**quantum mechanics**- The other sub-field is quantum mechanics. (wikipedia.org)
- When the objects being examined are sufficiently small, it becomes necessary to introduce the other major sub-field of mechanics: quantum mechanics. (wikipedia.org)
- The physics of very small particles, such as the electron, is more accurately described by quantum mechanics. (wikipedia.org)
- His work is concerned principally with the use of quantum mechanics to predict the properties of materials at the nanoscale. (wikipedia.org)
- The understanding of the interaction between light and matter following these developments was crucial for the development of quantum mechanics as a whole. (wikipedia.org)
- Laser science-i.e., research into principles, design and application of these devices-became an important field, and the quantum mechanics underlying the laser's principles was studied now with more emphasis on the properties of light[dubious - discuss], and the name quantum optics became customary. (wikipedia.org)
- In 1929 Hermann Weyl 's The theory of groups and quantum mechanics was published in German. (st-and.ac.uk)
- I have intentionally presented the more difficult portions of these problems of spin and second quantization in considerable detail, as they have been for the most part either entirely ignored or but hastily indicated in the large number of texts which have now appeared on quantum mechanics. (st-and.ac.uk)
- Casati is in fact principally known for the discovery of quantum dynamical localization phenomenon, that highlighted the relevance of chaos in quantum mechanics. (wikipedia.org)
- Heller is known for his work on time dependent quantum mechanics, and also for producing digital art based on the results of his numerical calculations. (wikipedia.org)
- Heller is principally known for pioneering a time-dependent wavepacket picture of quantum mechanics, which allowed the excited-state dynamics of large quantum mechanical systems to be understood without calculating eigenstates. (wikipedia.org)
- Heller's more recent work has focused on the study of two dimensional electron gases, quantum mirages in quantum corrals, scattering theory, few-body quantum mechanics, semiclassical methods, and freak waves in the ocean. (wikipedia.org)
- Many (though not all) of these studies make use of the time-dependent quantum mechanics ideas from his earlier work. (wikipedia.org)
- Such results would support the position that there is no way to explain the phenomena of quantum mechanics in terms of a more fundamental description of nature that is more in line with the rules of classical physics. (wikipedia.org)
- One feature of the theory of quantum mechanics under debate was the meaning of Heisenberg's uncertainty principle. (wikipedia.org)
- In 1935, Einstein, Boris Podolsky, and Nathan Rosen published a claim that quantum mechanics predicts that more information about a pair of entangled particles could be observed than Heisenberg's principle allowed, which would only be possible if information were travelling instantly between the two particles. (wikipedia.org)
- In 1964, John Stewart Bell proposed his now famous theorem, which states that no physical theory of hidden local variables can ever reproduce all the predictions of quantum mechanics. (wikipedia.org)
- Implicit in the theorem is the proposition that the determinism of classical physics is fundamentally incapable of describing quantum mechanics. (wikipedia.org)
- The results of the experiment could then be compared to what was predicted by local realism and those predicted by quantum mechanics. (wikipedia.org)
- The modern developments of relativity and quantum mechanics modify these laws insofar as they apply to higher speeds, very massive objects, and to the tiny elementary constituents of matter, such as electrons , protons , and neutrons . (britannica.com)
- The 20th-century subjects of quantum mechanics, crucial to treating the structure of matter, subatomic particles , superfluidity , superconductivity , neutron stars , and other major phenomena, and relativistic mechanics , important when speeds approach that of light, are forms of mechanics that will be discussed later in this section. (britannica.com)

**relativistic mechanics**- However, a number of modern sources do include relativistic mechanics, which in their view represents classical mechanics in its most developed and accurate form. (wikipedia.org)
- Non-relativistic mechanics also assumes that forces act instantaneously (see also Action at a distance). (wikipedia.org)

**fluid mechanics**- Geometric mechanics is a branch of mathematics applying particular geometric methods to many areas of mechanics, from mechanics of particles and rigid bodies to fluid mechanics to control theory. (wikipedia.org)
- Since Sir Isaac Newton originated the concept of viscosity, the study of liquids with strain rate dependent viscosity is also often called Non-Newtonian fluid mechanics. (wikipedia.org)
- Theoretical aspects of rheology are the relation of the flow/deformation behaviour of material and its internal structure (e.g., the orientation and elongation of polymer molecules), and the flow/deformation behaviour of materials that cannot be described by classical fluid mechanics or elasticity. (wikipedia.org)
- In practice, rheology is principally concerned with extending continuum mechanics to characterize flow of materials, that exhibits a combination of elastic, viscous and plastic behavior by properly combining elasticity and (Newtonian) fluid mechanics. (wikipedia.org)
- Dimensionless numbers in fluid mechanics are a set of dimensionless quantities that have an important role in the behaviour of fluids. (wikipedia.org)
- Springer Handbook of Experimental Fluid Mechanics. (wikipedia.org)

