Search results for: depth function
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 7770

Search results for: depth function

7770 Variations in the Frequency-Magnitude Distribution with Depth in Kalabsha Area, Aswan, South Egypt

Authors: Ezzat Mohamed El-Amin

Abstract:

Mapping the earthquake-size distribution in various tectonic regimes on a local to regional scale reveals statistically significant variations in the range of at least 0.4 to 2.0 for the b-value in the frequency-magnitude distribution. We map the earthquake frequency–magnitude distribution (b value) as a function of depth in the Reservoir Triggered Seismicity (RTS) region in Kalabsha region, in south Egypt. About 1680 well-located events recorded during 1981–2014 in the Kalabsha region are selected for the analysis. The earthquake data sets are separated in 5 km zones from 0 to 25 km depth. The result shows a systematic decrease in b value up to 12 km followed by an increase. The increase in b value is interpreted to be caused by the presence of fluids. We also investigate the spatial distribution of b value with depth. Significant variations in the b value are detected, with b ranging from b 0.7 to 1.19. Low b value areas at 5 km depth indicate localized high stresses which are favorable for future rupture.

Keywords: seismicity, frequency-magnitude, b-value, earthquake

Procedia PDF Downloads 532
7769 Numerical Solution of Manning's Equation in Rectangular Channels

Authors: Abdulrahman Abdulrahman

Abstract:

When the Manning equation is used, a unique value of normal depth in the uniform flow exists for a given channel geometry, discharge, roughness, and slope. Depending on the value of normal depth relative to the critical depth, the flow type (supercritical or subcritical) for a given characteristic of channel conditions is determined whether or not flow is uniform. There is no general solution of Manning's equation for determining the flow depth for a given flow rate, because the area of cross section and the hydraulic radius produce a complicated function of depth. The familiar solution of normal depth for a rectangular channel involves 1) a trial-and-error solution; 2) constructing a non-dimensional graph; 3) preparing tables involving non-dimensional parameters. Author in this paper has derived semi-analytical solution to Manning's equation for determining the flow depth given the flow rate in rectangular open channel. The solution was derived by expressing Manning's equation in non-dimensional form, then expanding this form using Maclaurin's series. In order to simplify the solution, terms containing power up to 4 have been considered. The resulted equation is a quartic equation with a standard form, where its solution was obtained by resolving this into two quadratic factors. The proposed solution for Manning's equation is valid over a large range of parameters, and its maximum error is within -1.586%.

Keywords: channel design, civil engineering, hydraulic engineering, open channel flow, Manning's equation, normal depth, uniform flow

Procedia PDF Downloads 182
7768 Numerical Modeling of the Depth-Averaged Flow over a Hill

Authors: Anna Avramenko, Heikki Haario

Abstract:

This paper reports the development and application of a 2D depth-averaged model. The main goal of this contribution is to apply the depth averaged equations to a wind park model in which the treatment of the geometry, introduced on the mathematical model by the mass and momentum source terms. The depth-averaged model will be used in future to find the optimal position of wind turbines in the wind park. K-E and 2D LES turbulence models were consider in this article. 2D CFD simulations for one hill was done to check the depth-averaged model in practise.

Keywords: depth-averaged equations, numerical modeling, CFD, wind park model

Procedia PDF Downloads 570
7767 RGB-D SLAM Algorithm Based on pixel level Dense Depth Map

Authors: Hao Zhang, Hongyang Yu

Abstract:

Scale uncertainty is a well-known challenging problem in visual SLAM. Because RGB-D sensor provides depth information, RGB-D SLAM improves this scale uncertainty problem. However, due to the limitation of physical hardware, the depth map output by RGB-D sensor usually contains a large area of missing depth values. These missing depth information affect the accuracy and robustness of RGB-D SLAM. In order to reduce these effects, this paper completes the missing area of the depth map output by RGB-D sensor and then fuses the completed dense depth map into ORB SLAM2. By adding the process of obtaining pixel-level dense depth maps, a better RGB-D visual SLAM algorithm is finally obtained. In the process of obtaining dense depth maps, a deep learning model of indoor scenes is adopted. Experiments are conducted on public datasets and real-world environments of indoor scenes. Experimental results show that the proposed SLAM algorithm has better robustness than ORB SLAM2.

