Liquid vector space

Last updated

The concept of a liquid vector space is part of condensed mathematics. [1] Liquid vector spaces are an alternative to topological vector spaces. [2]

Related Research Articles

<span class="mw-page-title-main">Pressure</span> Force distributed over an area

Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the pressure relative to the ambient pressure.

<span class="mw-page-title-main">Heat pump</span> System that transfers heat from one space to another

A heat pump is a device that uses work to transfer heat from a cool space to a warm space by transferring thermal energy using a refrigeration cycle, cooling the cool space and warming the warm space. In cold weather a heat pump can move heat from the cool outdoors to warm a house; the pump may also be designed to move heat from the house to the warmer outdoors in warm weather. As they transfer heat rather than generating heat, they are more energy-efficient than other ways of heating a home.

In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phonon is an excited state in the quantum mechanical quantization of the modes of vibrations for elastic structures of interacting particles. Phonons can be thought of as quantized sound waves, similar to photons as quantized light waves. However, photons are fundamental particles that can be individually detected, whereas phonons, being quasiparticles, are an emergent phenomenon.

<span class="mw-page-title-main">Vortex</span> Fluid flow revolving around an axis of rotation

In fluid dynamics, a vortex is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in the wake of a boat, and the winds surrounding a tropical cyclone, tornado or dust devil.

<span class="mw-page-title-main">Liquid nitrogen</span> Liquid state of nitrogen

Liquid nitrogenLN2—is nitrogen in a liquid state at low temperature. Liquid nitrogen has a boiling point of about −195.8 °C (−320 °F; 77 K). It is produced industrially by fractional distillation of liquid air. It is a colorless, mobile liquid whose viscosity is about one tenth that of acetone. Liquid nitrogen is widely used as a coolant.

Topological defects or solitons are irregularities or disruptions that occur within continuous fields or ordered states of matter. These defects, which can take various forms such as points, lines, or surfaces, are characterized by their stability and the fact that they cannot be 'smoothed out' or removed through continuous transformations of the field or material. They play a significant role in various areas of physics, including condensed matter physics, cosmology, and quantum field theory, and can have profound effects on the properties and behavior of the systems in which they occur.

<span class="mw-page-title-main">Thermal energy</span> Energy that is measured by temperature

The term "thermal energy" is used loosely in various contexts in physics and engineering, generally related to the kinetic energy of vibrating and colliding atoms in a substance. It can refer to several different well-defined physical concepts. These include the internal energy or enthalpy of a body of matter and radiation; heat, defined as a type of energy transfer ; and the characteristic energy of a degree of freedom, , in a system that is described in terms of its microscopic particulate constituents.

<span class="mw-page-title-main">Heat pipe</span> Heat-transfer device that employs phase transition

A heat pipe is a heat-transfer device that employs phase transition to transfer heat between two solid interfaces.

Cryogenic fuels are fuels that require storage at extremely low temperatures in order to maintain them in a liquid state. These fuels are used in machinery that operates in space where ordinary fuel cannot be used, due to the very low temperatures often encountered in space, and the absence of an environment that supports combustion. Cryogenic fuels most often constitute liquefied gases such as liquid hydrogen.

Liquid air is air that has been cooled to very low temperatures, so that it has condensed into a pale blue mobile liquid. It is stored in specialized containers, such as vacuum flasks, to insulate it from room temperature. Liquid air can absorb heat rapidly and revert to its gaseous state. It is often used for condensing other substances into liquid and/or solidifying them, and as an industrial source of nitrogen, oxygen, argon, and other inert gases through a process called air separation.

<span class="mw-page-title-main">Robert Coleman Richardson</span> American physicist

Robert Coleman Richardson was an American experimental physicist whose area of research included sub-millikelvin temperature studies of helium-3. Richardson, along with David Lee, as senior researchers, and then graduate student Douglas Osheroff, shared the 1996 Nobel Prize in Physics for their 1972 discovery of the property of superfluidity in helium-3 atoms in the Cornell University Laboratory of Atomic and Solid State Physics.

