Sharif Digital Repository

In this paper we present a new exact solution for scalar field with cosmological constant in cylindrical symmetry Associated cosmological models including a model that describes a cyclic universe are discussed  

In this study, the authors investigate the problem of source localisation based on the time difference of arrival (TDOA) in a group of sensors. Aiming to minimise the squared range-difference errors, the problem leads to a quadratically constrained quadratic programme. It is well known that this approach results in a non-convex optimisation problem. By proposing a relaxation technique, they show that the optimisation problem would be transformed to a convex one which can be solved by semi-definite programming (SDP) and Lagrange multiplier methods. Moreover, these methods offer the exact solution of the original problem and the affirmation of its uniqueness. In contrast to other complicated... 

Numerical and analytical exact solutions of diffusional release from a cylindrical polymeric matrix into an infinite medium have been developed in which the initial solute loading (A) is greater than solubility limit (Cs). Also, the effects of boundary layers on the drug release rate have been studied. The numerical solution is valid for any initial drug loading whereas analytical solution can be used for high values of drug loading. Comparisons have been made between numerical and analytical exact solutions in upper and lower bounds (A/Cs蠑1 and A/Cs→1) and previously presented approximate solution. The presented results validate the proposed numerical solution  

In this paper, we introduce a general framework for coinfection as cooperative susceptible-infected-removed (SIR) dynamics. We first solve the SIR model analytically for two symmetric cooperative contagions [L. Chen, Europhys. Lett. 104, 50001 (2013)10.1209/0295-5075/104/50001] and then generalize and solve the model exactly in the symmetric scenarios for three and more cooperative contagions. We calculate the transition points and order parameters, i.e., the total number of infected hosts. We show that the behavior of the system does not change qualitatively with the inclusion of more diseases. We also show analytically that there is a saddle-node-like bifurcation for two cooperative SIR... 

In this article, the homotopy analysis method has been applied to solve nonlinear differential equations of fractional order. The validity of this method has successfully been accomplished by applying it to find the solution of two nonlinear fractional equations. The results obtained by homotopy analysis method have been compared with those exact solutions. The results show that the solution of homotopy analysis method is good agreement with the exact solution. Crown  

We design a quasi-one-dimensional spin chain with engineered coupling strengths such that the natural dynamics of the spin chain evolves a single excitation localized at the left-hand site to any specified single-particle state on the whole chain. Our treatment is an exact solution to a problem which has already been addressed in approximate ways. As two important examples, we study the W states and Gaussian states of arbitrary width. © 2019 American Physical Society  

In this paper, we consider the problem of optimum rate adaptation and power allocation to maximize the delay-limited throughput (DLT) in a time-correlated 2×1 MISO Rayleigh fading channel with Hybrid ARQ in Chase-Combining mode (HARQ-CC). To this aim, we have first formulated the DLT equation based on the outage probability for 2×1 MISO-HARQ channel. We show that exact analytical calculation of the outage probability is not tractable. Therefore, we approximate the outage probability using a log-normal approximation approach. Based on such approximation, optimal rate and power allocations are derived. Finally, using Monte-Carlo simulation, we show that the approximation method provides... 

The free longitudinal vibration of tapered nanowires is investigated in the context of nonlocal continuum theory. The problem is studied for the nanowires with linearly varied radii under fixedfixed and fixedfree boundary conditions. In order to assess the problem in a more general form, a perturbation technique is proposed based on the Fredholm alternative theorem. The natural frequencies, corresponding mode shapes, and phase velocities of the tapered nanowires are derived analytically up to the second-order perturbation for different boundary conditions. The predicted results by the perturbation technique are successfully verified with those of the exact solution. The obtained results... 

We propose an approach for computing the general compromised solution of an LR fuzzy linear system by use of a ranking function when the coefficient matrix is a crisp m×n matrix. The solution is so that mean values of a compromised solution satisfies the corresponding crisp linear system. We show that if the corresponding crisp system is incompatible, then the fuzzy linear system lacks any solution. Otherwise, we solve a constrained least squares problem to compute a compromised solution. If the optimal value of the constrained least squares problem is zero, then we obtain the LR solution, namely the exact solution, of the system with respect to a ranking function. On the other hand, if the... 

The Adomian Decomposition Method is employed in the solution of the two dimensional laminar boundary layer of Falkner-Skan equation for wedge. This work aims at the solution of momentum equation in the case of accelerated flow and decelerated flow with separation. The Adomian Decomposition Method is provided an analytical solution in the form of an infinite power series. The effect of Adomian polynomials terms is considered on accuracy of the results. The velocity profiles in boundary layer are obtained. Results show a good accuracy compared to the exact solution. © 2007 Elsevier B.V. All rights reserved  

In this work the topological order at finite temperature in two-dimensional color code is studied. The topological entropy is used to measure the behavior of the topological order. Topological order in color code arises from the colored string-net structures. By imposing the hard constrained limit the exact solution of the entanglement entropy becomes possible. For finite size systems, by raising the temperature, one type of string-net structure is thermalized and the associative topological entropy vanishes. In the thermodynamic limit the underlying topological order is fragile even at very low temperatures. Taking first the thermodynamic limit and then the zero-temperature limit and vice... 

