Channel model and analysis for wireless underground sensor networks in soil medium

Wireless underground sensor networks (WUSNs) constitute one of the promising application areas of the recently developed wireless sensor networking techniques. The main difference between WUSNs and the terrestrial wireless sensor networks is the communication medium. The propagation characteristics of electromagnetic (EM) waves in soil and the significant differences between propagation in air prevent a straightforward characterization of the underground wireless channel. To this end, in this paper, advanced channel models are derived to characterize the underground wireless channel and the foundational issues for efficient communication through soil are discussed. In particular, the underground communication channel is modeled considering not only the propagation of EM waves in soil, but also other effects such as multipath, soil composition, soil moisture, and burial depth. The propagation characteristics are investigated through simulation results of path loss between two underground sensors. Moreover, based on the proposed channel model, the resulting bit error rate is analyzed for different network and soil parameters. Furthermore, the effects of variations in soil moisture are investigated through field measurement results. The theoretical analysis and the simulation results prove the feasibility of wireless communication in underground environment and highlight several important aspects in this field. This work will lead to the provision of a generic framework for underground wireless communication and the realization of WUSNs.     

On some new analytical solutionsforthe (2+1)-dimensional burgers equation and the special type of dodd_bullough_Mikhailov equation

Some new travelling wave transform methods are very importantfor obtaining analytical solutions of special type of nonlinear partial differentialequations (NLPDEs). Some of these solutions of NLPDEs may be inthe different forms such as rational function solutions, trigonometric functionsolutions, hyperbolic function solutions, exponential function solutions andJacobi elliptic function solutions. These forms tell us the various propertiesof the NLPDEs from scientifical applications to engineering.In this research, we have studied to obtain the analytical solution ofthe nonlinear (2+1)-dimensional Burgers equation which is named from JohannesMartinus Burgers and the nonlinear special type of the Dodd-Bullough-Mikhailov equation introduced to the literature by Roger Dodd, Robin Bullough,and Alexander Mikhailov.     

Analytical and numerical approaches to nerve impulse model of fractional-order

We consider a fractional-order nerve impulse model which is known as FitzHugh–Nagumo (F–N) model in this paper. Knowing the solutions of this model allows the management of the nerve impulses process. Especially, considering this model as fractional-order ensures to be able to analyze in detail because of the memory effect. In this context, first, we use an analytical solution and with the aim of this solution, we obtain numerical solutions by using two numerical schemes. Then, we demonstrate the walking wave-type solutions of the stated problem. These solutions include complex trigonometric functions, complex hyperbolic functions, and algebraic functions. In addition, the linear stability analysis is performed and the absolute error is occurred by comparing the numerical results with the analytical result. All of the results are depicted by tables and figures. This paper not only points out the exact and numerical solutions of the model but also compares the differences and the similarities of the stated solution methods. Therefore, the results of this paper are important and useful for either neuroscientists and physicists or mathematicians and engineers.     

A new collocation method for solution of mixed linear integro-differential-difference equations

Numerical solution of mixed linear integro-differential-difference equation is presented using Chebyshev collocation method. The aim of this article is to present an efficient numerical procedure for solving mixed linear integro-differential-difference equations. Our method depends mainly on a Chebyshev expansion approach. This method transforms mixed linear integro-differential-difference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system Maple10.     

On the Bessel Heat Equation Related to the Bessel Diamond Operator

In this article, we study the equation

$\frac{\partial }{\partial t}u(x,t)=c^{2}\Diamond _{B}^{k}u(x,t)$

with the initial condition u(x,0)=f(x) for x∈? _n ⁺ . The operator ? _B ^k is named to be Bessel diamond operator iterated k-times and is defined by

$\Diamond _{B}^{k}=\bigl[(B_{x_{1}}+B_{x_{2}}+\cdots +B_{x_{p}})^{2}-(B_{x_{p+1}}+\cdots +B_{x_{p+q}})^{2}\bigr]^{k},$

