Nonconservative forces

Nonequilibrium Steady State (NESS). The system is driven by external forces (either time dependent or nonconservative) in a stationary nonequilibrium state, where its properties do not change with time. The steady state is an irreversible nonequilibrium process that cannot be described by the Boltzmann-Gibbs distribution, where the average heat that is dissipated by the system (equal to the entropy production of the bath) is positive. 

A number of interesting effects occur in spatially periodically forced pattern forming systems with a nonconserved order parameter, which have been investigated during recent years [60-73, 120], Here we focus on nearly unexplored effects of spatially periodic forcing in system with a conserved order parameter, as they occur in phase separating systems which are forced by spatial temperature modulations and where thermodiffusion plays a crucial role. 

The dissipative term takes the form of a nonconservative force, Qk, acting on the generalized coordinate qk. 

This force, being one of a class of dissipative or frictional forces, is termed a nonconservative force, as are all forces that depend on velocity or time. 

Equation (3.200) is the expression for a nonconservative change in local entropy density, and allows the determination of the entropy production from the total change in entropy and the evaluation of the dependence of on flows and forces. 

Since the zero-order fields are known, these perturbation equations are linear, inhomogeneous, Stokes-type equations. Particular integrals are very easy to obtain. To do so we note that Eq. (191) is formally equivalent to Stokes equations in the presence of nonconservative external volume forces. If =fa lfiV denotes the dimensionless force per unit volume exerted by the surroundings at a point in the fluid, Stokes equations in nondimensional form become... 

Molecular parity nonconservation caused by the parity violating property of the elec-troweak force is discussed. Different approaches to the computation of these parity violating influences are outlined and recent predictions for parity violating effects in spectroscopically and biologically relevant molecules are reviewed. 

Climb is nonconservative motion because vacancies and/or interstitials must be absorbed or emitted (their number is not conserved). When a jog moves, it can either glide or climb. The special point to remember is that the glide plane of a jog is not the same as the glide plane of the dislocation on which is sits. If we force a dislocation jog to move on a plane, which is not its glide plane, it must adsorb or emit point defects, but it can glide. Since it is charged, it carries a current when it glides. 

In the context of vibrating mechanical systems, damping is the irreversible transition of mechanical energy into other forms of energy, mainly thermal energy, caused by nonconservative forces acting on the system. 

If desired, internal viscosity can be included by incorporating dashpots in parallel with the springs in the mechanical models. However, this introduces nonconservative forces into the problem. To avoid dealing with nonconservative forces, one can use momentum-space averages of the dashpot term as explained in DPL, Eq. 13C.2-2. We know of no molecular theory that can legitimize the use of dashpots in molecular models. 

Conservative forces due to gravity and elasticity are typically accounted for within the terms defining the potential energy of the system, while inertial forces are derived from the kinetic energy. Forces due to joint friction, tissue damping, and certain external forces are expressed as nonconservative generalized forces. 

A nonequilibrium steady state occurs if time-independent but nonconservative forces F(x) act on the system with a time-independent control parameter A. For such a system, a steady current is... 

For all issues relevant to the chemistry and physics of atoms, molecules, clusters, and solids only electromagnetic and — to a negligible extent — weak interactions, which are responsible for the radioactive /5-decay and the nonconservation of parity, contribute. The internal structure of hadrons, i.e., protons and neutrons built up by quarks governed by strong interactions and also gravitational forces, do not play any role and are therefore not covered by this presentation. 

This nonconservative (v — dependent) force is not derivable from a potential energy V in the manner of Eq. 1.50. If a Lagrangian function can nevertheless be found that obeys Eq. 1.57, the formulation of the Hamiltonian using Eq. 1.62 will still be valid. Recasting Eq. 1.64 in terms of the vector and scalar potentials (Eqs. 1.39 and 1.42), we obtain... 

Alternatively, Mortensen et al. ° suggest using two different approximate force expressions for the local nodes and the nonlocal repatoms. The two expressions will differ from the negative derivative of the energy only in the interface region. As with the previous method, this approach involves nonconservative forces. 

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