Keywords: RGB-D, SLAM, dense depth, depth map

Procedia PDF Downloads 103
7766 Correlation between Initial Absorption of the Cover Concrete, the Compressive Strength and Carbonation Depth

Authors: Bouzidi Yassine

Abstract:

This experimental work was aimed to characterize the porosity of the concrete cover zone using the capillary absorption test, and establish the links between open porosity characterized by the initial absorption, the compressive strength and carbonation depth. Eight formulations of workability similar made from ordinary Portland cement (CEM I 42.5) and a compound cement (CEM II/B 42.5) four of each type are studied. The results allow us to highlight the effect of the cement type. Indeed, concretes-based cement CEM II/B 42.5 carbonatent approximately faster than concretes-based cement CEM I 42.5. This effect is attributed in part to the lower content of portlandite Ca(OH)2 of concretes-based cement CEM II/B 42.5, but also the impact of the cement type on the open porosity of the cover concrete. The open porosity of concretes-based cement CEM I 42.5 is lower than that of concretes-based cement CEM II/B 42.5. The carbonation depth is a decreasing function of the compressive strength at 28 days and increases with the initial absorption. Through the results obtained, correlations between the quantity of water absorbed in 1 h, the carbonation depth at 180 days and the compressive strength at 28 days were performed in an acceptable manner.

Keywords: initial absorption, cover concrete, compressive strength, carbonation depth

Procedia PDF Downloads 301
7765 Analytical Solution for End Depth Ratio in Rectangular Channels

Authors: Abdulrahman Abdulrahman, Abir Abdulrahman

Abstract:

Free over-fall is an instrument for measuring discharge in open channels by measuring end depth. A comprehensive researchers investigated theoretically and experimentally brink phenomenon with various approaches for different cross-sectional shapes. Anderson's method, based on Boussinq's approximation and energy approach was used to derive a pressure distribution factor at end depth. Applying the one-dimensional momentum equation and the principles of limit slope analysis, a relevant analytical solution may be derived for brink depth ratio (EDR) in prismatic rectangular channel. Also relationships between end depth ratio and slope ratio for a given non-dimensional normal or critical depth with upstream supercritical flow regime are presented. Simple indirect procedure is used to estimate the end depth discharge ratio (EDD) for subcritical and supercritical flow using measured end depth. The comparison of this analysis with all previous theoretical and experimental studies showed an excellent agreement.

Keywords: analytical solution, brink depth, end depth, flow measurement, free over fall, hydraulics, rectangular channel

Procedia PDF Downloads 146
7764 The Implementation of Secton Method for Finding the Root of Interpolation Function

Authors: Nur Rokhman

Abstract:

A mathematical function gives relationship between the variables composing the function. Interpolation can be viewed as a process of finding mathematical function which goes through some specified points. There are many interpolation methods, namely: Lagrange method, Newton method, Spline method etc. For some specific condition, such as, big amount of interpolation points, the interpolation function can not be written explicitly. This such function consist of computational steps. The solution of equations involving the interpolation function is a problem of solution of non linear equation. Newton method will not work on the interpolation function, for the derivative of the interpolation function cannot be written explicitly. This paper shows the use of Secton method to determine the numerical solution of the function involving the interpolation function. The experiment shows the fact that Secton method works better than Newton method in finding the root of Lagrange interpolation function.

Keywords: Secton method, interpolation, non linear function, numerical solution

Procedia PDF Downloads 346
7763 Spectral Re-Evaluation of the Magnetic Basement Depth over Yola Arm of Upper Benue Trough Nigeria Using Aeromagnetic Data

Authors: Emberga Terhemb Opara Alexander, Selemo Alexader, Onyekwuru Samuel

Abstract:

The aeromagnetic data have been used to re-evaluate parts of the Upper Benue Trough Nigeria using spectral analysis technique in order to appraise the mineral accumulation potential of the area. The regional field was separated with a first order polynomial using polyfit program. The residual data was subdivided into 24 spectral blocks using OASIS MONTAJ software program. Two prominent magnetic depth source layers were identified. The deeper source depth values obtained ranges from 1.56km to 2.92km with an average depth of 2.37km as the magnetic basement depth while for the shallower sources, the depth values ranges from -1.17km to 0.98km with an average depth of 0.55km. The shallow depth source is attributed to the volcanic rocks that intruded the sedimentary formation and this could possibly be responsible for the mineralization found in parts of the study area.