where k is a positive integer, p+q=n, \(B_{x_{i}}=\frac{\partial ^{2}}{\partial x_{i}^{2}}+\frac{2v_{i}}{x_{i}}\frac{\partial }{\partial x_{i}},\) 2v _i =2α _i +1,\(\;\alpha _{i}>-\frac{1}{2}\), x _i >0, i=1,2,…,n, and n is the dimension of the ? _n ⁺ , u(x,t) is an unknown function of the form (x,t)=(x ₁,…,x _n ,t)∈? _n ⁺ ×(0,∞), f(x) is a given generalized function and c is a positive constant (see Levitan, Usp. Mat. 6(2(42)):102–143, 1951; Y?ld?r?m, Ph.D. Thesis, 1995; Y?ld?r?m and Sar?kaya, J. Inst. Math. Comput. Sci. 14(3):217–224, 2001; Y?ld?r?m, et al., Proc. Indian Acad. Sci. (Math. Sci.) 114(4):375–387, 2004; Sar?kaya, Ph.D. Thesis, 2007; Sar?kaya and Y?ld?r?m, Nonlinear Anal. 68:430–442, 2008, and Appl. Math. Comput. 189:910–917, 2007). We obtain the solution of such equation, which is related to the spectrum and the kernel, which is so called Bessel diamond heat kernel. Moreover, such Bessel diamond heat kernel has interesting properties and also related to the kernel of an extension of the heat equation.

     

A dynamic rationing policy for continuous-review inventory systems

Stock rationing is an inventory policy that allows differential treatment of customer classes without using separate inventories. In this paper, we propose a dynamic rationing policy for continuous-review inventory systems, which utilizes the information on the status of the outstanding replenishment orders. For both backordering and lost sales environments, we conduct simulation studies to compare the performance of the dynamic policy with the static critical level and the common stock policies and quantify the gain obtained. We propose two new bounds on the optimum dynamic rationing policy that enables us to tell how much of the potential gain the proposed dynamic policy realizes. We discuss the conditions under which stock rationing – both dynamic and static – is beneficial and assess the value of the dynamic policy.     

Spacelike helices in Minkowski 4-space $${E_1^4 }$$

In this paper, we give some characterizations for spacelike helices in Minkowski space–time E₁⁴{E_1^4}. We find the differential equations characterizing the spacelike helices and also give the integral characterizations for these curves in Minkowski space–time E₁⁴{E_1^4}.     

A collocation method to solve higher order linear complex differential equations in rectangular domains

In this article, a collocation method is developed to find an approximate solution of higher order linear complex differential equations with variable coefficients in rectangular domains. This method is essentially based on the matrix representations of the truncated Taylor series of the expressions in equation and their derivates, which consist of collocation points defined in the given domain. Some numerical examples with initial and boundary conditions are given to show the properties of the method. All results were computed using a program written in scientific WorkPlace v5.5 and Maple v12. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

What part of the concept of acceleration is difficult to understand: the mathematics, the physics, or both?

In this paper, details of student difficulties in understanding the concept of acceleration and the mathematical and physical/intuitive sources of these are delineated by utilizing the teaching experiment methodology. As a result of the study, two anchoring analogies are proposed that can be used as a diagnostic tool for students’ alternative conceptions. These can be used in teaching to highlight the peculiarity of acceleration concept. This study portrays how seeing acceleration as ‘rate of change’ of a quantity (velocity) and recognizing the consequences of such a definition are hindered in certain ways which in turn negatively affect learning the concept of force. This is also an example that illustrates that a rather “simple” mathematical concept (i.e., rate of change) for the expert can become a complex phenomenon when embedded in a physical concept (i.e., acceleration) which is consistently found to be as a misconception among learners at various levels that is widely occurring and very resistant to change.     

An arbitrary Lagrangian–Eulerian formulation for the numerical simulation of flow patterns generated by the hydromedusa Aequorea victoria

A new geometrically conservative arbitrary Lagrangian–Eulerian (ALE) formulation is presented for the moving boundary problems in the swirl-free cylindrical coordinates. The governing equations are multiplied with the radial distance and integrated over arbitrary moving Lagrangian–Eulerian quadrilateral elements. Therefore, the continuity and the geometric conservation equations take very simple form similar to those of the Cartesian coordinates. The continuity equation is satisfied exactly within each element and a special attention is given to satisfy the geometric conservation law (GCL) at the discrete level. The equation of motion of a deforming body is solved in addition to the Navier–Stokes equations in a fully-coupled form. The mesh deformation is achieved by solving the linear elasticity equation at each time level while avoiding remeshing in order to enhance numerical robustness. The resulting algebraic linear systems are solved using an ILU(k) preconditioned GMRES method provided by the PETSc library. The present ALE method is validated for the steady and oscillatory flow around a sphere in a cylindrical tube and applied to the investigation of the flow patterns around a free-swimming hydromedusa Aequorea victoria (crystal jellyfish). The calculations for the hydromedusa indicate the shed of the opposite signed vortex rings very close to each other and the formation of large induced velocities along the line of interaction while the ring vortices moving away from the hydromedusa. In addition, the propulsion efficiency of the free-swimming hydromedusa is computed and its value is compared with values from the literature for several other species.