Search results for: coupling equation

Authors: Naila Nasreen, Dianchen Lu

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This paper explores the dynamical behavior of the (2+1)-dimensional Boussinesq equation, which is a nonlinear water wave equation and is used to model wave packets in dispersive media with weak nonlinearity. This equation depicts how long wave made in shallow water propagates due to the influence of gravity. The (2+1)- dimensional Boussinesq equation combines the two-way propagation of the classical Boussinesq equation with the dependence on a second spatial variable, as that occurs in the two-dimensional Kadomstev- Petviashvili equation. This equation provides a description of head- on collision of oblique waves and it possesses some interesting properties. The governing model is discussed by the assistance of Ricatti equation mapping method, a relatively integration tool. The solutions have been extracted in different forms the solitary wave solutions as well as hyperbolic and periodic solutions. Moreover, the sensitivity analysis is demonstrated for the designed dynamical structural system’s wave profiles, where the soliton wave velocity and wave number parameters regulate the water wave singularity. In addition to being helpful for elucidating nonlinear partial differential equations, the method in use gives previously extracted solutions and extracts fresh exact solutions. Assuming the right values for the parameters, various graph in different shapes are sketched to provide information about the visual format of the earned results. This paper’s findings support the efficacy of the approach taken in enhancing nonlinear dynamical behavior. We believe this research will be of interest to a wide variety of engineers that work with engineering models. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complicated systems in a variety of fields, especially in ocean engineering.

Keywords: (2+1)-dimensional Boussinesq equation, solitary wave solutions, Ricatti equation mapping approach, nonlinear phenomena

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Authors: Yaping Zhao

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In the present study, the exact solutions for the steady response of quasi-linear systems under non-white wide-band random excitation are considered by means of the stochastic averaging method. The non linearity of the systems contains the power-law damping and the cross-product term of the power-law damping and displacement. The drift and diffusion coefficients of the Fokker-Planck-Kolmogorov (FPK) equation after averaging are obtained by a succinct approach. After solving the averaged FPK equation, the joint probability density function and the marginal probability density function in steady state are attained. In the process of resolving, the eigenvalue problem of ordinary differential equation is handled by integral equation method. Some new results are acquired and the novel method to deal with the problems in nonlinear random vibration is proposed.

Keywords: random vibration, stochastic averaging method, FPK equation, transition probability density

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Authors: Sumit Kumar Vishwakarma

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The aim of the paper is to investigate the influence of inhomogeneity associated with the elastic constants and density of the orthotropic medium. The inhomogeneity is considered as exponential function of depth. The impact of gravity had been discussed. Using the concept of separation of variables, the system of a partial differential equation (equation of motion) has been converted into ordinary differential equation, which is coupled in nature. It further reduces to a biquadratic equation whose roots were found by using MATLAB. A suitable boundary condition is employed to derive the dispersion equation in a closed-form. Numerical simulations had been performed to show the influence of the inhomogeneity parameter. It was observed that as the numerical values of increases, the phase velocity of Rayleigh waves decreases at a particular wavenumber. Graphical illustrations were drawn to visualize the effect of the increasing and decreasing values of the inhomogeneity parameter. It can be concluded that it has a remarkable bearing on the phase velocity as well as damping velocity.

Keywords: Rayleigh waves, orthotropic medium, gravity field, inhomogeneity

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Authors: C. Trapp, A. Vijay, M. Khorasani

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Decentralised micro-grids with sector coupling can combat the spatial and temporal intermittence of renewable energy by combining power, transportation and infrastructure sectors. Intelligent energy conversion concepts such as electrolysers, hydrogen engines and fuel cells combined with energy storage using intelligent batteries and hydrogen storage form the back-bone of such a system. This paper describes a micro-grid based on Photo-Voltaic cells, battery storage, innovative modular and scalable Anion Exchange Membrane (AEM) electrolyzer with an efficiency of up to 73%, high-pressure hydrogen storage as well as cutting-edge combustion-engine based Combined Heat and Power (CHP) plant with more than 85% efficiency at the university campus to address the challenges of decarbonization whilst eliminating the necessity for expensive high-voltage infrastructure.

