Search results for: complex non-linear partial differential equations

Authors: Zulfiqar Ali, Umar Saleem, Muhammad Junaid, Rizwan Tahir

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Gulzar Mahal is a heritage site located in the city of Bahawalpur, Pakistan. The site is under a process of degradation, as cracks are appearing on the walls, roofs, and floor around the building due to differential settlement. To preserve the integrity of the structure, a geotechnical distress evaluation was carried out to evaluate the causal factors and recommend remediation measures. The research involved the characterization of the problematic soil and analysis of the observed distress with respect to the geotechnical properties. Both conventional lab and field tests were used in conjunction with the unconventional techniques like; Electrical Resistivity Tomography (ERT) and FEA. The temporal, geophysical and geotechnical evaluations have concluded that the foundation soil over the past was subjected to variations in the land use, poor drainage patterns, overloading and fluctuations in groundwater table all contributing to the differential settlements manifesting in the form of the visible shear crack across the length and breadth of the building.

Keywords: differential settlement, distress evaluation, finite element analysis, Gulzar Mahal

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Authors: Israa Sh. Tawfic, Sema Koc Kayhan

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Given a large sparse signal, great wishes are to reconstruct the signal precisely and accurately from lease number of measurements as possible as it could. Although this seems possible by theory, the difficulty is in built an algorithm to perform the accuracy and efficiency of reconstructing. This paper proposes a new proved method to reconstruct sparse signal depend on using new method called Least Support Matching Pursuit (LS-OMP) merge it with the theory of Partial Knowing Support (PSK) given new method called Partially Knowing of Least Support Orthogonal Matching Pursuit (PKLS-OMP). The new methods depend on the greedy algorithm to compute the support which depends on the number of iterations. So to make it faster, the PKLS-OMP adds the idea of partial knowing support of its algorithm. It shows the efficiency, simplicity, and accuracy to get back the original signal if the sampling matrix satisfies the Restricted Isometry Property (RIP). Simulation results also show that it outperforms many algorithms especially for compressible signals.

Keywords: compressed sensing, lest support orthogonal matching pursuit, partial knowing support, restricted isometry property, signal reconstruction

Procedia PDF Downloads 243

Authors: Rouhollah Torabi, Ashkan Chavoshi, Sheyda Almasi, Shima Almasi

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In this paper the effect of impeller trim on centrifugal pump performance is studied and the most important effect which is decreasing the flow rate, differential head and efficiency is analyzed. For this case a low specific speed centrifugal pump is simulated with CFD. Total flow inside the pump including the secondary flow in sidewall gap which form internal leakage is modeled simultaneously in CFX software. The flow field in different area of pumps such as inside impeller, volute, balance holes and leakage through wear rings are studied. To validate the results experimental tests are done for various impeller diameters. Results also compared with analytic equations which predict pump performance with trimmed impeller.

Keywords: centrifugal pump, CFD, impeller, trim

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Authors: Nurudeen Oluwasola Lasisi

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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

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Authors: J.P. Henriques, E. R. Neto, G. Almeida, G. Ribeiro, J.V. Coutinho, A.B. Lugli

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Industry 4.0, or the Fourth Industrial Revolution, is transforming the relationship between people and machines. In this scenario, some technologies such as Cloud Computing, Internet of Things, Augmented Reality, Artificial Intelligence, Additive Manufacturing, among others, are making industries and devices increasingly intelligent. One of the most powerful technologies of this new revolution is the Digital Twin, which allows the virtualization of a real system or process. In this context, the present paper addresses the linear and nonlinear dynamic study of a didactic level plant using Digital Twin. In the first part of the work, the level plant is identified at a fixed point of operation, BY using the existing method of least squares means. The linearized model is embedded in a Digital Twin using Automation Studio® from Famous Technologies. Finally, in order to validate the usage of the Digital Twin in the linearized study of the plant, the dynamic response of the real system is compared to the Digital Twin. Furthermore, in order to develop the nonlinear model on a Digital Twin, the didactic level plant is identified by using the method proposed by Hammerstein. Different steps are applied to the plant, and from the Hammerstein algorithm, the nonlinear model is obtained for all operating ranges of the plant. As for the linear approach, the nonlinear model is embedded in the Digital Twin, and the dynamic response is compared to the real system in different points of operation. Finally, yet importantly, from the practical results obtained, one can conclude that the usage of Digital Twin to study the dynamic systems is extremely useful in the industrial environment, taking into account that it is possible to develop and tune controllers BY using the virtual model of the real systems.

