Search results for: Galerkin projection

Authors: N. H. Z. Abidin, N. F. M. Mokhtar, S. S. A. Gani

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The influence of diffusion of the thermal or known as Soret effect in a heated Binary fluid model with Coriolis force is investigated theoretically. The linear stability analysis is used, and the eigenvalue is obtained using the Galerkin method. The impact of the Soret and Coriolis force on the onset of stationary convection in a system is analysed with respect to various Binary fluid parameters and presented graphically. It is found that an increase of the Soret values, destabilize the Binary fluid layer system. However, elevating the values of the Coriolis force helps to lag the onset of convection in a system.

Keywords: Benard convection, binary fluid, Coriolis, Soret

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Authors: Alireza Akbari, Gelareh Babaee Khou

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Ground Penetrating Radar (GPR) is an important nondestructive remote sensing tool that has been used in both military and civilian fields. Recently, GPR imaging has attracted lots of attention in detection of subsurface shallow small targets such as landmines and unexploded ordnance and also imaging behind the wall for security applications. For the monostatic arrangement in the space-time GPR image, a single point target appears as a hyperbolic curve because of the different trip times of the EM wave when the radar moves along a synthetic aperture and collects reflectivity of the subsurface targets. With this hyperbolic curve, the resolution along the synthetic aperture direction shows undesired low resolution features owing to the tails of hyperbola. However, highly accurate information about the size, electromagnetic (EM) reflectivity, and depth of the buried objects is essential in most GPR applications. Therefore hyperbolic curve behavior in the space-time GPR image is often willing to be transformed to a focused pattern showing the object's true location and size together with its EM scattering. The common goal in a typical GPR image is to display the information of the spatial location and the reflectivity of an underground object. Therefore, the main challenge of GPR imaging technique is to devise an image reconstruction algorithm that provides high resolution and good suppression of strong artifacts and noise. In this paper, at first, the standard back-projection (BP) algorithm that was adapted to GPR imaging applications used for the image reconstruction. The standard BP algorithm was limited with against strong noise and a lot of artifacts, which have adverse effects on the following work like detection targets. Thus, an improved BP is based on cross-correlation between the receiving signals proposed for decreasing noises and suppression artifacts. To improve the quality of the results of proposed BP imaging algorithm, a weight factor was designed for each point in region imaging. Compared to a standard BP algorithm scheme, the improved algorithm produces images of higher quality and resolution. This proposed improved BP algorithm was applied on the simulation and the real GPR data and the results showed that the proposed improved BP imaging algorithm has a superior suppression artifacts and produces images with high quality and resolution. In order to quantitatively describe the imaging results on the effect of artifact suppression, focusing parameter was evaluated.

Keywords: algorithm, back-projection, GPR, remote sensing

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Authors: Mahtsente Tadese, Lalit Kumar, Richard Koech

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The aim of this study was to project and analyze climate change in the Awash River Basin (ARB) using bias-corrected Global and Regional Climate Model simulations. The analysis included a baseline period from 1986-2005 and two future scenarios (the 2050s and 2070s) under two representative concentration pathways (RCP4.5 and RCP8.5). Bias correction methods were evaluated using graphical and statistical methods. Following the evaluation of bias correction methods, the Distribution Mapping (DM) and Power Transformation (PT) were used for temperature and precipitation projection, respectively. The 2050s and 2070s RCP4 simulations showed an increase in precipitation during half of the months with 32 and 10%, respectively. Moreover, the 2050s and 2070s RCP8.5 simulation indicated a decrease in precipitation with 18 and 26%, respectively. The 2050s and 2070s RCP8.5 simulation indicated a significant decrease in precipitation in four of the months (February/March to May) with the highest decreasing rate of 34.7%. The 2050s and 2070s RCP4.5 simulation showed an increase of 0.48-2.6 °C in maximum temperature. In the case of RCP8.5, the increase rate reached 3.4 °C and 4.1 °C in the 2050s and 2070s, respectively. The changes in precipitation and temperature might worsen the water stress, flood, and drought in ARB. Moreover, the critical focus should be given to mitigation strategies and management options to reduce the negative impact. The findings of this study provide valuable information on future precipitation and temperature change in ARB, which will help in the planning and design of sustainable mitigation approaches in the basin.

Keywords: variability, climate change, Awash River Basin, precipitation

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Authors: Chen Zhang, Nan Chen

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High-dimensional process monitoring becomes increasingly important in many application domains, where usually the process distribution is unknown and much more complicated than the normal distribution, and the between-stream correlation can not be neglected. However, since the process dimension is generally much bigger than the reference sample size, most traditional nonparametric multivariate control charts fail in high-dimensional cases due to the curse of dimensionality. Furthermore, when the process goes out of control, the influenced variables are quite sparse compared with the whole dimension, which increases the detection difficulty. Targeting at these issues, this paper proposes a new nonparametric monitoring scheme for high-dimensional processes. This scheme first projects the high-dimensional process into several subprocesses using random projections for dimension reduction. Then, for every subprocess with the dimension much smaller than the reference sample size, a local nonparametric control chart is constructed based on the spatial rank test to detect changes in this subprocess. Finally, the results of all the local charts are fused together for decision. Furthermore, after an out-of-control (OC) alarm is triggered, a diagnostic framework is proposed. using the square-root LASSO. Numerical studies demonstrate that the chart has satisfactory detection power for sparse OC changes and robust performance for non-normally distributed data, The diagnostic framework is also effective to identify truly changed variables. Finally, a real-data example is presented to demonstrate the application of the proposed method.

