Solution Of Transport Problems Research Articles

A New Method for Optimal Solutions of Transportation Problems in LPP

The several standard and the existing proposed methods for optimality of transportation problems in linear programming problem are available. In this paper, we considered all standard and existing proposed methods and then we proposed a new method for optimal solution of transportation problems. The most attractive feature of this method is that it requires very simple arithmetical and logical calculation, that’s why it is very easy even for layman to understand and use. Some limitations and recommendations of future works are also mentioned of the proposed method. Several numerical examples have been illustrated, those gives the clear idea about the method. A programming code for this method has been written in Appendix of the paper.

English

English

THE AERODYNAMIC CHRACTERISTICS CALCULATION METHODOLOGY OF TWO-SHELL PARAGLIDERS

Currently, two-shell paragliders (TSP) find a sufficiently wide application, including the solution of transport problems. A two-shell paraglider is a soft wing, the form of which is supported by the high-speed pressure in the stream and it is a complex aeroelastic system. To determine the aerodynamic characteristics of such system the use of nonlinear aerodynamics and nonlinear theory of elasticity methods is required, it causes the significant computational difficulties. This paper studies the aerodynamic characteristics of various steady-state shapes of gliding parachutes, the calculation-experimental method of their calculation is proposed. It is shown that the replacement of the volumetric profile of TSP median surface allows to receive the results which correctly reflect the qualitative effects of stalled and attached flows. It leads to the assumption that such replacement was possible for obtaining data about the main patterns of parachute finite wings span flow. The aerodynamic characteristics data of TSP steady-state shapes allow to identify the regularities of their changes depending on parachute cutting shape, the deformations of its surface caused by the incoming flow or control actions. To solve the problem of gliding parachute stall, with a stream of air, the discrete vortex method with closed frameworks is used. This method allows to calculate the aerodynamic characteristics of parachutes. The middle surface airflow of TSP steady-state shape with the flow of an ideal incompressible fluid is examined. The parachute fabric permeability is not considered because the upper and lower TSP cloth is either made of low permeable or impermeable fabric. The stalled aerodynamic coefficients are determined by time averaging after calculations up to its larger values. The results of the calculations are given. The possibility of application the proposed methodology for calculation of TSP aerodynamic characteristics in the range of angles of attack to 10° and over 20° for the simplified calculation scheme with accuracy 10% is shown. At the same time, it is revealed that with the increase of soft wing elongation, it is important to consider its main surface curvature for more precise aerodynamic characteristics definition. The proposed methodology can be used for rapid assessments of aerodynamic forces at the design stage and in planning tube experiment. The obtained results can be useful in TSP design during the performance of the tube experiments.

Solute transport along a single fracture with a finite extent of matrix: A new simple solution and temporal moment analysis

A new simple and robust solution, based on uniform steady-state flow velocity, is developed for the problem of solute transport in a fracture-matrix system with a finite penetration depth of a radioactive contaminant into the rock matrix. The solution is an extension of Liu et al. (2017) to finite penetration depth and an alternative solution strategy to the problem solved by Sudicky et al. (1982). The solution takes the form of a convolution of two functions. The first function describes the probability density function of the residence time distribution of a conservative solute resulting merely from advection and Fickian dispersion. The second function is actually the impulse response of the fracture-matrix system in the case of a plug flow without any hydrodynamic dispersion. As a result, the effects of Fickian dispersion and matrix diffusion on solute transport are decoupled, and thus the resulting breakthrough curve can be analyzed in terms of those two functions. In addition to this, the derived Péclet numbers of those two functions, based on temporal moments, are also found to be associated with the derived Péclet number of the resulting breakthrough curve. By comparing the Péclet numbers of those two functions, the contribution of Fickian dispersion and matrix diffusion to solute spreading is determined in a straightforward way. This can aid to find out the dominating mechanism on solute transport, and therefore the performance of breakthrough curve can be approximated by only one function in some specific cases.

RAILWAY AND PORTS INTEGRATION SYSTEM AS SOLUTION OF ISLAND TRANSPORTATION PROBLEM (CASE STUDY SUMATRA ISLAND)

ABSTRACT
 The quality of Transportation system is one of island economic level determinant. Railway transportation evidently more efficient than road transportation. Trans-Sumatra railway construction can be a solution for transportation problem in Sumatra Island. This analysis integrated railway and port to improve economic development in 8 provinces on Sumatra using Spanning Tree and Dijkstra algorithm. It need 1965 kilometers of railway to connect all the 8 provinces. It also generates 1518 kilometers as the distance of Malahayati Port to Panjang Port connection. This integrated system can be a breakthrough solution for Sumatra transportation problem in economic development and the Malacca Strait traffic problem.
 Keywords: Trans-Sumatra railway, Minimum Route, Spanning Tree Algorithm, Dijkstra, Algorithm

Theoretical Insight into the Biodegradation of Solitary Oil Microdroplets Moving through a Water Column.