Keywords: industry 4.0, digital twin, system identification, linear and nonlinear models

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Authors: Usamah Al-Ali

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We explore the effect of expanding space on the exoticity of the matter supporting a traversable Lorentzian wormhole of zero radial tide whose line element is given by ds2 = dt^2 − a^2(t)[ dr^2/(1 − kr2 −b(r)/r)+ r2dΩ^2 in the context of General Relativity. This task is achieved by deriving the Einstein field equations for anisotropic matter field corresponding to the considered cosmological wormhole metric and performing a classification of their solutions on the basis of a variable equations of state (EoS) of the form p = ω(r)ρ. Explicit forms of the shape function b(r) and the scale factor a(t) arising in the classification are utilized to construct the corresponding energy-momentum tensor where the energy conditions for each case is investigated. While the violation of energy conditions is inevitable in case of static wormholes, the classification we performed leads to interesting solutions in which this violation is either reduced or eliminated.

Keywords: general relativity, Einstein field equations, energy conditions, cosmological wormhole

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Authors: Nahum Yustus Godi

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A three-dimensional numerical optimisation of combined microchannels with constructal solid, half hollow, and hollow circular fins is documented in this paper. The technique seeks to minimize peak temperature in the entire volume of the microchannel heat sink. The volume and axial length were all fixed, while the width of the microchannel could morph. High-density heat flux was applied at the bottom wall of the microchannel. The coolant employed to remove the heat deposited at the bottom surface of the microchannel was a single-phase fluid (water) in a forced convection laminar condition, and heat transfer was a conjugate problem. The unit cell symmetrical computation domain was discretised, and governing equations were solved using computational fluid dynamic (CFD) code. The results reveal that the combined microchannel with hollow circular fins and solid fins performed better at different Reynolds numbers. The numerical study was validated for the single microchannel without fins and found to be in good agreement with previous studies.

Keywords: constructal fins, complex heat exchangers, cooling technique, numerical optimisation

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Authors: Hamid Goharnejad, Milad Sadeghpoor Moalem, Mahmood Zakeri Niri, Leili Sadeghi Khalegh Abadi

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While there are many benefits to using reservoir dams, their break leads to destructive effects. From the viewpoint of International Committee of Large Dams (ICOLD), dam break means the collapse of whole or some parts of a dam; thereby the dam will be unable to hold water. Therefore, studying dam break phenomenon and prediction of its behavior and effects reduces losses and damages of the mentioned phenomenon. One of the most common types of reservoir dams is embankment dam. Overtopping in embankment dams occurs because of flood discharge system inability in release inflows to reservoir. One of the most important issues among managers and engineers to evaluate the performance of the reservoir dam rim when sliding into the storage, creating waves is large and long. In this study, the effects of floods which caused the overtopping of the dam have been investigated. It was assumed that spillway is unable to release the inflow. To determine outflow hydrograph resulting from dam break, numerical model using Flow-3D software and empirical equations was used. Results of numerical models and their comparison with empirical equations show that numerical model and empirical equations can be used to study the flood resulting from dam break.

Keywords: embankment dam break, empirical equations, Taleghan dam, Flow-3D numerical model

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Authors: Mohsun Rasim Alizada, Azar Inshalla Ahmdov

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Prompt photons are perhaps the most versatile tools for studying the dynamics of relativistic collisions of heavy ions. The study of photon radiation is of interest that in most hadron interactions, photons fly out as a background to other studied signals. The study of the birth of prompt photons in nucleon-nucleon collisions was previously carried out in experiments on Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). Due to the large energy of colliding nucleons, in addition to prompt photons, many different elementary particles are born. However, the birth of additional elementary particles makes it difficult to determine the accuracy of the effective section of the birth of prompt photons. From this point of view, the experiments planned on the Nuclotron-based Ion Collider Facility (NICA) complex will have a great advantage, since the energy obtained for colliding heavy ions will reduce the number of additionally born elementary particles. Of particular importance is the study of the processes of birth of prompt photons to determine the gluon leaving hadrons since the photon carries information about a rigid subprocess. At present, paper production of prompt photon in Compton scattering of quark-gluon and annihilation of quark–antiquark processes is investigated. The matrix elements Compton scattering of quark-gluon and annihilation of quark-antiquark pair processes has been written. The Square of matrix elements of processes has been calculated in FeynCalc. The phase volume of subprocesses has been determined. Expression to calculate the differential cross-section of subprocesses has been obtained: Given the resulting expressions for the square of the matrix element in the differential section expression, we see that the differential section depends not only on the energy of colliding protons, but also on the mass of quarks, etc. Differential cross-section of subprocesses is estimated. It is shown that the differential cross-section of subprocesses decreases with the increasing energy of colliding protons. Asymmetry coefficient with polarization of colliding protons is determined. The calculation showed that the squares of the matrix element of the Compton scattering process without and taking into account the polarization of colliding protons are identical. The asymmetry coefficient of this subprocess is zero, which is consistent with the literary data. It is known that in any single polarization processes with a photon, squares of matrix elements without taking into account and taking into account the polarization of the original particle must coincide, that is, the terms in the square of the matrix element with the degree of polarization are equal to zero. The coincidence of the squares of the matrix elements indicates that the parity of the system is preserved. The asymmetry coefficient of annihilation of quark–antiquark pair process linearly decreases from positive unit to negative unit with increasing the production of the polarization degrees of colliding protons. Thus, it was obtained that the differential cross-section of the subprocesses decreases with the increasing energy of colliding protons. The value of the asymmetry coefficient is maximal when the polarization of colliding protons is opposite and minimal when they are directed equally. Taking into account the polarization of only the initial quarks and gluons in Compton scattering does not contribute to the differential section of the subprocess.

