Search results for: transport of intensity equation

Authors: Shashank Patidar, Sumit Kumar, Atul Srivastava, Suneet Singh

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Present work is concerned with the numerical investigation of thermal response of biological tissues during laser-based photo-thermal therapy for destroying cancerous/abnormal cells with minimal damage to the surrounding normal cells. Light propagation through the biological sample is mathematically modelled by transient radiative transfer equation. In the present work, application of the Lattice Boltzmann Method is extended to analyze transport of short-pulse radiation in a participating medium.In order to determine the two-dimensional temperature distribution inside the tissue medium, the RTE has been coupled with Penne’s bio-heat transfer equation based on Fourier’s law by several researchers in last few years.

Keywords: lattice Boltzmann method, transient radiation transfer equation, dual phase lag model

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Authors: Jaroslav Masek, Juraj Camaj, Eva Nedeliakova

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The paper is focused on the operational model for transport the single wagon consignments on railway network by using two different models of train formation. The paper gives an overview of possibilities of improving the quality of transport services. Paper deals with two models used in problematic of train formatting - time continuously and time discrete. By applying these models in practice, the transport company can guarantee a higher quality of service and expect increasing of transport performance. The models are also applicable into others transport networks. The models supplement a theoretical problem of train formation by new ways of looking to affecting the organization of wagon flows.

Keywords: train formation, wagon flows, marshalling yard, railway technology

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Authors: Nadjet Brahmia

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The evolution of urban forms, the new aspects of mobility, the ways of life and economic models make public transport conventional collective low-performing on the majority of largest Algerian cities, particularly in the west of Algeria. On the other side, the information and communication technologies (ICT) open new eventualities to develop a new mode of transport which brings together both the tenders offered by the public service collective and those of the particular vehicle, suitable for urban requirements, social and environmental. Like the concrete examples made in the international countries in terms of on-demand transport systems (ODT) more particularly in the developed countries, this article has for objective the opportunity analysis to establish a service of ODT at the level of a few towns of Oran Wilaya, such a service will be subsequently spread on the totality of the Wilaya if not on the whole of Algeria. In this context, we show the different existing means of transport in the current network whose aim to illustrate the points of insufficiency accented in the present transport system, then we discuss the solutions that may exhibit a service of ODT to the problem studied all around the transport sector, to carry at the end to highlight the capabilities of ODT replying to the transformation of mobilities, this in the light of well-defined cases.

Keywords: mobility, on-demand transport, public transport collective, transport system

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Authors: Csaba I. Hencz, István Á. Harmati

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Nowadays the significance of road transport is gradually increasing. All transport companies are working in the same external environment where the speed of transport is defined by traffic rules. The main objective is to accelerate the speed of service and it is only dependent on the individual abilities of the managing members. These operational control units make decisions quickly (in a typically experiential and/or intuitive way). For this reason, support for these decisions is an important task. Our goal is to create a decision support model based on fuzzy signatures that can assist the work of operational management automatically. If the model sets parameters properly, the management of transport could be more economical and efficient.

Keywords: freight transport, decision support, information handling, fuzzy methods

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Authors: Santosh Kumar Biswal, Ramakar Jha

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Soil erosion is a slow and continuous process and one of the prominent problems across the world leading to many serious problems like loss of soil fertility, loss of soil structure, poor internal drainage, sedimentation deposits etc. In this paper remote sensing and GIS based methods have been applied for the determination of soil erosion and sediment yield. Tel River basin which is the second largest tributary of the river Mahanadi laying between latitude 19° 15' 32.4"N and, 20° 45' 0"N and longitude 82° 3' 36"E and 84° 18' 18"E chosen for the present study. The catchment was discretized into approximately homogeneous sub-areas (grid cells) to overcome the catchment heterogeneity. The gross soil erosion in each cell was computed using Universal Soil Loss Equation (USLE). Various parameters for USLE was determined as a function of land topography, soil texture, land use/land cover, rainfall, erosivity and crop management and practice in the watershed. The concept of transport limited accumulation was formulated and the transport capacity maps were generated. The gross soil erosion was routed to the catchment outlet. This study can help in recognizing critical erosion prone areas of the study basin so that suitable control measures can be implemented.