Keywords: random projection, high-dimensional process control, spatial rank, sequential change detection

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Authors: Y. Galerkin, L. Marenina

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Stator elements «Vane diffuser + crossover + return channel» of stages with different specific speed were investigated by CFD calculations. The regime parameter was introduced to present efficiency and loss coefficient performance of all elements together. Flow structure demonstrated advantages and disadvantages of design. Flow separation in crossovers was eliminated by its shape modification. Efficiency increased visibly. Calculated CFD performances are in acceptable correlation with predicted ones by engineering design method. The information obtained is useful for design method better calibration.

Keywords: vane diffuser, return channel, crossover, efficiency, loss coefficient, inlet flow angle

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Authors: Prodromos E. Atlamazoglou

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The method of moments combined with the method of symmetrical components is used for the analysis of interstitial hyperthermia applicators. The basis and testing functions are both piecewise sinusoids, qualifying our technique as a Galerkin one. The dielectric coatings are modeled by equivalent volume polarization currents, which are simply related to the conduction current distribution, avoiding in that way the introduction of additional unknowns or numerical integrations. The results of our method for a four dipole circular array, are in agreement with those already published in literature for a same hyperthermia configuration. Apart from being accurate, our approach is more general, more computationally efficient and takes into account the coupling between the antennas.

Keywords: hyperthermia, integral equations, insulated antennas, method of symmetrical components

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Authors: Alexandra Andrade Brandão Soares, Paulo Batista Gonçalves

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Using a modal expansion that satisfies the boundary and continuity conditions and expresses the modal couplings characteristic of cylindrical shells in the nonlinear regime, the equations of motion are discretized using the Galerkin method. The resulting algebraic equations are solved by the Newton-Raphson method, thus obtaining the nonlinear frequency-amplitude relation. Finally, a parametric analysis is conducted to study the influence of the geometry of the shell, the gradient of the functional material and vibration modes on the degree and type of nonlinearity of the cylindrical shell, which is the main contribution of this research work.

Keywords: cylindrical shells, dynamics, functionally graded material, nonlinear vibrations

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Authors: P. G. Romeo

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A Lie group is a highly sophisticated structure which is a smooth manifold whose underlying set of elements is equipped with the structure of a group such that the group multiplication and inverse-assigning functions are smooth. This structure was introduced by the Norwegian mathematician So- phus Lie who founded the theory of continuous groups. The Lie groups are well developed and have wide applications in areas including Mathematical Physics. There are several advances and generalizations for Lie groups and Lie groupoids is one such which is termed as a "many-object generalization" of Lie groups. A groupoid is a category whose morphisms are all invertible, obviously, every group is a groupoid but not conversely. Definition 1. A Lie groupoid G ⇒ M is a groupoid G on a base M together with smooth structures on G and M such that the maps α, β: G → M are surjective submertions, the object inclusion map x '→ 1x, M → G is smooth, and the partial multiplication G ∗ G → G is smooth. A bundle is a triple (E, p, B) where E, B are topological spaces p: E → B is a map. Space B is called the base space and space E is called total space and map p is the projection of the bundle. For each b ∈ B, the space p−1(b) is called the fibre of the bundle over b ∈ B. Intuitively a bundle is regarded as a union of fibres p−1(b) for b ∈ B parametrized by B and ’glued together’ by the topology of the space E. A cross-section of a bundle (E, p, B) is a map s: B → E such that ps = 1B. Example 1. Given any space B, a product bundle over B with fibre F is (B × F, p, B) where p is the projection on the first factor. Definition 2. A principal bundle P (M, G, π) consists of a manifold P, a Lie group G, and a free right action of G on P denoted (u, g) '→ ug, such that the orbits of the action coincide with the fibres of the surjective submersion π : P → M, and such that M is covered by the domains of local sections σ: U → P, U ⊆ M, of π. Definition 3. A Lie group bundle, or LGB, is a smooth fibre bundle (K, q, M ) in which each fibre (Km = q−1(m), and the fibre type G, has a Lie group structure, and for which there is an atlas {ψi: Ui × G → KUi } such that each {ψi,m : G → Km}, is an isomorphism of Lie groups. A morphism of LGB from (K, q, M ) to (K′, q′, M′) is a morphism (F, f ) of fibre bundles such that each Fm: Km → K′ is a morphism of Lie groups. In this paper, we will be discussing the Lie groupoid bundles. Here it is seen that to a Lie groupoid Ω on base B there is associated a collection of principal bundles Ωx(B, Ωx), all of which are mutually isomorphic and conversely, associated to any principal bundle P (B, G, p) there is a groupoid called the Ehresmann groupoid which is easily seen to be Lie. Further, some interesting properties of the category of Lie groupoids and bundles will be explored.

