Physics And Mathematics

Lenoir cycle The Lenoir cycle is an idealized thermodynamic cycle often used to model a pulse jet engine. It is based on the operation of an engine patented by Jean Joseph Etienne Lenoir in 1860. This engine is often thought of as the first commercially produced internal combustion engine. The absence of any compression process in the design leads to lower thermal efficiency than the more well known Otto cycle and Diesel cycle. the cycle, an ideal gas undergoes 1–2: Constant volume (isochoric) heat addition; 2–3: Isentropic expansion; 3–1: Constant pressure (isobaric) heat rejection. The expansion process is isentropic and hence involves no heat interaction. Energy is absorbed as heat during the isochoric heating and rejected as work during the isentropic expansion. Waste heat is rejected during the isobaric cooling which consumes some work.

Archimedes Principle Archimedes' principle (also spelled Archimedes's principle) states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially, is equal to the weight of the fluid that the body displaces. Archimedes' principle is a law of physics fundamental to fluid mechanics. It was formulated by Archimedes of Syracuse. Any object, totally or partially immersed in a fluid or liquid, is buoyed up by a force equal to the weight of the fluid displaced by the object. Archimedes' principle allows the buoyancy of any floating object partially or fully immersed in a fluid to be calculated. The downward force on the object is simply its weight. The upward, or buoyant, force on the object is that stated by Archimedes' principle above. Thus, the net force on the object is the difference between the magnitudes of the buoyant force and its weight. If this net force is positive, the object rises; if negative, the object sinks; and if zero, the object is neutrally buoyant—that is, it remains in place without either rising or sinking. In simple words, Archimedes' principle states that, when a body is partially or completely immersed in a fluid, it experiences an apparent loss in weight that is equal to the weight of the fluid displaced by the immersed part of the body(s).

🔴 Some facts about Sir ALBERT EINSTEIN:- 👉 J. Edgar Hoover's FBI hoped to unmask Einstein as a Soviet spy and maintained almost constant surveillance of Einstein. His FBI file totaled 1,800 pages. 👉Einstein's brain was removed without permission during his autopsy and was sent to be tested for its perceived secrets. 👉He often pretended not to be Albert Einstein due to frequent questions from the public on the street. 👉Not just a great scientist, Einstein was also a great musician. When his mother first enrolled him in violin lessons, he wasn't a big fan, but this soon changed when he heard Mozart whose music he loved and said that if he had not gone into physics, he likely would have become a musician. 👉 Einstein for president! He was actually asked if he'd take the position of the second president of Israel. Einstein turned it down though because he didn't have the right people skills. 👉People often use Einstein to represent a 'mad scientist'. This is because of his dishevelled look with unkept hair, and no socks. 👉He failed his first try on his entrance exam for college. This proves how important perseverance and hard work is! 👉Einstein was a pacifist- this means that he didn't agree with war or violence. 👉In 1911, he was invited to the first ever world physics conference. He was the youngest person there. 👉As an adult, he was really disorganised and he often forgot appointments. His amazing brain was so complex and was a bit all over the place so his lectures were a bit difficult to understand. 👉He published more than 300 scientific papers and over 150 non-scientific works. He received honorary doctorate degrees in science, medicine and philosophy from lots of European and American universities. 🔴 Sir ALBERT EINSTEIN is a great inspiration for me and for others too. we adore physics that's why we love sir Albert Einstein .❤️

Permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ε (epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in response to an applied electric field than a material with low permittivity, thereby storing more energy in the material. In electrostatics, the permittivity plays an important role in determining the capacitance of a capacitor.

The Butterfly Effect In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state. The term is closely associated with the work of mathematician and meteorologist Edward Norton Lorenz. He noted that the butterfly effect is derived from the metaphorical example of the details of a tornado (the exact time of formation, the exact path taken) being influenced by minor perturbations such as a distant butterfly flapping its wings several weeks earlier. Lorenz originally used a seagull causing a storm but was persuaded to make it more poetic with the use of a butterfly and tornado by 1972. He discovered the effect when he observed runs of his weather model with initial condition data that were rounded in a seemingly inconsequential manner. He noted that the weather model would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome. The idea that small causes may have large effects in weather was earlier acknowledged by French mathematician and engineer Henri Poincaré. American mathematician and philosopher Norbert Wiener also contributed to this theory. Lorenz's work placed the concept of instability of the Earth's atmosphere onto a quantitative base and linked the concept of instability to the properties of large classes of dynamic systems which are undergoing nonlinear dynamics and deterministic chaos.

Ball Lightning Ball lightning is a rare and unexplained phenomenon described as luminescent, spherical objects that vary from pea-sized to several meters in diameter. Though usually associated with thunderstorms, the observed phenomenon is reported to last considerably longer than the split-second flash of a lightning bolt, and is a phenomenon distinct from St. Elmo's fire. Some 19th-century reports describe balls that eventually explode and leave behind an odor of sulfur. Descriptions of ball lightning appear in a variety of accounts over the centuries and have received attention from scientists. An optical spectrum of what appears to have been a ball lightning event was published in January 2014 and included a video at high frame rate. Laboratory experiments have produced effects that are visually similar to reports of ball lightning, but how these relate to the supposed phenomenon remains unclear.