Keywords: sector coupling, micro-grids, energy self-sufficiency, decarbonization, AEM electrolysis, hydrogen CHP

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Authors: Kefale W. Yizengaw, Delele Worku Ayele, Jyh-Chiang Jiang

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The catalytic co-conversion of CO₂ and CH₄ to value-added compounds has become one of the promising approaches to addressing global climate change by having valuable fossil fuels. Thedirect co-conversion of CO₂ and CH₄ to value-added compounds is attractive but tremendously challenging because of both molecules' thermodynamic stability and kinetic inertness. In the present study, a single iridium atom doped and a single oxygen atom defect hematite (110)surface model catalyst, which can comprehend direct C–O coupling based on simultaneous activation of CO2 and CH4 was studied using density functional theory plus U (DFT + U)calculations. The presence of dual active sites on the Ir/Fe₂O₃(110)-OV surface catalyst enablesCO₂ activation on the Ir site and CH₄ activation at the defect site. The electron analysis for the theco-adsorption of CO₂ and CH₄ deals with the electron redistribution on the surface and clearly shows the synergistic effect for simultaneous CO₂ and CH₄ activation on Ir/α- Fe₂O₃(110)-OVsurface. The microkinetic analysis shows that the dissociation of CH4 to CH3 * and H* plays an excellent role in the C–O coupling. The coverage analysis for the intermediate products of the microkinetic simulation results indicates that C–O coupling is the reaction limiting step. Finally, after the CH₃O* intermediate product species is produced, the radical hydrogen species spontaneously diffuse to the CH3O* intermediate product to form methanol at around 490 [K]. The present work provides mechanistic and kinetic insights into the direct C–O coupling of CO₂and CH₄, which could help design more-efficient catalysts.

Keywords: co-conversion, C–O coupling, doping, oxygen vacancy, microkinetic

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Authors: Fahrudin Nugroho, Halim Hamadi, Yusril Yusuf, Pekik Nurwantoro, Ari Setiawan, Yoshiki Hidaka

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We investigate the Nikolaevskiy equation numerically using exponential time differencing method and pseudo-spectral method. This equation develops a long-wavelength modulation that behaves as a Nambu–Goldstone mode, and short-wavelength instability and exhibit turbulence. Using the autocorrelation analysis, the statistical properties of the turbulence governed by the equation are investigated. The autocorrelation then has been fitted with The Kohlrausch– Williams–Watts (KWW) expression. By varying the control parameter, we show a transition from compressed to stretched exponential for the auto-correlation function of Nikolaevskiy turbulence. The compressed exponential is an indicator of the existence of dynamical heterogeneity while the stretched indicates aging process. Thereby, we revealed the existence of dynamical heterogeneity and aging in the turbulence governed by Nikolaevskiy equation.

Keywords: compressed exponential, dynamical heterogeneity, Nikolaevskiy equation, stretched exponential, turbulence

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Authors: Anders Schou Simonsen, Thomas Condra, Kim Sørensen

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Various processes are modelled using a discrete phase, where particles are seeded from a source. Such particles can represent liquid water droplets, which are affecting the continuous phase by exchanging thermal energy, momentum, species etc. Discrete phases are typically modelled using parcel, which represents a collection of particles, which share properties such as temperature, velocity etc. When coupling the phases, the exchange rates are integrated over the cell, in which the parcel is located. This can cause spikes and fluctuating exchange rates. This paper presents an alternative method of coupling a discrete and a continuous plug flow phase. This is done using triangular parcels, which span between nodes following the dynamics of single droplets. Thus, the triangular parcels are propagated using the corner nodes. At each time step, the exchange rates are spatially integrated over the surface of the triangular parcels, which yields a smooth continuous exchange rate to the continuous phase. The results shows that the method is more stable, converges slightly faster and yields smooth exchange rates compared with the steam tube approach. However, the computational requirements are about five times greater, so the applicability of the alternative method should be limited to processes, where the exchange rates are important. The overall balances of the exchanged properties did not change significantly using the new approach.

Keywords: CFD, coupling, discrete phase, parcel

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Authors: Norhashidah Hj Mohd Ali, Teng Wai Ping

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In this paper, the formulation of a new group explicit method with a fourth order accuracy is described in solving the two-dimensional Helmholtz equation. The formulation is based on the nine-point fourth-order compact finite difference approximation formula. The complexity analysis of the developed scheme is also presented. Several numerical experiments were conducted to test the feasibility of the developed scheme. Comparisons with other existing schemes will be reported and discussed. Preliminary results indicate that this method is a viable alternative high accuracy solver to the Helmholtz equation.