Keywords: groupoid, lie group, lie groupoid, bundle

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Authors: Roberta Martino, Viviana Ventre

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From a theoretical point of view, the relationship between the risk associated with an investment and the expected value are directly proportional, in the sense that the market allows a greater result to those who are willing to take a greater risk. However, empirical evidence proves that this relationship is distorted in the minds of investors and is perceived exactly the opposite. To deepen and understand the discrepancy between the actual actions of the investor and the theoretical predictions, this paper analyzes the essential parameters used for the valuation of financial assets with greater attention to two elements: probability and the passage of time. Although these may seem at first glance to be two distinct elements, they are closely related. In particular, the error in the theoretical description of the relationship between risk and return lies in the failure to consider the impatience that is generated in the decision-maker when events that have not yet happened occur in the decision-making context. In this context, probability loses its objective meaning and in relation to the psychological aspects of the investor, it can only be understood as the degree of confidence that the investor has in the occurrence or non-occurrence of an event. Moreover, the concept of objective probability does not consider the inter-temporality that characterizes financial activities and does not consider the condition of limited cognitive capacity of the decision maker. Cognitive psychology has made it possible to understand that the mind acts with a compromise between quality and effort when faced with very complex choices. To evaluate an event that has not yet happened, it is necessary to imagine that it happens in your head. This projection into the future requires a cognitive effort and is what differentiates choices under conditions of risk and choices under conditions of uncertainty. In fact, since the receipt of the outcome in choices under risk conditions is imminent, the mechanism of self-projection into the future is not necessary to imagine the consequence of the choice and the decision makers dwell on the objective analysis of possibilities. Financial activities, on the other hand, develop over time and the objective probability is too static to consider the anticipatory emotions that the self-projection mechanism generates in the investor. Assuming that uncertainty is inherent in valuations of events that have not yet occurred, the focus must shift from risk management to uncertainty management. Only in this way the intertemporal dimension of the decision-making environment and the haste generated by the financial market can be cautioned and considered. The work considers an extension of the prospectus theory with the temporal component with the aim of providing a description of the attitude towards risk with respect to the passage of time.

Keywords: impatience, risk aversion, subjective probability, uncertainty

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Authors: Y.Galerkin, O. Solovieva

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Flow parameters are calculated in vaneless diffusers with relative width 0,014 – 0,10 constant along radii. Inlet flow angles and similarity criteria were varied. Information about flow structure is presented – meridian streamlines configuration, information on flow full development, flow separation. Polytrophic efficiency, loss and recovery coefficient are used to compare diffusers’ effectiveness. The sample of narrow diffuser optimization by conical walls application is presented. Three tampered variants of a wide diffuser are compared too. The work is made in the R&D laboratory “Gas dynamics of turbo machines” of the TU SPb.

Keywords: vaneless diffuser, relative width, flow angle, flow separation, loss coefficient, similarity criteria

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Authors: A.Beril Tugrul, Selahattin Cimen

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Dependency of humanity on the energy is ever-increasing today and the energy policies are reaching undeniable and un-ignorable dimensions steering the political events as well. Therefore, energy has the highest priority for Turkey like any other country. In this study, the energy supply security for Turkey evaluated according to the strategic criteria of energy policy. Under these circumstances, different alternatives are described and assessed with in terms of the energy expansion of Turkey. With this study, different opportunities in the energy expansion of Turkey is clarified and emphasized.

Keywords: energy policy, energy strategy, future projection, Turkey

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Authors: Ghulam Hussain, Herrington Lee, Comfort Paul, Jones Richard

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Background: To determine the functional limitations of the lower limbs or readiness to return to sport, most rehabilitation programs use some form of testing; however, it is still unknown what the pass criteria is. This study aims to investigate the differences between the dominant and non-dominant leg performances across several lower limb tasks, which are hop tests, two-dimensional (2D) frontal plane projection angle (FPPA) tests, and isokinetic muscle tests. This study also provides the reference values for the limb symmetry index (LSI) for the hop and isokinetic muscle strength tests. Twenty recreationally active participants were recruited, 11 males and 9 females (age 23.65±2.79 years; height 169.9±3.74 cm; and body mass 74.72±5.81 kg. All tests were undertaken on the dominant and non-dominant legs. These tests are (1) Hop tests, which include horizontal hop for distance and crossover hop tests, (2) Frontal plane projection angle (FPPA): 2D capturing from two different tasks, which are forward hop landing and squatting, and (3) Isokinetic muscle strength tests: four different muscles were tested: quadriceps, hamstring, ankle plantar flexor, and hip extensor muscles. The main outcome measurements were, for the (1) hop tests: maximum distance was taken when undertaking single/crossover hop for distance using a standard tape measure, (2) for the FPPA: the knee valgus angle was measured from the maximum knee flexion position using a single 2D camera, and (3) for the isokinetic muscle strength tests: three different variables were measured: peak torque, peak torque to body weight, and the total work to body weight. All the muscle strength tests have been applied in both concentric and eccentric muscle actions at a speed of 60°/sec. This study revealed no differences between the dominant and non-dominant leg performance, and 85% of LSI was achieved by the majority of the subjects in both hop and isokinetic muscle tests, and; therefore, one leg’s hop performance can define the other.