Keywords: spectral analysis, Upper Benue Trough, magnetic basement depth, aeromagnetic

Procedia PDF Downloads 419
7762 Throughput of Point Coordination Function (PCF)

Authors: Faisel Eltuhami Alzaalik, Omar Imhemed Alramli, Ahmed Mohamed Elaieb

Abstract:

The IEEE 802.11 defines two modes of MAC, distributed coordination function (DCF) and point coordination function (PCF) mode. The first sub-layer of the MAC is the distributed coordination function (DCF). A contention algorithm is used via DCF to provide access to all traffic. The point coordination function (PCF) is the second sub-layer used to provide contention-free service. PCF is upper DCF and it uses features of DCF to establish guarantee access of its users. Some papers and researches that have been published in this technology were reviewed in this paper, as well as talking briefly about the distributed coordination function (DCF) technology. The simulation of the PCF function have been applied by using a simulation program called network simulator (NS2) and have been found out the throughput of a transmitter system by using this function.

Keywords: DCF, PCF, throughput, NS2

Procedia PDF Downloads 537
7761 Effect of Fault Depth on Near-Fault Peak Ground Velocity

Authors: Yanyan Yu, Haiping Ding, Pengjun Chen, Yiou Sun

Abstract:

Fault depth is an important parameter to be determined in ground motion simulation, and peak ground velocity (PGV) demonstrates good application prospect. Using numerical simulation method, the variations of distribution and peak value of near-fault PGV with different fault depth were studied in detail, and the reason of some phenomena were discussed. The simulation results show that the distribution characteristics of PGV of fault-parallel (FP) component and fault-normal (FN) component are distinctly different; the value of PGV FN component is much larger than that of FP component. With the increase of fault depth, the distribution region of the FN component strong PGV moves forward along the rupture direction, while the strong PGV zone of FP component becomes gradually far away from the fault trace along the direction perpendicular to the strike. However, no matter FN component or FP component, the strong PGV distribution area and its value are both quickly reduced with increased fault depth. The results above suggest that the fault depth have significant effect on both FN component and FP component of near-fault PGV.

Keywords: fault depth, near-fault, PGV, numerical simulation

Procedia PDF Downloads 313
7760 Architecture Performance-Related Design Based on Graphic Parameterization

Authors: Wenzhe Li, Xiaoyu Ying, Grace Ding

Abstract:

Architecture plane form is an important consideration in the design of green buildings due to its significant impact on energy performance. The most effective method to consider energy performance in the early design stages is parametric modelling. This paper presents a methodology to program plane forms using MATLAB language, generating 16 kinds of plane forms by changing four designed parameters. DesignBuilder (an energy consumption simulation software) was proposed to simulate the energy consumption of the generated planes. A regression mathematical model was established to study the relationship between the plane forms and their energy consumption. The main finding of the study suggested that there was a cubic function relationship between the depth-ratio of U-shaped buildings and energy consumption, and there is also a cubic function relationship between the width-ratio and energy consumption. In the design, the depth-ratio of U-shaped buildings should not be less than 2.5, and the width-ratio should not be less than 2.

Keywords: graphic parameterization, green building design, mathematical model, plane form

Procedia PDF Downloads 120
7759 Depth Estimation in DNN Using Stereo Thermal Image Pairs

Authors: Ahmet Faruk Akyuz, Hasan Sakir Bilge

Abstract:

Depth estimation using stereo images is a challenging problem in computer vision. Many different studies have been carried out to solve this problem. With advancing machine learning, tackling this problem is often done with neural network-based solutions. The images used in these studies are mostly in the visible spectrum. However, the need to use the Infrared (IR) spectrum for depth estimation has emerged because it gives better results than visible spectra in some conditions. At this point, we recommend using thermal-thermal (IR) image pairs for depth estimation. In this study, we used two well-known networks (PSMNet, FADNet) with minor modifications to demonstrate the viability of this idea.