Keywords: explicit group method, finite difference, Helmholtz equation, five-point formula, nine-point formula

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Authors: Hassan Athari, Abdurrahim Bolukbasi, Dogan Ciloglu

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This study represented the respiratory alveoli system, and determined the trajectory of inhaled particles more accurately using the modified three-dimensional model with deformable walls of alveoli. The study also considered the tissue tension in the model to demonstrate the effect of lung. Tissue tensions are transferred by the lung parenchyma and produce the pressure gradient. This load expands the alveoli and establishes a sub-ambient (vacuum) pressure within the lungs. Thus, at the alveolar level, the flow field and movement of alveoli wall lead to an integrated effect. In this research, we assume that the three-dimensional alveolus has a visco-elastic tissue (walls). For accurate investigation of pulmonary tissue mechanical properties on particle transport and alveolar flow field, the actual relevance between tissue movement and airflow is solved by two-way FSI (Fluid Structure Interaction) simulation technique in the alveolus. Therefore, the essence of real simulation of pulmonary breathing mechanics can be achieved by developing a coupled FSI computational model. We, therefore conduct a series of FSI simulations over a range of tissue models and breathing rates. As a result, the fluid flows and streamlines have changed during present flexible model against the rigid models and also the two-way coupling particle trajectories have changed against the one-way particle coupling.

Keywords: FSI, two-way particle coupling, alveoli, CDF

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Authors: Talat Baran

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Palladium-catalyzed Suzuki coupling reactions are powerful ways for synthesis of biaryls compounds and so far different palladium sources as have been used in catalyst systems. However, the high cost of the ligands using as support materials for palladium ion and so researchers have explored alternative low-cost support materials such as silica, cellule and zeolite. A natural polymer chitosan is suitable for support material because of it unique properties such as eco-friendly, renewable, abundant, low cost, biodegradable and it has free reactive -NH2 and –OH groups. Especially, pendant amino groups of chitosan can easily react with carbonyl groups of aldehyde or ketone by Schiff base formation and thus palladium ions can coordinate with imine groups of Schiff base. This purpose, in this study, firstly a new chitosan Schiff base supported palladium (II) catalyst was synthesized and its chemical structure was characterized with FT-IR, SEM/EDAX, XRD, TG-DTG, ICP-OES and magnetic moment techniques. Then catalytic performance of the catalyst was investigated in Suzuki cross coupling reactions under simple and fast microwave heating methods. Also, recycle activity of palladium catalyst was tested under optimum condition and the catalyst showed long life time. At the end of catalytic performance tests of chitosan supported palladium (II) catalysts indicated high turnover numbers, turnover frequency and selectivity with very small loading catalyst

Keywords: catalyst, chitosan, Schiff base, Suzuki coupling

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Authors: Aria Ratmandanu

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Boson stars can be viewed as zero temperature ground state, Bose-Einstein condensates, characterized by enormous occupation numbers. Time-dependent spherically symmetric spacetime can be a model of Boson Star. We use (3+1) split of Einstein equation (ADM formulation of general relativity) to solve Einstein field equation coupled to a complex scalar field (Einstein-Klein-Gordon Equation) on time-dependent spherically symmetric spacetime, We get the result that Boson stars are pulsating stars with the frequency of oscillation equal to its density. We search for interior solution of Boson stars and get the T.O.V. (Tollman-Oppenheimer-Volkoff) equation for Boson stars. Using T.O.V. equation, we get the equation of state and the relation between pressure and density, its total mass and along with its gravitational Mass. We found that the hypothetical particle Axion could form a Boson star with the size of a milky way galaxy and make it a candidate for a dark galaxy, (a galaxy that consists almost entirely of dark matter).

Keywords: axion, boson star, dark galaxy, time-dependent spherically symmetric spacetime

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Authors: Kitjapat Phuvoravan, Phattaraphong Ponsorn

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In the design of Castellated beams (CB), the web post buckling acted by horizontal shear force is one of the important failure modes that have to be considered. It is also a dominant governing mode when design following the AISC 31 design guideline which is just published. However, the equation of the web post buckling given by the guideline is still questionable for most of the engineers. So the purpose of this paper is to study and provide a proposed equation for design the web post buckling with more simplified and convenient to use. The study is also including the improper of the safety factor given by the guideline. The proposed design equation is acquired by regression method based on the results of finite element analysis. An amount of Cellular beam simulated to study is modelled by using shell element, analysis with both geometric and material nonlinearity. The results of the study show that the use of the proposed equation to design the web post buckling in Castellated beams is more simple and precise for computation than the equations provided from the guideline.