Keywords: 2D FPPA, hop tests, isokinetic testing, LSI

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Authors: Sue Hershberger Yoder, Jon Yoder

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“The appearance does not hide the essence, it reveals it; it is the essence.”—Jean-Paul Sartre, Being and Nothingness Three decades ago, transarchitect Marcos Novak developed an early form of algorithmic animation he called “liquid architecture.” In that project, digitally floating forms morphed seamlessly in cyberspace without claiming to evolve or improve. Change itself was seen as inevitable. And although some imagistic moments certainly stood out, none was hierarchically privileged over another. That project challenged longstanding assumptions about creativity and artistic genius by posing infinite parametric possibilities as inviting alternatives to traditional notions of stability, originality, and evolution. Through ephemeral processes of printing, milling, and projecting, the exhibition “Liquid Illumination” destabilizes the solid foundations of fashion and architecture. The installation is neither worn nor built in the conventional sense, but—like the sensual art forms of fashion and architecture—it is still radically embodied through the logics and techniques of design. Appearances are everything. Surface pattern and color are no longer understood as minor afterthoughts or vapid carriers of dubious content. Here, they become essential but ever-changing aspects of precisely fabricated images. Fourteen silk “colorways” (a term from the fashion industry) are framed selections from ongoing experiments with intricate pattern and complex color configurations. Whether these images are printed on fabric, milled in foam, or illuminated through projection, they explore and celebrate the untapped potentials of the surficial and superficial. Some components of individual prints appear to float in front of others through stereoscopic superimpositions; some figures appear to melt into others due to subtle changes in hue without corresponding changes in value; and some layers appear to vibrate via moiré effects that emerge from unexpected pattern and color combinations. The liturgical atmosphere of Liquid Illumination is intended to acknowledge that, like the simultaneously sacred and superficial qualities of rose windows and illuminated manuscripts, artistic and religious ideologies are also always malleable. The intellectual provocation of this paper pushes the boundaries of current thinking concerning viable applications for fashion print designs and architectural images—challenging traditional boundaries between fine art and design. The opportunistic installation of digital printing, CNC milling, and video projection mapping in a gallery that is normally reserved for fine art exhibitions raises important questions about cultural/commercial display, mass customization, digital reproduction, and the increasing prominence of surface effects (color, texture, pattern, reflection, saturation, etc.) across a range of artistic practices and design disciplines.

Keywords: fashion, print design, architecture, projection mapping, image, fabrication

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Authors: G. N. Sekhar, P. G. Siddheshwar, G. Jayalatha, R. Prakash

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The problem of thermal convection in temperature and magnetic field sensitive Newtonian ferromagnetic liquid is studied in the presence of uniform vertical magnetic field and throughflow. Using a combination of Galerkin and shooting techniques the critical eigenvalues are obtained for stationary mode. The effect of Prandtl number (Pr > 1) on onset is insignificant and nonlinearity of non-buoyancy magnetic parameter M3 is found to have no influence on the onset of ferroconvection. The magnetic buoyancy number, M1 and variable viscosity parameter, V have destabilizing influences on the system. The effect of throughflow Peclet number, Pe is to delay the onset of ferroconvection and this effect is independent of the direction of flow.

Keywords: ferroconvection, magnetic field dependent viscosity, temperature dependent viscosity, throughflow

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Authors: Yasuyuki Takahashi, Hirotaka Shimada, Kyoko Saito

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Bone scintigraphy is widely used as a screening tool for bone metastases. However, the 180 to 240 minutes (min) waiting time after the intravenous (i.v.) injection of the tracer is both long and tiresome. To solve this shortcoming, a bone scan with a shorter waiting time is needed. In this study, we applied the Maximum Intensity Projection (MIP) and triple energy window (TEW) scatter correction to a whole body bone SPECT (Merged SPECT) and investigated shortening the waiting time. Methods: In a preliminary phantom study, hot gels of 99mTc-HMDP were inserted into sets of rods with diameters ranging from 4 to 19 mm. Each rod set covered a sector of a cylindrical phantom. The activity concentration of all rods was 2.5 times that of the background in the cylindrical body of the phantom. In the human study, SPECT images were obtained from chest to abdomen at 30 to 180 min after 99mTc- hydroxymethylene diphosphonate (HMDP) injection of healthy volunteers. For both studies, MIP images were reconstructed. Planar whole body images of the patients were also obtained. These were acquired at 200 min. The image quality of the SPECT and the planar images was compared. Additionally, 36 patients with breast cancer were scanned in the same way. The delectability of uptake regions (metastases) was compared visually. Results: In the phantom study, a 4 mm size hot gel was difficult to depict on the conventional SPECT, but MIP images could recognize it clearly. For both the healthy volunteers and the clinical patients, the accumulation of 99mTc-HMDP in the SPECT was good as early as 90 min. All findings of both image sets were in agreement. Conclusion: In phantoms, images from MIP with TEW scatter correction could detect all rods down to those with a diameter of 4 mm. In patients, MIP reconstruction with TEW scatter correction could improve the detectability of hot lesions. In addition, the time between injection and imaging could be shortened from that conventionally used for whole body scans.

