Modeling and Simulating Asymmetrical Conductance Changes in Gramicidin Pores

Abstract Gramicidin A is a small and well characterized peptide that forms an ion channel in lipid membranes. An important feature of gramicidin A (gA) pore is that its conductance is affected by the electric charges near the its entrance. This property has led to the application of gramicidin A as a biochemical sensor for monitoring and quantifying a number of chemical and enzymatic reactions. Here, a mathematical model of conductance changes of gramicidin A pores in response to the presence of electrical charges near its entrance, either on membrane surface or attached to gramicidin A itself, is presented. In this numerical simulation, a two dimensional computational domain is set to mimic the structure of a gramicidin A channel in the bilayer surrounded by electrolyte. The transport of ions through the channel is modeled by the Poisson-Nernst-Planck (PNP) equations that are solved by Finite Element Method (FEM). Preliminary numerical simulations of this mathematical model are in qualitative agreement with the experimental results in the literature. In addition to the model and simulations, we also present the analysis of the stability of the solution to the boundary conditions and the convergence of FEM method for the two dimensional PNP equations in our model.

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Application of the method of mathematical modeling for forecasting channel deformations at the underwater crossing of the main pipeline

SCIENCE & TECHNOLOGIES OIL AND OIL PRODUCTS PIPELINE TRANSPORTATION ◽

10.28999/2541-9595-2020-10-6-599-609 ◽

2020 ◽

Vol 10 (6) ◽

pp. 599-609

Author(s):

Valery А. Gruzdev ◽

◽

Georgy V. Mosolov ◽

Ekaterina A. Sabayda ◽

◽

...

Keyword(s):

Mathematical Modeling ◽

Mathematical Model ◽

Roughness Coefficient ◽

Computational Domain ◽

Channel Deformations ◽

Geological Surveys ◽

Kuban River ◽

The Stability ◽

Protective Structures

In order to determine the possibility of using the method of mathematical modeling for making long-term forecasts of channel deformations of trunk line underwater crossing (TLUC) through water obstacles, a methodology for performing and analyzing the results of mathematical modeling of channel deformations in the TLUC zone across the Kuban River is considered. Within the framework of the work, the following tasks were solved: 1) the format and composition of the initial data necessary for mathematical modeling were determined; 2) the procedure for assigning the boundaries of the computational domain of the model was considered, the computational domain was broken down into the computational grid, the zoning of the computational domain was performed by the value of the roughness coefficient; 3) the analysis of the results of modeling the water flow was carried out without taking the bottom deformations into account, as well as modeling the bottom deformations, the specifics of the verification and calibration calculations were determined to build a reliable mathematical model; 4) considered the possibility of using the method of mathematical modeling to check the stability of the bottom in the area of TLUC in the presence of man-made dumping or protective structure. It has been established that modeling the flow hydraulics and structure of currents, making short-term forecasts of local high-altitude reshaping of the bottom, determining the tendencies of erosion and accumulation of sediments upstream and downstream of protective structures are applicable for predicting channel deformations in the zone of the TLUC. In all these cases, it is mandatory to have materials from engineering-hydro-meteorological and engineering-geological surveys in an amount sufficient to compile a reliable mathematical model.

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A Mathematical Model of the Transition from the Normal Hematopoiesis to the Chronic and Accelerated Acute Stages in Myeloid Leukemia

10.20944/preprints202001.0236.v1 ◽

2020 ◽

Author(s):

Lorand Gabriel Parajdi ◽

Radu Precup ◽

Eduard Alexandru Bonci ◽

Ciprian Tomuleasa

Keyword(s):

Mathematical Model ◽

Stem Cells ◽

Bone Marrow ◽

Stability Analysis ◽

Myeloid Leukemia ◽

Transition Process ◽

Two Dimensional ◽

The Stability ◽

Theoretical Results

A mathematical model given by a two - dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.

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A Two-Dimensional Mathematical Model of Heat Propagation Equations and Their Significance for Soil Temperature

Symmetry ◽

10.3390/sym11040478 ◽

2019 ◽

Vol 11 (4) ◽

pp. 478 ◽

Cited By ~ 1

Author(s):

Anis Dhahbi ◽

Salah Boulaaras ◽

Taha Radwan ◽

Nadia Mezouar ◽

Khaled Zennir ◽

...

Keyword(s):

Mathematical Model ◽

Soil Temperature ◽

Heat Propagation ◽

Two Dimensional ◽

Mathematical Problems ◽

Different Depths ◽

Spatial Method ◽

The Stability ◽

Academic Year ◽

Real Experimental Data

In the context of the development of the research project (Boulaaras et al.) which was supported by the Deanship of Scientific Research of Qassim University under the Project No. 1140 during the academic year 2016/1437, this research will introduce a two dimensional mathematical model based on the finite elements spatial method combined with a finite differences time scheme applied to the diffusion equations. This model will be applied in the hypothetical example where the obtained results will be compared with the real experimental data. Such a comparison will allow to predict the soil temperature for different depths and at different time periods according to certain conditions on the weather and take into account the stability conditions of the used numerical method. It’s worthy of note that some of the concreted mathematical problems will be addressed by the experimental scientific theories of functional analysis and then the numerical simulation of the theoretical study will be provided thanks to sophisticated methods with more convergence and stability. This mathematical model would be reduced by means of physical measurement and also in charge of the physical cost.

