Mechanically Driven Branching of Bacterial Colonies

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Chiara Giverso ◽  
Marco Verani ◽  
Pasquale Ciarletta
Keyword(s):  
Mathematical Model ◽  
Surface Tension ◽  
Culture Medium ◽  
Chemotactic Response ◽  
Sharp Interface ◽  
Proper Choice ◽  
Pattern Selection ◽  
Analytical Analysis ◽  
Viscous Interaction ◽  
The Mathematical Model

A continuum mathematical model with sharp interface is proposed for describing the occurrence of patterns in initially circular and homogeneous bacterial colonies. The mathematical model encapsulates the evolution of the chemical field characterized by a Monod-like uptake term, the chemotactic response of bacteria, the viscous interaction between the colony and the underlying culture medium and the effects of the surface tension at the boundary. The analytical analysis demonstrates that the front of the colony is linearly unstable for a proper choice of the parameters. The simulation of the model in the nonlinear regime confirms the development of fingers with typical wavelength controlled by the size parameters of the problem, whilst the emergence of branches is favored if the diffusion is dominant on the chemotaxis or for high values of the friction parameter. Such results provide new insights on pattern selection in bacterial colonies and may be applied for designing engineered patterns.

scholarly journals The Muskat problem with surface tension and equal viscosities in subcritical $$L_p$$-Sobolev spaces

2021 ◽  
Author(s):  
Anca-Voichita Matioc ◽  
Bogdan-Vasile Matioc
Keyword(s):  
Mathematical Model ◽  
Surface Tension ◽  
Global Existence ◽  
Sobolev Spaces ◽  
Existence Of Solutions ◽  
Well Posedness ◽  
Global Existence Of Solutions ◽  
Muskat Problem ◽  
The Mathematical Model ◽  
Quasilinear Parabolic

AbstractIn this paper we establish the well-posedness of the Muskat problem with surface tension and equal viscosities in the subcritical Sobolev spaces $$W^s_p(\mathbb {R})$$ W p s ( R ) , where $${p\in (1,2]}$$ p ∈ ( 1 , 2 ] and $${s\in (1+1/p,2)}$$ s ∈ ( 1 + 1 / p , 2 ) . This is achieved by showing that the mathematical model can be formulated as a quasilinear parabolic evolution problem in $$W^{\overline{s}-2}_p(\mathbb {R})$$ W p s ¯ - 2 ( R ) , where $${\overline{s}\in (1+1/p,s)}$$ s ¯ ∈ ( 1 + 1 / p , s ) . Moreover, we prove that the solutions become instantly smooth and we provide a criterion for the global existence of solutions.

The Mathematical Model of Simulative Calculation for the Process of Airbag Landing

2014 ◽  
Vol 635-637 ◽  
pp. 228-232
Author(s):  
Jian He ◽  
Ji Sheng Ma ◽  
Da Lin Wu
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Finite Element Simulation ◽  
Calculation Method ◽  
Low Cost ◽  
Analytical Analysis ◽  
Heavy Equipment ◽  
Element Simulation ◽  
The Mathematical Model

Airbag is widely used in heavy equipment dropped field with its efficient cushion performance and low cost. The calculation method used now for the process of airbag landing mainly is simulative calculation: analytical analysis and finite element simulation, but there are less systematic introduction for the mathematical model behind these methods in past papers. This paper mainly does the summary for the mathematical model of vented airbag which is usually used.

The Influence of Surface Tension on Lubrication Characteristics

2010 ◽  
Vol 33 ◽  
pp. 627-630
Author(s):  
Jian Ping Liu ◽  
Xin Yi Zhang
Keyword(s):  
Mathematical Model ◽  
Surface Tension ◽  
Friction Coefficient ◽  
Experimental Results ◽  
Apparent Effect ◽  
Entrainment Velocity ◽  
Lubrication Performance ◽  
Increase Rate ◽  
Lubrication Characteristics ◽  
The Mathematical Model

The mathematical model was developed to account for viscosity induced by surface tension in the light of EDL theory. The effect of the EDL on the lubrication performance of lubricant for a composite sliding block-disc pair was investigated in considering surface tension. The experimental results showed the EDL has apparent effect on the friction coefficient, The lower of the entrainment velocity, the greater of the friction coefficient. With the increase of entrainment velocity, the increase rate of friction coefficient decreases. Thus, the established model could be used to well explain the effect of the surface tension of the EDL on the lubricating performance of a liquid.

Internal Flows in Microscopic Polymer Solution Droplets Evaporating on Flat Surfaces

2010 ◽  
Author(s):  
Shohei Yasumatsu ◽  
Narumi Nanri ◽  
Yu Yoshitake ◽  
Koichi Nakaso ◽  
Jun Fukai
Keyword(s):  
Mathematical Model ◽  
Surface Tension ◽  
Free Surface ◽  
Polymer Solution ◽  
Local Minimum ◽  
Flow Direction ◽  
Solute Concentration ◽  
Internal Flows ◽  
Initial Solute ◽  
The Mathematical Model