Keywords: annihilation of a quark-antiquark pair, coefficient of asymmetry, Compton scattering, effective cross-section

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Authors: J. Samuel, S. Al-Enezi, A. Al-Banna

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High-density polyethylene reinforced with carbon nanofibers (HDPE/CNF) have been prepared via melt processing using dialkylimidazolium tetrafluoroborate (ionic liquid) as a dispersion agent. The prepared samples were characterized by thermogravimetric (TGA) and differential scanning calorimetric (DSC) analyses. The samples blended with imidazolium ionic liquid exhibit higher thermal stability. DSC analysis showed clear miscibility of ionic liquid in the HDPE matrix and showed single endothermic peak. The melt rheological analysis of HDPE/CNF composites was performed using an oscillatory rheometer. The influence of CNF and ionic liquid concentration (ranging from 0, 0.5, and 1 wt%) on the viscoelastic parameters was investigated at 200 °C with an angular frequency range of 0.1 to 100 rad/s. The rheological analysis shows the shear-thinning behavior for the composites. An improvement in the viscoelastic properties was observed as the nanofiber concentration increases. The progress in the modulus values was attributed to the structural rigidity imparted by the high aspect ratio CNF. The modulus values and complex viscosity of the composites increased significantly at low frequencies. Composites blended with ionic liquid exhibit slightly lower values of complex viscosity and modulus over the corresponding HDPE/CNF compositions. Therefore, reduction in melt viscosity is an additional benefit for polymer composite processing as a result of wetting effect by polymer-ionic liquid combinations.

Keywords: high-density polyethylene, carbon nanofibers, ionic liquid, complex viscosity

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Authors: Hyun-Woo Cho

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Unexpected operational events or abnormalities of industrial processes have a serious impact on the quality of final product of interest. In terms of statistical process control, fault detection and diagnosis of processes is one of the essential tasks needed to run the process safely. In this work, nonlinear representation of process measurement data is presented and evaluated using a simulation process. The effect of using different representation methods on the diagnosis performance is tested in terms of computational efficiency and data handling. The results have shown that the nonlinear representation technique produced more reliable diagnosis results and outperforms linear methods. The use of data filtering step improved computational speed and diagnosis performance for test data sets. The presented scheme is different from existing ones in that it attempts to extract the fault pattern in the reduced space, not in the original process variable space. Thus this scheme helps to reduce the sensitivity of empirical models to noise.

Keywords: fault diagnosis, nonlinear technique, process data, reduced spaces

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Authors: Rouzbeh Ramezani, Renzo Di Felice

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Nowadays, removal of CO₂ as one of the major contributors to global warming using alternative solvents with high CO₂ absorption efficiency, is an important industrial operation. In this study, three amines, including 2-methylpiperazine, potassium sarcosinate and potassium lysinate as potential additives, were added to the potassium carbonate solution as a base solvent for CO₂ capture. In order to study the absorption performance of CO₂ in terms of loading capacity of CO₂ and absorption rate, the absorption experiments in a blend of additives with potassium carbonate were carried out using the vapor-liquid equilibrium apparatus at a temperature of 313.15 K, CO₂ partial pressures ranging from 0 to 50 kPa and at mole fractions 0.2, 0.3, and 0.4. Furthermore, the performance of CO₂ absorption in these blend solutions was compared with pure monoethanolamine and with pure potassium carbonate. Finally, a correlation with good accuracy was developed using the nonlinear regression analysis in order to predict CO₂ loading capacity.

