With use of the Trotter's technique simulation for one - dimensional XYZ Heisenberg systems of spin -1/2 have been performed. It is shown that the one- dimensional quantum systems can be transformed to the two- dimensional classical systyems by Trotter's technique. The extra dimension found to be like an imaginary time which has been related to the temperature of the system. Several chanis of one - dimensional spin systems are simulated by Monte Carlo method and the thermodynamic quantities of these are calculated at low temperature by means of this technique. Comparison is made with Bonner &Fisher's exact data which is found tobe in good agreement with their results.

Studying stock options is still a pristine area of research in the Iranian capital market. This is due to the lack of data as well as the complexity of valu-ation methodologies. In the present paper, using the Monte-Carlo simulation, we have estimated the value of stock options traded on Tehran Stock Exchange and examined whether the use of a control variate or antithetic variate augmented methods can lower the standard error of estimates. Furthermore, the estimated values of the three models under consideration, including of crude Monte-Carlo, control variates augmented Monte-Carlo, and antithetic variates augmented Mon-teCarlo are compared with each other and with options market prices. The results show that the standard error of the antithetic variate method is less than the crude method and control variate method. However, control variate augmented MonteCarlo model is more powerful than the crude Monte-Carlo and antithetic variate augmented Monte-Carlo method. Therefore, we can conclude that the control variate augmented Monte-Carlo model has a better performance in estimating the value of trading stock options and its estimated values are closer to the market prices.

Background and Aim: Liposuction is one of the most popular procedures for removing unwanted body fat deposits now. The conventional methods for liposuction however have many drawbacks; among them is long recovery time, scars, bruising, skin flaccidity and excessive blood loss. Considering the increasing demand for body sculpting, the need to improve these techniques is of vital importance. One of these newly proposed techniques is laser assisted lipolysis. Laser lipolysis is now widely used for body contouring and sculpting. Less trauma, bleeding and pain is among the main advantages of this method.Methods: Photons propagation and scattering within the biological tissues can effectively investigated by using numerical methods. In this study we used the Monte Carlo simulation method to simulate photons directions, absorption and scattering inside the tissue. This method uses a random number generator for photons creation, moving inside the tissue and termination. In this simulation we considered both the wavelength and fluence variations effects on the photon absorption rate and penetration depth inside the fat tissue.Results: Our study showed the increasing of penetration depth with decreasing of absorption coefficient. We observed that deepest penetration depth for 920 nm wavelength as it has lowest absorption coefficient. We also concluded that increasing the laser power (increase in fluence of laser) resulted in increasing the penetration depth of laser radiation.Increasing the radius of laser beam (decreasing the fluence) on the other hand resulted in reduction in penetration depth.Conclusion: Monte Carlo simulation of radiation propagation within the biological tissue has proved to be an efficient method. This method effectively simulates the physical components of laser radiation. Our findings indicate that to have laser lipolysis more efficient and safe, it is essential to choose suitable wavelength.

In this work, based on experimental observations and exact theoretical predictions, the kinetic scheme of RAFT polymerization is extended to a wider range of reactions such as irreversible intermediate radical terminations and reversible transfer reactions. The reactions which have been labeled as kinetic scheme are the more probable existing reactions as the theoretical point of view. The detailed kinetic scheme is applied to three kinds of RAFT polymerization system by utilizing the Monte Carlo simulation Method. To do this, a new approach of simulation method was used. In this approach, a multi-reaction step was used in each time step. Unknown kinetic rate constants have obtained by curve fitting of the simulation results and theoretical data, applying the least square method; or estimated by considering theoretical facts and experimental findings. The origin of the rate retardation and induction period has been understood by studying the main and pre-equilibrium stages of dithiobenzoate-mediated RAFT homo polymerization. A copolymerization system in the presence of RAFT agent has also been examined to confirm the capability of introduced simulation method in different monomer/RAFT agent systems. The simulation results were in excellent agreement with experimental data, which proves the validity and applicability of the Monte Carlo algorithm.