In the aftermath of oil spills in the sea, clouds of droplets drift into the seawater column and are carried away by sea currents. The fate of the drifting droplets is determined by natural attenuation processes, mainly dissolution into the seawater and biodegradation by oil-degrading microbial communities. Specifically, microbes have developed three fundamental strategies for accessing and assimilating oily substrates. Depending on their affinity for the oily phase and ability to proliferate in multicellular structures, microbes might either attach to the oil surface and directly uptake compounds from the oily phase, or grow suspended in the aqueous phase consuming solubilized oil, or form three-dimensional biofilms over the oil–water interface. In this work, a compound particle model that accounts for all three microbial strategies is developed for the biodegradation of solitary oil microdroplets moving through a water column. Under a set of educated hypotheses, the hydrodynamics and solute transport problems are amenable to analytical solutions and a closed-form correlation is established for the overall dissolution rate as a function of the Thiele modulus, the Biot number and other key parameters. Moreover, two coupled ordinary differential equations are formulated for the evolution of the particle size and used to investigate the impact of the dissolution and biodegradation processes on the droplet shrinking rate.

New Method to find initial basic feasible solution of Transportation Problem using MSDM

New Method to find initial basic feasible solution of Transportation Problem using MSDM

A reduced proper orthogonal decomposition (POD) element free Galerkin (POD-EFG) method to simulate two-dimensional solute transport problems and error estimate

One meshless method based on the variational weak form is the element free Galerkin method. The element free Galerkin (EFG) method is similar to the finite element method but the test and trial functions for the EFG method are chosen from moving least squares (MLS) approximations. The shape functions of MLS approximation don't have the δ-Kronecker property thus the essential boundary conditions (Dirichlet boundary conditions) can not be applied, directly. On the other hand, there are some shape functions that have the mentioned property. One of these functions is the radial point interpolation method (RPIM). In the current paper, we employ the shape functions of RPIM as the test and trial functions. We apply the EFG method based on the RPIM (EFG-RPIM) for solving two-dimensional solute transport problems. To reduce the used CPU time, the proper orthogonal decomposition (POD) approach has been combined with the EFG-RPIM technique. Also, the unconditional stability and convergence of POD-EFG-RPIM method are proved by the energy method. Finally, some numerical results have been reported to show the efficiency and computational order of the new method.

Direct and Inverse Modeling of Seawater Intrusion: A Perspective

ABSTRACT Sea Water Intrusion (SWI) is one of the major hydrological problem in coastal aquifers. This global issue is aggravated by increasing demands for freshwater in coastal regions. In this paper, different approaches of modeling SWI and the parameters affecting the process of SWI are introduced. This is followed by the discussion on the numerical models to solve the complex, three dimensional (3D) groundwater and solute transport problems in coastal aquifer. The importance of considering aquifer characteristics while modeling the groundwater system for flow and solute transport is emphasized. A brief discussion on previous methodology, novelty and limitations on direct simulation of SWI are tabulated. The significant aspects to be considered while direct modeling of coastal aquifers are discussed and the recent focus of research in this area of interest are stated. In direct modeling, information on aquifer parameters are often unknown, therefore, an inverse approach is explained briefly. The previous studies relating to determistic inverse modeling for coupled groundwater flow and solute transport problems reported in literature are summarized. The insights about prior information, estimated parameter sensitivities, variances and correlations are reported. The paper identifies some of the existing gaps in the modeling of SWI based on the previous work and provides comprehensive understanding on direct and deterministic inverse SWI modeling.

Evaluation of a logarithmic solution to the convection-dispersion equation obtained from boundary-layer theory

Introducing boundary-layer (BL) theory to solve problems of solute transport provides a simple and accurate alternative method to estimate transport parameters. Most BL solutions to the convection–...

