Rotational Diffusion
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Rotational Diffusion
Rotational diffusion is the rotational movement which acts upon any object such as particles, molecules, atoms when present in a fluid, by random changes in their orientations. Whilst the directions and intensities of these changes are statistically random, they do not arise randomly and are instead the result of interactions between particles. One example occurs in colloids, where relatively large insoluble particles are suspended in a greater amount of fluid. The changes in orientation occur from collisions between the particle and the many molecules forming the fluid surrounding the particle, which each transfer kinetic energy to the particle, and as such can be considered random due to the varied speeds and amounts of fluid molecules incident on each individual particle at any given time. The analogue to translational diffusion which determines the particle's position in space, rotational diffusion randomises the orientation of any particle it acts on. Anything in a solutio ...
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Randomly Rotating Sphere
In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if the probability distribution is known, the frequency of different outcomes over repeated events (or "trials") is predictable.Strictly speaking, the frequency of an outcome will converge almost surely to a predictable value as the number of trials becomes arbitrarily large. Non-convergence or convergence to a different value is possible, but has probability zero. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often as 4. In this view, randomness is not haphazardness; it is a measure of uncertainty of an outcome. Randomness applies to concepts of chance, probability, and information entropy. The fields of ...
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Protein–protein Interaction
Protein–protein interactions (PPIs) are physical contacts of high specificity established between two or more protein molecules as a result of biochemical events steered by interactions that include electrostatic forces, hydrogen bonding and the hydrophobic effect. Many are physical contacts with molecular associations between chains that occur in a cell or in a living organism in a specific biomolecular context. Proteins rarely act alone as their functions tend to be regulated. Many molecular processes within a cell are carried out by molecular machines that are built from numerous protein components organized by their PPIs. These physiological interactions make up the so-called interactomics of the organism, while aberrant PPIs are the basis of multiple aggregation-related diseases, such as Creutzfeldt–Jakob and Alzheimer's diseases. PPIs have been studied with many methods and from different perspectives: biochemistry, quantum chemistry, molecular dynamics, signal trans ...
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Journal De Physique
The ''European Physical Journal'' (or ''EPJ'') is a joint publication of EDP Sciences, Springer Science+Business Media, and the Società Italiana di Fisica. It arose in 1998 as a merger and continuation of ''Acta Physica Hungarica'', ''Anales de Física'', ''Czechoslovak Journal of Physics'', ''Il Nuovo Cimento'', ''Journal de Physique'', ''Portugaliae Physica'' and ''Zeitschrift für Physik''. The journal is published in various sections, covering all areas of physics. History In the late 1990s, Springer and EDP Sciences decided to merge ''Zeitschrift für Physik'' and ''Journal de Physique''. With the addition of ''Il Nuovo Cimento'' from the Societa Italiana di Fisica, the ''European Physical Journal'' commenced publication in January 1998. Now ''EPJ'' is a merger and continuation of ''Acta Physica Hungarica'', ''Anales de Fisica'', ''Czechoslovak Journal of Physics'', ''Il Nuovo Cimento'', ''Journal de Physique'', ''Portugaliae Physica'' and ''Zeitschrift für Physik''. The sh ...
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Time Constant
In physics and engineering, the time constant, usually denoted by the Greek letter (tau), is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system.Concretely, a first-order LTI system is a system that can be modeled by a single first order differential equation in time. Examples include the simplest single-stage electrical RC circuits and RL circuits. The time constant is the main characteristic unit of a first-order LTI system. In the time domain, the usual choice to explore the time response is through the step response to a step input, or the impulse response to a Dirac delta function input. In the frequency domain (for example, looking at the Fourier transform of the step response, or using an input that is a simple sinusoidal function of time) the time constant also determines the bandwidth of a first-order time-invariant system, that is, the frequency at which the output signal power drops to half the value it has at ...
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Moment Of Inertia
The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rate of rotation. It is an extensive (additive) property: for a point mass the moment of inertia is simply the mass times the square of the perpendicular distance to the axis of rotation. The moment of inertia of a rigid composite system is the sum of the moments of inertia of its component subsystems (all taken about the same axis). Its simplest definition is the second moment of mass with respect to distance from an axis. For bodies constrained to rotate in a plane, only their moment of inertia about an axis ...
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Principal Axis (mechanics)
The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rate of rotation. It is an extensive (additive) property: for a point mass the moment of inertia is simply the mass times the square of the perpendicular distance to the axis of rotation. The moment of inertia of a rigid composite system is the sum of the moments of inertia of its component subsystems (all taken about the same axis). Its simplest definition is the second moment of mass with respect to distance from an axis. For bodies constrained to rotate in a plane, only their moment of inertia about an axis p ...
