مجله بین المللی محاسبات و مدل سازی ریاضی
سال سوم شماره 4 (Autumn 2013)

Modern control systems widely use network to decrease the implementation cost and also increase the performance. Although they have several advantages, they suffer from some limitations and deficiencies. Packet loss is one of the main limitations which affect the control system in different conditions and finally can lead to system instability. To prevent such problems it is important to model the system properly. In this paper, a new function has been proposed for error modeling. Moreover, different influences of system parameters and packet loss on error function have been investigated and it has been determined that changes of which parameter has more contribution on packet effect in error function. Considering these parameters is very critical in designing systems.

Tetracycline (TC) is a broad spectrum of antibiotic which is used to cure infectious diseases and cancer. It can cause harmful side effects due to its high absorption in all organs. On the other hand graphene is appropriate to carry drug and release it to special target, organ or cell. It may decrease the side effects of the drug dramatically by using low dosage of medicine. Graphene oxide (GO) is able to adsorb the molecule of TC via π-π stacking. Base on this mechanism, simulation of TC molecule onto graphene nano sheets was adjusted. Study of force in the z direction illustrated that TC is closed to graphene via carbon (C8) phenolic ring then it rotates and is again closed to the graphene from amino group side. This case is adsorption equilibrium and total energy of the system is -6800eV.

An approximation technique is considered for computing transmission and reflection coefficients for plane waves propagating through stratified slabs. The propagation of elastic pulse through a planar slab is derived from first principles using straightforward time-dependent method. The paper ends with calculations of enhancement factor for the elastic plane wave and it is shown that it depends on the velocity ratio of the wave in two different media but not the incident wave form. The result, valid for quite arbitrary incident pulses and quite arbitrary slab inhomogeneities, agrees with that obtained by time-independent methods, but uses more elementary methods.

Severe Tropical Cyclones associated with surges frequently hits the coastal region of Bangladesh. For a reliable hydrodynamic model to simulate the severity of such cyclones, it is necessary to incorporate the meteorological and hydrological inputs properly. In order to incorporate the coastlines and the island boundaries properly in the numerical scheme a very fine grid resolution along the coastal belts is necessary. Consideration of very fine resolution involves more memory, CPU time in the solution process and invites problem of complexity in the model or numerical instability. In this study we use the boundary-fitted curvilinear grids where the complete boundary of the analysis area and each Island are represented by four curves and they are defined by four functions. Using appropriate transformations of independent coordinates, the curvilinear physical domains are transformed to a square one and also each island boundary transforms to a rectangle within this square domain. The vertically integrated shallow water equations are transformed to the new space domain and then the regular explicit finite difference scheme is used to solve the shallow water equations, where the problem domain is divided into 100× 129 grid points. The model is applied to compute the water levels due to astronomical tide and surges associated with Cyclone Sidr (2007) and Cyclone Aila (2009) that hit the coast of Bangladesh. The computed results along the coastal belt of Bangladesh are found to be reasonably accurate.

In this paper, we use game theory to describe the emergence of self-organization and consequent pattern formation through communicative cooperation in Bacillus subtilis colonies. The emergence of cooperative regime is modelled as an n-player Assurance game, with the bacterial colonies as individual players. The game is played iteratively through cooperative communication, and mediated by exchange of information about the local environment between the different bacterial colonies comprising the system. The iteration causes the interactive system to grow and produce beautiful complex spatial patterns signaling the emergence of self-organization.In laboratory, we have the bacterial growth environment mimicked in Petri dish, where chemical stress is introduced in a three- fold manner: through modification of nutrition and substrate amounts and introducing an antibiotic in the system. In our model, bacteria colonies, treated asindividual players, interact within the environment and grow according to a set of rules. The rules capture the biotic processes that allow bacteria to grow in the hostile environment, and cope with the stress. We find the effects of sophisticated communications and information-sharing between bacterial colonies to be a vital determinant for bacterial growth, which is manifested in the Petri dish as complex spatial patterns, often at fractal scales.As a formal description of the above game, we model the emergence of this cooperative behaviour as finite deterministic automata, whose transition function is informed by the Assurance game pay-off. Consequently, the exercise allows us to derive a grammar that provides the rules for describing the bacterial interactions leading to the emergence of the spatial structures.

In this paper, an interesting and easy method to solve the multi-dimensional knapsack problem is presented. Although it belongs to the combinatorial optimization, but the proposed method belongs to the decision making field in mathematics. In order to, initially efficiency values for every item is calculated then items are ranked by using Multiple Criteria Decision Making (MCDA). Finally, items are selected in according to their rank.

Nonlinear problems are more challenging and almost complex to be solved. A recently developed Homotopy Perturbation Method (HPM) is introduced. This method is used to represent the system as a less complicated (almost linear) model. To verify the effectiveness, HPM based model is compared with the nonlinear dynamic in both open and closed loop PI controlled. The error indices are approximation of possible uncertainties which may be occurred. The simulation results reveal the ability of the proposed method.

Fixed charge solid transportation problem (FCSTP) is one of the main and most important problems in transportation and network research areas. To tackle such an NP-hard problem, An Electromagnetism-like algorithm (EM) is employed. To the best of our knowledge, EM has been considered for any kind of transportation problems. Due to the significant role of parameters on the algorithm’s performance, a calibration in EM is carried out with the aid of a set of experimental design. The efficiency of employed parameters is measured by the experimental design method. To evaluate the performance of the proposed EM, a computational study has been conducted and the associated results obtained by the EM are compared with simulated annealing algorithm (SA).