<span class="mw-page-title-main">Volatility (chemistry)</span> Tendency of a substance to vaporize

In chemistry, volatility is a material quality which describes how readily a substance vaporizes. At a given temperature and pressure, a substance with high volatility is more likely to exist as a vapour, while a substance with low volatility is more likely to be a liquid or solid. Volatility can also describe the tendency of a vapor to condense into a liquid or solid; less volatile substances will more readily condense from a vapor than highly volatile ones. Differences in volatility can be observed by comparing how fast substances within a group evaporate when exposed to the atmosphere. A highly volatile substance such as rubbing alcohol will quickly evaporate, while a substance with low volatility such as vegetable oil will remain condensed. In general, solids are much less volatile than liquids, but there are some exceptions. Solids that sublimate such as dry ice or iodine can vaporize at a similar rate as some liquids under standard conditions.

<span class="mw-page-title-main">Absorption refrigerator</span> Refrigerator that uses a heat source

An absorption refrigerator is a refrigerator that uses a heat source to provide the energy needed to drive the cooling process. Solar energy, burning a fossil fuel, waste heat from factories, and district heating systems are examples of convenient heat sources that can be used. An absorption refrigerator uses two coolants: the first coolant performs evaporative cooling and then is absorbed into the second coolant; heat is needed to reset the two coolants to their initial states. Absorption refrigerators are commonly used in recreational vehicles (RVs), campers, and caravans because the heat required to power them can be provided by a propane fuel burner, by a low-voltage DC electric heater or by a mains-powered electric heater. Absorption refrigerators can also be used to air-condition buildings using the waste heat from a gas turbine or water heater in the building. Using waste heat from a gas turbine makes the turbine very efficient because it first produces electricity, then hot water, and finally, air-conditioning—trigeneration.

Condensing boilers are water heaters typically used for heating systems that are fueled by gas or oil. When operated in the correct circumstances, a heating system can achieve high efficiency by condensing water vapour found in the exhaust gases in a heat exchanger to preheat the circulating water. This recovers the latent heat of vaporisation, which would otherwise have been wasted. The condensate is sent to a drain. In many countries, the use of condensing boilers is compulsory or encouraged with financial incentives.

<span class="mw-page-title-main">Deposition (phase transition)</span> Phase transition of matter from gaseous directly to solid

Deposition is the phase transition in which gas transforms into solid without passing through the liquid phase. Deposition is a thermodynamic process. The reverse of deposition is sublimation and hence sometimes deposition is called desublimation.

<span class="mw-page-title-main">Vapor-compression refrigeration</span> Refrigeration process

Vapour-compression refrigeration or vapor-compression refrigeration system (VCRS), in which the refrigerant undergoes phase changes, is one of the many refrigeration cycles and is the most widely used method for air conditioning of buildings and automobiles. It is also used in domestic and commercial refrigerators, large-scale warehouses for chilled or frozen storage of foods and meats, refrigerated trucks and railroad cars, and a host of other commercial and industrial services. Oil refineries, petrochemical and chemical processing plants, and natural gas processing plants are among the many types of industrial plants that often utilize large vapor-compression refrigeration systems. Cascade refrigeration systems may also be implemented using two compressors.

<span class="mw-page-title-main">Condenser (laboratory)</span> Laboratory apparatus used to condense vapors

In chemistry, a condenser is laboratory apparatus used to condense vapors – that is, turn them into liquids – by cooling them down.

<i>The Feynman Lectures on Physics</i> Textbook by Richard Feynman

The Feynman Lectures on Physics is a physics textbook based on some lectures by Richard Feynman, a Nobel laureate who has sometimes been called "The Great Explainer". The lectures were presented before undergraduate students at the California Institute of Technology (Caltech), during 1961–1963. The book's co-authors are Feynman, Robert B. Leighton, and Matthew Sands.

Condensed mathematics is a theory developed by Dustin Clausen and Peter Scholze which aims to unify various mathematical subfields, including topology, complex geometry, and algebraic geometry.

The TQ-15 is a gas-generator cycle rocket engine burning liquid methane and liquid oxygen under development by Landspace. The most recent version of the TQ engine family, the TQ-15A, is intended to power the second stage of LandSpace's upgraded Zhuque-2 rocket.

References

  1. "liquid vector space in nLab". ncatlab.org. Retrieved 2023-11-07.
  2. Scholze, Peter. "Lectures on Analytic Geometry: Lecture III: Condensed ℝ-vector spaces" (PDF). Retrieved 7 November 2023.