Analytical model for advective-dispersive transport involving flexible boundary inputs, initial distributions and zero-order productions

A novel solution method is presented which leads to an analytical model for the advective-dispersive transport in a semi-infinite domain involving a wide spectrum of boundary inputs, initial distributions, and zero-order productions. The novel solution method applies the Laplace transform in combination with the generalized integral transform technique (GITT) to obtain the generalized analytical solution. Based on this generalized analytical expression, we derive a comprehensive set of special-case solutions for some time-dependent boundary distributions and zero-order productions, described by the Dirac delta, constant, Heaviside, exponentially-decaying, or periodically sinusoidal functions as well as some position-dependent initial conditions and zero-order productions specified by the Dirac delta, constant, Heaviside, or exponentially-decaying functions. The developed solutions are tested against an analytical solution from the literature. The excellent agreement between the analytical solutions confirms that the new model can serve as an effective tool for investigating transport behaviors under different scenarios. Several examples of applications, are given to explore transport behaviors which are rarely noted in the literature. The results show that the concentration waves resulting from the periodically sinusoidal input are sensitive to dispersion coefficient. The implication of this new finding is that a tracer test with a periodic input may provide additional information when for identifying the dispersion coefficients. Moreover, the solution strategy presented in this study can be extended to derive analytical models for handling more complicated problems of solute transport in multi-dimensional media subjected to sequential decay chain reactions, for which analytical solutions are not currently available.

Assessment of uncertainty in discrete fracture network modeling using probabilistic distribution method.

There have been widespread concerns about solute transport problems in fractured media, e.g. the disposal of high-level radioactive waste in geological fractured rocks. Numerical simulation of particle tracking is gradually being employed to address these issues. Traditional predictions of radioactive waste transport using discrete fracture network (DFN) models often consider one particular realization of the fracture distribution based on fracture statistic features. This significantly underestimates the uncertainty of the risk of radioactive waste deposit evaluation. To adequately assess the uncertainty during the DFN modeling in a potential site for the disposal of high-level radioactive waste, this paper utilized the probabilistic distribution method (PDM). The method was applied to evaluate the risk of nuclear waste deposit in Beishan, China. Moreover, the impact of the number of realizations on the simulation results was analyzed. In particular, the differences between the modeling results of one realization and multiple realizations were demonstrated. Probabilistic distributions of 20 realizations at different times were also obtained. The results showed that the employed PDM can be used to describe the ranges of the contaminant particle transport. The high-possibility contaminated areas near the release point were more concentrated than the farther areas after 5E6 days, which was 25,400 m2.

Entropy‐based critical reaction time for mixing‐controlled reactive transport

AbstractEntropy‐based metrics, such as the dilution index, have been proposed to quantify dilution and reactive mixing in solute transport problems. In this work, we derive the transient advection dispersion equation for the entropy density of a reactive plume. We restrict our analysis to the case where the concentration distribution of the transported species is Gaussian and we observe that, even in case of an instantaneous complete bimolecular reaction, dilution caused by dispersive processes dominates the entropy balance at early times and results in the net increase of the entropy density of a reactive species. Successively, the entropy of the reactant decreases until it vanishes. We show the existence of a unique critical value of dilution, which corresponds to the complete consumption of one of the reactants. This critical dilution index is independent of advective and dispersive processes, and depends only on the dimensionality of the problem, on the stoichiometry of the reaction and on the initial concentrations of the reactants. Furthermore, we provide simple analytical expressions to compute the critical reaction time, i.e., the time at which the critical dilution index is reached, for selected flow configurations. Our results show that, differently from the critical dilution index, the critical reaction time depends on solute transport processes such as advection and hydrodynamic dispersion.

Solute transport along a single fracture in a porous rock: a simple analytical solution and its extension for modeling velocity dispersion

A simple and robust solution is developed for the problem of solute transport along a single fracture in a porous rock. The solution is referred to as the solution to the single-flow-path model and takes the form of a convolution of two functions. The first function is the probability density function of residence-time distribution of a conservative solute in the fracture-only system as if the rock matrix is impermeable. The second function is the response of the fracture-matrix system to the input source when Fickian-type dispersion is completely neglected; thus, the effects of Fickian-type dispersion and matrix diffusion have been decoupled. It is also found that the solution can be understood in a way in line with the concept of velocity dispersion in fractured rocks. The solution is therefore extended into more general cases to also account for velocity variation between the channels. This leads to a development of the multi-channel model followed by detailed statistical descriptions of channel properties and sensitivity analysis of the model upon changes in the model key parameters. The simulation results obtained by the multi-channel model in this study fairly well agree with what is often observed in field experiments—i.e. the unchanged Peclet number with distance, which cannot be predicted by the classical advection-dispersion equation. In light of the findings from the aforementioned analysis, it is suggested that forced-gradient experiments can result in considerably different estimates of dispersivity compared to what can be found in natural-gradient systems for typical channel widths.