Keywords: merged SPECT, MIP, TEW scatter correction, 99mTc-HMDP

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Authors: E. Tchandao Mangamana, V. Cariou, E. Vigneau, R. Glele Kakai, E. M. Qannari

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A new definition of a latent variable associated with a dataset makes it possible to propose variants of the PLS2 regression and the multi-block PLS (MB-PLS). We shall refer to these variants as Rd-PLS regression and Rd-MB-PLS respectively because they are inspired by both Redundancy analysis and PLS regression. Usually, a latent variable t associated with a dataset Z is defined as a linear combination of the variables of Z with the constraint that the length of the loading weights vector equals 1. Formally, t=Zw with ‖w‖=1. Denoting by Z' the transpose of Z, we define herein, a latent variable by t=ZZ’q with the constraint that the auxiliary variable q has a norm equal to 1. This new definition of a latent variable entails that, as previously, t is a linear combination of the variables in Z and, in addition, the loading vector w=Z’q is constrained to be a linear combination of the rows of Z. More importantly, t could be interpreted as a kind of projection of the auxiliary variable q onto the space generated by the variables in Z, since it is collinear to the first PLS1 component of q onto Z. Consider the situation in which we aim to predict a dataset Y from another dataset X. These two datasets relate to the same individuals and are assumed to be centered. Let us consider a latent variable u=YY’q to which we associate the variable t= XX’YY’q. Rd-PLS consists in seeking q (and therefore u and t) so that the covariance between t and u is maximum. The solution to this problem is straightforward and consists in setting q to the eigenvector of YY’XX’YY’ associated with the largest eigenvalue. For the determination of higher order components, we deflate X and Y with respect to the latent variable t. Extending Rd-PLS to the context of multi-block data is relatively easy. Starting from a latent variable u=YY’q, we consider its ‘projection’ on the space generated by the variables of each block Xk (k=1, ..., K) namely, tk= XkXk'YY’q. Thereafter, Rd-MB-PLS seeks q in order to maximize the average of the covariances of u with tk (k=1, ..., K). The solution to this problem is given by q, eigenvector of YY’XX’YY’, where X is the dataset obtained by horizontally merging datasets Xk (k=1, ..., K). For the determination of latent variables of order higher than 1, we use a deflation of Y and Xk with respect to the variable t= XX’YY’q. In the same vein, extending Rd-MB-PLS to the path modeling setting is straightforward. Methods are illustrated on the basis of case studies and performance of Rd-PLS and Rd-MB-PLS in terms of prediction is compared to that of PLS2 and MB-PLS.

Keywords: multiblock data analysis, partial least squares regression, path modeling, redundancy analysis

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Authors: Y. Galerkin, K. Soldatova, A. Drozdov

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The 6th version of Universal modeling method for centrifugal compressor stage calculation is described. Identification of the new mathematical model was made. As a result of identification the uniform set of empirical coefficients is received. The efficiency definition error is 0,86 % at a design point. The efficiency definition error at five flow rate points (except a point of the maximum flow rate) is 1,22 %. Several variants of the stage with 3D impellers designed by 6th version program and quasi three-dimensional calculation programs were compared by their gas dynamic performances CFD (NUMECA FINE TURBO). Performance comparison demonstrated general principles of design validity and leads to some design recommendations.

Keywords: compressor design, loss model, performance prediction, test data, model stages, flow rate coefficient, work coefficient

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Authors: Ibrahim Aliyu Isah, Mohd Mansor Ismail, Salim Hassan, Norsida Bint Man

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Global and National contributions of Extension Agents in income derive through stingless beekeeping production as acknowledged globally as a new source of wealth creation, which contributes significantly to the positive, sustainable economic growth of Malaysia. A common specie, Trigona itama, production through effective utilization of highly competent agents of extension services led to high increase of output that guaranteed high income and sustainability to farmers throughout the study areas. A study on impacts of extension services on stingless bee production and its profitability and sustainability in both Peninsular Malaysia and East (Sarawak) Malaysia was conducted with the following objectives: (i) to examined various impacts of extension services on sustainability as variables in enhancing stingless beekeeping production for positive profitability. (ii) to determine the profitability and sustainability of stingless beekeeping production in the study area through transfer of technology and human resources development. The study covers a sample of beekeepers in ten states of Peninsular Malaysia and Sarawak. The sample size of 87 respondents were selected out of the population and 54 of filled questionnaires were retrieved. Capital budgeting analysis was carried out and economic performance was evaluated. Data collected was analysed using SPSS version 23.0. Correlation and Regression analyses were used. The capital budgeting analysis and government incentive schemes was incorporated in the applied projection of stingless bee farms. The result of Net Present Value (NPV) is determined as an accepted projection to the financial appraisal. The NPV in the study indicated positive outcome of production that can generate positive income and indicated efficient yield of investment and Profitability index (PI). In summary, it is possible for the extension services to increase output and hence increase profit which is sustainable for growth and development of agricultural sector in Malaysia.

