A SIMULATION FOR ENERGY DISSIPATION IN PHYSICAL SYSTEMS
A SIMULATION FOR ENERGY DISSIPATION IN PHYSICAL SYSTEMS
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Date
1988-09
Authors
NGADDA, YAKUBU,
HUNIRA
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Abstract
ABSTRACT
A formalism for energy dissipation in physical systems using
coupled oscillators is hereby presented. The model demonstrates
energy transfer from a free translational motion of a centre of mass
into intrinsic modes represented by four oscillators of the same
force constant. First, from the classical energy of the system, the
kinetic and potential energy matrices are deduced. These matrices
are used to transform the natural modes of vibration into normal
coordinates which decouple the vibration into the various modes with
particular frequencies. This transformation has been done through
the application of Lagrangian dynamics. A classically decoupled
total Hamiltonian obtained is written in terms of its quantum mechanical
equivalence. The time-independent Schrodinger's equation applied to the
decoupled Hamiltonian of the system quantizes it, giving the usual
quantum mechanical eigenvalues and eigenfunctions for both intrinsic
and translational motions.
Collective amplitudes of the motion, or the dissipation functions
of the internal excitation energy, obtained as a multiple integral in
terms of the translational and intrinsic wave functions is solved
analytically exactly.
Numerical values of the normalized collective amplitudes have
been computed and examples of probability distributions for the
intrinsic excitation are presented graphically.
Description
Department of Physics,
Ahmadu Bello University,
Zaria.
Keywords
SIMULATION,, ENERGY,, DISSIPATION,, PHYSICAL,, SYSTEMS