Keywords: Universal Soil Loss Equation (USLE), GIS, land use, sediment yield,

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

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

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

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Authors: G. Sivakumar, T. Pratyusha, D. Gupta, W. Shen

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To get ohmic contact between the cathode and organic semiconductor, transport layers are introduced between the active layer and the electrodes. Generally zinc oxide or titanium dioxide are used as electron transport layer. When electron transport layer is doped with lithium, the resultant film exhibited superior electronic properties, which enables faster electron transport. Doping is accomplished by heat treatment of films with Lithium salts. Li-doped films. We fabricated organic solar cell using PTB7(poly(3-hexylthiopene-2,5- diyl):PCBM(phenyl-C61-butyric acid methyl ester) and found that the solar cells prepared using Li doped films had better performance in terms of efficiency when compared to the undoped transport layers.

Keywords: electron transport layer, higher efficiency, lithium doping, ohmic contact

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Authors: N. Dahbi, M. Daoudi

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This paper deals with the use of computational method based on Monte Carlo simulation in order to investigate the transport phenomena of the electron in HgCdTe narrow band gap semiconductor. Via this method we can evaluate the time dependence of the transport parameters: velocity, energy and mobility of electrons through matter (HgCdTe).

Keywords: Monte Carlo, transport parameters, HgCdTe, computational mechanics

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Authors: Praveen Kumar, R. Uma, R. P. Sharma

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This study investigates the generation of turbulence in a deep-fluid environment using a damped 1D-modified nonlinear Schrödinger equation model. The well-known damped modified nonlinear Schrödinger equation (d-MNLS) is solved using numerical methods. Artificial damping is added to the MNLS equation, and turbulence generation is investigated through a numerical simulation. The numerical simulation employs a finite difference method for temporal evolution and a pseudo-spectral approach to characterize spatial patterns. The results reveal a recurring periodic pattern in both space and time when the nonlinear Schrödinger equation is considered. Additionally, the study shows that the modified nonlinear Schrödinger equation disrupts the localization of structure and the recurrence of the Fermi-Pasta-Ulam (FPU) phenomenon. The energy spectrum exhibits a power-law behavior, closely following Kolmogorov's spectra steeper than k⁻⁵/³ in the inertial sub-range.

Keywords: water waves, modulation instability, hydrodynamics, nonlinear Schrödinger's equation

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Authors: Jamal Takhchi

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The understanding of vibration propagation in complex structures such as automotive body in white remains a challenging issue in car design regarding NVH performances. The current analysis is limited to the low frequency range where modal concepts are dominant. Higher frequencies, between 200 and 1000 Hz, will become critical With the rise of electrification. EVs annoying sounds are mostly whines created by either Gears or e-motors between 300 Hz and 2 kHz. Structural intensity analysis was Experienced a few years ago on finite element models. The application was promising but limited by the fact that the propagating 3D intensity vector field is masked by a rotational Intensity field. This rotational field should be filtered using a differential operator. The expression of this operator in the framework of finite element modeling is not yet known. The aim of the proposed work is to implement this operator in the current dynamic solver (NASTRAN) of Stellantis and develop the Expected methodology for the mid-frequency structural analysis of electrified vehicles.

Keywords: structural intensity, NVH, body in white, irrotatational intensity

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Authors: Meruyert Zhassybayeva, Kuralay Yesmukhanova, Ratbay Myrzakulov

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Integrable nonlinear differential equations are an important class of nonlinear wave equations that admit exact soliton solutions. All these equations have an amazing property which is that their soliton waves collide elastically. One of such equations is the (1+1)-dimensional Fokas-Lenells equation. In this paper, we have constructed an integrable (2+1)-dimensional Fokas-Lenells equation. The integrability of this equation is ensured by the existence of a Lax representation for it. We obtained its bilinear form from the Hirota method. Using the Hirota method, exact one-soliton and two-soliton solutions of the (2 +1)-dimensional Fokas-Lenells equation were found.

