Density functional theory of freezing for soft interactions in two dimensions

A density functional theory of two-dimensional freezing is presented for a soft interaction potential that scales as inverse cube of particle distance. This repulsive potential between parallel, induced dipoles is realized for paramagnetic colloids on an interface, which are additionally exposed to an external magnetic field. An extended modified weighted density approximation which includes correct triplet correlations in the liquid state is used. The theoretical prediction of the freezing transition is in good agreement with experimental and simulation data.Comment: 7 pages, 3 figures, submitted 200

Superparamagnetic colloids in viscous fluids

The influence of a magnetic field on the aggregation process of superparamagnetic colloids has been well known on short time for a few decades. However, the influence of important parameters, such as viscosity of the liquid, has received only little attention. Moreover, the equilibrium state reached after a long time is still challenging on some aspects. Indeed, recent experimental measurements show deviations from pure analytical models in extreme conditions. Furthermore, current simulations would require several years of computing time to reach equilibrium state under those conditions. In the present paper, we show how viscosity influences the characteristic time of the aggregation process, with experimental measurements in agreement with previous theories on transient behaviour. Afterwards, we performed numerical simulations on equivalent systems with lower viscosities. Below a critical value of viscosity, a transition to a new aggregation regime is observed and analysed. We noticed this result can be used to reduce the numerical simulation time from several orders of magnitude, without modifying the intrinsic physical behaviour of the particles. However, it also implies that, for high magnetic fields, granular gases could have a very different behaviour from colloidal liquids

SIMULATION OF OSCILLATIONS OF THE CENTER OF MASS OF THE TRACTOR WITH TRACKED PROPULSION UNIT

To increase the traction force of tractors while simultaneously reducing the specific pressure on the soil, one of the effective ways is the use of a tracked propulsion unit. The article considers a variant of a tracked propulsion unit, installed separately on each drive axle of the tractor instead of wheels. The basis of the developed design of the tracked propulsion unit is the trackbed, which reduces the pressure on the ground and increases adhesion to the soil. The results of simulation modeling of the rectilinear movement of a tractor with a tracked propulsion unit along grain stubble are presented. Realizations of oscillations of the front, sprung and rear, unsprung axles and the tractor frame were obtained. Oscillations in the ordinates of the reference surface were modeled as a random process with specified values corresponding to the reference surface of the grain stubble. The simulation results showed acceptable oscillation values of the tractor frame with the proposed propulsion design. The proposed propulsion unit can be easily installed on a tractor instead of wheels and, if necessary, can also be easily dismantled. Purpose. Investigation of oscillations of the center of mass of a tractor with a tracked propulsion unit using simulation modeling in the MATLAB Simulink environment. Methodology. Methods of mathematical modeling and analysis were used in the article. Results. The parameters showing the effectiveness of using a tracked propulsion unit instead of wheels on a tractor of traction class 6 are obtained. Practical implications. The results obtained can be applied in the design of tractors to determine the acceptable parameters of the tracked propulsion unit