Keywords: thermal stereo matching, deep neural networks, CNN, Depth estimation

Procedia PDF Downloads 233
7758 Scour Depth Prediction around Bridge Piers Using Neuro-Fuzzy and Neural Network Approaches

Authors: H. Bonakdari, I. Ebtehaj

Abstract:

The prediction of scour depth around bridge piers is frequently considered in river engineering. One of the key aspects in efficient and optimum bridge structure design is considered to be scour depth estimation around bridge piers. In this study, scour depth around bridge piers is estimated using two methods, namely the Adaptive Neuro-Fuzzy Inference System (ANFIS) and Artificial Neural Network (ANN). Therefore, the effective parameters in scour depth prediction are determined using the ANN and ANFIS methods via dimensional analysis, and subsequently, the parameters are predicted. In the current study, the methods’ performances are compared with the nonlinear regression (NLR) method. The results show that both methods presented in this study outperform existing methods. Moreover, using the ratio of pier length to flow depth, ratio of median diameter of particles to flow depth, ratio of pier width to flow depth, the Froude number and standard deviation of bed grain size parameters leads to optimal performance in scour depth estimation.

Keywords: adaptive neuro-fuzzy inference system (ANFIS), artificial neural network (ANN), bridge pier, scour depth, nonlinear regression (NLR)

Procedia PDF Downloads 180
7757 Experimental Study of Local Scour Depth around Cylindrical Bridge Pier

Authors: Mohammed T. Shukri

Abstract:

The failure of bridges due to excessive local scour during floods poses a challenging problem to hydraulic engineers. The failure of bridges piers is due to many reasons such as localized scour combined with general riverbed degradation. In this paper, we try to estimate the temporal variation of scour depth at nonuniform cylindrical bridge pier, by experimental work conducted in hydraulic laboratories of Gaziantep University Civil Engineering Department on a flume having dimensions of 8.3 m length, 0.8 m width and 0.9 m depth. The experiments will be carried on 20 cm depth of sediment layer having d50=0.4 mm. Three bridge pier shapes having different scaled models will be constructed in a 1.5m of test section in the channel.

Keywords: scour, local scour, bridge piers, scour depth

Procedia PDF Downloads 221
7756 Influence of Channel Depth on the Performance of Wavy Fin Absorber Solar Air Heater

Authors: Abhishek Priyam, Prabha Chand

Abstract:

Channel depth is an important design parameter to be fixed in designing a solar air heater. In this paper, a mathematical model has been developed to study the influence of channel duct on the thermal performance of solar air heaters. The channel depth has been varied from 1.5 cm to 3.5 cm for the mass flow range 0.01 to 0.11 kg/s. Based on first law of thermodynamics, the channel depth of 1.5 cm shows better thermal performance for all the mass flow range. Also, better thermohydraulic performance has been found up to 0.05 kg/s, and beyond this, thermohydraulic efficiency starts decreasing. It has been seen that, with the increase in the mass flow rate, the difference between thermal and thermohydraulic efficiency increases because of the increase in pressure drop. At lower mass flow rate, 0.01 kg/s, the thermal and thermohydraulic efficiencies for respective channel depth remain the same.

Keywords: channel depth, thermal efficiency, wavy fin, thermohydraulic efficiency

Procedia PDF Downloads 340
7755 Variation with Depth of Physico-Chemical, Mineralogical and Physical Properties of Overburden over Gneiss Basement Complex in Minna Metropolis, North Central Nigeria

Authors: M. M. Alhaji, M. Alhassan, A. M. Yahaya

Abstract:

Soil engineers pay very little or no attention to variation in the mineralogical and consequently, the geotechnical properties of overburden with depth on basement complexes, a situation which can lead to sudden failure of civil engineering structures. Soil samples collected at depths ranging from 0.5m to 4.0m at 0.5m intervals, from a trial pit dogged manually to depth of 4.0m on an overburden over gneiss basement complex, was evaluated for physico-chemical, mineralogical and physical properties. This is to determine the variation of these properties with depth within the profile of the strata. Results showed that sodium amphibolite and feldspar, which are both primary minerals dominate the overall profile of the overburden. Carbon which dominates the lower profile of the strata was observed to alter to gregorite at upper section of the profile. Organic matter contents and cation exchange capacity reduces with increase in depth while lost on ignition and pH were relatively constant with depth. The index properties, as well as natural moisture contents, increases from 0.5m to between 1.0m to 1.5m depth after which the values reduced to constant values at 3.0m depth. The grain size analysis shows high composition of sand sized particles with silts of low to non-plasticity. The maximum dry density (MDD) values are generally relatively high and increases from 2.262g/cm³ at 0.5m depth to 2.410g/cm³ at 4.0m depth while the optimum moisture content (OMC) reduced from 9.8% at 0.5m depth to 6.7% at 4.0m depth.

Keywords: Gneiss basement complex, mineralogical properties, North Central Nigeria, physico-chemical properties, physical properties, overburden soil

Procedia PDF Downloads 107
7754 On a Univalent Function and the Integral Means of Its Derivative

Authors: Shatha S. Alhily

Abstract:

The purpose of this research paper is to show all the possible values of the pth power of the integrable function which make the integral means of the derivative of univalent function existing and finite.

Keywords: derivative, integral means, self conformal maps, univalent function

Procedia PDF Downloads 594
7753 Mechanistic Study of Composite Pavement Behavior in Heavy Duty Area

Authors: Makara Rith, Young Kyu Kim, Seung Woo Lee

Abstract:

In heavy duty areas, asphalt pavement constructed as entrance roadway may expose distresses such as cracking and rutting during service life. To mitigate these problems, composite pavement with a roller-compacted concrete base may be a good alternative; however, it should be initially investigated. Structural performances such as fatigue cracking and rut depth may be changed due to variation of some design factors. Therefore, this study focuses on the variation effect of material modulus, layer thickness and loading on composite pavement performances. Stress and strain at the critical location are determined and used as the input of transfer function for corresponding distresses to evaluate the pavement performance. Also, composite pavement satisfying the design criteria may be selected as a design section for heavy duty areas. Consequently, this investigation indicates that composite pavement has the ability to eliminate fatigue cracking in asphalt surfaces and significantly reduce rut depth. In addition, a thick or strong rigid base can significantly reduce rut depth and prolong fatigue life of this layer.

Keywords: composite pavement, ports, cracking, rutting

Procedia PDF Downloads 160
7752 Solution of the Nonrelativistic Radial Wave Equation of Hydrogen Atom Using the Green's Function Approach

Authors: F. U. Rahman, R. Q. Zhang

Abstract:

This work aims to develop a systematic numerical technique which can be easily extended to many-body problem. The Lippmann Schwinger equation (integral form of the Schrodinger wave equation) is solved for the nonrelativistic radial wave of hydrogen atom using iterative integration scheme. As the unknown wave function appears on both sides of the Lippmann Schwinger equation, therefore an approximate wave function is used in order to solve the equation. The Green’s function is obtained by the method of Laplace transform for the radial wave equation with excluded potential term. Using the Lippmann Schwinger equation, the product of approximate wave function, the Green’s function and the potential term is integrated iteratively. Finally, the wave function is normalized and plotted against the standard radial wave for comparison. The outcome wave function converges to the standard wave function with the increasing number of iteration. Results are verified for the first fifteen states of hydrogen atom. The method is efficient and consistent and can be applied to complex systems in future.

Keywords: Green’s function, hydrogen atom, Lippmann Schwinger equation, radial wave

Procedia PDF Downloads 355
7751 A Compressor Map Optimizing Tool for Prediction of Compressor Off-Design Performance

Authors: Zhongzhi Hu, Jie Shen, Jiqiang Wang

Abstract:

A high precision aeroengine model is needed when developing the engine control system. Compared with other main components, the axial compressor is the most challenging component to simulate. In this paper, a compressor map optimizing tool based on the introduction of a modifiable β function is developed for FWorks (FADEC Works). Three parameters (d density, f fitting coefficient, k₀ slope of the line β=0) are introduced to the β function to make it modifiable. The comparison of the traditional β function and the modifiable β function is carried out for a certain type of compressor. The interpolation errors show that both methods meet the modeling requirements, while the modifiable β function can predict compressor performance more accurately for some areas of the compressor map where the users are interested in.