**Springer-Verlag**- Addison-Wesley Arnold, Vladimir (1966), "Sur la géométrie différentielle des groupes de Lie de dimension infine et ses applications a l'hydrodynamique des fluides parfaits", Annales de l'Institut Fourier, 16: 319-361, doi:10.5802/aif.233 Arnold, Vladimir (1978), Mathematical Methods for Classical Mechanics, Springer-Verlag Bloch, Anthony (2003). (wikipedia.org)

**analytical mechanics**- These advances, made predominantly in the 18th and 19th centuries, extend substantially beyond Newton's work, particularly through their use of analytical mechanics. (wikipedia.org)
- Symplectic geometry and analytical mechanics. (wikipedia.org)

**Newtonian**- In physics, classical mechanics, also known as Newtonian mechanics, is one of two major sub-fields of mechanics developed principally by Isaac Newton and Gottfried Wilhelm Leibniz. (wikipedia.org)
- The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology, though textbook authors often consider Newtonian mechanics, along with Lagrangian mechanics and Hamiltonian mechanics, as the three main formalisms of classical mechanics. (wikipedia.org)
- In case that objects become extremely heavy, deviations from Newtonian mechanics become apparent and can be quantified by using the Parameterized post-Newtonian formalism. (wikipedia.org)
- The earliest development of classical mechanics is often referred to as Newtonian mechanics. (wikipedia.org)

**20th century**- The term classical mechanics was coined in the early 20th century. (wikipedia.org)

**Lagrangian**- Later, more abstract and general methods were developed, leading to the reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. (wikipedia.org)

**continuum**- Research in the Continuum Mechanics and Industrial Mathematics (CMIM) group focuses on the mathematical description of processes that are of key importance to many industrial companies. (strath.ac.uk)
- Such relationships are then amenable to mathematical treatment by the established methods of continuum mechanics. (wikipedia.org)

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- Classical mechanics is sometimes considered a branch of applied mathematics. (britannica.com)

**phenomena**- The classical numbers in transport phenomena of mass, momentum, and energy are principally analyzed by the ratio of effective diffusivities in each transport mechanism. (wikipedia.org)

**numerical**- it will also interest numerical analysts in engineering mechanics. (hugendubel.de)

**pioneers**- The Bell test has its origins in the debate between Einstein and other pioneers of quantum physics, principally Niels Bohr. (wikipedia.org)

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**particles**- In classical mechanics the laws are initially formulated for point particles in which the dimensions, shapes, and other intrinsic properties of bodies are ignored. (britannica.com)

**conserved quantities**- Smale's paper on Topology and Mechanics investigates the conserved quantities arising from Noether's theorem when a Lie group of symmetries acts on a mechanical system, and defines what is now called the momentum map (which Smale calls angular momentum), and he raises questions about the topology of the energy-momentum level surfaces and the effect on the dynamics. (wikipedia.org)

**work**- One of the principal ideas of geometric mechanics is reduction, which goes back to Jacobi's elimination of the node in the 3-body problem, but in its modern form is due to K. Meyer (1973) and independently J.E. Marsden and A. Weinstein (1974), both inspired by the work of Smale (1970). (wikipedia.org)

**behavior**- Within classical mechanics are sub-fields, including those that describe the behavior of solids, liquids and gases. (wikipedia.org)

**Classical**- Classical mechanics is concerned with the set of physical laws describing the motion of bodies under the influence of a system of forces. (wikipedia.org)
- Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies. (wikipedia.org)
- Classical mechanics provides extremely accurate results when studying large objects that are not extremely heavy (i.e. their Schwarzschild radius is negligibly small for a given application) and speeds not approaching the speed of light. (wikipedia.org)
- When neither quantum nor classical mechanics apply and the objects are not extremely heavy, such as at the quantum level with high speeds, quantum field theory (QFT) becomes applicable. (wikipedia.org)
- The following introduces the basic concepts of classical mechanics. (wikipedia.org)
- In reality, the kind of objects that classical mechanics can describe always have a non-zero size. (wikipedia.org)
- Classical mechanics uses common-sense notions of how matter and forces exist and interact. (wikipedia.org)

**modern**- As a modern subject, geometric mechanics has its roots in four works written in the 1960s. (wikipedia.org)

**industrial**- Schlafly's father, John Bruce Stewart, was a machinist and salesman of industrial equipment, principally for Westinghouse. (wikipedia.org)

**second edition**- These ideas, and particularly those of Smale were central in the second edition of Foundations of Mechanics (Abraham and Marsden, 1978). (wikipedia.org)

**time**- During this time he received training and experience working in aircraft and engine mechanics, skills which he would later put to good use during his driving career. (wikipedia.org)
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**structure**- Geometric mechanics applies principally to systems for which the configuration space is a Lie group, or a group of diffeomorphisms, or more generally where some aspect of the configuration space has this group structure. (wikipedia.org)
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**taken**- Mechanics is generally taken to mean the study of the motion of objects (or their lack of motion) under the action of given forces. (britannica.com)

**common**- While attending lectures in mechanics at the Franklin Institute, Philadelphia, PA, Norcross principally studied arts and sciences, beyond his common [elem. (wikipedia.org)

**transport**- Mechanics and Energetics of Biological Transport by Prof. Dr. Erich Heinz (auth. (rockridgebrothers.com)