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Bistability
In a dynamical system, bistability means the system has two stable equilibrium states. Something that is bistable can be resting in either of two states. An example of a mechanical device which is bistable is a light switch. The switch lever is designed to rest in the "on" or "off" position, but not between the two. Bistable behavior can occur in mechanical linkages, electronic circuits, nonlinear optical systems, chemical reactions, and physiological and biological systems. In a conservative force field, bistability stems from the fact that the potential energy has two local minima, which are the stable equilibrium points. These rest states need not have equal potential energy. By mathematical arguments, a local maximum, an unstable equilibrium point, must lie between the two minima. At rest, a particle will be in one of the minimum equilibrium positions, because that corresponds to the state of lowest energy. The maximum can be visualized as a barrier between them. A sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bistability Graph
In a dynamical system, bistability means the system has two stable equilibrium states. Something that is bistable can be resting in either of two states. An example of a mechanical device which is bistable is a light switch. The switch lever is designed to rest in the "on" or "off" position, but not between the two. Bistable behavior can occur in mechanical linkages, electronic circuits, nonlinear optical systems, chemical reactions, and physiological and biological systems. In a conservative force field, bistability stems from the fact that the potential energy has two local minima, which are the stable equilibrium points. These rest states need not have equal potential energy. By mathematical arguments, a local maximum, an unstable equilibrium point, must lie between the two minima. At rest, a particle will be in one of the minimum equilibrium positions, because that corresponds to the state of lowest energy. The maximum can be visualized as a barrier between them. A sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optical Bistability
In optics, optical bistability is an attribute of certain optical devices where two resonant transmissions states are possible and stable, dependent on the input. Optical devices with a feedback mechanism, e.g. a laser, provide two methods of achieving bistability. *Absorptive bistability utilizes an absorber to block light inversely dependent on the intensity of the source light. The first bistable state resides at a given intensity where no absorber is used. The second state resides at the point where the light intensity overcomes the absorber's ability to block light. *Refractive bistability utilizes an optical mechanism that changes its refractive index inversely dependent on the intensity of the source light. The first bistable state resides at a given intensity where no optical mechanism is used. The second state resides at the point where a certain light intensity causes the light to resonate to the corresponding refractive index. This effect is caused by two factors *Nonline ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hysteresis
Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of the moment often form a loop or hysteresis curve, where there are different values of one variable depending on the direction of change of another variable. This history dependence is the basis of memory in a hard disk drive and the remanence that retains a record of the Earth's magnetic field magnitude in the past. Hysteresis occurs in ferromagnetic and ferroelectric materials, as well as in the deformation of rubber bands and shape-memory alloys and many other natural phenomena. In natural systems it is often associated with irreversible thermodynamic change such as phase transitions and with internal friction; and dissipation is a common side effect. Hysteresis can be found in physics, chemistry, engineering, biology, and economics. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Digit
Binary may refer to: Science and technology Mathematics * Binary number, a representation of numbers using only two digits (0 and 1) * Binary function, a function that takes two arguments * Binary operation, a mathematical operation that takes two arguments * Binary relation, a relation involving two elements * Binary-coded decimal, a method for encoding for decimal digits in binary sequences * Finger binary, a system for counting in binary numbers on the fingers of human hands Computing * Binary code, the digital representation of text and data * Bit, or binary digit, the basic unit of information in computers * Binary file, composed of something other than human-readable text ** Executable, a type of binary file that contains machine code for the computer to execute * Binary tree, a computer tree data structure in which each node has at most two children Astronomy * Binary star, a star system with two stars in it * Binary planet, two planetary bodies of compara ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apoptosis
Apoptosis (from grc, ἀπόπτωσις, apóptōsis, 'falling off') is a form of programmed cell death that occurs in multicellular organisms. Biochemical events lead to characteristic cell changes (morphology) and death. These changes include blebbing, cell shrinkage, nuclear fragmentation, chromatin condensation, DNA fragmentation, and mRNA decay. The average adult human loses between 50 and 70 billion cells each day due to apoptosis. For an average human child between eight and fourteen years old, approximately twenty to thirty billion cells die per day. In contrast to necrosis, which is a form of traumatic cell death that results from acute cellular injury, apoptosis is a highly regulated and controlled process that confers advantages during an organism's life cycle. For example, the separation of fingers and toes in a developing human embryo occurs because cells between the digits undergo apoptosis. Unlike necrosis, apoptosis produces cell fragments called apoptotic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cellular Differentiation