Keywords: absorption rate, carbon dioxide, CO2 capture, global warming, loading capacity

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Authors: Seema Paul, John Mango Magero, Prosun Bhattacharya, Zahra Kalantari, Steve W. Lyon

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The purpose of this review paper is to develop an understanding of lake hydrodynamics and the potential climate impact on the Lake Victoria (LV) catchment scale. This paper briefly discusses the main problems of lake hydrodynamics and its’ solutions that are related to quality assessment and climate effect. An empirical methodology in modeling and mapping have considered for understanding lake hydrodynamic and visualizing the long-term observational daily, monthly, and yearly mean dataset results by using geographical information system (GIS) and Comsol techniques. Data were obtained for the whole lake and five different meteorological stations, and several geoprocessing tools with spatial analysis are considered to produce results. The linear regression analyses were developed to build climate scenarios and a linear trend on lake rainfall data for a long period. A potential evapotranspiration rate has been described by the MODIS and the Thornthwaite method. The rainfall effect on lake water level observed by Partial Differential Equations (PDE), and water quality has manifested by a few nutrients parameters. The study revealed monthly and yearly rainfall varies with monthly and yearly maximum and minimum temperatures, and the rainfall is high during cool years and the temperature is high associated with below and average rainfall patterns. Rising temperatures are likely to accelerate evapotranspiration rates and more evapotranspiration is likely to lead to more rainfall, drought is more correlated with temperature and cloud is more correlated with rainfall. There is a trend in lake rainfall and long-time rainfall on the lake water surface has affected the lake level. The onshore and offshore have been concentrated by initial literature nutrients data. The study recommended that further studies should consider fully lake bathymetry development with flow analysis and its’ water balance, hydro-meteorological processes, solute transport, wind hydrodynamics, pollution and eutrophication these are crucial for lake water quality, climate impact assessment, and water sustainability.

Keywords: climograph, climate scenarios, evapotranspiration, linear trend flow, rainfall event on LV, concentration

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Authors: Jiwon Park, Jihae Hur, Kukjae Kim, Hansoo Kim

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In this study, outriggers, which are horizontal structures connecting a building core to distant columns to increase the lateral stiffness of a tall building, are used to reduce differential axial shortening in a tall building. Therefore, the outriggers in tall buildings are used to serve the dual purposes of reducing the lateral displacement and reducing the differential axial shortening. Since the location of the outrigger greatly affects the effectiveness of the outrigger in terms of the lateral displacement at the top of the tall building and the maximum differential axial shortening, the optimum locations of the dual-purpose outriggers can be determined by an optimization method. Because the floors where the outriggers are installed are given as integer numbers, the conventional gradient-based optimization methods cannot be directly used. In this study, a piecewise quadratic interpolation method is used to resolve the integrality requirement posed by the optimum locations of the dual-purpose outriggers. The optimal solutions for the dual-purpose outriggers are searched by linear scalarization which is a popular method for multi-objective optimization problems. It was found that increasing the number of outriggers reduced the maximum lateral displacement and the maximum differential axial shortening. It was also noted that the optimum locations for reducing the lateral displacement and reducing the differential axial shortening were different. Acknowledgment: This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science and ICT (NRF-2017R1A2B4010043) and financially supported by Korea Ministry of Land, Infrastructure and Transport(MOLIT) as U-City Master and Doctor Course Grant Program.

Keywords: concrete structure, optimization, outrigger, tall building

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Authors: Habib Akbarzadeh Bengar, Mohammad Asadi Kiadehi, Ali Rameeh

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The result of the past earthquakes has shown that insufficient amount of stirrups and brittle behavior of concrete lead to the shear and flexural failure in reinforced concrete (RC) members. In this paper, an analytical model proposed to predict the nonlinear behavior of RC and SFRC elements and frames. In this model, some important parameter such as shear effect, varying axial load, and longitudinal bar buckling are considered. The results of analytical model were verified with experimental tests. The results of verification have shown that the proposed analytical model can predict the nonlinear behavior of RC and SFRC members and also frames accurately. In addition, the results have shown that use of steel fibers increased bearing capacity and ductility of RC frame. Due to this enhancement in shear strength and ductility, insufficient amount of stirrups, which resulted in shear failure, can be offset with usage of the steel fibers. In addition to the steps taken, to analyze the effects of fibers percentages on the bearing capacity and ductility of frames parametric studies have been performed to investigate of these effects.