A New and Efficient Proposed Approach to Find Initial Basic Feasible Solution of a Transportation Problem

In this research, a new and efficient approach of finding an initial basic feasible solution to transportation problems is proposed. The proposed approach is named “Inverse Coefficient of Variation Method (ICVM)”, and the method is illustrated with seven numerical examples. Six existing methods; North West Corner Method (NWCM), Column Minimum Method (CMM), Least Cost Method (LCM), Row Minimum Method (RMM),Vogel’s Approximation Method (VAM), and Allocation Table Method (ATM) were compared with the proposed approach. It can be said conclusively that the proposed Inverse Coefficient of Variation Method (ICVM) provides an improved Initial Basic Feasible Solution to all the transportation problems used in the experiment. Further, the new method leads to the optimal solution to many of the problems considered.

Solving a fuzzy fixed charge solid transportation problem using batch transferring by new approaches in meta-heuristic

Nowadays finding effective solution for transportation problem is one of the main issues both in industries and academia. According to the real world, in this paper it is assumed that the products are transferred in batches in a fixed charge transportation problem. Furthermore, the fuzzy values are used according to the parameters value in the real world. In addition, six meta-heuristics are utilized in order to solve the presented model. Most of these algorithms are firstly used for a mathematical model in transportation problem literature. Because of the importance of tuning the parameters in solving the given problem, the Taguchi method is used. Finally, computational results with different problem sizes are studied and analyzed.

A general polynomial solution to convection–dispersion equation using boundary layer theory

A number of models have been established to simulate the behaviour of solute transport due to chemical pollution, both in croplands and groundwater systems. An approximate polynomial solution to convection–dispersion equation (CDE) based on boundary layer theory has been verified for the use to describe solute transport in semi-infinite systems such as soil column. However, previous studies have only proposed low order polynomial solutions such as parabolic and cubic polynomials. This paper presents a general polynomial boundary layer solution to CDE. Comparison with exact solution suggests the prediction accuracy of the boundary layer solution varies with the order of polynomial expression and soil transport parameters. The results show that prediction accuracy increases with increasing order up to parabolic or cubic polynomial function and with no distinct relationship between accuracy and order for higher order polynomials (\(n\geqslant 3\)). Comparison of two critical solute transport parameters (i.e., dispersion coefficient and retardation factor), estimated by the boundary layer solution and obtained by CXTFIT curve-fitting, shows a good agreement. The study shows that the general solution can determine the appropriate orders of polynomials for approximate CDE solutions that best describe solute concentration profiles and optimal solute transport parameters. Furthermore, the general polynomial solution to CDE provides a simple approach to solute transport problems, a criterion for choosing the right orders of polynomials for soils with different transport parameters. It is also a potential approach for estimating solute transport parameters of soils in the field.

Three new methods to find initial basic feasible solution of transportation problems

Three new methods to find initial basic feasible solution of transportation problems

多种算法求解运输问题的比较分析

运输问题作为一类特殊的线性规划问题，传统上的表上作业法，求解过程比较繁琐。随着计算机技术的发展，各种软件发挥了重要的作用，例如MATLAB、Lingo以及Excel等软件。本文根据运筹学中线性规划的单纯形法、运输问题的表上作业法，以及决策理论中的优化决策思想，通过实例对几种软件求解运输问题最优解的方法进行了对比分析。 As a special kind of linear programming problem, the traditional table on the operation method of the transport problem, its solution process is more complicated. With the development of computer technology, a variety of software plays an important role, such as MATLAB, Lingo and Excel and other software. Based on the Simplex method of linear programming in transportation research, the table operation method of transportation problem and the optimal decision making in decision theory, this paper makes a comparative analysis of several methods to solve the optimal solution of transportation problem.

OFSTF Method- An Optimal Solution for Transportation Problem

In this paper a different approach OFSTF (Origin, First, Second, Third, and Fourth quadrants) Method is applied for finding a feasible solution for transportation problems directly. The proposed method is a unique, it gives always feasible (may be optimal for some extant) solution without disturbance of degeneracy condition. This method takes least iterations to reach optimality. A numerical example is solved to check the validity of the proposed method and degeneracy problem is also discussed.