Keywords: castellated beam, web opening, web post buckling, design equation

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Authors: Olayiwola Moruf Oyedunsi

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This paper discusses the Modified Variational Iteration Method (MVIM) for the solution of nonlinear Burgers’ equation arising in longitudinal dispersion phenomena in fluid flow through porous media. The method is an elegant combination of Taylor’s series and the variational iteration method (VIM). Using Maple 18 for implementation, it is observed that the procedure provides rapidly convergent approximation with less computational efforts. The result shows that the concentration C(x,t) of the contaminated water decreases as distance x increases for the given time t.

Keywords: modified variational iteration method, Burger’s equation, porous media, partial differential equation

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Authors: Sisi Xia, Dezhuan Tao, Junyan Yang, Weiting Xiong

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Under the background of Chinese urbanization changing from incremental development to stock development, the completion of urban public service facilities is essential to urban spatial quality. As public services facilities is a huge and complicated system, clarifying the various types of internal rules associated with the land market price is key to optimizing spatial layout. This paper takes Wuxi City as a representative sample location and establishes the digital analysis platform using urban price and several high-precision big data acquisition methods. On this basis, it analyzes the coupling relationship between different public service categories and land price, summarizing the coupling patterns of urban public facilities distribution and urban land price fluctuations. Finally, the internal mechanism within each of the two elements is explored, providing the reference of the optimum layout of urban planning and public service facilities.

Keywords: public service facilities, land price, urban spatial morphology, big data

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Authors: Ming Su, Ziqiang Mu

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This paper proposes a synthesis method for nonuniform linear antenna arrays that combine Gaussian process regression (GPR) and genetic algorithm (GA). In this method, the GPR model can be used to calculate the array radiation pattern in the presence of mutual coupling effects, and then the GA is used to optimize the excitations and locations of the elements so as to generate the desired radiation pattern. In this paper, taking a 9-element nonuniform linear array as an example and the desired radiation pattern corresponding to a Chebyshev distribution as the optimization objective, optimize the excitations and locations of the elements. Finally, the optimization results are verified by electromagnetic simulation software CST, which shows that the method is effective.

Keywords: nonuniform linear antenna arrays, GPR, GA, mutual coupling effects, active element pattern

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Authors: Minna Theres James, Nirmal K Sebastian, Shoubhik Mandal, Pramita Mishra, R Ganesan, P S Anil Kumar

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We report the temperature-dependent evolution of Raman spectra of type-II Dirac semimetal (DSM) NiTe2 (001) in the form of bulk single crystal and a nanoflake (200 nm thick) for the first time. A physical model that can quantitatively explain the evolution of out of plane A1g and in-plane E1g Raman modes is used. The non-linear variation of peak positions of the Raman modes with temperature is explained by anharmonic three-phonon and four-phonon processes along with thermal expansion of the lattice. We also observe prominent effect of electron-phonon coupling from the variation of FWHM of the peaks with temperature, indicating the metallicity of the samples. Raman mode E1 1g corresponding to an in plane vibration disappears on decreasing the thickness from bulk to nanoflake.

Keywords: raman spectroscopy, type 2 dirac semimetal, nickel telluride, phonon-phonon coupling, electron phonon coupling, transition metal dichalcogonide

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Authors: M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous movement disorder that often appears in the elderly. PD is induced by a loss of dopamine secretion. Some drugs increase the secretion of dopamine. In this paper, we will simply study the stability of PD models as a nonlinear delay differential equation. After a period of taking drugs, these act as positive feedback and increase the tremors of patients, and then, the differential equation has positive coefficients and the system is unstable under these conditions. We will present a set of suggested modifications to make the system more compatible with the biodynamic system. When giving a set of numerical examples, this research paper is concerned with the mathematical analysis, and no clinical data have been used.