Keywords: Fokas-Lenells equation, integrability, soliton, the Hirota bilinear method

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Authors: Julius A. Ademokoya, Grace C. Ilori

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Extreme public transport difficulty for persons with disabilities (PWDs) has always been one of the challenges which these individuals experience on a daily basis in Nigeria. Private and public transport vehicles are not disability- friendly. Operators of public transport are often very intolerant of PWDs' conditions. Indeed, many Nigerians believe it is luxury for PWDs to engage in public transport. They are rarely expected to be seen in public much less going to places via public transport means. Initiatives by a few Nigerian states to develop and implement public transport policies for PWDs, therefore, were a huge relief for them and some concerned Nigerians. A few years ago, three southwest Nigerian states (Lagos, Ondo, and Ekiti) came up with some legislative welfare provisions (including transport programmes) for PWDs. This study, therefore, sought to ascertain levels of awareness and implementation of public policies among the PWDs and those expected to implement the policies. The study adopted a mixed method research. Findings across the three states showed that: (1) awareness of public policies among PWDs is low and (2) a considerable scope of the policies is not yet implemented. Recommendations are, therefore, made on how to improve on awareness and implementation of transport policies for PWDs in three south-west Nigerian states.

Keywords: awareness, disability rights, implementation persons with disability, transport policies

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Authors: Zhuang He, Andrei Kotousov

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All current experimental methods for determination of stress intensity factors are based on the assumption that the state of stress near the crack tip is plane stress. Therefore, these methods rely on strain and displacement measurements made outside the near crack tip region affected by the three-dimensional effects or by process zone. In this paper, we develop and validate an experimental procedure for the evaluation of stress intensity factors from the measurements of the out-of-plane displacements in the surface area controlled by 3D effects. The evaluation of stress intensity factors is possible when the process zone is sufficiently small, and the displacement field generated by the 3D effects is fully encapsulated by K-dominance region.

Keywords: digital image correlation, stress intensity factors, three-dimensional effects, transverse displacement

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Authors: Ognjen Vukovic

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Chern-Simons equation represents the cornerstone of quantum physics. The question that is often asked is if the aforementioned equation can be successfully applied to the interaction in international financial markets. By analysing the time series in financial theory, it is proved that Chern-Simons equation can be successfully applied to financial time-series. The aforementioned statement is based on one important premise and that is that the financial time series follow the fractional Brownian motion. All variants of Chern-Simons equation and theory are applied and analysed. Financial theory time series movement is, firstly, topologically analysed. The main idea is that exchange rate represents two-dimensional projections of three-dimensional Brownian motion movement. Main principles of knot theory and topology are applied to financial time series and setting is created so the Chern-Simons equation can be applied. As Chern-Simons equation is based on small particles, it is multiplied by the magnifying factor to mimic the real world movement. Afterwards, the following equation is optimised using Solver. The equation is applied to n financial time series in order to see if it can capture the interaction between financial time series and consequently explain it. The aforementioned equation represents a novel approach to financial time series analysis and hopefully it will direct further research.

Keywords: Brownian motion, Chern-Simons theory, financial time series, econophysics

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Authors: Jiahui Song

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The application of an electric field can cause poration at cell membranes. This includes the outer plasma membrane, as well as the membranes of intracellular organelles. In order to analyze and predict such electroporation effects, it becomes necessary to first evaluate the electric fields and the transmembrane voltages. This information can then be used to assess changes in the pore formation energy that finally yields the pore distributions and their radii based on the Smolchowski equation. The dynamic pore model can be achieved by including a dynamic aspect and a dependence on the pore population density into the pore formation energy equation. These changes make the pore formation energy E(r) self-adjusting in response to pore formation without causing uncontrolled growth and expansion. By using dynamic membrane tension, membrane electroporation in response to a 180kV/cm trapezoidal pulse with a 10 ns on time and 1.5 ns rise- and fall-times is discussed. Poration is predicted to occur at times beyond the peak at around 9.2 ns. Modeling also yields time-dependent distributions of the membrane pore population after multiple pulses. It shows that the pore distribution shifts to larger values of the radius with multiple pulsing. Molecular dynamics (MD) simulations are also carried out for a fixed field of 0.5 V/nm to demonstrate nanopore formation from a microscopic point of view. The result shows that the pore is predicted to be about 0.9 nm in diameter and somewhat narrower at the central point.