The computational burdens and more accurate approximations for the estimation of the failure probability are the main concerns in the structural reliability analyses. The Monte Carlo simulation (MCS) method can simply provide an accurate estimation for the failure probability, but it is a time-consuming method for complex reliability engineering problems with a low failure probability and may efficiently approximate the failure probability. In this paper, the efficiency of MCS for the computations of the performance function is improved using a random-weighted method known as the random-weighted MCS (RWMC) method. By using the weighted exponential function, the weights of random data points generated by MCS are adjusted by selecting the random point in the design space. The convergence performances including the computational burdens for evaluating the limit sate function and the accuracy of failure probabilities of RWMC are compared with MCS by using several nonlinear and complex mathematical and structural problems with normal and no-normal random variables. The results indicate that the proposed RWMC method can estimate the accurate results with the less computational burdens, about 100 to 1000 times faster than MCS.

Introduction: Most beta and gamma radiation radioisotopes used for treatment are not suitable for imaging. The bremsstrahlung images on a conventional gamma camera helped to localize the radionuclide within and outside of the lesion. Secondary scattering of gamma rays of higher energy and bremsstrahlung causes contamination in the energy window and reducing the contrast and resolution of the images and the quantization validation of the images cannot be performed. Therefore, the accuracy of scatter correction methods is of great importance. The method involves the use of energy window, empirically selected broad bremsstrahlung energy to enhance the signal to noise ratio and a wiener restoration filter to compensate for system blur. Materials and Methods: To simulate and validate the system, a water bottle containing Phosphorus-32 (P32) radio was taken. GATE package was used to determine the spectrum of bremsstrahlung radiation from P32 inside the liver and Zubal phantom was used to model a liver. Importantly, simulations were performed in the presence of a collimator without collimator and the collimator function was calculated. Zubal Phantom was also used to model liver imaging. The Wiener filter was used as a resolution adjuster. Results: Despite the small number of electrons reaching the collimator, a considerable spectrum is produced. Collimator function and simulated liver image were calculated. No significant change in resolution was observed after using the Weiner filter. Conclusion: The energy spectrum of the beams was altered after collimation to the collimator. Also, the shape of the energy spectrum was influenced by the type of tissue and size of the patient. The results had shown that planar gamma camera imaging and quantitation of P32 can be done. There is no compelling reason to suggest that the Wiener filter is useful in planning a Plane.

A direct Monte Carlo Method is used to simulate the effect of tri-and tetra-functional branching on molecular weight distribution in emulsion polymerization of butadiene. Butadiene polymerization due to high extent of transfer to C=C bonds of polymer chains, can be used as a modeL to study the effect of tri-and tetra-functional branching on Polymer Microstructure. In this simulation, elementary reactions included propagation, chain transfer to Monomer, termination by disproportionation, transfer to C-H bonds (BN3) and C=C bonds (BN4) of growing and dead polymer chains. The initial polymerization volume of the simulation was 105 nm3. The ratio of monomer to initiator concentration and initiator to polymer particles were 500 and 2.5,  respectively. As the conversion was increased from 20% to 75%, the molecular weight  distribution became bimodal. The maximum of the second peak of the bimodal distribution moved to higher molecular weights as the conversion was increased. Tetra-functional branching had little effect on number average molecular Weight, but it had a significant effect on weight average molecular weight. Therefore, weight average molecular weight is more suitable for characterization of emulsion polymerization systems with high extent of tetra-functional branching.

Quantifying source contribution of aeolian sediments is essential to prioritize sources and mitigate wind erosion. The objective of this research is quantifying uncertainty associated with results of sediment fingerprinting method using Monte-Carlo simulation technique in the Sirjan plain. Six sediment samples were collected from the sand sheets and forty source samples consisting Qt (n=13); Qc (n=17); Qsg (n=5); and Dc (n=5) were collected from geological spatial sources in the surrounding area. Concentration of eight geochemical elements were measured in both sample group. A two-stage statistical method including Kruskal Wallis H test and a stepwise discriminant function analysis applied for discriminating of aeolian sediment sources. Based on two-stage statistical method, four geochemical properties consisting Fe, K, Mg and Cu were selected as optimum fingerprints. The Qc and Dc were recognized as dominant sources for aeolian sediments in the study area and also, full uncertainty or full range (0-100%) calculated for some source contributions. Therefore, management activities for mitigation of wind erosion should establish at the Qc and Dc source regions. This technique has great potential for quantifying source contribution of aeolian sediments at other area with active wind erosion.