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Search Results: 1 - 10 of 17 matches for " Pirooz Mohazzabi "
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Foucault Pendulum and Other Coriolis Effects in Inertial Frames  [PDF]
Pirooz Mohazzabi
Journal of Applied Mathematics and Physics (JAMP) , 2017, DOI: 10.4236/jamp.2017.55089
Abstract: The purpose of this research is to show that Foaucault pendulum as well as other Coriolis effects, which are normally studied in a rotating coordinate system, can also be analyzed in a fixed reference frame. To this end, Foucault pendulum and other Coriolis effects are studied in inertial reference frames. The approach is simple, yet rigorous, and the results are exactly the same as those obtained in non-inertial reference frames but without resorting to some of the assumptions that are needed in rotating coordinate systems.
The Work of a Normal Force  [PDF]
Pirooz Mohazzabi
Journal of Applied Mathematics and Physics (JAMP) , 2017, DOI: 10.4236/jamp.2017.55098
Abstract: It is shown that an impulsive force acting on a particle perpendicular to its velocity vector cannot change its direction of motion without increasing its kinetic energy. If the particle’s kinetic energy is to remain unchanged, the impulsive force must have a component in the direction opposite to the direction of motion. This situation is also realized in the case of a continuous force acting perpendicular to the velocity vector of the particle, when the particle's motion is viewed as a sequence of infinitesimal steps.
Damping of a Simple Pendulum Due to Drag on Its String  [PDF]
Pirooz Mohazzabi, Siva P. Shankar
Journal of Applied Mathematics and Physics (JAMP) , 2017, DOI: 10.4236/jamp.2017.51013
Abstract: A basic classical example of simple harmonic motion is the simple pendulum, consisting of a small bob and a massless string. In a vacuum with zero air resistance, such a pendulum will continue to oscillate indefinitely with a constant amplitude. However, the amplitude of a simple pendulum oscillating in air continuously decreases as its mechanical energy is gradually lost due to air resistance. To this end, it is generally perceived that the main role in the dissipation of mechanical energy is played by the bob of the pendulum, and that the string’s contribution is negligible. The purpose of this research is to experimentally investigate the merit of this assumption. Thus, we experimentally investigate the damping of a simple pendulum as a function of its string diameter and compare that to the contribution from its bob. We find out that although in some cases the effect of the string might be small or even negligible, in general the string can play a significant role, and in some cases even a greater role on the damping of the pendulum than its bob.
Numerical Solution of Differential Equations by Direct Taylor Expansion  [PDF]
Pirooz Mohazzabi, Jennifer L. Becker
Journal of Applied Mathematics and Physics (JAMP) , 2017, DOI: 10.4236/jamp.2017.53053
Abstract: A variation of the direct Taylor expansion algorithm is suggested and applied to several linear and nonlinear differential equations of interest in physics and engineering, and the results are compared with those obtained from other algorithms. It is shown that the suggested algorithm competes strongly with other existing algorithms, both in accuracy and ease of application, while demanding a shorter computation time.
Maxwell-Boltzmann Distribution in Solids  [PDF]
Pirooz Mohazzabi, Siva P. Shankar
Journal of Applied Mathematics and Physics (JAMP) , 2018, DOI: 10.4236/jamp.2018.63052
Abstract: The velocity distribution functions of particles in one- and three-dimensional harmonic solids are investigated through molecular dynamics simulations. It is shown that, as in the case of dense fluids, these distribution functions still obey the Maxwell-Boltzmann law and the assumption of molecular chaos remains valid even at low temperatures.
Average Speed in Projectile Motion and in General Motion of a Particle  [PDF]
Chloe T. Calderon, Pirooz Mohazzabi
Journal of Applied Mathematics and Physics (JAMP) , 2018, DOI: 10.4236/jamp.2018.67130
Abstract: We calculate the average speed of a projectile in the absence of air resistance, a quantity that is missing from the treatment of the problem in the literature. We then show that this quantity is equal to the time-average instantaneous speed of the projectile, but different from its space-average instantaneous speed. It is then shown that this behavior is shared by general motion of all particles regardless of the dimensionality of motion and the nature of the forces involved. The equality of average speed and time-average instantaneous speed can be useful in situations where the calculation of one is more difficult than the other. Thus, making it more efficient to calculate one by calculating the other.
Premelting, Pressure Melting, and Regelation of Ice Revisited  [PDF]
Chloe T. Calderon, Pirooz Mohazzabi
Journal of Applied Mathematics and Physics (JAMP) , 2018, DOI: 10.4236/jamp.2018.611183
Abstract: In this article we review some of the most important and relevant literature on the properties of ice. We focus on three of its surface properties, namely, the slipperiness of ice, the phenomena of a string under load passing through a block of ice without cutting the block in half, and pressure melting and adhesion of blocks of ice. We then provide an argument for the most plausible factor responsible for each of these effects.
Approximate and Invariant Solutions of a Mathematical Model Describing a Simple One-Dimensional Blood Flow of Variable Density  [PDF]
Ranis Ibragimov, Nail Ibragimov, Pirooz Mohazzabi
Journal of Applied Mathematics and Physics (JAMP) , 2017, DOI: 10.4236/jamp.2017.56111
Abstract: We examine governing equations that could be used to model a one-dimensional blood flow within a pulsating elastic artery that is represented by a tube of varying cross-section. The model is considered from two perspectives. The first represents a singular perturbation theory providing explicit approximate solutions to the model, and the second is based on group theoretical modeling that provides exact solutions in implicit form. The main goal is to compare these two approaches and lay out the advantages and disadvantages of each approach.
A New Formulation of Maxwell’s Equations in Clifford Algebra  [PDF]
Pirooz Mohazzabi, Norbert J. Wielenberg, Gary Clark Alexander
Journal of Applied Mathematics and Physics (JAMP) , 2017, DOI: 10.4236/jamp.2017.58130
Abstract: A new unification of the Maxwell equations is given in the domain of Clifford algebras with \"\"in a fashion similar to those obtained with Pauli and Dirac algebras. It is shown that the new electromagnetic field multivector can be obtained from a potential function that is closely related to the scalar and the vector potentials of classical electromagnetics. Additionally it is shown that the gauge transformations of the new multivector and its potential function and the Lagrangian density of the electromagnetic field are in agreement with the transformation rules of the second-rank antisymmetric electromagnetic field tensor, in contrast to the results obtained by applying other versions of Clifford algebras.
Archimedes’ Principle Revisited  [PDF]
Pirooz Mohazzab
Journal of Applied Mathematics and Physics (JAMP) , 2017, DOI: 10.4236/jamp.2017.54073
Abstract: Based on Newton’s third law of motion, we present a different but quite general analysis of Archimedes’ principle. This analysis explains the reduction in apparent weight of a submerged object in all cases, regardless of its position in the fluid. We also study the case in which the object rests on the bottom of the container where the net hydrostatic force on it is downward, and explain where in this case the reduction in the apparent weight comes from.
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