Keywords: extension services, impacts, profitability and sustainability, Sarawak and peninsular Malaysia, trigona itama production

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Authors: Shreeyam, Ranjan Kumar Sah, Shivangi

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Recognizing and solving handwritten mathematical expressions can be a challenging task, particularly when certain characters are segmented and classified. This project proposes a solution that uses Convolutional Neural Network (CNN) and image processing techniques to accurately solve various types of equations, including arithmetic, quadratic, and trigonometric equations, as well as logical operations like logical AND, OR, NOT, NAND, XOR, and NOR. The proposed solution also provides a graphical solution, allowing users to visualize equations and their solutions. In addition to equation solving, the platform, called CNNCalc, offers a comprehensive learning experience for students. It provides educational content, a quiz platform, and a coding platform for practicing programming skills in different languages like C, Python, and Java. This all-in-one solution makes the learning process engaging and enjoyable for students. The proposed methodology includes horizontal compact projection analysis and survey for segmentation and binarization, as well as connected component analysis and integrated connected component analysis for character classification. The compact projection algorithm compresses the horizontal projections to remove noise and obtain a clearer image, contributing to the accuracy of character segmentation. Experimental results demonstrate the effectiveness of the proposed solution in solving a wide range of mathematical equations. CNNCalc provides a powerful and user-friendly platform for solving equations, learning, and practicing programming skills. With its comprehensive features and accurate results, CNNCalc is poised to revolutionize the way students learn and solve mathematical equations. The platform utilizes a custom-designed Convolutional Neural Network (CNN) with image processing techniques to accurately recognize and classify symbols within handwritten equations. The compact projection algorithm effectively removes noise from horizontal projections, leading to clearer images and improved character segmentation. Experimental results demonstrate the accuracy and effectiveness of the proposed solution in solving a wide range of equations, including arithmetic, quadratic, trigonometric, and logical operations. CNNCalc features a user-friendly interface with a graphical representation of equations being solved, making it an interactive and engaging learning experience for users. The platform also includes tutorials, testing capabilities, and programming features in languages such as C, Python, and Java. Users can track their progress and work towards improving their skills. CNNCalc is poised to revolutionize the way students learn and solve mathematical equations with its comprehensive features and accurate results.

Keywords: AL, ML, hand written equation solver, maths, computer, CNNCalc, convolutional neural networks

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Authors: Y. Galerkin, A. Rekstin, K. Soldatova

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Universal modeling method well proven for industrial compressors was applied for design of the high flow rate supersonic stage. Results were checked by ANSYS CFX and NUMECA Fine Turbo calculations. The impeller appeared to be very effective at transonic flow velocities. Stator elements efficiency is acceptable at design Mach numbers too. Their loss coefficient versus inlet flow angle performances correlates well with Universal modeling prediction. The impeller demonstrated ability of satisfactory operation at design flow rate. Supersonic flow behavior in the impeller inducer at the shroud blade to blade surface Φdes deserves additional study.

Keywords: centrifugal compressor stage, supersonic impeller, inlet flow angle, loss coefficient, return channel, shock wave, vane diffuser

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Authors: K. Khanafer

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The aim of this investigation was to validate the fluid-structure interaction (FSI) model of type B aortic dissection with our experimental results from a bench-top-model. Another objective was to study the relationship between the size of a septectomy that increases the outflow of the false lumen and its effect on the values of the differential of pressure between true lumen and false lumen. FSI analysis based on Galerkin’s formulation was used in this investigation to study flow pattern and hemodynamics within a flexible type B aortic dissection model using boundary conditions from our experimental data. The numerical results of our model were verified against the experimental data for various tear size and location. Thus, CFD tools have a potential role in evaluating different scenarios and aortic dissection configurations.

Keywords: aortic dissection, fluid-structure interaction, in vitro model, numerical

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Authors: A. P. Mikhailovich, V. V. Fomin, E. M. Agapitov, V. E. Rogachev, E. A. Kostousova, E. S. Perekhodova