Keywords: Parkinson's disease, stability, simulation, two delay differential equation

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Authors: C. Pallis

Abstract:

Induced-Gravity inflation is a model of chaotic inflation where the inflaton is identified with a Higgs-like modulus whose the vacuum expectation value controls the gravitational strength. Thanks to a strong enough coupling between the inflaton and the Ricci scalar curvature, inflation is attained even for subplanckian values of the inflaton with the corresponding effective theory being valid up to the Planck scale. In its simplest realization, induced-gravity inflation is based on a quatric potential and a quadratic non-minimal coupling and the inflationary observables turn out to be in agreement with the Planck data. Its supersymmetrization can be formulated within no-scale Supergravity employing two gauge singlet chiral superfields and applying a continuous $R$ and a discrete Zn symmetry to the proposed superpotential and Kahler potential. Modifying slightly the non-minimal coupling to Gravity, the model can account for the recent results of BICEP2. These modifications can be also accommodated beyond the no-scale SUGRA considering the fourth order term of the Kahler potential which mixes the inflaton with the accompanying non-inflaton field and small deviations from the prefactor $-3$ encountered in the adopted Kahler potential.

Keywords: cosmology, supersymmetric models, supergravity, modified gravity

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Authors: Elvis Adam Alhassan, Kaiyu Tian, Akos Konadu, Ernest Zamanah, Michael Jackson Adjabui, Ibrahim Justice Musah, Esther Agyeiwaa Owusu, Emmanuel K. A. Agyeman

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In this paper, how to solve simultaneous equations using the Elvis improved method is shown. The Elvis improved method says; to make one variable in the first equation the subject; make the same variable in the second equation the subject; equate the results and simplify to obtain the value of the unknown variable; put the value of the variable found into one equation from the first or second steps and simplify for the remaining unknown variable. The difference between our Elvis improved method and the substitution method is that: with Elvis improved method, the same variable is made the subject in both equations, and the two resulting equations equated, unlike the substitution method where one variable is made the subject of only one equation and substituted into the other equation. After describing the Elvis improved method, findings from 100 secondary students and the views of 5 secondary tutors to demonstrate the effectiveness of the method are presented. The study's purpose is proved by hypothetical examples.

Keywords: simultaneous equations, substitution method, elimination method, graphical method, Elvis improved method

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Authors: Haowen Xi

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We propose and solve exactly a class of non-linear generalization of the Black-Scholes process of stochastic differential equations describing price bubble and crashes dynamics. As a result of nonlinear positive feedback, the faster-than-exponential price positive growth (bubble forming) and negative price growth (crash forming) are found to be the power-law finite-time singularity in which bubbles and crashes price formation ending at finite critical time tc. While most literature on the market bubble and crash process focuses on the nonlinear positive feedback mechanism aspect, very few studies concern the noise level on the same process. The present work adds to the market bubble and crashes literature by studying the external sources noise influence on the critical time tc of the bubble forming and crashes forming. Two main results will be discussed: (1) the analytical expression of expected value of the critical time is found and unexpected critical slowing down due to the coupling external noise is predicted; (2) numerical simulations of the nonlinear stochastic equation is presented, and the probability distribution of Prob(tc) is found to be the inverse gamma function.

Keywords: bubble, crash, finite-time-singular, numerical simulation, price dynamics, stochastic differential equations

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Authors: Esmael Makarian, Ayub Elyasi, Fatemeh Saberi, Olusegun Stanley Tomomewo

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Geothermal reservoirs (GTRs) have garnered global recognition as a sustainable energy source. The Thermo-Hydro-Mechanical-Chemical (THMC) integration coupling proves to be a practical and effective method for optimizing production in GTRs. The study outcomes demonstrate that THMC coupling serves as a versatile and valuable tool, offering in-depth insights into GTRs and enhancing their operational efficiency. This is achieved through temperature analysis and pressure changes and their impacts on mechanical properties, structural integrity, fracture aperture, permeability, and heat extraction efficiency. Moreover, THMC coupling facilitates potential benefits assessment and risks associated with different geothermal technologies, considering the complex thermal, hydraulic, mechanical, and chemical interactions within the reservoirs. However, THMC-coupling utilization in GTRs presents a multitude of challenges. These challenges include accurately modeling and predicting behavior due to the interconnected nature of processes, limited data availability leading to uncertainties, induced seismic events risks to nearby communities, scaling and mineral deposition reducing operational efficiency, and reservoirs' long-term sustainability. In addition, material degradation, environmental impacts, technical challenges in monitoring and control, accurate assessment of resource potential, and regulatory and social acceptance further complicate geothermal projects. Addressing these multifaceted challenges is crucial for successful geothermal energy resources sustainable utilization. This paper aims to illuminate the challenges and opportunities associated with THMC coupling in enhanced geothermal systems. Practical solutions and strategies for mitigating these challenges are discussed, emphasizing the need for interdisciplinary approaches, improved data collection and modeling techniques, and advanced monitoring and control systems. Overcoming these challenges is imperative for unlocking the full potential of geothermal energy making a substantial contribution to the global energy transition and sustainable development.