Keywords: high-intensity, nanosecond, dynamics, electroporation

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Authors: Ramin Mirzada

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This research investigates the valuation of public transport importance in decreasing congestion and in introduction of bus rapid transit in Kabul city. The main concern and main problem of the Kabul city public transport is traffic congestion. When buses and trams are stuck in traffic jams, it is clear that they fall behind from the schedule and this cause lots of problem for Kabul residence. In this research, the main attention has been given to improve current public transport in Kabul city which Public transport has large share almost 50% share among all mode. The main purpose of this research is to improve public transport system, to examine the demand and the supply of public transport in Kabul city, and to improve public transport system by introducing Bus rapid transit (BRT) system in Kabul city. The data which is used in this research is gathered by Transport Ministry, Kabul Municipality and Japan Cooperation Agency in Afghanistan (JICA). Urban transportation modeling system (UTMS) which is also known as traditional four-step modeling is used as the methodology of this research. The outcome of this research shows that by improving public transport which is local bus system mostly congestion problem of Kabul city become solve, and for those lanes which has the high demand and has more congestion, it is needed to introduce bus rapid transit system.

Keywords: transportation, planning, public transport, bus rapid transit, Kabul, Afghanistan

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Authors: Tao Zhao, Xianshuo Xu

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Low-carbon public passenger transport is an important part of low carbon city. The CO₂ emissions of public passenger transport in Tianjin from 1995 to 2010 are estimated with IPCC CO₂ counting method, which shows that the total CO₂ emissions of Tianjin public passenger transport have gradually become stable at 1,425.1 thousand tons. And then the CO₂ emissions of the buses, taxies, and rail transits are calculated respectively. A CO₂ emission of 829.9 thousand tons makes taxies become the largest CO₂ emissions source among the public passenger transport in Tianjin. Combining with passenger volume, this paper analyzes the CO₂ emissions proportion of the buses, taxies, and rail transits compare the passenger transport rate with the proportion of CO₂ emissions, as well as the CO₂ emissions change of per 10,000 people. The passenger volume proportion of bus among the three public means of transport is 72.62% which is much higher than its CO₂ emissions proportion of 36.01%, with the minimum number of CO₂ emissions per 10,000 people of 4.90 tons. The countermeasures to reduce CO₂ emissions of public passenger transport in Tianjin are to develop rail transit, update vehicles and use alternative fuel vehicles.

Keywords: public passenger transport, carbon emissions, countermeasures, China

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Authors: Brahmia Nadjet

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The growing needs of displacements led advanced countries in this field install new specific transport systems, able to palliate any deficiencies, especially when regular public transport does not adequately meet the requests of users. In this context, on-demand transport systems (ODT) are very efficient; they rely on techniques based on the location of trip generators which should be assured effectively with the use of operators responsible of the advance reservation, planning and organization, and studying the different ODT criteria (organizational, technical, geographical, etc.). As the advanced countries in the field of transport, some developing countries are involved in the adaptation of the new technologies to reduce the deficit in their communication system. This communication presents the study of an ODT implementation in the west of Algeria, by developing the Geomatics side of the study. This part requires the use of specific systems (such as GIS, RDBMS), so we developed the process through an application in an environment of mobility by using the computer tools dedicated to the management of the entities related to the transport field.

Keywords: ODT, geomatics, GIS, transport systems

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Authors: Paschal A. Ochang, Emmanuel C. Oji

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The Duffing’s Equation is a second order system that is very important because they are fundamental to the behaviour of higher order systems and they have applications in almost all fields of science and engineering. In the biological area, it is useful in plant stem dependence and natural frequency and model of the Brain Crash Analysis (BCA). In Engineering, it is useful in the study of Damping indoor construction and Traffic lights and to the meteorologist it is used in the prediction of weather conditions. However, most Problems in real life that occur are non-linear in nature and may not have analytical solutions except approximations or simulations, so trying to find an exact explicit solution may in general be complicated and sometimes impossible. Therefore we aim to find out if it is possible to obtain one analytical fixed point to the non-linear ordinary equation using fixed point analytical method. We started by exposing the scope of the Duffing’s equation and other related works on it. With a major focus on the fixed point and fixed point iterative scheme, we tried different iterative schemes on the Duffing’s Equation. We were able to identify that one can only see the fixed points to a Damped Duffing’s Equation and not to the Undamped Duffing’s Equation. This is because the cubic nonlinearity term is the determining factor to the Duffing’s Equation. We finally came to the results where we identified the stability of an equation that is damped, forced and second order in nature. Generally, in this research, we approximate the solution of Duffing’s Equation by converting it to a system of First and Second Order Ordinary Differential Equation and using Fixed Point Iterative approach. This approach shows that for different versions of Duffing’s Equations (damped), we find fixed points, therefore the order of computations and running time of applied software in all fields using the Duffing’s equation will be reduced.

