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🔗 Mathematics 🔗 Physics

The Fresnel integrals S(x) and C(x) are two transcendental functions named after Augustin-Jean Fresnel that are used in optics and are closely related to the error function (erf). They arise in the description of near-field Fresnel diffraction phenomena and are defined through the following integral representations:

The simultaneous parametric plot of S(x) and C(x) is the Euler spiral (also known as the Cornu spiral or clothoid).

🔗 Physics

A Bose–Einstein condensate (BEC) is a state of matter (also called the fifth state of matter) which is typically formed when a gas of bosons at low densities is cooled to temperatures very close to absolute zero (-273.15 °C). Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which point microscopic quantum phenomena, particularly wavefunction interference, become apparent macroscopically. A BEC is formed by cooling a gas of extremely low density, about one-hundred-thousandth (1/100,000) the density of normal air, to ultra-low temperatures.

This state was first predicted, generally, in 1924–1925 by Albert Einstein following a paper written by Satyendra Nath Bose, although Bose came up with the pioneering paper on the new statistics.

🔗 Computing 🔗 Physics 🔗 Systems 🔗 Systems/Cybernetics

Bremermann's limit, named after Hans-Joachim Bremermann, is a limit on the maximum rate of computation that can be achieved in a self-contained system in the material universe. It is derived from Einstein's mass-energy equivalency and the Heisenberg uncertainty principle, and is c²/h ≈ 1.36 × 10⁵⁰ bits per second per kilogram. This value is important when designing cryptographic algorithms, as it can be used to determine the minimum size of encryption keys or hash values required to create an algorithm that could never be cracked by a brute-force search.

For example, a computer with the mass of the entire Earth operating at the Bremermann's limit could perform approximately 10⁷⁵ mathematical computations per second. If one assumes that a cryptographic key can be tested with only one operation, then a typical 128-bit key could be cracked in under 10⁻³⁶ seconds. However, a 256-bit key (which is already in use in some systems) would take about two minutes to crack. Using a 512-bit key would increase the cracking time to approaching 10⁷² years, without increasing the time for encryption by more than a constant factor (depending on the encryption algorithms used).

The limit has been further analysed in later literature as the maximum rate at which a system with energy spread ${\displaystyle \Delta E}$ can evolve into an orthogonal and hence distinguishable state to another, ${\displaystyle \Delta t={\frac {\pi \hbar }{2\Delta E}}.}$ In particular, Margolus and Levitin have shown that a quantum system with average energy E takes at least time ${\displaystyle \Delta t={\frac {\pi \hbar }{2E}}}$ to evolve into an orthogonal state. However, it has been shown that access to quantum memory in principle allows computational algorithms that require arbitrarily small amount of energy/time per one elementary computation step.

🔗 Physics 🔗 Physics/Fluid Dynamics

A Feynman sprinkler, also referred to as a Feynman inverse sprinkler or as a reverse sprinkler, is a sprinkler-like device which is submerged in a tank and made to suck in the surrounding fluid. The question of how such a device would turn was the subject of an intense and remarkably long-lived debate.

A regular sprinkler has nozzles arranged at angles on a freely rotating wheel such that when water is pumped out of them, the resulting jets cause the wheel to rotate; both a Catherine wheel and the aeolipile ("Hero's engine") work on the same principle. A "reverse" or "inverse" sprinkler would operate by aspirating the surrounding fluid instead. The problem is now commonly associated with theoretical physicist Richard Feynman, who mentions it in his bestselling memoirs Surely You're Joking, Mr. Feynman! The problem did not originate with Feynman, nor did he publish a solution to it.

🔗 Physics 🔗 Physics/relativity 🔗 Chemistry

Relativistic quantum chemistry combines relativistic mechanics with quantum chemistry to explain elemental properties and structure, especially for the heavier elements of the periodic table. A prominent example of such an explanation is the color of gold: due to relativistic effects, it is not silvery like most other metals.