Keywords: geothermal reservoirs, THMC coupling, interdisciplinary approaches, challenges and opportunities, sustainable utilization

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Authors: Ali Dehgan Moroozeh, B. Farhadi Bansouleh

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Evapotranspiration is one of the most important components of the hydrological cycle. Evapotranspiration (ETo) is an important variable in water and energy balances on the earth’s surface, and knowledge of the distribution of ET is a key factor in hydrology, climatology, agronomy and ecology studies. Many researchers have a valid relationship, which is a function of climate factors, to estimate the potential evapotranspiration presented to the plant water stress or water loss, prevent. The FAO-Penman method (PM) had been recommended as a standard method. This method requires many data and these data are not available in every area of world. So, other methods should be evaluated for these conditions. When sufficient or reliable data to solve the PM equation are not available then Hargreaves equation can be used. The Hargreaves equation (HG) requires only daily mean, maximum and minimum air temperature extraterrestrial radiation .In this study, Hargreaves method (HG) were evaluated in 12 stations in the North West region of Iran. Results of HG and M.HG methods were compared with results of PM method. Statistical analysis of this comparison showed that calibration process has had significant effect on efficiency of Hargreaves method.

Keywords: evapotranspiration, hargreaves, equation, FAO-Penman method

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Authors: A. Zerarka, W. Djoudi

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The method developed in this work uses a generalised coth and csch funtions method to construct new exact travelling solutions to the nonlinear lattice equation. The technique of the homogeneous balance method is used to handle the appropriated solutions.

Keywords: coth functions, csch functions, nonlinear partial differential equation, travelling wave solutions

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Authors: Wenxue Xu

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Fluid resistance damper is an important damping element to attenuate vehicle vibration. It converts vibration energy into thermal energy dissipation through oil throttling. It is a typical fluid-solid-heat coupling problem. A complete three-dimensional flow-structure-thermal coupling dynamics simulation model of a gas-filled fluid-resistance damper was established. The flow-condition-based interpolation (FCBI) method and direct coupling calculation method, the unit's FCBI-C fluid numerical analysis method and iterative coupling calculation method are used to achieve the damper dynamic response of the piston rod under sinusoidal excitation; the air chamber inflation pressure, spring compression characteristics, constant flow passage cross-sectional area and oil parameters, etc. The system parameters, excitation frequency, and amplitude and other excitation parameters are analyzed and compared in detail for the effects of differential pressure characteristics, velocity characteristics, flow characteristics and dynamic response of valve opening, floating piston response and piston rod output force characteristics. Experiments were carried out on some simulation analysis conditions. The results show that the node-based FCBI (flow-condition-based interpolation) fluid numerical analysis method and direct coupling calculation method can better guarantee the conservation of flow field calculation, and the calculation step is larger, but the memory is also larger; if the chamber inflation pressure is too low, the damper will become cavitation. The inflation pressure will cause the speed characteristic hysteresis to increase, and the sealing requirements are too strict. The spring compression characteristics have a great influence on the damping characteristics of the damper, and reasonable damping characteristic needs to properly design the spring compression characteristics; the larger the cross-sectional area of the constant flow channel, the smaller the maximum output force, but the more stable when the valve plate is opening.