Keywords: nonlinear analysis, SFRC frame, shear failure, varying an axial load

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Authors: M. A. Tayfun, M. A. Alkhalidi

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The exact theoretical expression describing the probability distribution of nonlinear sea-surface elevations derived from the second-order narrowband model has a cumbersome form that requires numerical computations, not well-disposed to theoretical or practical applications. Here, the same narrowband model is re-examined to develop a simpler closed-form approximation suitable for theoretical and practical applications. The salient features of the approximate form are explored, and its relative validity is verified with comparisons to other readily available approximations, and oceanic data.

Keywords: ocean waves, probability distributions, second-order nonlinearities, skewness coefficient, wave steepness

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Authors: Ankita Shukla, Tiratha Raj Singh

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Colorectal cancer (CRC) imposes serious mortality burden worldwide and it has been increasing for past consecutive years. Continuous efforts have been made so far to diagnose the disease condition and to identify the root cause for it. In this study, we performed the pathway level as well as the differential gene expression studies for CRC. We analyzed the gene expression profile GSE24514 from Gene Expression Omnibus (GEO) along with the gene pathways involved in the CRC. This analysis helps us to understand the behavior of the genes that have shown differential expression through their targeted pathways. Pathway analysis for the targeted genes covers the wider area which therefore decreases the possibility to miss the significant ones. This will prove to be beneficial to expose the ones that have not been given attention so far. Through this analysis, we attempt to understand the various neighboring genes that have close relationship to the targeted one and thus proved to be significantly controlling the CRC. It is anticipated that the identified hub and neighboring genes will provide new directions to look at the pathway level differently and will be crucial for the regulatory processes of the disease.

Keywords: mismatch repair, microsatellite instability, carcinogenesis, morbidity

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Authors: Sadia Arshad, Ayesha Sohail, Sana Javed, Khadija Maqbool, Salma Kanwal

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The dynamical study of the carriers play an essential role in the evolution and global transmission of infectious diseases and will be discussed in this study. To make this approach novel, we will consider the fractional order model which is generalization of integer order derivative to an arbitrary number. Since the integration involved is non local therefore this property of fractional operator is very useful to study epidemic model for infectious diseases. An extended numerical method (ODE solver) is implemented on the model equations and we will present the simulations of the model for different values of fractional order to study the effect of carriers on transmission dynamics. Global dynamics of fractional model are established by using the reproduction number.

Keywords: Fractional differential equation, Numerical simulations, epidemic model, transmission dynamics

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Authors: Jurriaan Gillissen

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This work is concerned with stabilizing the numerical integration of the Navier-Stokes equation (NSE), backwards in time. Applications involve the detection of sources of, e.g., sound, heat, and pollutants. Stable reverse numerical integration of parabolic differential equations is also relevant for image de-blurring. While the literature addresses the reverse integration problem of the advection-diffusion equation, the problem of numerical reverse integration of the NSE has, to our knowledge, not yet been addressed. Owing to the presence of viscosity, the NSE is irreversible, i.e., when going backwards in time, the fluid behaves, as if it had a negative viscosity. As an effect, perturbations from the perfect solution, due to round off errors or discretization errors, grow exponentially in time, and reverse integration of the NSE is inherently unstable, regardless of using an implicit time integration scheme. Consequently, some sort of filtering is required, in order to achieve a stable, numerical, reversed integration. The challenge is to find a filter with a minimal adverse affect on the accuracy of the reversed integration. In the present work, we explore an adjoint gradient method (AGM) to achieve this goal, and we apply this technique to two-dimensional (2D), decaying turbulence. The AGM solves for the initial velocity field u0 at t = 0, that, when integrated forward in time, produces a final velocity field u1 at t = 1, that is as close as is feasibly possible to some specified target field v1. The initial field u0 defines a minimum of a cost-functional J, that measures the distance between u1 and v1. In the minimization procedure, the u0 is updated iteratively along the gradient of J w.r.t. u0, where the gradient is obtained by transporting J backwards in time from t = 1 to t = 0, using the adjoint NSE. The AGM thus effectively replaces the backward integration by multiple forward and backward adjoint integrations. Since the viscosity is negative in the adjoint NSE, each step of the AGM is numerically stable. Nevertheless, when applied to turbulence, the AGM develops instabilities, which limit the backward integration to small times. This is due to the exponential divergence of phase space trajectories in turbulent flow, which produces a multitude of local minima in J, when the integration time is large. As an effect, the AGM may select unphysical, noisy initial conditions. In order to improve this situation, we propose two remedies. First, we replace the integration by a sequence of smaller integrations, i.e., we divide the integration time into segments, where in each segment the target field v1 is taken as the initial field u0 from the previous segment. Second, we add an additional term (regularizer) to J, which is proportional to a high-order Laplacian of u0, and which dampens the gradients of u0. We show that suitable values for the segment size and for the regularizer, allow a stable reverse integration of 2D decaying turbulence, with accurate results for more then O(10) turbulent, integral time scales.

