Energy gradient, definition

This definition of thermal diffusivity gives the impression that it is simply a mathematical factor but, as Hands points out10, it is the parameter that relates heat flow to the energy gradient, analogous to thermal conductivity relating heat flow to the temperature gradient. 

We now discuss the A = +1 CD in more detail. Three features will be stressed which describe the saddle behaviour of the MO. The first has already been discussed in connection with the definition of dia-batic MO cmves [6a,b] asymptotic to the R— oo three-body breakup threshold. Each stiff MO, with positive energy gradient at il = 0, has fixed quantum numbers (nA,0,m) and is the precursor of a complete in-saddle sequence of MO whose other members are all promoted MO with quantum numbers (ha, = even, m). The promoted MO show avoided crossings with other members of the sequence [6c]. The dia-batic connection of all avoided crossings connects the stiff precmsor MO near il = 0 with the R oo three-body break-up threshold. Note that the precursor MO are those e with positive gradient near J2 = 0 in Fig. la and are therefore easily recognised. 

Optimization—that is, minimization of the energy gradient—of a reactant, reaction intermediate (if existing), or product is usually straightforward and the only caveat is to make sure that its corresponding Hessian is positive definite. However, characterization and optimization of a transition structure constitute more difficult tasks and different algorithms [16,17] have been developed to this end. The located transition structure must fulfill the following four requirements, also known as Mclver-Komornicki conditions [18] ... 

The development gradient-corrected XC functionals has definitely been one of the keys to the recent surge in the popularity of DFT. Nevertheless, such functionals could not have had as much impact had it not been for the concurrent development of analytic DFT energy gradients, the first derivatives of the DFT total energy with respect to any of the nuclear coordinates. Without... 

Minimum exposure times must be observed in order to reach the requisite S/N ratio. As per EN 1435 and EN 584-1, for the different ranges of utilization (energy, wall thickness), definite film elasses are prescribed. They are characterized by the minimum gradient-to-noise ratios. Based on this, one can calculate the minimum values for the S/N ratio based on the IP systems. The exposure time and the device parameter sensitivity and dynamics (latitude) must be adjusted accordingly, with an availability of an at least 12 bit system for the digitalization. 

We divide by Avogadro s number to convert the partial molar Gibbs free energy to a molecular quantity, and the minus sign enters because the force and the gradient are in opposing directions. Recalling the definition of chemical potential [Eq. (8.13)], we write jUj + RT In aj = ii2 + RT In 7jC, where aj... 

Because of the influence of potential gradients, the work function depends on the position of the point to which the electron is transferred. As in the definition of surface potential, a point a) situated in the vacuum just outside the metal is regarded as the terminal point of transfer. It is assumed, moreover, that when the transfer has been completed, the velocity of the electron is close to zero (i.e., no kinetic energy is imparted on it). 

Active transport. The definition of active transport has been a subject of discussion for a number of years. Here, active transport is defined as a membrane transport process with a source of energy other than the electrochemical potential gradient of the transported substance. This source of energy can be either a metabolic reaction (primary active transport) or an electrochemical potential gradient of a substance different from that which is actively transported (secondary active transport). 

The banded coherency spectrum has an analogous definition (Yeung and Pope 1993) where the energy spectra are replaced with the spectra integrated over a finite wavenumber band. From the spectral time-evolution equations, it is easily shown that, in the absence of mean scalar gradients, the time evolution of the coherency spectrum is governed by 1 dPap Tap 1 Taa 1 Tpp ... 

The absolute value of the pressure gradient is used for all dissipation calculations. Although the pressure-induced flow is in different directions for a positive- and negative-valued pressure gradient operation, the dissipation level, however, is identical. Viscous energy dissipation is always positive definite. 

Fig. 1. The ground state energies of a Z = 90 hydrogen-like atom obtainedfrom the Dirac (D) andfrom the Levy-Leblond (L) equations as functions of the nonlinear parameters. In the upper-rowfgures (Dl and LI) the a (abscissa) and (3 (ordinate) dependence ofE is displayed when L and S are set equal to the values corresponding to the exact solutions. In the lower-row figures (D2 and L2 ) the L (abscissa) and S (ordinate) dependence of E is displayed when a and 5 are set equal to the exact value. The arrows show directions of the gradient their length is proportional to the value of the gradient The solid line crossing the saddle corresponds to the functions andLl) or S = Sj (L) D2 and L2. For the definitions of thesefunctions see text.

Since /(r) is the electrostatic potential energy per unit charge, the gradient of this parameter with distance must be equal to the force acting on a unit charge - which is the definition of the electric field. Hence it follows that... 

Heat (Definitions and Selected General References) A form, of energy. The mean energy transferred from one system to another system as a result of purely thermal interactions (temperature gradients) is called heat Refs 1) J.A. Randall Heat , J. Wiley and Sons, New York (1913) 2) T. Preston. J.R. Cotter Theory of Heat , Macmillan and Co., London (1919) 3) G.N. Lewis M. Randall Thermodynamics , McGraw Hill, New York... 

---