Keywords: damping, Duffing's equation, fixed point analysis, second order differential, stability analysis

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Authors: Paul Dunst, Ing. Tobias Hemsel, Ing. Habil. Walter Sextro

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The use of fine powders with high cohesive and adhesive properties leads to challenges during transport, mixing and dosing in industrial processes, which have not been satisfactorily solved so far. Due to the increased contact forces at the transporting parts (e. g. pipe-wall and transport screws), conventional transport systems and also vibratory conveyors reach their limits. Often, flowability increasing additives that need to be removed again in later process steps are the only option to achieve wanted transport results. A rather new ultrasound-assisted powder transport system showed to overcome some of the issues by manipulating the effective friction between powder and transport pipe. Within this contribution, the transport mechanism will be introduced shortly, together with preliminary transport results. As the tangential force of the transport pipe and the powder is the main influencing factor within the transport process, a test stand for measuring tangential forces of a powder-wall contact in the presence of an ultrasonic vibration orthogonal to the contact plane was built. Measurements for a sample powder show that the effective tangential force can already be significantly reduced at very low ultrasonic amplitude. As a result of the measurements, an empirical model for the relationship of tangential force, contact parameters and ultrasonic excitation is presented. This model was used to adjust the driving parameters of the powder transport system, resulting in better performance.

Keywords: powder transport, ultrasound, friction, friction manipulation, vibratory conveyor

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Authors: Ayda Nikkar, Roghayye Ahmadiasl

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In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.

Keywords: homotopy perturbation method, Whitham–Broer–Kaup (WBK) equation, Modified Boussinesq, Approximate Long Wave

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Authors: Md Abdullah Al Faruque, Ram Balachandar

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Sudden change of bed condition is frequent in open channel flow. Change of bed condition affects the turbulence characteristics in both streamwise and wall-normal direction. Understanding the turbulence intensity in open channel flow is of vital importance to the modeling of sediment transport and resuspension, bed formation, entrainment, and the exchange of energy and momentum. A comprehensive study was carried out to understand the extent of the effect of Reynolds number and bed roughness on different turbulence characteristics in an open channel flow. Four different bed conditions (impervious smooth bed, impervious continuous rough bed, pervious rough sand bed, and impervious distributed roughness) and two different Reynolds numbers were adopted for this cause. The effect of bed roughness on different turbulence characteristics is seen to be prevalent for most of the flow depth. Effect of Reynolds number on different turbulence characteristics is also evident for flow over different bed, but the extent varies on bed condition. Although the same sand grain is used to create the different rough bed conditions, the difference in turbulence characteristics is an indication that specific geometry of the roughness has an influence on turbulence characteristics. Roughness increases the contribution of the extreme turbulent events which produces very large instantaneous Reynolds shear stress and can potentially influence the sediment transport, resuspension of pollutant from bed and alter the nutrient composition, which eventually affect the sustainability of benthic organisms.

Keywords: open channel flow, Reynolds Number, roughness, turbulence

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Authors: Kiyoumars Roushangar, Saeid Sadaghian

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Although accurate sediment load prediction is very important in planning, designing, operating and maintenance of water resources structures, the transport mechanism is complex, and the deterministic transport models are based on simplifying assumptions often lead to large prediction errors. In this research, firstly, two intelligent ANN methods, Radial Basis and General Regression Neural Networks, are adopted to model of total sediment load transport into Madani Dam reservoir (north of Iran) using the measured data and then applicability of the sediment transport methods developed by Engelund and Hansen, Ackers and White, Yang, and Toffaleti for predicting of sediment load discharge are evaluated. Based on comparison of the results, it is found that the GRNN model gives better estimates than the sediment rating curve and mentioned classic methods.