Keywords: time reversed integration, parabolic differential equations, adjoint gradient method, two dimensional turbulence

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Authors: Priyanka Ghosh, Priti Kumar Roy

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Every year a considerable number of people die due to methyl alcohol poisoning, in which most of them die even before proper treatment. This work gives a simple and cheap first aid to those affected individuals by the administration of activated charcoal. In this article, we emphasise on the adsorption capability of activated charcoal for the treatment of poisoning and use an impulsive differential equation to study the effect of activated charcoal during adsorption. We also investigate the effects of various parameters on the adsorption which are incorporated in the model system.

Keywords: activated charcoal, adsorption, impulsive differential equation, methanol poisoning

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Authors: Shuang Zhao, Shintaro Ito, Yoshihiro Ohba, Hiroshi Katagiri

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We present the synthesis and single-crystal X-ray crystallography of a Cu(II) complex(bmn-bpy) of a pyridine-naphthoimidazole-based ligand containing two naphthoimidazoles as the chromophores and a vacant coordination site on Cu(II).

Keywords: synthesis, Cu(II) complex, single-crystal X-ray crystallography

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Authors: Graziano Chesi

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The topological entropy plays a key role in linear dynamical systems, allowing one to establish the existence of stabilizing feedback controllers for linear systems in the presence of communications constraints. This paper addresses the determination of a robust value of the topological entropy in nonlinear dynamical systems, specifically the largest value of the topological entropy over all linearized models in a region of interest of the state space. It is shown that a sufficient condition for establishing upper bounds of the sought robust value of the topological entropy can be given in terms of a semidefinite program (SDP), which belongs to the class of convex optimization problems.

Keywords: non-linear system, communication constraint, topological entropy

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Authors: Mahdi Kiani, Hassan Salarieh, Aria Alasty, S. Mahdi Darbandi

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The design and implementation of the hybrid control method for a three-pole active magnetic bearing (AMB) is proposed in this paper. The system is inherently nonlinear and conventional nonlinear controllers are a little complicated, while the proposed hybrid controller has a piecewise linear form, i.e. linear in each sub-region. A state-feedback hybrid controller is designed in this study, and the unmeasurable states are estimated by an observer. The gains of the hybrid controller are obtained by the Linear Quadratic Regulator (LQR) method in each sub-region. To evaluate the performance, the designed controller is implemented on an experimental setup in static mode. The experimental results show that the proposed method can efficiently stabilize the three-pole AMB system. The simplicity of design, domain of attraction, uncomplicated control law, and computational time are advantages of this method over other nonlinear control strategies in AMB systems.

Keywords: active magnetic bearing, three pole AMB, hybrid control, Lyapunov function

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Authors: Brayden Mi

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Reverse time migration has been widely used in the Petroleum exploration industry to reveal subsurface images and to detect rock and fluid properties since the early 1980s. The seismic technology involves the construction of a velocity model through interpretive model construction, seismic tomography, or full waveform inversion, and the application of the reverse-time propagation of acquired seismic data and the original wavelet used in the acquisition. The methodology has matured from 2D, simple media to present-day to handle full 3D imaging challenges in extremely complex geological conditions. Conventional Ultrasound computed tomography (USCT) utilize travel-time-inversion to reconstruct the velocity structure of an organ. With the velocity structure, USCT data can be migrated with the “bend-ray” method, also known as migration. Its seismic application counterpart is called Kirchhoff depth migration, in which the source of reflective energy is traced by ray-tracing and summed to produce a subsurface image. It is well known that ray-tracing-based migration has severe limitations in strongly heterogeneous media and irregular acquisition geometries. Reverse time migration (RTM), on the other hand, fully accounts for the wave phenomena, including multiple arrives and turning rays due to complex velocity structure. It has the capability to fully reconstruct the image detectable in its acquisition aperture. The RTM algorithms typically require a rather accurate velocity model and demand high computing powers, and may not be applicable to real-time imaging as normally required in day-to-day medical operations. However, with the improvement of computing technology, such a computational bottleneck may not present a challenge in the near future. The present-day (RTM) algorithms are typically implemented from a flat datum for the seismic industry. It can be modified to accommodate any acquisition geometry and aperture, as long as sufficient illumination is provided. Such flexibility of RTM can be conveniently implemented for the application in USCT imaging if the spatial coordinates of the transmitters and receivers are known and enough data is collected to provide full illumination. This paper proposes an implementation of a full 3D RTM algorithm for USCT imaging to produce an accurate 3D acoustic image based on the Phase-shift-plus-interpolation (PSPI) method for wavefield extrapolation. In this method, each acquired data set (shot) is propagated back in time, and a known ultrasound wavelet is propagated forward in time, with PSPI wavefield extrapolation and a piece-wise constant velocity model of the organ (breast). The imaging condition is then applied to produce a partial image. Although each image is subject to the limitation of its own illumination aperture, the stack of multiple partial images will produce a full image of the organ, with a much-reduced noise level if compared with individual partial images.

