical constants, and second using finite element method including adsorption kinetic and the switch of Dirichlet to Neumann condition.

Keywords: AMCs, FOUP, cross-contamination, adsorption, diffusion, numerical analysis, wafers, Dirichlet to Neumann, finite elements methods, Fick’s law, optimization

Procedia PDF Downloads 506

Authors: Moataz Medhat, Essam E. Khalil, Hatem Haridy

Abstract:

In the present study, a numerical simulation study is used to 3-D model the steady-state combustion of a staged natural gas flame in a 300 kW swirl-stabilized burner, using ANSYS solver to find the highest combustion efficiency by changing the inlet air swirl number and burner quarl angle in a furnace and showing the effect of flue gas recirculation, type of fuel and staging. The combustion chamber of the gas turbine is a cylinder of diameter 1006.8 mm, and a height of 1651mm ending with a hood until the exhaust cylinder has been reached, where the exit of combustion products which have a diameter of 300 mm, with a height of 751mm. The model was studied by 15 degree of the circumference due to axisymmetric of the geometry and divided into a mesh of about 1.1 million cells. The numerical simulations were performed by solving the governing equations in a three-dimensional model using realizable K-epsilon equations to express the turbulence and non-premixed flamelet combustion model taking into consideration radiation effect. The validation of the results was done by comparing it with other experimental data to ensure the agreement of the results. The study showed two zones of recirculation. The primary one is at the center of the furnace, and the location of the secondary one varies by changing the quarl angle of the burner. It is found that the increase in temperature in the external recirculation zone is a result of increasing the swirl number of the inlet air stream. Also it was found that recirculating part of the combustion products back to the combustion zone decreases pollutants formation especially nitrogen monoxide.

Keywords: burner selection, natural gas, analysis, recirculation

Procedia PDF Downloads 161

Authors: William Albeiro Alvarez, Gloria Patricia Jaramillo, Ivan Reinaldo Sarmiento

Abstract:

Understanding the behavior of individuals and the different human factors that influence the choice when faced with a complex system such as transportation is one of the most complicated aspects of measuring in the components that constitute the modeling of route choice due to that various behaviors and driving mode directly or indirectly affect the choice. During the last two decades, with the development of information and communications technologies, new data collection techniques have emerged such as GPS, geolocation with mobile phones, apps for choosing the route between origin and destination, individual service transport applications among others, where an interest has been generated to improve discrete choice models when considering the incorporation of these developments as well as psychological factors that affect decision making. This paper implements a discrete choice model that proposes and estimates a hybrid model that integrates route choice models and latent variables based on the observation on the route of a sample of public taxi drivers from the city of Medellín, Colombia in relation to its behavior, personality, socioeconomic characteristics, and driving mode. The set of choice options includes the routes generated by the individual service transport applications versus the driver's choice. The hybrid model consists of measurement equations that relate latent variables with measurement indicators and utilities with choice indicators along with structural equations that link the observable characteristics of drivers with latent variables and explanatory variables with utilities.

Keywords: behavior choice model, human factors, hybrid model, real time data

Procedia PDF Downloads 152

Authors: Nattamon Srithammee, Ratchanikorn Chonchaiya

Abstract:

This study explores the impact of Augmented Reality (AR) technology on mathematics education, focusing on Area and Volume concepts at Phra Dabos School in Thailand. We developed a mobile augmented reality application to present these mathematical concepts innovatively. Using a mixed-methods approach, we assessed the knowledge of 79 students before and after using the application. The results showed a significant improvement in students' understanding of Area and Volume, with average test scores increasing from 3.70 to 9.04 (p < 0.001, Cohen's d = 2.05). Students also reported increased engagement and satisfaction. Our findings suggest that augmented reality technology can be a valuable tool in mathematics education, particularly for enhancing the understanding of abstract concepts like Area and Volume. This study contributes to research on educational technology in STEM education and provides insights for educators and educational technology developers.

Keywords: augmented reality, mathematics education, area and volume, educational technology, STEM education

Procedia PDF Downloads 24

Authors: Ganiyu Samson Okunlola, Ladanu Abiodun Ajala, Olaide Oluwaseun Adegbayo

Abstract:

Since the usefulness of articulated vehicles is becoming more apparent and the diesel consumption of these vehicles constitutes a major portion of operating costs, development of mathematical model for their diesel consumption is of a great importance. Therefore, the present work developed a quantitative relationship between diesel consumption and vehicle age, annual use and cost of maintenance of the different makes of articulated vehicles. The vehicles selected for the study were FIAT 682 T3, IVECO 19036 and M.A.N. Diesel 19.240. The operating parameters for 90 vehicles of different age groups were recorded. Multiple regression models for diesel consumption of articulated vehicles of different makes were developed. From the analysis of results, it can be concluded that as the age of the vehicles increases, the diesel consumption increases. Also, as the diesel consumption increases, the cost of maintenance increases and there is a subsequent decrease in annual use. Moreover, FIAT 682 T3 and IVECO 19036 should be replaced at 7 years of age while M.A.N diesel should be replaced at 8 years of age. These are the ages where the diesel consumption becomes abnormal and uneconomical and they are points of optimal overhaul.

