On the two-dimensional rotational body of maximal Newtonian resistance

We investigate, by means of computer simulations, shapes of nonconvex bodies that maximize resistance to their motion through a rarefied medium, considering that bodies are moving forward and at the same time slowly rotating. A two-dimensional geometric shape that confers to the body a resistance very close to the theoretical supremum value is obtained, improving previous results.Comment: This is a preprint version of the paper published in J. Math. Sci. (N. Y.), Vol. 161, no. 6, 2009, 811--819. DOI:10.1007/s10958-009-9602-

Billiard scattering on rough sets: two-dimensional case

The notion of a rough two-dimensional (convex) body is introduced, and to each rough body there is assigned a measure on T3 describing billiard scattering on the body. The main result is characterization of the set of measures generated by rough bodies. This result can be used to solve various problems of least aerodynamical resistance

High frequency limit of the Transport Cross Section and boundedness of the Total Cross Section in scattering by an obstacle with impedance boundary conditions

The scalar scattering of the plane wave by a strictly convex obstacle with impedance boundary conditions is considered. The uniform boundedness of the Total Cross Section for all values of frequencies is proved. The high frequency limit of the Transport Cross Section is founded and presented as a classical functional of the variational theory

Force acting on a rough disk spinning in a flow of noninteracting particles

Pressure force exerted on a rough disk spinning in a flow of noninteracting particles is determined by considering that a flow of point particles impinges on a body spinning around a fixed point. The rough disk is identical with the sequence of sets and thus the sets can be viewed as successive approximations of the rough disk. A proper choice of sequence of sets shows that the characteristic of billiard scattering is independent of n, and the billiard scattering on the rough set is defined. The pressure force exerted on the disk is independent of its angular velocity and that the characteristic of the interaction that is the moment of the pressure force slows down the rotation of the rough disk. The transverse force aligned with the instantaneous velocity of the front point of the body results in Magnus effect

ELECTROCHEMICAL CHARACTERISTICS OF BIMETALLIC IMPLANT FOR OSTEOSYNTHESIS

The article presents experimental results of electrochemical characteristics of bimetallic implants in experiment

On the minimum and maximum averaged resistance problem of moving bodies

A body moving in a rarefied medium of point fixed particles is considered. The center of mass of the body moves with a constant speed, and, moreover, the body executes slow rotational motions. The resistance force of the medium to the body's motion is defined. The concept of a rough body is introduced, and it is proved that the ratio between the resistance of the rough body and that of the smooth body corresponding to it lies in the limits from 0.969 up to 2. © 2007 Springer Science+Business Media, Inc

On Newton's problem of a body of least aerodynamic resistance

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Short-term memory in a sparse clock neural network

We propose a model of short-term (working) memory in a clock neural network. The retrieval dynamics of a strongly diluted version of the model is solved. The related phase diagrams reflecting fixed point retrieval behaviour of the system are also obtained and discussed

Neural networks : iterative unlearning algorithm converging to the projector rule matrix

The iterative unlearning algorithm for connectivity self-correction is proposed. No presentation of patterns during the iteration process is required. Starting from the Hebbian connectivity, the convergence of the (rescaled) iterated connection matrix to the projector rule one is proven, for arbitrary set of p < N binary patterns