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Milan Batista

Publications and source records attributed to Milan Batista.

28 records · Page 2Linked to original sources
arXiv2008

A Method for Solving Cyclic Block Penta-diagonal Systems of Linear Equations

A method for solving cyclic block three-diagonal systems of equations is generalized for solving a block cyclic penta-diagonal system of equations. Introducing a special form of two new variables the original system is split into three block pentagonal systems, which can be solved by the known methods. As such method belongs to class of direct methods without pivoting. Implementation of the algorithm is discussed in some details and the numerical examples are present.

cs.MS↗
arXiv2007

A Note On Steady Flow of Incompressible Fluid Between Two Co-rotating Disks

The article provides an analytical solution of the Navier-Stokes equations for the case of the steady flow of an incompressible fluid between two uniformly co-rotating disks. The solution is derived from the asymptotical evolution of unknown components of velocity and pressure in a radial direction--in contrast to the Briter-Pohlhausen analytical solution, which is supported by simplified Navier-Stokes equations. The obtained infinite system of ordinary differential equations forms recurrent relations from which unknown functions can be calculated successively. The first and second approximations of solution are solved analytically and the third and fourth approximations of solutions are solved numerically. The numerical example demonstrates agreements with results obtained by other authors using different methods.

physics.flu-dyn↗
arXiv2006

Quantum cards and quantum rods

Quantum mechanical analysis of a rigid rod with one end fixed to a flat table is presented. It is shown, that for a macroscopic rod the ground state is orientationally delocalized only if the table is absolutely horizontal. In this latter case the rod, assumed to be initally in the upright orientation, falls down symmetrically and simultaneously in both directions, as claimed by Tegmark and Wheeler. In addition, the time of fall is calculated using WKB wavefunctions representing energy eigenstates near the barrier summit.

quant-ph↗
arXiv2006

The Falling Time of an Inverted Plane Pendulum

The article provides the formula for the calculation the falling time of inverted pendulum. The result is expressed in terms of elliptic integrals of first kind. The asymptotic formula for small initial inclination value is also provided.

physics.class-ph↗
arXiv2006

On the Mutual Coefficient of Restitution in Two Car Collinear Collisions

In the paper two car collinear collisions are discussed using Newton's law of mechanics, conservation of energy and linear constitutive law connecting impact force and crush. Two ways of calculating the mutual restitution coefficient are given: one based on car masses and one based on car stiffness. A numerical example of an actual test is provided.

physics.soc-ph↗
arXiv2005

Steady Motion of a Rigid Disk of Finite Thickness on a Horizontal Plane

The article discusses the steady motion of a rigid disk of finite thickness rolling on its edge on a horizontal plane under the influence of gravity. The governing equations are presented and two cases allowing for a steady state solution are considered: rolling on consistently rough ground and rolling on perfectly smooth ground. The conditions of steady motion are derived for both kinds of ground and it is shown that the possible steady motion of a disk is either on a straight line in a circle. Also oscillations about steady state are discussed and conditions for stable motion are established.

physics.class-ph↗