Tag: Index
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Rocket Propulsion
Introduction Rocket propulsion refers to the means by which rockets generate thrust to move forward. It is the fundamental principle that enables space travel. The principle that underpins rocket propulsion is Newton’s Third Law of Motion: for every action, there is an equal and opposite reaction. Basic Physics of Rocket Propulsion In rocket propulsion, a…
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Velocity Dispersion
Introduction Velocity dispersion refers to the statistical spread in velocities of particles in a system. It is a measure of how much the velocities of the particles deviate from the mean. The concept is widely used in physics and astronomy, especially in the study of galaxies and clusters of galaxies. Basic Understanding In a system…
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Centrifugal Force
Introduction Centrifugal force is often described as a ‘fictitious’ or ‘pseudo’ force because it does not arise due to a physical interaction between objects. It is a perceived force that acts on a body moving in a circular path, appearing to push it away from the center of the path. Basic Understanding The term ‘centrifugal…
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Maser
Introduction A maser is a device that produces coherent electromagnetic waves through amplification by stimulated emission. The term “maser” is an acronym for “Microwave Amplification by Stimulated Emission of Radiation”. Masers are the microwave-frequency precursor to the better-known laser (Light Amplification by Stimulated Emission of Radiation). Basic Working Principle The basic principle of a maser…
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Square-Integrable Functions
Introduction Square-integrable functions play a fundamental role in areas of physics such as quantum mechanics, signal processing, and optics. These are functions for which the integral of the square of the absolute value is finite. Definition A function defined over a measure space is said to be square-integrable if: This is commonly seen in the…
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Oberth Effect
Introduction The Oberth effect is a principle in astrodynamics and astronautics that states that the efficiency of a rocket’s propulsion system increases as the speed of the rocket increases. Named after the German scientist Hermann Oberth, who first described the effect, it is a fundamental principle used in mission planning and design for interplanetary travel.…
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Knudsen Number
Introduction The Knudsen number is a dimensionless number in fluid dynamics which describes the relative importance of molecular diffusion over molecular momentum transfer in a gas. It is named after the Danish physicist Martin Knudsen. Definition The Knudsen number is defined as the ratio of the molecular mean free path to a characteristic physical length…
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Magnons
Introduction Magnons are quasiparticles associated with the collective excitation of electron spin waves in a magnetic lattice. They are the fundamental excitation of a spin system and carry both energy and spin. Quantum Description of Magnons The energy of a magnon is quantized in units of , where is the frequency of the spin wave.…
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Phonons
Introduction Phonons are quasiparticles that represent the quantization of vibrational modes in a crystal lattice. These vibrations contribute significantly to the thermal and electrical properties of materials. Phonon as a Quantum Harmonic Oscillator At low energies, the vibrations of a crystal lattice can be described by harmonic oscillators. When quantum mechanics is applied to these…
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Bessel Functions
Introduction Bessel functions, named after Friedrich Bessel, are canonical solutions to Bessel’s differential equation: This equation arises in many physical problems, including heat conduction, vibrations of circular membranes, and quantum mechanics. Bessel Functions of the First Kind The Bessel function of the first kind is defined by the series: Alternatively, it can be expressed as…