Decker equation

The determination of the pressure inside the diamond anvil cell requires a calibrated standard. The most commonly used standard is the R-line ( E —> Aj) emission from ruby. The wavelengths of the ruby Rj and Rj lines have been accurately calibrated as a function of pressure using fixed point standards [86] and the measured lattice constant of NaCl in conjunction with the Decker equation of state [87-89]. The shift rate of the lower energy Rj line is normally used to calibrate pressure. The room temperature Ri shift rate is linear up to 200 kbar (0.365 A/kbar (- 0.759 cm Vkbar)) [87]. Above 200 kbar, the shift becomes non-linear and has been quantified empirically [90-93]. The currently accepted Rj line wavelength calibration is valid up to 800 kbar and can be expressed [91] by... 

Even nowadays, a DNS of the turbulent flow in, e.g., a lab-scale stirred vessel at a low Reynolds number (Re = 8,000) still takes approximately 3 months on 8 processors and more than 17 GB of memory (Sommerfeld and Decker, 2004). Hence, the turbulent flows in such applications are usually simulated with the help of the Reynolds Averaged Navier- Stokes (RANS) equations (see, e.g., Tennekes and Lumley, 1972) which deliver an averaged representation of the flow only. This may lead, however, to poor results as to small-scale phenomena, since many of the latter are nonlinearly dependent on the flow field (Rielly and Marquis, 2001). 

MSN. 180. T. Petrosky and I. Prigogine, Limits to causality and delocalization in classical field theory, in Evolution Equations and Their Applications in Physical and Life Sciences, G. Lumer and L. Weis, eds., Marcel Decker, New York, 2000. 

Lichtenstein and Schulz (5) studied the disappearance of aldrin over a 5-year period from a Wisconsin soil, both for a single application of 25 pounds per acre and for five annual applications of 5 pounds per acre. Soil was analyzed for dieldrin and aldrin. The data for the single application indicated that dieldrin decomposition is first-order with a half life of 4.2 years, which is similar to the results found by Decker et al. for Illinois soils. If the dieldrin first-order decomposition curve is extrapolated to zero time, a value of 24% is obtained to "represent the efficiency of conversion of aldrin to dieldrin—again similar to Illinois results. Assuming that the addition of 24% as much dieldrin is an approximately equivalent situation to the addition of aldrin, the accumulated residue for the case of five annual additions can be calculated according to the equation ... 

Borole (IV in Figure 14) has been used to synthesize a plethora of sandwich and half-sandwich stmctures it is the bora analog of cyclopentadiene. Borole is an antiaromatic system see Antiaromatic Compound), and only the blue pentaphenyl derivative has been prepared. The general route to borole complexes consists of complexation under dehydrogenation of 2- or 3-borolenes, which are prepared from [Mg(butadiene)]x and RBX2. Thus, the heating of either isomer of borolene with Co2(CO)g produces [(borole)Co(CO)2]2 (47) (equation 60) from which further cobalt borole complexes are prepared (equation 61). CpCo(borole) (48) can be made from (47) by Cp transfer from the labile 20-electron nickelocene (equation 61). Pyrolysis of (48) at 160-180 °C gives a triple-decker complex (49) in nearly quantitative yield, which in turn can be cleaved by Cp into (48) and the bis(borole)cobaltate anion (50 ) (Scheme 34). 

Table III. Radiochemical yields determined by Decker et al. at 45 C in oxygen excess (P02 > 2 lO Pa) 14). Comparison to theoretical ones predicted with equations 6-11.

Cook RK (1957) Variation of elastic constants and static strains with hydrostatic pressure a method for calculation from ultrasonic measurements. J Acoust Soc Am 29 445-449 David WIF (1992) Transformations in neutron powder diffraction. Physica B 180 181 567-574 Decker DL (1971) High-pressure equations of state forNaCl, KCl, and CsCl. J ApplPhys 42 3239-3244 Decker DL, Petersen S, Debray D, Lambert M (1979) Pressure-induced ferroelastic phase transition in Pb3(P04)2 A neutron diffraction study. Phys Rev B 19 3552-3555 Eggert JH, Xu L-W, Che R-Z, Chen L-C, Wang J-F (1992) High-pressure refractive index measurements of 4 1 methanol ethanol. J Appl Phys 72 2453-2461... 

In tests of the correction equations by means of random specimens, Newkirk and Bruce [9.11] found good agreement with Eq. (9-10) of Decker, Asp, and Harker. On the other hand, the data of Aoki et al. [9.12] show better agreement between experiment and theory for the Schulz method than that of Decker et al. However, in judging the validity of correction equations one must always keep in mind the necessity not only of a truly random specimen, but also of a close match between the actual x-ray optics (nature of incident beam and width of counter slit) and those assumed in the derivation of the equations. 

In Ref. [33] Decker et al. analyzed the photopolymerization kinetics of polyurethane-acrylate resins using the bimolecular and monomolecular termination models given by equations (4.11) and (4.16). They considered ranges of conversion where the models show linearity and they differentiated three polymerization states with different termination types ... 

The main developments in experimental techniques for measuring high pressure to obtain reliable pressure sensors are extensively discussed by Decker et al. [42]. These include (1) the establishment of a primary pressure scale using a free piston gauge (2) the selection and precise measurement of identifiable phase transitions as fixed pressure points and (3) the use of interpolation and extrapolation techniques for continuous-pressure calibration based on changes in resistance, volume, or optical spectra (based on an equation of state). An alternative method of estimating absolute pressure in isotropically compressed materials is based on measurements of ultrasonic velocity [43, 44]. 

Decker DL (1966) Equation of state of sodium chloride. J Appl Phys 37 5012... 

Decker DL (1971) High-pressure equation of state for NaCl, KCl, and CsCl. J Appl Phys 42 3239... 

A trinuclear Co2Sn species was obtained while treating 316 with GpCo(C2H4)2. This compound 317 can be viewed as an extremely slipped 34 VE triple-decker sandwich compound (see COMC (1995) and COMC (1982)), as it contains a bridging 1,2,4-triphospholyl 77 -bonded to one and 7] -bonded to the other CpCo unit (Equation (50)). ... 

Unfortunately, as a quadruple decker was obtained (which contained however only iron), no further results in this potentially very interesting area were published until then. A somewhat related dinuclear compound has been obtained while attempting the synthesis of l-formyl-l, 2, 3, 4, 5 -pentamethylcobaltocene. This compound was only made in situ as it rearranged into dimeric species 362 by redox disproportionation with radical coupling (Equation (62)). ... 

It is incorrect to assemble a fluid—particle interaction force by simply combining via a linear addition a number of forces obtained for various canonical cases. Many authors—see, e.g., Sokolichin and Eigenberger (1994), Lahey (1995), Hill et al (1995), Decker and Sommerfeld (2000), Lain et al (2000), Derksen (2003), Hibiki and Ishii (2007), Niceno et al (2008), Tabib et al (2008), and Dhotre et al (2009)— pursue this simple approach. While this procedure may be allowed for mere creeping flow conditions, generally it is not due to the notorious nonlinear character of the Navier—Stokes equation. 

In RANS-based simulations, the focus is on the average fluid flow as the complete spectrum of turbulent eddies is modeled and remains unresolved. When nevertheless the turbulent motion of the particles is of interest, this can only be estimated by invoking a stochastic tracking method mimicking the instantaneous turbulent velocity fluctuations. Various particle dispersion models are available, such as discrete random walk models (among which the eddy lifetime or eddy interaction model) and continuous random walk models usually based on the Langevin equation (see, e.g.. Decker and... 

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