Keywords: beta function, compressor map, interpolation error, map optimization tool

Procedia PDF Downloads 231
7750 An Online 3D Modeling Method Based on a Lossless Compression Algorithm

Authors: Jiankang Wang, Hongyang Yu

Abstract:

This paper proposes a portable online 3D modeling method. The method first utilizes a depth camera to collect data and compresses the depth data using a frame-by-frame lossless data compression method. The color image is encoded using the H.264 encoding format. After the cloud obtains the color image and depth image, a 3D modeling method based on bundlefusion is used to complete the 3D modeling. The results of this study indicate that this method has the characteristics of portability, online, and high efficiency and has a wide range of application prospects.

Keywords: 3D reconstruction, bundlefusion, lossless compression, depth image

Procedia PDF Downloads 41
7749 View Synthesis of Kinetic Depth Imagery for 3D Security X-Ray Imaging

Authors: O. Abusaeeda, J. P. O. Evans, D. Downes

Abstract:

We demonstrate the synthesis of intermediary views within a sequence of X-ray images that exhibit depth from motion or kinetic depth effect in a visual display. Each synthetic image replaces the requirement for a linear X-ray detector array during the image acquisition process. Scale invariant feature transform, SIFT, in combination with epipolar morphing is employed to produce synthetic imagery. Comparison between synthetic and ground truth images is reported to quantify the performance of the approach. Our work is a key aspect in the development of a 3D imaging modality for the screening of luggage at airport checkpoints. This programme of research is in collaboration with the UK Home Office and the US Dept. of Homeland Security.

Keywords: X-ray, kinetic depth, KDE, view synthesis

Procedia PDF Downloads 226
7748 Algorithm Research on Traffic Sign Detection Based on Improved EfficientDet

Authors: Ma Lei-Lei, Zhou You

Abstract:

Aiming at the problems of low detection accuracy of deep learning algorithm in traffic sign detection, this paper proposes improved EfficientDet based traffic sign detection algorithm. Multi-head self-attention is introduced in the minimum resolution layer of the backbone of EfficientDet to achieve effective aggregation of local and global depth information, and this study proposes an improved feature fusion pyramid with increased vertical cross-layer connections, which improves the performance of the model while introducing a small amount of complexity, the Balanced L1 Loss is introduced to replace the original regression loss function Smooth L1 Loss, which solves the problem of balance in the loss function. Experimental results show, the algorithm proposed in this study is suitable for the task of traffic sign detection. Compared with other models, the improved EfficientDet has the best detection accuracy. Although the test speed is not completely dominant, it still meets the real-time requirement.

Keywords: convolutional neural network, transformer, feature pyramid networks, loss function

Procedia PDF Downloads 64
7747 The Effect of the Side-Weir Crest Height to Scour in Clay-Sand Mixed Sediments

Authors: F. A. Saracoglu Varol, H. Agaccıoglu

Abstract:

Experimental studies to investigate the depth of the scour conducted at a side-weir intersection located at the 1800 curved flume which located Hydraulic Laboratory of Yıldız Technical University, Istanbul, Turkey. Side weirs were located at the middle of the straight part of the main channel. Three different lengths (25, 40 and 50 cm) and three different weir crest height (7, 10 and 12 cm) of the side weir placed on the side weir station. There is no scour when the material is only kaolin. Therefore, the cohesive bed was prepared by properly mixing clay material (kaolin) with 31% sand in all experiments. Following 24h consolidation time, in order to observe the effect of flow intensity on the scour depth, experiments were carried out for five different upstream Froude numbers in the range of 0.33-0.81. As a result of this study the relation between scour depth and upstream flow intensity as a function of time have been established. The longitudinal velocities decreased along the side weir; towards the downstream due to overflow over the side-weirs. At the beginning, the scour depth increases rapidly with time and then asymptotically approached constant values in all experiments for all side weir dimensions as in non-cohesive sediment. Thus, the scour depth reached equilibrium conditions. Time to equilibrium depends on the approach flow intensity and the dimensions of side weirs. For different heights of the weir crest, dimensionless scour depths increased with increasing upstream Froude number. Equilibrium scour depths which formed 7 cm side-weir crest height were obtained higher than that of the 12 cm side-weir crest height. This means when side-weir crest height increased equilibrium scour depths decreased. Although the upstream side of the scour hole is almost vertical, the downstream side of the hole is inclined.