Keywords: vehicle, overhaul, age, uneconomical, diesel, consumption

Procedia PDF Downloads 251

Authors: Nurudeen Oluwasola Lasisi

Abstract:

Newcastle disease is a highly contagious disease of birds caused by a para-myxo virus. In this paper, we presented Novel quarantine-adjusted incident and linear incident of Newcastle disease model equations. We considered the dynamics of transmission and control of Newcastle disease. The existence and uniqueness of the solutions were obtained. The existence of disease-free points was shown, and the model threshold parameter was examined using the next-generation operator method. The sensitivity analysis was carried out in order to identify the most sensitive parameters of the disease transmission. This revealed that as parameters β,ω, and ᴧ increase while keeping other parameters constant, the effective reproduction number R_ev increases. This implies that the parameters increase the endemicity of the infection of individuals. More so, when the parameters μ,ε,γ,δ_1, and α increase, while keeping other parameters constant, the effective reproduction number R_ev decreases. This implies the parameters decrease the endemicity of the infection as they have negative indices. Analytical results were numerically verified by the Differential Transformation Method (DTM) and quantitative views of the model equations were showcased. We established that as contact rate (β) increases, the effective reproduction number R_ev increases, as the effectiveness of drug usage increases, the R_ev decreases and as the quarantined individual decreases, the R_ev decreases. The results of the simulations showed that the infected individual increases when the susceptible person approaches zero, also the vaccination individual increases when the infected individual decreases and simultaneously increases the recovery individual.

Keywords: disease-free equilibrium, effective reproduction number, endemicity, Newcastle disease model, numerical, Sensitivity analysis

Procedia PDF Downloads 45

Authors: Shrikant Ghadage

Abstract:

Study of shock waves generated in the Scramjet engine is typically restricted to pressure, temperature, density, entropy and Mach number variation across the shock wave. The present work discusses the impact of inlet shock wave angles on the specific impulse of the Scramjet engine. A mathematical analysis has done for the isentropic hypersonic flow of air flowing through a Scramjet with hydrogen fuel at an altitude of 30 km. Analysis has been done in order to get optimum shock wave angle to achieve maximum impulse. Since external drag has excluded from the analysis, the losses due to friction are not considered for the present analysis. When Mach number of the airflow at the entry of the nozzle reaches unity, then that flow is choked. This condition puts limitations on increasing the inlet shock wave angle. As inlet shock wave angle increases, speed of the flow entering into the nozzle decreases, which results in an increase in the specific impulse of the engine. When the speed of the flow at the entry of the nozzle reduces below sonic speed, then there is no further increase in the specific impulse of the engine. Here the Conclusion is the thrust and specific impulse of a scramjet engine, which increases gradually with an increase in inlet shock wave angle up to the condition when airflow speed reaches sonic velocity at the exit of the combustor. In addition to that, variation in drag force at the inlet of the scramjet and variation in hypersonic flow conditions at every stage of the scramjet also studied in order to understand variation on flow characteristics with respect to flow deflection angle. Essentially, it helps in designing inlet profile for the Scramjet engine to achieve optimum specific impulse.

Keywords: hypersonic flow, scramjet, shock waves, specific impulse, mathematical analysis

Procedia PDF Downloads 168

Authors: Hui Fang Huang Su, Leanne Lai, Pei-Fen Li, Mei-Hwei Ho, Yu-Wen Chiu

Abstract:

This study aimed to provide a practical, systematic, and comprehensive intervention for children with Autism Spectrum Disorder (ASD). A pilot study of quasi-experimental pre-post intervention with control group design was conducted to evaluate if the mathematical intervention (Project MIND - Math Is Not Difficult) increases the math comprehension of children with ASD Children with ASD in the primary grades (K-1, 2) participated in math interventions to enhance their math comprehension and cognitive ability. The Bracken basic concept scale was used to evaluate subjects’ language skills, cognitive development, and school readiness. The study found that our systemic interventions of Project MIND significantly improved the mathematical and cognitive abilities in children with autism. The results of this study may lead to a major change in effective and adequate health care services for children with ASD and their families. All statistical analyses were performed with the IBM SPSS Statistics Version 25 for Windows. The significant level was set at 0.05 P-value.

Keywords: autism, mathematics, technology, family

Procedia PDF Downloads 105

Authors: Mohamed El Hattab

Abstract:

The Supercritical carbon dioxide (SFE) and the focused microwave-assisted hydrodistillation (FMAHD) were employed to isolate the volatile fraction of the brown alga Dictyopteris membranacea from the crude extract. The volatiles fractions obtained were analyzed by GC/MS. The major compounds in this case: dictyopterene A, 6-butylcyclohepta-1,4-diene, Undec-1-en-3-one, Undeca-1,4-dien-3-one, (3-oxoundec-4-enyl) sulphur, tetradecanoic acid, hexadecanoic acid, 3-hexyl-4,5-dithia-cycloheptanone and albicanol (this later is present only in the FMAHD oil) are identified by comparing their mass spectra with those reported on the commercial MS data base and also on our previously work. A kinetic study realized on both extraction processes and followed by an external standard quantification has allowed the study of the mass percent evolution of the major compounds in the two oils, an empirical mathematical modelling was used to describe their kinetic extraction.

Keywords: dictyopteris membranacea, extraction techniques, mathematical modeling, volatile oils

Procedia PDF Downloads 428