Cellular differentiation is the process in which a stem cell alters from one type to a differentiated one. Usually, the cell changes to a more specialized type. Differentiation happens multiple times during the development of a multicellular organism as it changes from a simple zygote to a complex system of tissues and cell types. Differentiation continues in adulthood as adult stem cells divide and create fully differentiated daughter cells during tissue repair and during normal cell turnover. Some differentiation occurs in response to antigen exposure. Differentiation dramatically changes a cell's size, shape, membrane potential, metabolic activity, and responsiveness to signals. These changes are largely due to highly controlled modifications in gene expression and are the study of epigenetics. With a few exceptions, cellular differentiation almost never involves a change in the DNA sequence itself. Although metabolic composition does get altered quite dramaticall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cell Cycle
The cell cycle, or cell-division cycle, is the series of events that take place in a cell that cause it to divide into two daughter cells. These events include the duplication of its DNA (DNA replication) and some of its organelles, and subsequently the partitioning of its cytoplasm, chromosomes and other components into two daughter cells in a process called cell division. In cells with nuclei ( eukaryotes, i.e., animal, plant, fungal, and protist cells), the cell cycle is divided into two main stages: interphase and the mitotic (M) phase (including mitosis and cytokinesis). During interphase, the cell grows, accumulating nutrients needed for mitosis, and replicates its DNA and some of its organelles. During the mitotic phase, the replicated chromosomes, organelles, and cytoplasm separate into two new daughter cells. To ensure the proper replication of cellular components and division, there are control mechanisms known as cell cycle checkpoints after each of the key steps ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stimuli
A stimulus is something that causes a physiological response. It may refer to: *Stimulation **Stimulus (physiology), something external that influences an activity **Stimulus (psychology), a concept in behaviorism and perception *Stimulus (economics) **For government spending as stimulus, see Fiscal policy **For an increase in money designed to speed growth, see Monetary policy *The input to an input/output system, especially in computers See also *Stimulus bill (other), in economics *Economic Stimulus Act of 2008, United States *2008 Chinese economic stimulus plan *2008 European Union stimulus plan *American Recovery and Reinvestment Act of 2009 The American Recovery and Reinvestment Act of 2009 (ARRA) (), nicknamed the Recovery Act, was a stimulus package enacted by the 111th U.S. Congress and signed into law by President Barack Obama in February 2009. Developed in response to the Gr ... * Stimulus Package, an add-on for the video game ''Modern Warfare 2 {{d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bifurcation Theory
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior. Bifurcations occur in both continuous systems (described by ordinary, delay or partial differential equations) and discrete systems (described by maps). The name "bifurcation" was first introduced by Henri Poincaré in 1885 in the first paper in mathematics showing such a behavior. Henri Poincaré also later named various types of stationary points and classified them . Bifurcation types It is useful to divide bifurcations into two principal classes: * Local bifurcations, which can b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pitchfork Bifurcation
In bifurcation theory, a field within mathematics, a pitchfork bifurcation is a particular type of local bifurcation where the system transitions from one fixed point to three fixed points. Pitchfork bifurcations, like Hopf bifurcations, have two types – supercritical and subcritical. In continuous dynamical systems described by ODEs—i.e. flows—pitchfork bifurcations occur generically in systems with symmetry. Supercritical case The normal form of the supercritical pitchfork bifurcation is : \frac=rx-x^3. For r0 there is an unstable equilibrium at x = 0, and two stable equilibria at x = \pm\sqrt. Subcritical case The normal form for the subcritical case is : \frac=rx+x^3. In this case, for r0 the equilibrium at x=0 is unstable. Formal definition An ODE : \dot=f(x,r)\, described by a one parameter function f(x, r) with r \in \mathbb satisfying: : -f(x, r) = f(-x, r)\,\, (f is an odd function), :\begin \frac(0, r_0) &= 0, & \frac(0, r_0) &= 0, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marginal Stability
In the theory of dynamical systems and control theory, a linear time-invariant system is marginally stable if it is neither asymptotically stable nor unstable. Roughly speaking, a system is stable if it always returns to and stays near a particular state (called the steady state), and is unstable if it goes farther and farther away from any state, without being bounded. A marginal system, sometimes referred to as having neutral stability, is between these two types: when displaced, it does not return to near a common steady state, nor does it go away from where it started without limit. Marginal stability, like instability, is a feature that control theory seeks to avoid; we wish that, when perturbed by some external force, a system will return to a desired state. This necessitates the use of appropriately designed control algorithms. In econometrics, the presence of a unit root in observed time series, rendering them marginally stable, can lead to invalid regression results rega ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical Systems Theory
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called ''continuous dynamical systems''. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle. When difference equations are employed, the theory is called ''discrete dynamical systems''. When the time variable runs over a set that is discrete over some intervals and continuous over other intervals or is any arbitrary time-set such as a Cantor set, one gets dynamic equations on time scales. Some situations may also be modeled by mixed operators, such as differential-difference equations. This theory deals with the long-term qualitative behav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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