Fundamental measures functional

The simulation results for coexistence properties are from Hoover and Ree [24] and the value of L is from the work of Ohnesorge et al. [135], The result from Barker s SCF theory [94] is from the leading term (order a ) in an expansion of the mean square displacement in powers of a = (p p/p) - 1 and may be an underestimate of the true value from that theory, SCF, self-consistent field LJD, Lennard-Jones and Devonshine MWDA, modified weighted-density approximation GELA, generalized effective liquid approximation FMF, fundamental measures functional. 

DFT has been much less successful for the soft repulsive sphere models. The definitive study of DFT for such potentials is that of Laird and Kroll [186] who considered both the inverse power potentials and the Yukawa potential. They showed that none of the theories existing at that time could describe the fluid to bcc transitions correctly. As yet, there is no satisfactory explanation for the failure of the DFTs considered by Laird and Kroll for soft potentials. However, it appears that some progress with such systems can be made within the context of Rosenfeld s fundamental measures functionals [130]. 

In general, different approximations are invoked for the hard-core contribution and the attractive contribution to the free energy functional. For the hardcore contribution, two accurate approximations can be obtained from the fundamental measure theory [108] and the weighted density approximation... 

The fundamental measurement in photochemistry/femtochemistry is the measurement of the yield Y per absorbed photon for the photochemical reaction (or equivalently cross section ), often as a function of optical wavelength ha>, absorbed optical fluence Fa, angle of incidence of the light to the surface d, and polarization of the light relative to the surface normal , i.e., as Y hot),FOJ,6i,POJ). A good indicator for hot electron (or more generally hot carrier) induced photochemistry is when the variation of (/ , ()i, ) parallels that for absorption of the light in the metal substrate. Direct adsorbate photochemistry behaves quite differently when the transition dipole is perpendicular to the surface [129]. There is, however, some... 

Here pt and pj denote the fractional populations of states i and j (p( = exp —Ei/kT /q in thermal equilibrium, where q is the partition function) pm and pn denote the corresponding fractional populations of the energy levels, and dm and dn the degeneracies (pf = pm/dm, etc.). The absorption intensity Gji9 and the Einstein coefficients and Bji9 are fundamental measures of the line strength between the individual states i and j they are related to each other by the general equations... 

The fundamental transfer function of a sensor is determined by the properties of the transducer principles chosen when setting up a signal path. Static sensor performance is defined by the static transfer function that describes the relationship between the output signal Uout and the input signal 0 (Eqs. 3.8 and 3.9) and additional parameters such as the measurement range, attainable sensitivity, resolution, and desired accuracy [8]. 

For the two fundamental thermodynamical functions (total and free energy) U and A are always used U signifies the heat developed in a process, or, in other words, the total amount of heat which can be measured in a calorimeter, and A the corresponding maximum work supplied in isothermal processes. This method of description, which frequently differs in sign from that hitherto customary, seemed to me advantageous for the following reasons —... 

Consider an excitation function a v) of an ion-molecule reaction for which, in order to simplify the discussion, any consideration of internal energy may be ignored. This can be included (and must be for any real system). It complicates the situation and some indication of this is given in the footnotes accompanying the following discussion. The excitation function, which summarizes the energy dependence of the integral reactive cross section for the particular reactive channel under consideration, is the fundamental measure of the total reaction efficiency for that... 

Perera, A. 2009. Bridge function and fundamental measure theory A test in dimension one. Molecular Physics. 107, 2251. 

Lutsko, J. E. 2008. J. Chem. Phys. Density functional theory of inhomogeneous liquids. 11. A fundamental measure approach. 128 184711. 

A more versatile version of the DFT has been introduced by Rosenfeld (1989) and Rosenfeld et al. (1996) and is known as the fundamental measure theory (FMT). In this approach, only one integrand is required, and thus the excess free energy functional is expressed as ... 

Tarazona, P. Density functional for hard sphere crystals A fundamental measure approach. 2000. Phys. Rev. Lett. 84 694. 

Thermodynamic logic often seems to be complex. This apparent complexity arises because the fundamental equilibrium functions cannot be measured directly. Equilibria are governed by energy and entropy through the Eirst and Second Laws, but unfortunately there are no energy or entropy meters to measure these quantities. Instead, inferences about equilibria are indirect and drawn from observations of quantities that can be measured, such as temperature, pressure, work, heat capacities, concentrations, or electrical potentials. Thermodynamics is a business of making clever inferences about unmeasurable quantities from observable ones, by various means. 

Let A be any convex body and denote its fundamental measures and r function by... 

By observing a comprehensive set of safety principles [2], the operators of plants will achieve the nuclear safety objectives. In this process, the measures that are taken to keep radiation exposure in all operational states to levels as low as reasonably achievable, and to minimize the likelihood of an accident that might lead to loss of normal control of the source of the radiation, are essential. For nuclear power plants, the safety objectives are ensured by fulfilling the three fundamental safety functions (FSFs) described in Section 2.2. 

Figure 16. The counterion density near a charged wall for the DFT scheme. Conditions as in Fig. 14. DFT denotes the density functional theory based on the fundamental measure theory [78], and WDA denotes the weighted density approximation based on the generalized Carnahan-Starling equation [75].

The defence in depth concept provides an overall strategy for safety measures and features of nuclear power plants. When properly applied, it ensures that no single human or mechanical failure leads to danger to the public, and even combinations of failures that are only remotely possible would lead to little or no injury. Defence in depth helps to establish that the three fundamental safety functions (controlling the power, eooling the fuel and confining the radioactive material) are preserved, and that radioaetive materials do not reach people or the environment. 

The incident monochromatic photon-to-current conversion efficiency (IPCE), sometimes referred to also as the external quantum efficiency (EQE), is another fundamental measurement of the performance of a device. The IPCE value corresponds to the photocurrent density generated in the external circuit under monochromatic illumination of the DSSC divided by the photon flux that strikes the cell [6]. From such an experiment, the IPCE as a function of wavelength can be calculated from the following formula ... 

It will be assumed that there is some exact functional relationship between the independent variable and the dependent variable that can be represented as y,. = F (Xj) and it is this functional relationship that one seeks to approximate by some mathematical /(x,., Q, Cj, C ) function. Sources of error in the measured value of the dependent variable can come about because of fundamental measurement errors in both the value of the independent and/or dependent variable. Thus for any particular measured value of y one can write ... 

The yield of electrons depends on the temperature of the filament and on the fundamental degree of difficulty in separating the electrons from the metal. The latter is measured in electron volts as a work function, ([). 

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