Sharif Digital Repository

An improvement to the Direct Discrete Method (DDM), also known as the Cell Method, has been discussed. The improvement is based on a duality theorem between the primal and dual complexes. Also, the analog counterpart of the Integral operator has been derived in this paper. The multi-group neutron diffusion is then derived, directly in a discrete algebraic form, according to this procedure. A numerical example has shown that this method would yield a high order of convergence (approximately 4.6) if its parameters are adjusted suitably. Finally, the method is applied to the 2D IAEA benchmark problem, and has shown to yield accurate solutions with a reasonably low number of unknowns  

A space dependent model for the second moment of a stochastic field has been presented. The derivation procedure is simple and avoids non-physical assumptions for completeness. Moreover, a program has been developed which obtains the solutions to this equation in the three dimensional space. Two benchmarks, namely the fissile cube and the subcritical slab, show the accuracy of the results obtained using this method  

Recently, deep convolutional neural networks (DCNN) that leverage the adversarial training framework for image restoration and enhancement have significantly improved the processed images' sharpness. Surprisingly, although these DCNNs produced crispier images than other methods visually, they may get a lower quality score when popular measures are employed for evaluating them. Therefore it is necessary to develop a quantitative metric to reflect their performances, which is well-aligned with the perceived quality of an image. Famous quantitative metrics such as Peak signal-to-noise ratio (PSNR), The structural similarity index measure (SSIM), and Perceptual Index (PI) are not well-correlated... 

The stochastic behavior of a point reactor is modeled with a system of Ito stochastic differential equations. This new approach does not require computing the square root of a matrix which is a great computational advantage. Moreover, the derivation procedure clearly demonstrates the mathematical approximations involved in the final formulation. Three numerical benchmarks show the accuracy of this model in predicting the mean and variance of the neutron and precursor population in a point reactor  

The most general basis for approximating the transport equation has been studied. The application of the Gram-Schmidt procedure has been shown to unify the complete class of functions (polynomial type or non-polynomial type), applicable to this equation. The completeness of the series of functions is proved. A generalized version of the Fick's law is introduced. It is shown that the spectrum of the transport equation obtained by this method agrees with the conventional methods of obtaining the spectrum  

Obtaining the set of algebraic equations that directly correspond to a physical phenomenon has been viable in the recent direct discrete method (DDM). Although this method may find its roots in physical and geometrical considerations, there are still some degrees of freedom that one may suspect optimize-able. Here we have used the information embedded in the corresponding adjoint equation to form a local functional, which in turn by its minimization, yield suitable dual mesh positioning  

Many of the physical macroscopic quantities could be explained as the result of a collection of microscopic particles which act independent of each-other, in a linear fashion. Since the physical laws of the interaction of these particles with their surrounding medium are non-deterministic, one could think of these particles as the generators of a linear stochastic field. In this paper, we have introduced a derivation which has yielded an equation for the spatiotemporal correlations in such a field. The derivation is simple and extendable to include the behavior of many physical particles. A simple numerical algorithm has been devised to solve the obtained initial value integrodifferential... 

A novel method is introduced which allows the higher order perturbative solution of a linear operator with a time variant coefficient. This method employs a form of raising and lowering operators which generate higher and lower order harmonics from a given harmonic. The analysis has been applied to the point kinetics equations with a monotone oscillatory reactivity to place bounds on the relative error of the linearization method frequently employed in the power reactor noise techniques. As a result, the maximum permissible reactivity amplitude for a given reactor as a function of frequency has been obtained such that regular power reactor noise methods remain accurate enough. Three... 

Power reactor noise analysis is one of the most powerful tools in online monitoring and diagnostics of nuclear power reactors. Unfortunately, since such an analysis belongs to the non-linear “parametric excitation” realm, its theoretical aspects and relations have been mostly carried out after linearization. In this paper a general framework, i.e. the Ladder Expansion Method, is developed to convert such equations to a series of coupled linear equations, up to any desired accuracy. This method is then applied to the single mode random fluctuations of the absorption cross sections in a power reactor which is modelled by the multigroup diffusion equation with multiple delayed neutron groups. A... 

The time-dependent diffusion of neutrons in a spheroid as a function of the focal distance has been studied. The solution is based on an orthogonal basis and an extrapolation distanced related boundary condition for the spheroidal geometry. It has been shown that spheres and disks are two limiting cases for the spheroids, for which there is a smooth transition for the systems properties between these two limits. Furthermore, it is demonstrated that a slight deformation from a sphere does not affect the fundamental mode properties, to the first order. The calculations for both multiplying and non-multiplying media have been undertaken, showing good agreement with direct Monte Carlo... 

Accurate calculation of kinetic parameters is of utmost importance in the safety analysis of a nuclear reactor. In the current paper, two approaches are investigated to evaluate these parameters in energy phase space. In the first approach, these parameters are derived from an energy-continuous form of the forward and adjoint transport equations and then integrals with respect to the energy variable are replaced by weighted summations over the energy groups, while in the second approach these parameters are extracted from the multi-group forward equation and its associate adjoint equation in which their multigroup constants are weighted by forward spectrum. The difference of weighting... 

In this paper, we consider a dual-sourcing model with constant demand and stochastic lead times. Two suppliers may be different in terms of purchasing prices and lead-time parameters. The ordering takes place when the inventory level depletes to a reorder level, and the order is split among two suppliers. Unlike previous works in the order splitting literature, the supply lead time between vendor and buyer as well as unit purchasing prices is considered to be order quantity dependent. The proposed model finds out the optimal reorder point, order quantity and splitting proportion, using a solution procedure. Numerical results show that neglecting the relationship between ordering batch size... 

Adsorption of human serum proteins (Albumin and total protein) onto high purity synthesis nano-hydroxyapatite (HA), Ca 10(PO 4) 6(OH) 2, has been studied in a wide temperature range by UV-visible spectrophotometer. Adsorption isotherm is basically important to describe how solutes interact with adsorbent, andiscriticalinoptimizing the use of adsorbent. Inthe present study, the experimental results werefitted tothe Langmuir, Freundlich, Temkin and Dubinin-Radushkevich (DR) models to obtain the characteristic parameters of each model and square of the correlation coefficients (R 2). According to the results, the DR isotherm model had the best agreement with the experimental data. The effect of...