Keywords: illumination, reverse time migration (RTM), ultrasound computed tomography (USCT), wavefield extrapolation

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Authors: Abdulbaset Saad, Adel Younis, Zuomin Dong

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For design optimization with high-dimensional expensive problems, an effective and efficient optimization methodology is desired. This work proposes a series of modification to the Differential Evolution (DE) algorithm for solving computation Intensive Black-Box Problems. The proposed methodology is called Radial Basis Meta-Model Algorithm Assisted Differential Evolutionary (RBF-DE), which is a global optimization algorithm based on the meta-modeling techniques. A meta-modeling assisted DE is proposed to solve computationally expensive optimization problems. The Radial Basis Function (RBF) model is used as a surrogate model to approximate the expensive objective function, while DE employs a mechanism to dynamically select the best performing combination of parameters such as differential rate, cross over probability, and population size. The proposed algorithm is tested on benchmark functions and real life practical applications and problems. The test results demonstrate that the proposed algorithm is promising and performs well compared to other optimization algorithms. The proposed algorithm is capable of converging to acceptable and good solutions in terms of accuracy, number of evaluations, and time needed to converge.

Keywords: differential evolution, engineering design, expensive computations, meta-modeling, radial basis function, optimization

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Authors: Fazl Ullah, Rahmat Ullah

Abstract:

This paper shows a comprehensive learning focused on the optimization of gas production in shale gas reservoirs through hydraulic fracturing. Shale gas has emerged as an important unconventional vigor resource, necessitating innovative techniques to enhance its extraction. The key objective of this study is to examine the influence of fracture parameters on reservoir productivity and formulate strategies for production optimization. A sophisticated model integrating gas flow dynamics and real stress considerations is developed for hydraulic fracturing in multi-stage shale gas reservoirs. This model encompasses distinct zones: a single-porosity medium region, a dual-porosity average region, and a hydraulic fracture region. The apparent permeability of the matrix and fracture system is modeled using principles like effective stress mechanics, porous elastic medium theory, fractal dimension evolution, and fluid transport apparatuses. The developed model is then validated using field data from the Barnett and Marcellus formations, enhancing its reliability and accuracy. By solving the partial differential equation by means of COMSOL software, the research yields valuable insights into optimal fracture parameters. The findings reveal the influence of fracture length, diversion capacity, and width on gas production. For reservoirs with higher permeability, extending hydraulic fracture lengths proves beneficial, while complex fracture geometries offer potential for low-permeability reservoirs. Overall, this study contributes to a deeper understanding of hydraulic cracking dynamics in shale gas reservoirs and provides essential guidance for optimizing gas production. The research findings are instrumental for energy industry professionals, researchers, and policymakers alike, shaping the future of sustainable energy extraction from unconventional resources.

Keywords: fluid-solid coupling, apparent permeability, shale gas reservoir, fracture property, numerical simulation

Procedia PDF Downloads 73

Authors: James A. Adeyanju, John O. Olajide, Akinbode A. Adedeji

Abstract:

A predictive mathematical model based on the fundamental principles of mass transfer was developed to simulate the moisture content and oil content during Deep-Fat Frying (DFF) process of dodo. The resulting governing equation, that is, partial differential equation that describes rate of moisture loss and oil uptake was solved numerically using explicit Finite Difference Technique (FDT). Computer codes were written in MATLAB environment for the implementation of FDT at different frying conditions and moisture loss as well as oil uptake simulation during DFF of dodo. Plantain samples were sliced into 5 mm thickness and fried at different frying oil temperatures (150, 160 and 170 ⁰C) for periods varying from 2 to 4 min. The comparison between the predicted results and experimental data for the validation of the model showed reasonable agreement. The correlation coefficients between the predicted and experimental values of moisture and oil transfer models ranging from 0.912 to 0.947 and 0.895 to 0.957, respectively. The predicted results could be further used for the design, control and optimization of deep-fat frying process.