The term relativistic effects was developed in light of the history of quantum mechanics. Initially quantum mechanics was developed without considering the theory of relativity. Relativistic effects are those discrepancies between values calculated by models that consider and that do not consider relativity. Relativistic effects are important for the heavier elements with high atomic numbers. In the most common layout of the periodic table, these elements are shown in the lower area. Examples are the lanthanides and actinides.

Relativistic effects in chemistry can be considered to be perturbations, or small corrections, to the non-relativistic theory of chemistry, which is developed from the solutions of the Schrödinger equation. These corrections affect the electrons differently depending on the electron speed relative to the speed of light. Relativistic effects are more prominent in heavy elements because only in these elements do electrons attain sufficient speeds for the elements to have properties that differ from what non-relativistic chemistry predicts.

🔗 Biography 🔗 Physics 🔗 Biography/science and academia 🔗 Astronomy 🔗 Physics/Biographies 🔗 Biophysics

Thomas Gold (also known as Tommy Gold), (May 22, 1920 – June 22, 2004) was an Austrian-born astrophysicist, a professor of astronomy at Cornell University, a member of the U.S. National Academy of Sciences, and a Fellow of the Royal Society (London). Gold was one of three young Cambridge scientists who in 1948 proposed the now mostly abandoned "steady state" hypothesis of the universe. Gold's work crossed academic and scientific boundaries, into biophysics, astronomy, aerospace engineering, and geophysics.

🔗 Mathematics 🔗 Physics 🔗 Systems 🔗 Systems/Dynamical systems

The Abelian sandpile model, also known as the Bak–Tang–Wiesenfeld model, was the first discovered example of a dynamical system displaying self-organized criticality. It was introduced by Per Bak, Chao Tang and Kurt Wiesenfeld in a 1987 paper.

The model is a cellular automaton. In its original formulation, each site on a finite grid has an associated value that corresponds to the slope of the pile. This slope builds up as "grains of sand" (or "chips") are randomly placed onto the pile, until the slope exceeds a specific threshold value at which time that site collapses transferring sand into the adjacent sites, increasing their slope. Bak, Tang, and Wiesenfeld considered process of successive random placement of sand grains on the grid; each such placement of sand at a particular site may have no effect, or it may cause a cascading reaction that will affect many sites.

The model has since been studied on the infinite lattice, on other (non-square) lattices, and on arbitrary graphs (including directed multigraphs). It is closely related to the dollar game, a variant of the chip-firing game introduced by Biggs.

🔗 Physics

The free will theorem of John H. Conway and Simon B. Kochen states that if we have a free will in the sense that our choices are not a function of the past, then, subject to certain assumptions, so must some elementary particles. Conway and Kochen's paper was published in Foundations of Physics in 2006. In 2009 they published a stronger version of the theorem in the Notices of the AMS. Later, in 2017, Kochen elaborated some details.

🔗 Physics 🔗 Physics/Fluid Dynamics

Granular convection, or granular segregation, is a phenomenon where granular material subjected to shaking or vibration will exhibit circulation patterns similar to types of fluid convection. It is sometimes described as the Brazil nut effect when the largest particles end up on the surface of a granular material containing a mixture of variously sized objects; this derives from the example of a typical container of mixed nuts, where the largest will be Brazil nuts. The phenomenon is also known as the muesli effect since it is seen in packets of breakfast cereal containing particles of different sizes but similar density, such as muesli mix.

Under experimental conditions, granular convection of variously sized particles has been observed forming convection cells similar to fluid motion. The convection of granular flows is becoming a well-understood phenomenon.

🔗 Spaceflight 🔗 Physics 🔗 Alternative Views

A quantum vacuum thruster (QVT or Q-thruster) is a theoretical system hypothesized to use the same principles and equations of motion that a conventional plasma thruster would use, namely magnetohydrodynamics (MHD), to make predictions about the behavior of the propellant. However, rather than using a conventional plasma as a propellant, a QVT would interact with quantum vacuum fluctuations of the zero-point field.

The concept is controversial and generally not considered physically possible. However, if QVT systems were possible they could eliminate the need to carry propellant, being limited only by the availability of energy.