Keywords: clay-sand mixed sediments, scour, side weir, hydraulic structures

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7746 Closed Forms of Trigonometric Series Interms of Riemann’s ζ Function and Dirichlet η, λ, β Functions or the Hurwitz Zeta Function and Harmonic Numbers

Authors: Slobodan B. Tričković

Abstract:

We present the results concerned with trigonometric series that include sine and cosine functions with a parameter appearing in the denominator. We derive two types of closed-form formulas for trigonometric series. At first, for some integer values, as we know that Riemann’s ζ function and Dirichlet η, λ equal zero at negative even integers, whereas Dirichlet’s β function equals zero at negative odd integers, after a certain number of members, the rest of the series vanishes. Thus, a trigonometric series becomes a polynomial with coefficients involving Riemann’s ζ function and Dirichlet η, λ, β functions. On the other hand, in some cases, one cannot immediately replace the parameter with any positive integer because we shall encounter singularities. So it is necessary to take a limit, so in the process, we apply L’Hospital’s rule and, after a series of rearrangements, we bring a trigonometric series to a form suitable for the application of Choi-Srivastava’s theorem dealing with Hurwitz’s zeta function and Harmonic numbers. In this way, we express a trigonometric series as a polynomial over Hurwitz’s zeta function derivative.

Keywords: Dirichlet eta lambda beta functions, Riemann's zeta function, Hurwitz zeta function, Harmonic numbers

Procedia PDF Downloads 61
7745 Estimation of Slab Depth, Column Size and Rebar Location of Concrete Specimen Using Impact Echo Method

Authors: Y. T. Lee, J. H. Na, S. H. Kim, S. U. Hong

Abstract:

In this study, an experimental research for estimation of slab depth, column size and location of rebar of concrete specimen is conducted using the Impact Echo Method (IE) based on stress wave among non-destructive test methods. Estimation of slab depth had total length of 1800×300 and 6 different depths including 150 mm, 180 mm, 210 mm, 240 mm, 270 mm and 300 mm. The concrete column specimen was manufactured by differentiating the size into 300×300×300 mm, 400×400×400 mm and 500×500×500 mm. In case of the specimen for estimation of rebar, rebar of ∅22 mm was used in a specimen of 300×370×200 and arranged at 130 mm and 150 mm from the top to the rebar top. As a result of error rate of slab depth was overall mean of 3.1%. Error rate of column size was overall mean of 1.7%. Mean error rate of rebar location was 1.72% for top, 1.19% for bottom and 1.5% for overall mean showing relative accuracy.

Keywords: impact echo method, estimation, slab depth, column size, rebar location, concrete

Procedia PDF Downloads 313
7744 Stability Analysis of SEIR Epidemic Model with Treatment Function

Authors: Sasiporn Rattanasupha, Settapat Chinviriyasit

Abstract:

The treatment function adopts a continuous and differentiable function which can describe the effect of delayed treatment when the number of infected individuals increases and the medical condition is limited. In this paper, the SEIR epidemic model with treatment function is studied to investigate the dynamics of the model due to the effect of treatment. It is assumed that the treatment rate is proportional to the number of infective patients. The stability of the model is analyzed. The model is simulated to illustrate the analytical results and to investigate the effects of treatment on the spread of infection.

