External energy, defined

The fitting of electronegativities and hardnesses is done independently of each other with the help of a reformulation of the fluctuating charge model in terms of a linear response model [117, 120, 210], In the presence of an external potential the electrostatic energy defined in Eq. (9-35) is ... 

Life is a system which is spatially defined by a semipermeable compartment of its own making and which is self-sustaining by transforming external energy/nutrients by its own process of components production. ... 

To put the previous statement into perspective it is necessary to stipulate that any macrosystem with well-defined values of its extensive parameters is made up of myriads of individual particles, each of which may be endowed with an unspecified internal energy, within a wide range consistent with all external constraints. The instantaneous distribution of energy among the constituent particles, adding up to the observed macroscopic energy, defines a microstate. It is clear that any given macrostate could arise as the result of untold different microstates. 

Perhaps it is most useful to define a chemical laser simply as one in which the population inversion is produced by a chemical reaction. This includes cases in which energetic precursors may be supplied externally or produced by external energy input, and in fact all known chemical lasers are initiated or driven by some external energy input. We exclude lasers in which the inversion is produced directly in the primary process of photodissociation. Possible chemical laser systems and mechanisms have been reviewed282-286. We will discuss here a few particular cases. 

Atomic absorption spectrometry is a method of elemental analysis which exploits the property of atoms of being excited by external energy in the form of electromagnetic radiation (photons) with well defined frequencies. 

In (2.44), we have split the total potential energy of the system of N particles into two parts the potential energy of the interaction among the N—l particles and the interaction of one particle, chosen as particle 1, with the 2V— 1 particles. Once we fix the configuration of particle 1 at Xi, the rest of the system can be viewed as a system in an external field defined by B. ... 

External Work Defined as a Change in Free Energy of the System and Surroundings... 

An explosion is a self-propagating, particulary rapid combustion process that is initiated by an ignition and proceeds without external energy or air. The explosion of a solvent vapor air mixture is possible only within a specific solvent concentration range, defined by the lower and upper ignition limits (explosion limits) which are specified in volume percent or grams per cubic meter of solvent in the solvent vapor-air mixture at 101,3 kPa. 

When the number of repeating units in a polymer chain is low, that is when the molecular weight of the polymer is low (2000-10000 g mol ), the polymer is defined as a resin, provided it possesses sufficient numbers of active sites in its structures for chemical cross-linking to occur. The resins can form three-dimensional network structures if sufficient external energy (heat/light/radiation) is applied, with or without the use of any other chemical(s) in their finished state. They are free flowing materials of low viscosity. Polyester resins, epoxy resins, and polyurethane resins are examples of this type of polymer. This book contains descriptions of the different types of resins derived from various vegetable oils. 

The Langevin dynamics can be applied to an individual fluctuating trajectory. The convention in the first law dW = dU + 6q is that a work applied to the system is positive as is heat transferred into the environment. For a particle in equilibrium (/= 0 and constant X), no work is applied to the system and hence an increase in internal energy, defined by the position in the potential dU = dxV)dx = —8q, must be associated with heat taken up from the reservoir. Applying work to the particle either requires a time-dependent potential V(jc,A(t)) and (or) an external force Jc,A(x)). The change in work applied to the particle becomes d W = dV/dX)dX + fdx where the first term arises from changing the potential at fixed particle position. The heat dissipated into the medium is... 

FIGURE 1 The major components of a laser include a gain medium where the light is amplified, an external energy source to produce the population inversion, and an optical resonator or laser cavity which provides feedback to the gain medium and establishes a well-defined laser beam. 

This definition of the relativistic many-body energy involves both electrostatic and magnetic interactions between pairs of electrons. Effects due to the Lamb shift and errors associated with the non-additivity of the electronic energy and the energy due to nuclear motion are neglected in the present discussion. The decomposition of the total energy defined by Eq. (3) has the attractive feature that it represents, to order (Za) in the external field potential and to order in the electron-electron interaction, a precise... 

The question whether the component will survive in fact hinges on Ur- The energy Ur is related to the chain relaxation capability (CRC) which has been defined (2-4) as the amount of external energy dissipated by relaxation in a unit of time per unit weight of pol5nner. 

Sufficient free volume is essential for these processes. An increase in Vf results in an increase in the number of conformational changes in the chains enhancing the chain relaxation capability (CRC) (Brostow and Macip 1989 Doolittle 1951 Akinay et al. 2001). Brostow and Macip (1989) defined CRC as the amount of external energy dissipated by a relaxation process in a unit of time and unit mass of the polymer. The excess energy that cannot be dissipated by relaxational processes can go into destructive processes (irreversible changes in response to an applied force and/or temperature such as bond fracture and plastic deformation). The theory of the chain relaxation capability is discussed in detail in several references (Akinay et al. 2002 Brostow and Kubat 1996 Brostow 2000 Brostow et al. 2000 Brostow et al. 1999a, b). 

We thus can conclude that putting the energy term into 6ui instead of 6u2 increases both the acceptance probability and the CPU time. As the efficiency (t]) of a MC algorithm is usually defined by the number of accepted trial moves divided by the CPU time, the algorithm can be optimized by an intelligent division of the energy between 6ui and 6u2. There are three parts of the total external energy which are usually put into 6ui or 6u2 ... 

Alternatively, authors have repeatedly invoked the internal pressure of water as an explanation of the rate enhancements of Diels-Alder reactions in this solvent ". They were probably inspired by the well known large effects of the external pressure " on rates of cycloadditions. However, the internal pressure of water is very low and offers no valid explanation for its effect on the Diels-Alder reaction. The internal pressure is defined as the energy required to bring about an infinitesimal change in the volume of the solvents at constant temperature pi = (r)E / Due to the open and... 

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