Keywords: sediment transport, dam reservoir, RBF, GRNN, prediction

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Authors: D. Tloczynski

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The main aim of this article is to present a balance of the decade of Polish air transport market in the European Union having taking into account selected entities of the aviation market. This article analyzes the functioning of the Polish air transport market after the Polish accession to the European Union. During the study two main areas were pointed: shipping activity and activity of the airports. The most important benefits of integration and the benefits of introducing of the open sky policy were indicated. The last part of the article presents the perspectives of development of air traffic.

Keywords: air transport, airports, development air transport, European Union, Poland

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Authors: Sachin Kumar

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Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

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Authors: Djemai Bara, Mohamed Faouzi Mahboub, Djamila Bennaceur-Doumaz

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In this work, the role of the preformed plasma created on the front face of a target, irradiated by a high intensity short pulse laser, in the framework of ion acceleration process, modeled by Target Normal Sheath Acceleration (TNSA) mechanism, is studied. This plasma is composed of cold ions governed by fluid equations and non-thermal & trapped with densities represented by a "Cairns-Gurevich" equation. The self-similar solution of the equations shows that electronic trapping and the presence of non-thermal electrons in the pre-plasma are both responsible in ion acceleration as long as the proportion of energetic electrons is not too high. In the case where the majority of electrons are energetic, the electrons are accelerated directly by the ponderomotive force of the laser without the intermediate of an accelerating plasma wave.

Keywords: Cairns-Gurevich Equation, ion acceleration, plasma expansion, pre-plasma

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Authors: Chor Nejmeddine, Ines Ben Omrane, Mohamed Abdelwahed

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In this paper, we present a posteriori analysis of the discretization of the heat equation by spectral element method. We apply Euler's implicit scheme in time and spectral method in space. We propose two families of error indicators, both of which are built from the residual of the equation and we prove that they satisfy some optimal estimates. We present some numerical results which are coherent with the theoretical ones.

Keywords: heat equation, spectral elements discretization, error indicators, Euler

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Authors: Jingya Liu, Yue Wu, Jiabin Luo

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This work investigates an intermodal transportation system for delivering goods from a Regional Distribution Centre to supermarkets on the Isle of Wight (IOW) via the port of Southampton or Portsmouth in the UK. We consider this integrated logistics chain as a 3-echelon transportation system. In such a system, there are two types of transport methods used to deliver goods across the Solent Channel: one is accompanied transport, which is used by most supermarkets on the IOW, such as Spar, Lidl and Co-operative food; the other is unaccompanied transport, which is used by Aldi. Five transport scenarios are studied based on different transport modes and ferry routes. The aim is to determine an optimal delivery plan for supermarkets of different business scales on IOW, in order to minimise the total running cost, fuel consumptions and carbon emissions. The problem is modelled as a vehicle routing problem with time windows and solved by genetic algorithm. The computing results suggested that accompanied transport is more cost efficient for small and medium business-scale supermarket chains on IOW, while unaccompanied transport has the potential to improve the efficiency and effectiveness of large business scale supermarket chains.

Keywords: genetic algorithm, intermodal transport system, Isle of Wight, optimization, supermarket

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Authors: Emad K. Jaradat, Ala’a Al-Faqih

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Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two-dimensional Schrodinger equation

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Authors: A. Suparmi, C. Cari, M. Yunianto, B. N. Pratiwi

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D-dimensional Dirac equations of q-deformed shape invariant potentials were solved using supersymmetric quantum mechanics (SUSY QM) in the case of exact spin symmetry. The D dimensional radial Dirac equation for shape invariant potential reduces to one-dimensional Schrodinger type equation by an appropriate variable and parameter change. The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial D dimensional Dirac equation that have reduced to one dimensional Schrodinger type equation. The SUSY operator was used to generate the D dimensional relativistic radial wave functions, the relativistic energy equation reduced to the non-relativistic energy in the non-relativistic limit.

Keywords: D-dimensional dirac equation, non-central potential, SUSY QM, radial wave function

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