Volume 16, Issue 3-4 -

In the paper, based on the theory of neurodynamics, the nine-dimensional one-compartment complex model of CA1 pyramid neuron developed by David Golomb [ J. Neurophysiol ., 96 (2006), 1912–1926] is reduced, and the two-dimensional reduced neuron model is obtained for the first time. According to the definition of the minimal model, the nine-dimensional complex dynamic model has first be reduced to the minimal models. Then the minimal model is reduced into the two-dimensional model by the model reduction theory of neurodynamics and the polynomial regression algorithm. Finally, dynamic characteristics of the two-dimensional reduced neuron model are analyzed and discussed in detail by the neurodynamic analysis methods. When the stimulation current gradually increases from zero, the two-dimensional reduced neuron model undergoes the saddle-node bifurcation. It is equivalent to a bistable integrator and has the common dynamic properties of the integrator such as definite threshold value and class 2 neural excitability. The investigation provides a simple and convenient method to investigate deeply the high-dimensional complex neuron model’s dynamic characteristics and functions by the neurodynamic theory. Moreover, it is helpful to know the dynamic characteristics of the hippocampal neuron.

In this work, we describe a numerical method which enables an efficient computation of membrane gas permeation processes that involve multiple membrane stages and multiple gas components. The utilized numerical approach is a collocation method equipped with a grid adaptation strategy based on a dependable error estimate of the numerical approximation. The comparison of the results provided by the collocation method with those calculated from an experimentally validated finite difference method has demonstrated that the accuracy of both numerical approximations is practically the same. However, the current procedure is characterized by a much better computational efficiency that allows to considerably reduce the computational time. This is a crucial feature when combining computation of membrane permeation processes with optimization algorithms. In such a setting the computation of the permeation process is frequently repeated and naturally, results in long computational times when the efficiency is not adequately improved.

The article presents results of multi-criteria optimization of air nozzle topology. The optimization in the CFD has been recently developed since equations of flow in porous media were applied among others governing equations. Optimization is a seeking for extremum of an objective function with respect to the function constraints. With this definition in mind, the optimization by using a continuous adjoint for the current cases is a finding such channel topology which minimizes for example pressure or energy loss when the constraints of objective function are in the form of flow governing equations of momentum and continuity. This methodology of optimization makes a design process faster comparing to the methods related to Design of Experiments (DoE). However, for the sake of flow governing equations nonlinearity, the continuous adjoint method can be successfully applied only in relatively simply and steady-state cases. The reason is of possibility of finding the global extremum of the objective function only for that kind of cases. The results of optimization of two selected cases are presented in the article and show advantages and limitations of the method applied. The continuous adjoint simulation results indicate the nozzles design directions and can be applied in industry with limited reliability. The object of research reported in the article is the nozzle which is augmented equipment used with a pneumatic pulsator. The pulsators are devices that utilize an air stream to destruct vaults created in loose material structure. The pulsator productivity equipped with a nozzle depends on outlet pressure. Therefore, the optimization problem was stated so that pressure loss is to be as low as possible.

In loose material beds above silo outlets or in vertical channels immovable vaults can occur limiting or making impossible the downward movement of the loose material. To prevent vault creation or to destroy vault by aeration and separation of the loose material from encasing walls, a pneumatic pulsator can be applied. In order to optimize the head design, the flow phenomena were numerically simulated and the channels were preliminarily designed. The data obtained from simulation were also used as a basis for setting up an experimental stand to validate simulation results. During air flow in the channels due to frictional heat is produced, which is discharged from the pulsator to the environment. To increase the heat transfer in pneumatic pulsator, the external surfaces of channel are finned. Numerical simulations carried out conduction and convection heat transfer in the fins, and the results illustrated the temperature distribution on the surface of the body, the temperature distribution in the fins, stress distribution, value of factor of safety, the static displacement of the body and the distribution of air temperature along with the speed vectors. The results were compared with experimental and analytical results that confirm their correctness. The results confirm the rational design of the body in terms of thermal. The obtained temperature distribution using CFD agrees approximately with the values measured during the tests.

The present paper deals with the numerical solution of magnetohydrodynamic (MHD) flow of Williamson fluid model over a stretching cylinder. The governing partial differential equation of Williamson fluid is converted into an ordinary differential equation using similarity transformations along with boundary layer approach, which is then solved numerically by applying the shooting method in conjunction with Runge–Kutta–Fehlberg method. The effect of different parameters on velocity profile is thoroughly examined through graphs and tables.

In order to study the dynamic compression mechanical properties of engineering rock under high strain rate （10 0 ~10 2 S −1 ）loads, dynamic compression tests of three common engineering rocks (marble, sandstone and granite) taken from the Qinling Mountain are studied subjected to five different kinds of shock air pressure using Φ 100 mm split Hopkinson pressure bar test system improved with purple copper waveform shaper. The dynamic compression stress-strain curves, dynamic compressive strength, peak strain, energy absorption rate and elastic modulus of three rocks variation with strain rate are researched. The dynamic compression failure modes under different strain rates are analyzed. Then the three-dimensional numerical simulations of waveform shaper shaping effects and stress wave propagation in the SHPB tests are carried out to reproduce the test results. The research results show that the dynamic compression stress-strain curves show certain discreteness, and there is an obvious rebound phenomenon after the peak. With the increase in strain rate, the dynamic compressive strength, peak strain and energy absorption rate are all in a certain degree of increase, but the elastic modulus have no obvious change trend. Under the same strain rate, the dynamic compressive strength of granite is greatest while of sandstone is least. With the increase in strain rate, the margin of increase in peak strain and energy absorption rate of granite is greatest while of sandstone is least. The failure modes of the sample experience a developing process from outside to inside with the increase of strain rate.

Free convection boundary layer flow past a semi-infinite vertical plate in a doubly stratified fluid-saturated porous medium in the presence of constant suction/injection is analyzed. The flow in the porous medium is described by the Brinkman–Forchheimer-based model. A suitable coordinate transformation is introduced, and the obtained system of non-similar, coupled and nonlinear partial differential equations is solved numerically using the spectral quasi-linearization method. The effects of buoyancy parameter, Darcy number, Forchheimer parameter, suction/injection parameter, thermal and solutal stratification parameters on the dimensionless velocity, temperature and concentration are presented graphically. Further, the local skin friction coefficient, heat and mass transfer rates are presented graphically.

This paper deals with a discrete Nicholson’s blowflies model. By using contraction mapping fixed point theorem, we obtain sufficient conditions for the existence of unique almost periodic positive solution. Moreover, we investigate exponential stability of the almost periodic positive solution by Liapunov functional. We obtain new results and complement the previously obtained results in the past literatures.

In this work we study one of the most important applications of symmetries to physical problems, namely the construction of conservation laws. Conservation laws have important place for applications of differential equations and solutions, also in all physics applications. And so, this study deals conservation laws of first- and second-type nonlinear (NL) reaction diffusion equations. We used Ibragimov’s approach for finding conservation laws for these equations. And then, we found exact solutions of first- and second-type NL reaction diffusion equations with Lie-point symmetries.