Keywords: frying, moisture loss, modelling, oil uptake

Procedia PDF Downloads 450

Authors: Abdelaziz Sheba Abdelrahman

Abstract:

Compost enriched with actinomyces and Bacillus polymyxa algae as a Partial Substitute for Mineral N in Ewaise Mango Orchards Organic fertiliser, compost enriched with actinomyces, and the biofertilizer Bacillus polymyxa algae were used as a partial replacement for mineral N fertiliser in Ewaise mango orchards during the 2019 and 2020 seasons. When compared to using mineral N alone, the results showed that reducing the percentage of mineral N fertiliser from 100 to 50% and using compost enriched with actinomyces at 25 to 50% and Bacillus polymyxa had an announced promotion on leaf area, total chlorophylls, leaf N, P, and K, yield, and fruit quality. The use of compost enriched with actinomyces and Bacillus polymyxa, as well as mineral N, resulted in a significant decrease in nitrite in the pulp. Reducing mineral N to 25% of the suitable N had a negative impact on yield. The application of appropriate N via 50% inorganic N + compost enriched with actinomyces at 50% + Bacillus polymyxa algae increased yield quantitatively and qualitatively in Ewaise mango orchards. This promised treatment significantly reduced nitrite levels in the pulp fruit.

Keywords: bacillus polymyxa algae, fertiliser, biofertilizer, ewaise mango

Procedia PDF Downloads 113

Authors: J. Juan Peña, J. Morales, J. García-Ravelo, J. García-Martínez

Abstract:

It is known that by introducing alternative forms of exponential and logarithmic functions, the Tsallis entropy Sᵩ is itself a generalization of Shannon entropy S. In this work, from a deformation through a scaling function applied to the differential operator, it is possible to generate a q-deformed calculus as well as a q-deformed arithmetic, which not only allows generalizing the exponential and logarithmic functions but also any other standard function. The updated q-deformed differential operator leads to an updated integral operator under which the functions are integrated together with a weight function. For each differentiable function, it is possible to identify its q-deformed partner, which is useful to generalize other algebraic relations proper of the original functions. As an application of this proposal, in this work, a generalization of exponential and logarithmic functions is studied in such a way that their relationship with the thermodynamic functions, particularly the entropy, allows us to have a q-deformed expression of these. As a result, from a particular scaling function applied to the differential operator, a q-deformed arithmetic is obtained, leading to the generalization of the Tsallis entropy.

Keywords: q-calculus, q-deformed arithmetic, entropy, exponential functions, thermodynamic functions

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Authors: Biaou Jean-Baptiste Kouchoro, Anissa Meziane, Philippe Micheau, Mathieu Renier, Nicolas Quaegebeur

Abstract:

Numerous experimental and numerical studies have shown the interest of the local defects resonance (LDR) for the Non-Destructive Testing of metallic and composite plates. Indeed, guided ultrasonic waves such as Lamb waves, which are increasingly used for the inspection of these flat structures, enable the generation of local resonance phenomena by their interaction with a damaged area, allowing the detection of defects. When subjected to a large amplitude motion, a nonlinear behavior can predominate in the damaged area. This work presents a 2D Finite Element Model of the local resonance of a 12 mm long and 5 mm deep Flat Bottom Hole (FBH) in a 6 mm thick aluminum plate under the excitation induced by an incident A0 Lamb mode. The analysis of the transient response of the FBH enables the precise determination of its resonance frequencies and the associate modal deformations. Then, a linear parametric study varying the geometrical properties of the FBH highlights the sensitivity of the resonance frequency with respect to the plate thickness. It is demonstrated that the resonance effect disappears when the ratio of thicknesses between the FBH and the plate is below 0.1. Finally, the nonlinear behavior of the FBH is considered and studied introducing geometrical (taken into account the nonlinear component of the strain tensor) nonlinearities that occur at large vibration amplitudes. Experimental analysis allows observation of the resonance effects and nonlinear response of the FBH. The differences between these experimental results and the numerical results will be commented on. The results of this study are promising and allow to consider more realistic defects such as delamination in composite materials.

Keywords: guided waves, non-destructive testing, dynamic field testing, non-linear ultrasound/vibration

Procedia PDF Downloads 135