To control the formation process of polymer thin films from polymer solution droplets using inkjet printings, internal flows of the droplets on substrates are studied. In our previous study [1], internal flow of polymer solution droplets receding on a lyophobic surface was experimentally visualized. It was found that the direction of the circulation flow in the droplet depended on the solvent and the initial solute concentration. In particular, the flow direction of polystyrene-anisole solution was reversed as the initial solute concentration increased. In this study, to clarify this reason, the conservation equations of momentum, energy and mass on two-dimensional cylindrical coordinate are numerically solved using a finite element method. The mathematical model considers the free convections derived by the dependencies of the density and surface tension on the solute concentration. As a result, the dependences of the calculated velocities on the initial solute concentration agree qualitatively with the experiments. The mathematical model predicts that double circulation flows appear after a single flow develops at high initial solute concentrations, while double circulations do not develop at low concentrations. It is concluded that the difference between the flow directions investigated experimentally is due to such a change of the flow structure. The distribution of the surface tension on the free surface is also discussed. When a local minimum of the surface tension appears on the free surface, the double circulations develop. According to the result for a low contact angle, the local minimum point shifts toward the axis of symmetry with a lapse of time, and finally erases the double circulations.

GROWTH OF A GAS BUBBLE IN A SUPERSATURATED LIQUID UNDER THE EFFECT OF VARIANT CASES OF SURFACE TENSION

2011 ◽  
Vol 25 (22) ◽  
pp. 3053-3070 ◽  
Author(s):  
S. A. MOHAMMADEIN ◽  
K. G. MOHAMED
Keyword(s):  
Mathematical Model ◽  
Surface Tension ◽  
Growth Process ◽  
Gas Bubble ◽  
Adjustment Factor ◽  
Surface Tension Effect ◽  
Factor B ◽  
Adjustment Factors ◽  
The Mathematical Model ◽  
Special Case

In this paper, the growth of a gas bubble in a supersaturated liquid is discussed for a constant and variable cases of surface tension effect. The mathematical model is solved analytically by using the method of Plesset and Zwick18 after modified it. The growth process is affected by: diffusion coefficient D, Jacob number Ja, surface tension σ, adjustment factor b and void fraction ϕ0. The famous formula of Plesset and Zwick is produced as a special case of the results at some values of the adjustment factors. Moreover, for some values of the adjustment factors, good approximation is obtained when a comparison between our results and the result that produced by Hashemi et al., 9 who solved the problem with the method of combining variables.

Hydrodynamics of Liquid Motion in Straight-Line Capillaries

2019 ◽  
Vol 942 ◽  
pp. 110-120
Author(s):  
Irina Lobanova ◽  
Vladimir Meshheryakov ◽  
Aleksey Kalinichenko ◽  
Anatoly Surzhikov
Keyword(s):  
Mathematical Model ◽  
Surface Tension ◽  
Full Scale ◽  
Liquid Motion ◽  
Straight Line ◽  
Capillary Size ◽  
The Mathematical Model

The paper considers the mathematical model of liquid motion in straight-line capillaries. The proposed mathematical model shows the liquid motion in slit-like capillaries, with regard to the density, viscosity and surface tension of liquids, the capillary size, and the angle of capillary inclination to the horizontal. The modeling results are proved by full-scale experiments.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

RESEARCH OF INDICATORS OF A VEHICLE WITH A DIESEL WORKING ON DIESEL AND DIESEL GAS CYCLES USING THE MATHEMATICAL MODEL

2020 ◽  
pp. 14-19
Author(s):  
Serhii Kovbasenko ◽  
Andriy Holyk ◽  
Serhii Hutarevych
Keyword(s):  
Mathematical Model ◽  
Diesel Engine ◽  
Environmental Performance ◽  
Energy Performance ◽  
Dual Fuel ◽  
Fuel System ◽  
Compressed Natural Gas ◽  
Diesel Vehicles ◽  
Diesel Cycle ◽  
The Mathematical Model

The features of an advanced mathematical model of motion of a truck with a diesel engine operating on the diesel and diesel gas cycles are presented in the article. As a result of calculations using the mathematical model, a decrease in total mass emissions as a result of carbon monoxide emissions is observed due to a decrease in emissions of nitrogen oxides and emissions of soot in the diesel gas cycle compared to the diesel cycle. The mathematical model of a motion of a truck on a city driving cycle according to GOST 20306-90 allows to study the fuel-economic, environmental and energy indicators of a diesel and diesel gas vehicle. The results of the calculations on the mathematical model will make it possible to conclude on the feasibility of converting diesel vehicles to using compressed natural gas. Object of the study – the fuel-economic, environmental and energy performance diesel engine that runs on dual fuel system using CNG. Purpose of the study – study of changes in fuel, economic, environmental and energy performance of vehicles with diesel engines operating on diesel and diesel gas cycles, according to urban driving cycle modes. Method of the study – calculations on a mathematical model and comparison of results with road tests. Bench and road tests, results of calculations on the mathematical model of motion of a truck with diesel, working on diesel and diesel gas cycles, show the improvement of environmental performance of diesel vehicles during the converting to compressed natural gas in operation. Improvement of environmental performance is obtained mainly through the reduction of soot emissions and nitrogen oxides emissions from diesel gas cycle operations compared to diesel cycle operations. The results of the article can be used to further develop dual fuel system using CNG. Keywords: diesel engine, diesel gas engine, CNG

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

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