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Angular Velocity
In physics, angular velocity or rotational velocity ( or ), also known as angular frequency vector,(UP1) is a pseudovector representation of how fast the angular position or orientation of an object changes with time (i.e. how quickly an object rotates or revolves relative to a point or axis). The magnitude of the pseudovector represents the ''angular speed'', the rate at which the object rotates or revolves, and its direction is normal to the instantaneous plane of rotation or angular displacement. The orientation of angular velocity is conventionally specified by the right-hand rule.(EM1) There are two types of angular velocity. * Orbital angular velocity refers to how fast a point object revolves about a fixed origin, i.e. the time rate of change of its angular position relative to the origin. * Spin angular velocity refers to how fast a rigid body rotates with respect to its center of rotation and is independent of the choice of origin, in contrast to orbital angular ve ...
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Diffusion Equation
The diffusion equation is a parabolic partial differential equation. In physics, it describes the macroscopic behavior of many micro-particles in Brownian motion, resulting from the random movements and collisions of the particles (see Fick's laws of diffusion). In mathematics, it is related to Markov processes, such as random walks, and applied in many other fields, such as materials science, information theory, and biophysics. The diffusion equation is a special case of the convection–diffusion equation, when bulk velocity is zero. It is equivalent to the heat equation under some circumstances. Statement The equation is usually written as: where is the density of the diffusing material at location and time and is the collective diffusion coefficient for density at location ; and represents the vector differential operator del. If the diffusion coefficient depends on the density then the equation is nonlinear, otherwise it is linear. The equation above applies wh ...
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Equipartition Theorem
In classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. The original idea of equipartition was that, in thermal equilibrium, energy is shared equally among all of its various forms; for example, the average kinetic energy per degree of freedom in translational motion of a molecule should equal that in rotational motion. The equipartition theorem makes quantitative predictions. Like the virial theorem, it gives the total average kinetic and potential energies for a system at a given temperature, from which the system's heat capacity can be computed. However, equipartition also gives the average values of individual components of the energy, such as the kinetic energy of a particular particle or the potential energy of a single spring. For example, it predicts that every atom in a monatomic ideal ...
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Biophysics
Biophysics is an interdisciplinary science that applies approaches and methods traditionally used in physics to study biological phenomena. Biophysics covers all scales of biological organization, from molecular to organismic and populations. Biophysical research shares significant overlap with biochemistry, molecular biology, physical chemistry, physiology, nanotechnology, bioengineering, computational biology, biomechanics, developmental biology and systems biology. The term ''biophysics'' was originally introduced by Karl Pearson in 1892.Roland Glaser. Biophysics: An Introduction'. Springer; 23 April 2012. . The term ''biophysics'' is also regularly used in academia to indicate the study of the physical quantities (e.g. electric current, temperature, stress, entropy) in biological systems. Other biological sciences also perform research on the biophysical properties of living organisms including molecular biology, cell biology, chemical biology, and biochemistry. Overview ...
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David Merritt
David Roy Merritt (born November 16, 1955 in Los Angeles) is an American astrophysicist. Until 2017 he was a professor at the Rochester Institute of Technology in Rochester, New York. He received in 1982 his PhD in Astrophysical Sciences from Princeton University with thesis advisor Jeremiah P. Ostriker and held postdoctoral positions at the University of California, Berkeley and the Canadian Institute for Theoretical Astrophysics in Toronto. Merritt's fields of specialization include dynamics and evolution of galaxies, supermassive black holes, and computational astrophysics. Merritt is a former Chair of the Division on Dynamical Astronomy of the American Astronomical Society. He is a founding member of the Center for Computational Relativity and Gravitation at RIT. His scientific contributions include Osipkov–Merritt models, black hole spin flips, the Leonard–Merritt mass estimator, the M–sigma relation, stellar systems with negative temperatures, and the Schw ...
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Supermassive Black Hole
A supermassive black hole (SMBH or sometimes SBH) is the largest type of black hole, with its mass being on the order of hundreds of thousands, or millions to billions of times the mass of the Sun (). Black holes are a class of astronomical objects that have undergone gravitational collapse, leaving behind spheroidal regions of space from which nothing can escape, not even light. Observational evidence indicates that almost every large galaxy has a supermassive black hole at its Central massive object, center. For example, the Milky Way has a Galactic Center#Supermassive black hole, supermassive black hole in its Galactic Center, corresponding to the Astronomical radio source, radio source Sagittarius A*. Accretion (astrophysics), Accretion of Interstellar medium, interstellar gas onto supermassive black holes is the process responsible for powering Active galactic nucleus, active galactic nuclei (AGNs) and quasars. Two supermassive black holes have been directly imaged by the ...
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