Hypersonic Speed In aerodynamics, a hypersonic speed is one that exceeds five times the speed of sound, often stated as starting at speeds of Mach 5 and above. The precise Mach number at which a craft can be said to be flying at hypersonic speed varies, since individual physical changes in the airflow (like molecular dissociation and ionization) occur at different speeds, these effects collectively become important around Mach 5-10. The hypersonic regime can also be alternatively defined as speeds where specific heat capacity changes with the temperature of the flow as kinetic energy of the moving object is converted into heat.

If you fell into a black hole, you would get stretched out like spaghetti! This is scientifically known as "spaghettification", and happens when "the gravity wants to sort of stretch you in one direction and squeeze you in another," according to Joe Polchinski, a physicist at the University of California, Santa Barbara.

▶️ A collider is a type of particle accelerator which brings two opposing particle beams together such that the particles collide. Colliders may either be ring accelerators or linear accelerators. ▶️ Colliders are used as a research tool in particle physics by accelerating particles to very high kinetic energy and letting them impact other particles. Analysis of the byproducts of these collisions gives scientists good evidence of the structure of the subatomic world and the laws of nature governing it. These may become apparent only at high energies and for tiny periods of time, and therefore may be hard or impossible to study in other ways.

Ramanujan‘s achievements were all about elegance, depth, and surprise beautifully intertwined. Unfortunately, Ramanujan contracted a fatal illness in England in 1918. He convalesced there for more than a year and returned to India in 1919. His condition then worsened, and he died on 26 April 1920. One might expect that a dying man would stop working and await his fate. However, Ramanujan spent his last year producing some of his most profound mathematics. It has been more than a century, however, his mathematical discoveries are still alive and flourishing. "Ramanujan is important not just as a mathematician but because of what he tells us that the human mind can do”. "Someone with his ability is so rare and so precious that we can't afford to lose them. A genius can arise anywhere in the world. It is our good fortune that he was one of us. It is unfortunate that too little of Ramanujan’s life and work, esoteric though the latter is, seems to be known to most of us".

🔴Ramanujan: The Man Who Knew Infinity Srinivasa Ramanujan (1887-1920), the man who reshaped twentieth-century mathematics with his various contributions in several mathematical domains, including mathematical analysis, infinite series, continued fractions, number theory, and game theory is recognized as one of history's greatest mathematicians. Leaving this world at the youthful age of 32, Ramanujan made significant contributions to mathematics that only a few others could match in their lifetime. Surprisingly, he never received any formal mathematics training. Most of his mathematical discoveries were based only on intuition and were ultimately proven correct. With its humble and sometimes difficult start, his life story is just as fascinating as his incredible work. Every year, Ramanujan’s birth anniversary on December 22 is observed as National Mathematics Day. Born in Erode, Tamil Nadu, India, Ramanujan demonstrated an exceptional intuitive grasp of mathematics at a young age. Despite being a mathematical prodigy, Ramanujan's career did not begin well. He received a college scholarship in 1904, but he quickly lost it by failing in nonmathematical subjects. Another attempt at college in Madras (now Chennai) ended in failure when he failed his First Arts exam. It was around this time that he began his famous notebooks. He drifted through poverty until 1910 when he was interviewed by R. Ramachandra Rao, secretary of the Indian Mathematical Society. Rao was initially sceptical of Ramanujan, but he eventually recognised his abilities and supported him financially. Srinivasa Ramanujan began developing his theories in mathematics and published his first paper in 1911. He was mentored at Cambridge by GH Hardy, a well-known British mathematician who encouraged him to publish his findings in a number of papers. In 1918, Ramanujan became the second Indian to be included as a Fellow of the Royal Society. 🔴Ramanujan’s major contributions to mathematics: Ramanujan's contribution extends to mathematical fields such as complex analysis, number theory, infinite series, and continued fractions. Infinite series for pi: In 1914, Ramanujan found a formula for infinite series for pi, which forms the basis of many algorithms used today. Finding an accurate approximation of π (pi) has been one of the most important challenges in the history of mathematics. Game theory: Ramanujan discovered a long list of new ideas for solving many challenging mathematical problems that have given great impetus to the development of game theory. His contribution to game theory is purely based on intuition and natural talent and is unmatched to this day. Mock theta function: He elaborated on the mock theta function, a concept in the field of modular forms of mathematics. Ramanujan number: 1729 is known as the Ramanujan number which is the sum of the cubes of two numbers 10 and 9. Circle Method: Ramanujan, along with GH Hardy, invented the circle method which gave the first approximations of the partition of numbers beyond 200. This method contributed significantly to solving the notorious complex problems of the 20th century, such as Waring's conjecture and other additional questions. Theta Function: Theta function is a special function of several complex variables. German mathematician Carl Gustav Jacob Jacobi invented several closely related theta functions known as Jacobi theta functions. Theta function was studied by extensively Ramanujan who came up with the Ramanujan theta function, that generalizes the form of Jacobi theta functions and also captures general properties. Ramanujan theta function is used to determine the critical dimensions in Bosonic string theory, superstring theory, and M-theory. Other notable contributions by Ramanujan include hypergeometric series, the Riemann series, the elliptic integrals, the theory of divergent series, and the functional equations of the zeta function.