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Instability of erodible beds

Journal of Fluid Mechanics ◽

10.1017/s0022112070001210 ◽

1970 ◽

Vol 42 (2) ◽

pp. 225-244 ◽

Cited By ~ 190

Author(s):

Frank Engelund

Keyword(s):

Mathematical Model ◽

Internal Friction ◽

Potential Flow ◽

Transport Mechanism ◽

Flow Analysis ◽

Two Dimensional ◽

Alluvial Channel ◽

The Stability ◽

Vorticity Transport ◽

Erodible Beds

The stability of a sand bed in an alluvial channel is investigated by a two-dimensional mathematical model, based on the vorticity transport equation. The model takes account of the internal friction and describes the non-uniform distribution of the suspended sediment. It turns out that the inclusion of the friction and of a definite model of the sediment transport mechanism leads to results rather different from those obtained previously by potential-flow analysis.

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A Mathematical Model of the Transition from Normal Hematopoiesis to the Chronic and Accelerated-Acute Stages in Myeloid Leukemia

Mathematics ◽

10.3390/math8030376 ◽

2020 ◽

Vol 8 (3) ◽

pp. 376

Author(s):

Lorand Gabriel Parajdi ◽

Radu Precup ◽

Eduard Alexandru Bonci ◽

Ciprian Tomuleasa

Keyword(s):

Mathematical Model ◽

Stem Cells ◽

Bone Marrow ◽

Stability Analysis ◽

Myeloid Leukemia ◽

Transition Process ◽

Two Dimensional ◽

The Stability ◽

Theoretical Results

A mathematical model given by a two-dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated-acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated-acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.

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Discrete transparent boundary conditions for the two-dimensional leap-frog scheme

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2020052 ◽

2020 ◽

Author(s):

Christophe Besse ◽

Jean-Francois Coulombel ◽

Pascal Noble

Keyword(s):

Boundary Conditions ◽

Normal Mode Analysis ◽

Mode Analysis ◽

General Strategy ◽

Computational Domain ◽

Two Dimensional ◽

Transparent Boundary Conditions ◽

Finite Difference Approximations ◽

Four Corners ◽

The Stability

We develop a general strategy in order to implement approximate discrete transparent boundary conditions for finite difference approximations of the two-dimensional transport equation. The computational domain is a rectangle equipped with a Cartesian grid. For the two-dimensional leap-frog scheme, we explain why our strategy provides with explicit numerical boundary conditions on the four sides of the rectangle and why it does not require prescribing any condition at the four corners of the computational domain. The stability of the numerical boundary condition on each side of the rectangle is analyzed by means of the so-called normal mode analysis. Numerical investigations for the full problem on the rectangle show that strong instabilities may occur when coupling stable strategies on each side of the rectangle. Other coupling strategies yield promising results.

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TO THE STABILITY OF TANK VEHICLES IN THE BRAKE MODE

Avtoshliakhovyk Ukrayiny ◽

10.33868/0365-8392-2019-1-257-27-32 ◽

2019 ◽

pp. 27-32

Author(s):

Denys Popelysh ◽

Yurii Seluk ◽

Sergyi Tomchuk

Keyword(s):

Mathematical Model ◽

Control Systems ◽

Distribution Systems ◽

Traffic Accidents ◽

Road Traffic ◽

Center Of Mass ◽

Dynamic Processes ◽

Course Stability ◽

The Stability ◽

Tank Vehicles

This article discusses the question of the possibility of improving the roll stability of partially filled tank vehicles while braking. We consider the dangers associated with partially filled tank vehicles. We give examples of the severe consequences of road traffic accidents that have occurred with tank vehicles carrying dangerous goods. We conducted an analysis of the dynamic processes of fluid flow in the tank and their influence on the basic parameters of the stability of vehicle. When transporting a partially filled tank due to the comparability of the mass of the empty tank with the mass of the fluid being transported, the dynamic qualities of the vehicle change so that they differ significantly from the dynamic characteristics of other vehicles. Due to large displacements of the center of mass of cargo in the tank there are additional loads that act vehicle and significantly reduce the course stability and the drivability. We consider the dynamics of liquid sloshing in moving containers, and give examples of building a mechanical model of an oscillating fluid in a tank and a mathematical model of a vehicle with a tank. We also considered the method of improving the vehicle’s stability, which is based on the prediction of the moment of action and the nature of the dynamic processes of liquid cargo and the implementation of preventive actions by executive mechanisms. Modern automated control systems (anti-lock brake system, anti-slip control systems, stabilization systems, braking forces distribution systems, floor level systems, etc.) use a certain list of elements for collecting necessary parameters and actuators for their work. This gives the ability to influence the course stability properties without interfering with the design of the vehicle only by making changes to the software of these systems. Keywords: tank vehicle, roll stability, mathematical model, vehicle control systems.

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