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Metastability
In chemistry and physics, metastability is an intermediate energetic state within a dynamical system other than the system's state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. If the ball is only slightly pushed, it will settle back into its hollow, but a stronger push may start the ball rolling down the slope. Bowling pins show similar metastability by either merely wobbling for a moment or tipping over completely. A common example of metastability in science is isomerisation. Higher energy isomers are long lived because they are prevented from rearranging to their preferred ground state by (possibly large) barriers in the potential energy. During a metastable state of finite lifetime, all state-describing parameters reach and hold stationary values. In isolation: *the state of least energy is the only one the system will inhabit for an indefinite length of time, until more external energy is added to the system (unique "absolu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metastable Phase
In chemistry and physics, metastability is an intermediate Energy level, energetic state within a dynamical system other than the system's ground state, state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. If the ball is only slightly pushed, it will settle back into its hollow, but a stronger push may start the ball rolling down the slope. Bowling pins show similar metastability by either merely wobbling for a moment or tipping over completely. A common example of metastability in science is isomerisation. Higher energy isomers are long lived because they are prevented from rearranging to their preferred ground state by (possibly large) barriers in the potential energy. During a metastable state of finite lifetime, all state-describing parameters reach and hold stationary values. In isolation: *the state of least energy is the only one the system will inhabit for an indefinite length of time, until more external energy is added to t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinetic Stability
In chemistry and physics, metastability is an intermediate energetic state within a dynamical system other than the system's state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. If the ball is only slightly pushed, it will settle back into its hollow, but a stronger push may start the ball rolling down the slope. Bowling pins show similar metastability by either merely wobbling for a moment or tipping over completely. A common example of metastability in science is isomerisation. Higher energy isomers are long lived because they are prevented from rearranging to their preferred ground state by (possibly large) barriers in the potential energy. During a metastable state of finite lifetime, all state-describing parameters reach and hold stationary values. In isolation: *the state of least energy is the only one the system will inhabit for an indefinite length of time, until more external energy is added to the system (unique "absolut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
States Of Matter
In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma. Different states are distinguished by the ways the component particles (atoms, molecules, ions and electrons) are arranged, and how they behave collectively. In a solid, the particles are tightly packed and held in fixed positions, giving the material a definite shape and volume. In a liquid, the particles remain close together but can move past one another, allowing the substance to maintain a fixed volume while adapting to the shape of its container. In a gas, the particles are far apart and move freely, allowing the substance to expand and fill both the shape and volume of its container. Plasma is similar to a gas, but it also contains charged particles (ions and free electrons) that move independently and respond to electric and magnetic fields. Beyond the classical states of matter, a wide variety o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metastate
In statistical mechanics, the metastate is a probability measure on the space of all thermodynamic states for a system with quenched randomness. The term metastate, in this context, was first used in by Charles M. Newman and Daniel L. Stein in 1996.. Two different versions have been proposed: 1) The Aizenman-Wehr construction, a canonical ensemble approach, constructs the metastate through an ensemble of states obtained by varying the random parameters in the Hamiltonian outside of the volume being considered. 2) The Newman- Stein metastate, a microcanonical ensemble In statistical mechanics, the microcanonical ensemble is a statistical ensemble that represents the possible states of a mechanical system whose total energy is exactly specified. The system is assumed to be isolated in the sense that it canno ... approach, constructs an empirical average from a deterministic (i.e., chosen independently of the randomness) subsequence of finite-volume Gibbs distributions. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
States Of Matter
In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma. Different states are distinguished by the ways the component particles (atoms, molecules, ions and electrons) are arranged, and how they behave collectively. In a solid, the particles are tightly packed and held in fixed positions, giving the material a definite shape and volume. In a liquid, the particles remain close together but can move past one another, allowing the substance to maintain a fixed volume while adapting to the shape of its container. In a gas, the particles are far apart and move freely, allowing the substance to expand and fill both the shape and volume of its container. Plasma is similar to a gas, but it also contains charged particles (ions and free electrons) that move independently and respond to electric and magnetic fields. Beyond the classical states of matter, a wide variety o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemical Kinetics
Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is different from chemical thermodynamics, which deals with the direction in which a reaction occurs but in itself tells nothing about its rate. Chemical kinetics includes investigations of how experimental conditions influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that also can describe the characteristics of a chemical reaction. History The pioneering work of chemical kinetics was done by German chemist Ludwig Wilhelmy in 1850. He experimentally studied the rate of inversion of sucrose and he used integrated rate law for the determination of the reaction kinetics of this reaction. His work was noticed 34 years later by Wilhelm Ostwald. In 1864, Peter Waage and Cato Guldberg published the law ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-equilibrium Thermodynamics
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of macroscopic quantities (non-equilibrium state variables) that represent an extrapolation of the variables used to specify the system in thermodynamic equilibrium. Non-equilibrium thermodynamics is concerned with transport processes and with the rates of chemical reactions. Almost all systems found in nature are not in thermodynamic equilibrium, for they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems and to chemical reactions. Many systems and processes can, however, be considered to be in equilibrium locally, thus allowing description by currently known equilibrium thermodynamics. Nevertheless, some natural systems and processes remain beyond the scope of equilibrium thermodynamic methods due to the exis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
White Noise
In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density. The term is used with this or similar meanings in many scientific and technical disciplines, including physics, acoustical engineering, telecommunications, and statistical forecasting. White noise refers to a statistical model for signals and signal sources, not to any specific signal. White noise draws its name from white light, although light that appears white generally does not have a flat power spectral density over the visible band. In discrete time, white noise is a discrete signal whose samples are regarded as a sequence of serially uncorrelated random variables with zero mean and finite variance; a single realization of white noise is a random shock. In some contexts, it is also required that the samples be independent and have identical probability distribution (in other words independent and identically distribu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermal Fluctuations
In statistical mechanics, thermal fluctuations are random deviations of an atomic system from its average state, that occur in a system at equilibrium.In statistical mechanics they are often simply referred to as fluctuations. All thermal fluctuations become larger and more frequent as the temperature increases, and likewise they decrease as temperature approaches absolute zero. Thermal fluctuations are a basic manifestation of the temperature of systems: A system at nonzero temperature does not stay in its equilibrium microscopic state, but instead randomly samples all possible states, with probabilities given by the Boltzmann distribution. Thermal fluctuations generally affect all the degrees of freedom of a system: There can be random vibrations (phonons), random rotations ( rotons), random electronic excitations, and so forth. Thermodynamic variables, such as pressure, temperature, or entropy, likewise undergo thermal fluctuations. For example, for a system that has an equ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Neuroscience
Computational neuroscience (also known as theoretical neuroscience or mathematical neuroscience) is a branch of neuroscience which employs mathematics, computer science, theoretical analysis and abstractions of the brain to understand the principles that govern the development, structure, physiology and cognitive abilities of the nervous system. Computational neuroscience employs computational simulations to validate and solve mathematical models, and so can be seen as a sub-field of theoretical neuroscience; however, the two fields are often synonymous. The term mathematical neuroscience is also used sometimes, to stress the quantitative nature of the field. Computational neuroscience focuses on the description of biologically plausible neurons (and neural systems) and their physiology and dynamics, and it is therefore not directly concerned with biologically unrealistic models used in connectionism, control theory, cybernetics, quantitative psychology, machine le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time-invariant System
In control theory, a time-invariant (TI) system has a time-dependent system function that is not a direct function of time. Such systems are regarded as a class of systems in the field of system analysis. The time-dependent system function is a function of the time-dependent input function. If this function depends ''only'' indirectly on the time-domain (via the input function, for example), then that is a system that would be considered time-invariant. Conversely, any direct dependence on the time-domain of the system function could be considered as a "time-varying system". Mathematically speaking, "time-invariance" of a system is the following property: :''Given a system with a time-dependent output function , and a time-dependent input function , the system will be considered time-invariant if a time-delay on the input directly equates to a time-delay of the output function. For example, if time is "elapsed time", then "time-invariance" implies that the relationship betwe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
