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Excitable Medium
An excitable medium is a nonlinear dynamical system which has the capacity to propagate a wave of some description, and which cannot support the passing of another wave until a certain amount of time has passed (known as the refractory time). A forest is an example of an excitable medium: if a wildfire burns through the forest, no fire can return to a burnt spot until the vegetation has gone through its refractory period and regrown. In chemistry, oscillating reactions are excitable media, for example the Belousov–Zhabotinsky reaction and the Briggs–Rauscher reaction. Cell excitability is the change in membrane potential that is necessary for cellular responses in various tissues. The resting potential forms the basis of cell excitability and these processes are fundamental for the generation of graded and action potentials. Normal and pathological activities in the heart and brain can be modelled as excitable media. A group of spectators at a sporting event are an excita ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Nonlinear Dynamical System
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it. At any given time, a dynamical system has a state representing a point in an appropriate state space. This state is often given by a tuple of real numbers or by a vector in a geometrical m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Partial Differential Equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to how is thought of as an unknown number to be solved for in an algebraic equation like . However, it is usually impossible to write down explicit formulas for solutions of partial differential equations. There is, correspondingly, a vast amount of modern mathematical and scientific research on methods to numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity, and stability. Among the many open questions are the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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. O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Dynamical Systems
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it. At any given time, a dynamical system has a state representing a point in an appropriate state space. This state is often given by a tuple of real numbers or by a vector in a geometr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Leon Glass
Leon Glass (born 1943) is an American scientist who has studied various aspects of the application of mathematical and physical methods to biology, with special interest in vision, cardiac arrhythmia, and genetic networks. Biography Leon Glass was born in Brooklyn, NY where he attended Erasmus Hall High School (Class of 1959) and majored in Chemistry at Brooklyn College (Class of 1963). He obtained a Ph.D. in Chemistry in 1968 from the University of Chicago studying theory of atomic motions in simple liquids. He was a Postdoctoral Fellow in Machine Intelligence and Perception (University of Edinburgh), Theoretical Biology (University of Chicago), and Physics and Astronomy (University of Rochester). In 1975, Glass joined the Department of Physiology at McGill University, where he is now Professor and the Isadore Rosenfeld Chair in Cardiology. He was awarded a Guggenheim Fellowship in 1994 and is a Fellow of the Royal Society of Canada (1998), the American Physical Society ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Autowave
Autowaves are self-supporting non-linear waves in active media (i.e. those that provide distributed energy sources). The term is generally used in processes where the waves carry relatively low energy, which is necessary for synchronization or switching the active medium. Introduction Relevance and significance In 1980, the Soviet scientists G.R. Ivanitsky, V.I. Krinsky, A.N. Zaikin, A.M. Zhabotinsky, B.P. Belousov became winners of the highest state award of the USSR, Lenin Prize "''for the discovery of a new class of autowave processes and the study of them in disturbance of stability of the distributed excitable systems''." A brief history of autowave researches The first who studied actively the self-oscillations was Academician AA Andronov, and the term "''auto-oscillations''" in Russian terminology was introduced by AA Andronov in 1928. His followers from Lobachevsky University further contributed greatly to the development of ''autowave theory''. The s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Fibrillation
Fibrillation is the rapid, irregular, and unsynchronized contraction of muscle fibers. An important occurrence is with regard to the heart. Cardiology There are two major classes of cardiac fibrillation: atrial fibrillation and ventricular fibrillation. * Atrial fibrillation is an irregular and uncoordinated contraction of the cardiac muscle of atria. It can be a chronic condition, usually treated with anticoagulation and sometimes with conversion to normal sinus rhythm. In this condition the normal electrical pulses coming from the sinoatrial node are overwhelmed by disorganized electrical impulses usually originating in the roots of the pulmonary veins, leading to irregular conduction of impulses to the ventricles which generate the heartbeat. * Ventricular fibrillation is an irregular and uncoordinated contraction of the cardiac muscle of ventricles. It is a common cause of cardiac arrest and is usually fatal if not reversed by defibrillation. Fibrillation may sometime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Tachycardia
Tachycardia, also called tachyarrhythmia, is a heart rate that exceeds the normal resting rate. In general, a resting heart rate over 100 beats per minute is accepted as tachycardia in adults. Heart rates above the resting rate may be normal (such as with exercise) or abnormal (such as with electrical problems within the heart). Complications Tachycardia can lead to fainting. When the rate of blood flow becomes too rapid, or fast blood flow passes on damaged endothelium, it increases the friction within vessels resulting in turbulence and other disturbances. According to the Virchow's triad, this is one of the three conditions that can lead to thrombosis (i.e., blood clots within vessels). Causes Some causes of tachycardia include: * Adrenergic storm * Anaemia * Anxiety * Atrial fibrillation * Atrial flutter * Atrial tachycardia * Atrioventricular reentrant tachycardia * AV nodal reentrant tachycardia * Brugada syndrome * Circulatory shock and its various ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Mexican Wave
The wave (known as a Mexican wave or stadium wave outside of North America) is an example of metachronal rhythm achieved in a packed stadium when successive groups of spectators briefly stand, yell, and raise their arms. Immediately upon stretching to full height, the spectator returns to the usual seated position. The result is a wave of standing spectators that travels through the crowd, even though individual spectators never move away from their seats. In many large arenas the crowd is seated in a contiguous circuit all the way around the sport field, and so the wave is able to travel continuously around the arena; in discontiguous seating arrangements, the wave can instead reflect back and forth through the crowd. When the gap in seating is narrow, the wave can sometimes pass through it. Usually only one wave crest will be present at any given time in an arena, although simultaneous, counter-rotating waves have been produced. The wave appeared in US sports events in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Cellular Automata
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling. A cellular automaton consists of a regular grid of ''cells'', each in one of a finite number of '' states'', such as ''on'' and ''off'' (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its ''neighborhood'' is defined relative to the specified cell. An initial state (time ''t'' = 0) is selected by assigning a state for each cell. A new ''generation'' is created (advancing ''t'' by 1), according to some fixed ''rule'' (generally, a mathematical function) that determines the new state of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |