Dissipative Systems

Also found in: Dictionary.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Dissipative Systems


mechanical systems whose total mechanical energy (the sum of kinetic and potential energy) decreases upon motion, changing into other forms of energy, such as heat. This process is called the process of dissipation of mechanical energy; it arises because of the presence of various forces of resistance (friction), which are also called dissipative forces. Examples of dissipative systems include a solid body moving along the surface of another solid in the presence of friction and a liquid or gas, among whose particles forces of viscosity (viscous friction) act upon motion.

The motion of dissipative systems may be retarded (damped) or accelerated. For example, the oscillations of a weight suspended from a spring will decay because of resistance from the surroundings and because of internal (viscous) resistance arising in the material of the spring itself upon deformation. On the other hand, the motion of a load along a rough inclined plane, which occurs when the sliding force is greater than the force of friction, will be accelerated. In this case the velocity v of the load, and consequently its kinetic energy T = mv2/2, where m is the mass of the load, are constantly increasing, but this increase proceeds more slowly than the decrease in potential energy Π = mgh (g is the acceleration of gravity and h is the height of the weight). As a result, the total mechanical energy of the weight, T + Π, is constantly decreasing.

The concept of dissipative systems is also applied in physics to nonmechanical systems in all cases when the energy of an orderly process is transformed into energy of a disorderly process—in the final analysis, into thermal energy. Thus, a system of circuits in which oscillations of electric current occur that die out because of the presence of resistance is also a dissipative system; in this case the electrical energy becomes joule heat.

Under terrestrial conditions, because of the inevitable presence of forces of resistance, virtually all systems in which no energy input from without takes place are dissipative systems. They may be regarded as conservative systems—that is, systems in which the conservation of mechanical energy takes place—only approximately, if forces of resistance are not taken into account. However, a nonconservative system may also not be a dissipative system, if the dissipation of energy in it is compensated for by the intake of energy from without. For example, the balance wheel of a clock, taken separately, is a dissipative system because of the presence of frictional resistance, and its oscillations (just as those of the weight) will decay. However, with a periodic input of energy from without by means of a spring or descending weight, the dissipation of energy is compensated, and the balance wheel performs self-oscillations.


The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
positively invariant manifolds for dissipative systems. Iterative method for the construction of invariant grid is discussed in section 3.3.
Focusing on mathematical methods for dissipative system complexity and mathematical biology, Vakulenko (mechanical engineering, Russian Academy of Sciences) considers the problem of the emergence of complexity in dissipative systems and chaos, stability, and evolution for genetic networks.
an energy dissipative system that can assume several to many conformations, will tend too take up one, or frequently return to one, that maximizes the entropy production from the energy gradients it is dissipating--to a degree consistent with that system's survival.
(21.) Also see our study "Dissipative Systems and Sustainability", published in Theoretical and Applied Economics 3(3), 2008 (the ideas from the study also have been presented and debated within the 4/2007 session of the Seminar).
(e) A key complexity insight is that of selforganization via bifurcation and dissipative systems, which Macintosh and MacLean (1999) have used to discuss their work in organizational change.
He pointed out that a wide class of systems existed - he called them dissipative systems - that tended to lose energy over time.
My argument in that earlier study fell into two distinct parts: a positive part, where classical mechanical systems displaying unequivocal temporal asymmetry were cited - dissipative systems, typical of engineering physics and chaos theory; and a negative part, where a standard argument in favour of the alleged symmetry (that which pretends to deduce a universal reversibility of motion from the invariance of some Lagrangian equations of motions) was criticized.
I was similarly stunned when, after providing the class with a brief introduction to chemical dissipative systems (a topic that combines thermodynamics and the law of time), the students immediately, clearly, made numerous connections to the text that gave them access to Bambara's ideas.
Dissipative systems operate inefficiently, and hence require large heat sinks.
When r = 0, [A.sub.0] is a stable matrix and [f.sub.0](t) = [p.sub.A](t) but when [mathematical expression not reproducible] we can obtain dissipative systems with unstable dynamics and the possibility of generating multiscroll attractors.
Other topics of the 20 reviews include lipid rafts, Rydberg state wavepackets, the quantum mechanics of dissipative systems, semiclassical initial value treatments of atoms and molecules, and heat capacity in proteins.