Keywords: basic reproduction number, local stability, SEIR epidemic model, treatment function

Procedia PDF Downloads 483
7743 Case-Wise Investigation of Body-Wave Propagation in a Cross-Anisotropic Soil Exhibiting Inhomogeneity along Depth

Authors: Sumit Kumar Vishawakarma, Tapas Ranjan Panihari

Abstract:

The article investigates the propagation behavior of SV-wave, SH-wave, and P-wave in a continuously inhomogeneous cross-anisotropic material, where the material properties such as Young's moduli, shear modulus, and density vary as an arbitrary continuous function of depth. In the considered model, Hook's law, strain-displacement relations along with equilibrium equations have been used to derive the governing equation. The mathematical formulation of this physical problem gives rise to an eigenvalue problem with displacement components as fundamental variables. This leads to achieving the closed-form expressions for quasi-wave velocities of SV-wave, SH-wave, and P-wave in the considered framework. These characteristics of wave propagation along with the above-stated variation have been scrutinized based on their numerical results. This parametric study reveals that wave velocity remarkably fluctuates as the magnitude of inhomogeneity parameters increases and decreases. The prominent effect has been shown depicting the dependence of wave velocity on the degree of material anisotropy. The influence of phase angle and depth of the medium has been remarkably established. The present study may facilitate the theoretical foundation and practical application in the field of earthquake source mechanisms.

Keywords: cross-anisotropic, inhomogeneity, P-wave, SH-wave, SV-wave, shear modulus, Young’s modulus

Procedia PDF Downloads 85
7742 Application of Genetic Algorithm with Multiobjective Function to Improve the Efficiency of Photovoltaic Thermal System

Authors: Sonveer Singh, Sanjay Agrawal, D. V. Avasthi, Jayant Shekhar

Abstract:

The aim of this paper is to improve the efficiency of photovoltaic thermal (PVT) system with the help of Genetic Algorithms with multi-objective function. There are some parameters that affect the efficiency of PVT system like depth and length of the channel, velocity of flowing fluid through the channel, thickness of the tedlar and glass, temperature of inlet fluid i.e. all above parameters are considered for optimization. An attempt has been made to the model and optimizes the parameters of glazed hybrid single channel PVT module when two objective functions have been considered separately. The two objective function for optimization of PVT module is overall electrical and thermal efficiency. All equations for PVT module have been derived. Using genetic algorithms (GAs), above two objective functions of the system has been optimized separately and analysis has been carried out for two cases. Two cases are: Case-I; Improvement in electrical and thermal efficiency when overall electrical efficiency is optimized, Case-II; Improvement in electrical and thermal efficiency when overall thermal efficiency is optimized. All the parameters that are used in genetic algorithms are the parameters that could be changed, and the non-changeable parameters, like solar radiation, ambient temperature cannot be used in the algorithm. It has been observed that electrical efficiency (14.08%) and thermal efficiency (19.48%) are obtained when overall thermal efficiency was an objective function for optimization. It is observed that GA is a very efficient technique to estimate the design parameters of hybrid single channel PVT module.

Keywords: genetic algorithm, energy, exergy, PVT module, optimization

Procedia PDF Downloads 572
7741 Integration of Quality Function Deployment and Modular Function Deployment in Product Development

Authors: Naga Velamakuri, Jyothi K. Reddy

Abstract:

Quality must be designed into a product and not inspected has become the main motto of all the companies globally. Due to the rapidly increasing technology in the past few decades, the nature of demands from the consumers has become more sophisticated. To sustain this global revolution of innovation in production systems, companies have to take steps to accommodate this technology growth. In this process of understanding the customers' expectations, all the firms globally take steps to deliver a perfect output. Most of these techniques also concentrate on the consistent development and optimization of the product to exceed the expectations. Quality Function Deployment(QFD) and Modular Function Deployment(MFD) are such techniques which rely on the voice of the customer and help deliver the needs. In this paper, Quality Function Deployment and Modular Function Deployment techniques which help in converting the quantitative descriptions to qualitative outcomes are discussed. The area of interest would be to understand the scope of each of the techniques and the application range in product development when these are applied together to any problem. The research question would be mainly aimed at comprehending the limitations using modularity in product development.

Keywords: quality function deployment, modular function deployment, house of quality, methodology

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