Keywords: damper, fluid-structure-thermal coupling, heat generation, heat transfer

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Authors: Itissam Abuiziah

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In several hydraulic systems, it is necessary to calculate the head losses which depend on the resistance flow friction factor in Darcy equation. Computing the resistance friction is based on implicit Colebrook-White equation which is considered as the standard for the friction calculation, but it needs high computational cost, therefore; several explicit approximation methods are used for solving an implicit equation to overcome this issue. It follows that the relative error is used to determine the most accurate method among the approximated used ones. Steel, cast iron and polyethylene pipe materials investigated with practical diameters ranged from 0.1m to 2.5m and velocities between 0.6m/s to 3m/s. In short, the results obtained show that the suitable method for some cases may not be accurate for other cases. For example, when using steel pipe materials, Zigrang and Silvester's method has revealed as the most precise in terms of low velocities 0.6 m/s to 1.3m/s. Comparatively, Halland method showed a less relative error with the gradual increase in velocity. Accordingly, the simulation results of this study might be employed by the hydraulic engineers, so they can take advantage to decide which is the most applicable method according to their practical pipe system expectations.

Keywords: Colebrook–White, explicit equation, friction factor, hydraulic resistance, implicit equation, Reynolds numbers

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Authors: Manisha Kankarej

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The purpose of this paper is to show a relation between CR structure and F-structure satisfying polynomial equation. In this paper, we have checked the significance of CR structure and F-structure on Integrability conditions and Nijenhuis tensor. It was proved that all the properties of Integrability conditions and Nijenhuis tensor are satisfied by CR structures and F-structure satisfying polynomial equation.

Keywords: CR-submainfolds, CR-structure, integrability condition, Nijenhuis tensor

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Authors: Matheus Fernando Pereira, Varese Salvador Timoteo

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In this work, we have solved the two-dimensional advection-diffusion equation numerically for a spatially dependent solute dispersion along non-uniform flow with a pulse type source in order to make a systematic study on the influence of medium heterogeneity, initial flow velocity, and initial dispersion coefficient parameters on the solutions of the equation. The behavior of the solutions is then investigated as we change the three parameters independently. Our results show that even though the parameters represent different physical features of the system, the effect on their variation is very similar. We also observe that the effects caused by the parameters on the concentration depend on the distance from the source. Finally, our numerical results are in good agreement with the exact solutions for all values of the parameters we used in our analysis.

Keywords: advection-diffusion equation, dispersion, numerical methods, pulse-type source

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Authors: Ted Silva

Abstract:

Dietrich de Velsa's Équation à un inconnu / Equation to an Unknown hybridizes art cinema style with the sexually explicit aesthetics of pornography to envision a uniquely queer world unmoored by heteronormative influence. This stylization evokes the memory of a queer history that once approximated such a prospect. With this historical and political context in mind, this paper utilizes formal analysis to assess how the film frames queer sexual encounters as tender acts of care, sometimes literally mending physical wounds. However, Equation to Unknown also highlights the transience of these sexual exchanges. By emphasizing the homogeneity of the protagonist’s sexual conquests, the film reveals that these practices have a darker meaning when the men reject the individualized connection to pursue purely visceral gratification. Given the lack of diversity or even recognizable identifying factors, the men become more anonymous to each other the more they pair up. Ultimately, Equation to an Unknown both celebrates and problematizes its vision of a queer utopia, highlighting areas in the community wherein intimacy and care flourish and locating those spots in which they are neglected.

Keywords: pornography studies, queer cinema, French cinema, history

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Authors: Tomoaki Hashimoto

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Recent technological advance has prompted significant interest in developing the control theory of quantum systems. Following the increasing interest in the control of quantum dynamics, this paper examines the control problem of Schrödinger equation because quantum dynamics is basically governed by Schrödinger equation. From the practical point of view, stochastic disturbances cannot be avoided in the implementation of control method for quantum systems. Thus, we consider here the robust stabilization problem of Schrödinger equation against stochastic disturbances. In this paper, we adopt model predictive control method in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. The objective of this study is to derive the stability criterion for model predictive control of Schrödinger equation under stochastic disturbances.

Keywords: optimal control, stochastic systems, quantum systems, stabilization

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Authors: Boualem Chetti

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The dynamic characteristics of a three-lobe journal bearing lubricated with micropolar fluids are determined by the linear stability theory. Lubricating oil containing additives and contaminants is modeled as micropolar fluid. The modified Reynolds equation is obtained using the micropolar lubrication theory and the finite difference technique has been used to solve it. The dynamic characteristics in terms of stiffness, damping coefficients, the critical mass and whirl ratio are determined for various values of size of material characteristic length and the coupling number. The computed results show compared with Newtonian fluids, that micropolar fluid exhibits better stability.

Keywords: three-lobe bearings, micropolar fluid, dynamic characteristics, stability analysis

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