Based on the Euler–Bernoulli beam model and the modified strain gradient theory, the size-dependent forced vibration of sandwich microbeams with a functionally graded (FG) core is presented. The equation of motion and the corresponding classical and nonclassical boundary conditions are derived using the Hamilton’s principle. An exact solution of the governing equation is developed for sandwich beams with various boundary conditions and subjected to an arbitrarily distributed harmonic transverse load. Finally, parametric studies are presented to investigate the effects of geometric ratios, length scale parameters, power index, boundary conditions, layup, and thickness of the FG layer on the... 

The Block method approach to solve EIT problem leads to an exact solution if the measurements are done without error. Non-iterative method is a feasible approach on solving 3D EIT forward problem. However, the effect of the measurement error has not been considered in this method yet. In this article, the 3D model of EIT with block method has been considered. The required equations to solve the forward problem are then generated. To solve the forward problem, non-iterative method has been employed. Effect of the measurement error on forward problem for a 3D model of EIT are generated. It has been shown that for a sample 3D model, measurement error can propagate exponentially. ©2007 IEEE  

In association with multi-inhomogeneity problems, a special class of eigenstrains is discovered to give rise to disturbance stresses of interesting nature. Some previously unnoticed properties of Eshelby's tensors prove useful in this accomplishment. Consider the set of nested similar ellipsoidal domains {Ω1, Ω2,⋯,ΩN+1}, which are embedded in an infinite isotropic medium. Suppose that Ωt= {x|x ∈ ℝ3, ∑p=13 x p2/ap2 ≤ ξt 2}, which 0 ≤ ξ1 < ξ2 < ⋯ < ξN+1 and ξ t a p , p=1,2,3 are the principal half axes of Ω t . Suppose, the distribution of eigenstrain, ε ij *(x) over the regions Γ t =Ω t+1-Ω t , t=1,2,⋯,N can be expressed as εij*(x)={f ijkl⋯mt(∑p=13 x p2/ap2)xkx l⋯xm, x∈ Γ, 0, x ∈ Ω1∪(ℝ3 -... 

We propose a robust deviation framework to deal with uncertain component reliabilities in the constrained redundancy optimization problem (CROP) in series-parallel reliability systems. The proposed model is based on a linearized binary version of standard nonlinear integer programming formulations of this problem. We extend the linearized model to address uncertainty by assuming that the component reliabilities belong to an interval uncertainty set, where only upper and lower bounds are known for each component reliability, and develop a Min-Max regret model to handle data uncertainty. A key challenge is that, because the deterministic model involves nonlinear functions of the uncertain... 

Rectangular plates on distributed elastic foundations are widely employed in footings and raft foundations of variety of structures. In particular, mounted columns and single footings may partially occupy the rectangular plate of any kind. This study deals with free vibration problem of thin rectangular plates on Winkler and Pasternak elastic foundation model which is distributed over a particular arbitrary area of the plate. Closed form solutions are developed through solving the governing differential equations of plates. Moreover, a novel mathematical approach is proposed to find the exact analytical solution of free vibration of plates with mixed or fully-clamped boundary conditions.... 

In this paper, an analytical solution for the nonlinear free vibration of a conservative oscillator is presented. The nonlinear governing equation is solved by employing the Variational Iteration Method (VIM). This method is based on the use of Lagrange multipliers for identification of optimal values of parameters in a function. Obtained results reveal that the proposed method is very effective, simple and exact. In the present investigation, the results of this method are compared with those of the Homotopy Analysis Method (HAM), as well as those predicted by the Runge-Kutta method. The excellent accuracy of the obtained results is demonstrated by comparing them with available analytical... 

In this paper, the responses of shape memory polymer (SMP) helical springs under axial force are studied both analytically and numerically. In the analytical solution, we first derive the response of a cylindrical tube under torsional loadings. This solution can be used for helical springs in which both the curvature and pitch effects are negligible. This is the case for helical springs with large ratios of the mean coil radius to the cross sectional radius (spring index) and also small pitch angles. Making use of this solution simplifies the analysis of the helical springs to that of the torsion of a straight bar with circular cross section. The 3D phenomenological constitutive model... 

Investigation of response of reinforced concrete (RC) structures due to axisymmetric macrocell corrosion of rebars is of concern after propagation of microcracks within the concrete medium. The geometry, boundary and interfaces conditions of the present problem are identical to those stated in part I. As seen in the companion paper, the exact solution to the boundary value problem corresponding to the uncracked steel-rust-concrete composite was possible. After appearance of the microcracks the concrete behavior becomes nonlinear anisotropic with post-cracking softening, and the associated problem is analytically intractable. Therefore, it is proposed to employ a novel meshless method, namely...