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Woody vegetation among the upper limit of its habitat is a sensitive indicator of biota reaction to regional climate changes. Quantitative assessment of temporal and spatial changes in the distribution of trees and plant biocenoses calls for the development of new modeling approaches based upon selected data from measurements on the ground level and ultra-resolution aerial photography. Statistical models were developed for the study area located in the Polar Urals. These models allow obtaining probabilistic estimates for placing Siberian Larch trees into one of the three age intervals, namely 1-10, 11-40 and over 40 years, based on the Weilbull distribution of the maximum horizontal crown projection. Authors developed the distribution map for larch trees with crown diameters exceeding twenty centimeters by deciphering aerial photographs made by a UAV from an altitude equal to fifty meters. The total number of larches was equal to 88608, forming the following distribution row across the abovementioned intervals: 16980, 51740, and 19889 trees. The results demonstrate that two processes can be observed in the course of recent decades: first is the intensive forestation of previously barren or lightly wooded fragments of the study area located within the patches of wood, woodlands, and sparse stand, and second, expansion into mountain tundra. The current expansion of the Siberian Larch in the region replaced the depopulation process that occurred in the course of the Little Ice Age from the late 13ᵗʰ to the end of the 20ᵗʰ century. Using data from field measurements of Siberian larch specimen biometric parameters (including height, diameter at root collar and at 1.3 meters, and maximum projection of the crown in two orthogonal directions) and data on tree ages obtained at nine circular test sites, authors developed a model for artificial neural network including two layers with three and two neurons, respectively. The model allows quantitative assessment of a specimen's age based on height and maximum crone projection values. Tree height and crown diameters can be quantitatively assessed using data from aerial photographs and lidar scans. The resulting model can be used to assess the age of all Siberian larch trees. The proposed approach, after validation, can be applied to assessing the age of other tree species growing near the upper tree boundaries in other mountainous regions. This research was collaboratively funded by the Russian Ministry for Science and Education (project No. FEUG-2023-0002) and Russian Science Foundation (project No. 24-24-00235) in the field of data modeling on the basis of artificial neural network.

Keywords: treeline, dynamic, climate, modeling

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Authors: Sendi Zohra, Belhadjsalah Hedi, Labergere Carl, Saanouni Khemais

Abstract:

The modeling of mechanical problems including both material and geometric nonlinearities with Finite Element Method (FEM) remains challenging. Meshless methods offer special properties to get rid of well-known drawbacks of the FEM. The main objective of Meshless Methods is to eliminate the difficulty of meshing and remeshing the entire structure by simply insertion or deletion of nodes, and alleviate other problems associated with the FEM, such as element distortion, locking and others. In this study, a robust numerical implementation of an Element Free Galerkin Method for an elastoplastic coupled to damage problem is presented. Several results issued from the numerical simulations by a DynamicExplicit resolution scheme are analyzed and critically compared with Element Finite Method results. Finally, different numerical examples are carried out to demonstrate the efficiency of this method.

Keywords: damage, dynamic explicit, elastoplasticity, isotropic hardening, meshless

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Authors: Haci Mehmet Guzey, Levent Acar

Abstract:

In this paper, a novel decentralized controller is developed for linear systems with nonlinear unknown interconnections. A model linear decoupled system is assigned for each system. By using the difference actual and model state dynamics, the problem is formulated as inverse problem. Then, the interconnected dynamics are approximated by using Galerkin’s expansion method for inverse problems. Two different sets of orthogonal basis functions are utilized to approximate the interconnected dynamics. Approximated interconnections are utilized in the controller to cancel the interconnections and decouple the systems. Subsequently, the interconnected systems behave as a collection of decoupled systems.

Keywords: decentralized control, inverse problems, large scale systems, nonlinear interconnections, basis functions, system identification

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Authors: Merbouha Barka, K. H. Benrahou, A. Fakrar, A. Tounsi, E. A. Adda Bedia

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This paper presents an analytical investigation on the buckling and postbuckling behaviors of thick functionally graded plates subjected to thermal load .Material properties are assumed to be temperature dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. The formulations are based on first order shear deformation plate theory taking into account Von Karman nonlinearity and initial geometrical imperfection. By applying Galerkin method, closed-form relations of postbuckling equilibrium paths for simply supported plates are determined. Analysis is carried out to show the effects of material and geometrical properties, in-plane boundary restraint, and imperfection on the buckling and postbuckling loading capacity of the plates.

Keywords: functionally graded materials, postbuckling, first order shear deformation theory, imperfection

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Authors: Shaidatul Azdawiyah Abdul Talib, Wan Mohd Razi Idris, Liew Ju Neng, Tukimat Lihan, Muhammad Zamir Abdul Rasid

Abstract:

Climate change has received great attention worldwide due to the impact of weather causing extreme events. Rainfall and temperature are crucial weather components associated with climate change. In Malaysia, increasing temperatures and changes in rainfall distribution patterns lead to drought and flood events involving agricultural areas, especially rice fields. Muda Agricultural Development Authority (MADA) is the largest rice growing area among the 10 granary areas in Malaysia and has faced floods and droughts in the past due to changing climate. Changes in rainfall and temperature patter affect rice yield. Therefore, trend analysis is important to identify changes in temperature and rainfall patterns as it gives an initial overview for further analysis. Six locations across the MADA area were selected based on the availability of meteorological station (MetMalaysia) data. Historical data (1991 to 2020) collected from MetMalaysia and future climate projection by multi-model ensemble of climate model from CMIP5 (CNRM-CM5, GFDL-CM3, MRI-CGCM3, NorESM1-M and IPSL-CM5A-LR) have been analyzed using Mann-Kendall test to detect the time series trend, together with standardized precipitation anomaly, rainfall anomaly index, precipitation concentration index and temperature anomaly. Future projection data were analyzed based on 3 different periods; early century (2020 – 2046), middle century (2047 – 2073) and late-century (2074 – 2099). Results indicate that the MADA area does encounter extremely wet and dry conditions, leading to drought and flood events in the past. The Mann-Kendall (MK) trend analysis test discovered a significant increasing trend (p < 0.05) in annual rainfall (z = 0.40; s = 15.12) and temperature (z = 0.61; s = 0.04) during the historical period. Similarly, for both RCP 4.5 and RCP 8.5 scenarios, a significant increasing trend (p < 0.05) was found for rainfall (RCP 4.5: z = 0.15; s = 2.55; RCP 8.5: z = 0.41; s = 8.05;) and temperature (RCP 4.5: z = 0.84; s = 0.02; RCP 8.5: z = 0.94; s = 0.05). Under the RCP 4.5 scenario, the average temperature is projected to increase up to 1.6 °C in early century, 2.0 °C in the middle century and 2.4 °C in the late century. In contrast, under RCP 8.5 scenario, the average temperature is projected to increase up to 1.8 °C in the early century, 3.1 °C in the middle century and 4.3 °C in late century. Drought is projected to occur in 2038 and 2043 (early century); 2052 and 2069 (middle century); and 2095, 2097 to 2099 (late century) under RCP 4.5 scenario. As for RCP 8.5 scenario, drought is projected to occur in 2021, 2031 and 2034 (early century); and 2069 (middle century). No drought is projected to occur in the late century under the RCP 8.5 scenario. Thus, this information can be used for the analysis of the impact of climate change scenarios on rice growth and yield besides other crops found in MADA area. Additionally, this study, it would be helpful for researchers and decision-makers in developing applicable adaptation and mitigation strategies to reduce the impact of climate change.

Keywords: climate projection, drought, flood, rainfall, RCP 4.5, RCP 8.5, temperature

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Authors: T. H. Young, Y. J. Tsai

Abstract:

A method for determining the stress distribution of a rectangular plate subjected to two pairs of arbitrarily distributed in-plane edge shear loads is proposed, and the free vibration and buckling of such a rectangular plate are investigated in this work.  The method utilizes two stress functions to synthesize the stress-resultant field of the plate with each of the stress functions satisfying the biharmonic compatibility equation. The sum of stress-resultant fields due to these two stress functions satisfies the boundary conditions at the edges of the plate, from which these two stress functions are determined. Then, the free vibration and buckling of the rectangular plate are investigated by the Galerkin method. Numerical results obtained by this work are compared with those appeared in the literature, and good agreements are observed.

Keywords: stress analysis, free vibration, plate buckling, nonuniform in-plane edge shear

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Authors: Tai-Ping Chang

Abstract:

In the present study, the effects on chaotic motion of single-walled carbon nanotube (SWCNT) due to the linear and nonlinear damping are investigated. By using the Hamilton’s principle, the nonlinear governing equation of the single-walled carbon nanotube embedded in a matrix is derived. The Galerkin’s method is adopted to simplify the integro-partial differential equation into a nonlinear dimensionless governing equation for the SWCNT, which turns out to be a forced Duffing equation. The variations of the Lyapunov exponents of the SWCNT with damping and harmonic forcing amplitudes are investigated. Based on the computations of the top Lyapunov exponent, it is concluded that the chaotic motion of the SWCNT occurs when the amplitude of the periodic excitation exceeds certain value, besides, the chaotic motion of the SWCNT occurs with small linear damping and tiny nonlinear damping.

Keywords: chaotic motion, damping, Lyapunov exponents, single-walled carbon nanotube

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Authors: M. J. Uddin, M. M. Rahman

Abstract:

Transient natural convective flow dynamics of nanofluids in a horizontal homocentric annulus using nonhomogeneous dynamic model has been experimented numerically. The simulation is carried out for four different shapes of the inner wall, which is either cylindrical, elliptical, square or triangular. The outer surface of the annulus is maintained at constant low temperature while the inner wall is maintained at a uniform temperature; higher than the outer one. The enclosure is permeated by a uniform magnetic field having variable orientation. The Brownian motion and thermophoretic deposition phenomena of the nanoparticles are taken into account in model construction. The governing nonlinear momentum, energy, and concentration equations are solved numerically using Galerkin weighted residual finite element method. To find the best performer, the local Nusselt number is demonstrated for different shapes of the inner wall. The heat transfer enhancement for different nanofluids for four different shapes of the inner wall is exhibited.

Keywords: nanofluids, annulus, nonhomogeneous dynamic model, heat transfer

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Authors: Shangerganesh Lingeshwaran

Abstract:

In this presentation, we have performed numerical simulations for a reaction-diffusion equation with various nonlinear density-dependent diffusion operators and proliferation functions. The mathematical model represented by parabolic partial differential equation is considered to study the invasion of gliomas (the most common type of brain tumors) and to describe the growth of cancer cells and response to their treatment. The unknown quantity of the given reaction-diffusion equation is the density of cancer cells and the mathematical model based on the proliferation and migration of glioma cells. A standard Galerkin finite element method is used to perform the numerical simulations of the given model. Finally, important observations on the each of nonlinear diffusion functions and proliferation functions are presented with the help of computational results.

Keywords: glioma invasion, nonlinear diffusion, reaction-diffusion, finite eleament method

Procedia PDF Downloads 207