arXiv subjects

Mohammad Amirian Matlob

Publications and source records attributed to Mohammad Amirian Matlob.

3 recordsLinked to original sources

arXiv2020

A new approach to solving multi-order fractional equations using BEM and Chebyshev matrix

In this paper, the boundary element method is combined with Chebyshev operational matrix technique to solve two-dimensional multi-order time-fractional partial differential equations; nonlinear and linear in respect to spatial and temporal variables, respectively. Fractional derivatives are estimated by Caputo sense. Boundary element method is used to convert the main problem into a system of a multi-order fractional ordinary differential equation. Then, the produced system is approximated by Chebyshev operational matrix technique, ans its condition number is analyzed. Accuracy and efficiency of the proposed hybrid scheme are demonstrated by solving three different types of two-dimensional time fractional convection-diffusion equations numerically. The convergent rates are calculated for different meshing within the boundary element technique. Numerical results are given by graphs and tables for solutions and different type of error norms.

math.AP↗

arXiv2019

The Role of Topology in the Synchronization of Neuronal Networks Based on the Hodgkin-Huxley Model

Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon that can be seen in the brain. The network topology has a remarkable impact on both the function and the dynamics of neural networks. In this research, synchronization of neural networks is scrutinized through creating various topologies. These networks include both excitatory and inhibitory neurons. We investigate the dynamics of different networks by random rewiring of the synaptic connections. In this manner, a regular network transforms into a small-world network and then becomes a random network. Coherence level which is measured and utilized as the criteria to analyze synchronicity, experiencing a sharp increase as the network changes into the small-world network and growing steadily by the end. On the other hand, a decreasing trend of coherence level is revealed starting from a complete excitatory network and gradually increasing of inhibitory neurons. Thus, the coherence level reaches approximately zero in a complete inhibitory network. By increasing the number of neurons in the network, the degree of synchronization follows a power-law distribution; however, the number of synaptic connections of each neuron and their conductance have a positive impact on synchronization. By applying the model to a C-elegance neural network, not only the mentioned parameters but also the role of the degree distribution are highlighted.

physics.bio-ph↗

arXiv2017

The Concepts and Applications of Fractional Order Differential Calculus in Modelling of Viscoelastic Systems: A primer

Viscoelasticity and related phenomena are of great importance in the study of mechanical properties of material especially, biological materials. Certain materials show some complex effects in mechanical tests, which cannot be described by standard linear equation (SLE) mostly owing to shape memory effect during deformation. Recently, researchers have been applying fractional calculus in order for probing viscoelasticity of such materials with a high precision. Fractional calculus is a powerful tool for modeling complex phenomenon. In this tutorial based paper, we try present clear descriptions of the fractional calculus, its techniques and its implementation. The intention is to keep the details to a minimum while still conveying a good idea of what and how can be done with this powerful tool. We try to expose the reader to the basic techniques that are used to solve the fractional equations analytically and/or numerically. More specifically, modeling the shape memory phenomena with this powerful tool are studied from different perspectives, as well as presented some physical interpretation in this case. Moreover, in order to show the relationship between fractional models and standard linear equations, a fractal system comprising spring and damper elements is considered, and the constitutive equation is approximated with a fractional element. Finally, after a brief literature review, two fractional models are utilized to investigate the viscoelasticity of the cell, and the comparison is made among them, experimental data, and previous models. Verification results indicate that not only does the fractional model match the experimental data well, but it also can be a good substitute for previously used models.

physics.bio-ph↗