Test-particle model

Sagarik, K. R, Ahlrichs, R., and Erode, S., Intermolecular potentials for ammonia based on the test particle model and the coupled pair functional method. Mol. Phys. 57, 1247-1264 (1986). 

K. P. Sagarik, R. Ahlrichs, and S. Brode, Mol. Phys., 57, 1247 (1986). Intermolecular Potentials for Ammonia Based on the Test Particle Model and the Coupled Pair Functional Method. 

K. P. Sagarik and R. Ahlrichs, /. Chem. Phys., 86, 5117 (1987). A Test Particle Model Potential for Formamide and Molecular Dynamics Simulations of the Liquid. 

Beck, T. L., Quantum path integral extension of Widom s test particle method for chemical potentials with application to isotope effects on hydrogen solubilities in model solids, J. Chem. Phys. 1992, 96, 7175-7177... 

Nevertheless, direct test particle calculations have been of great conceptual importance, particularly in cases where there is a consensus on the relevance of simplified model solutes [2-4, 6, 9, 10,41 15]. The related particle insertion techniques are used for simulating phase equilibria, as discussed in Chap. 10. 

Vrabec, J. Loth, A. Fischer, J., Vapour liquid equilibria of Lennard-Jones model mixtures from the NPT plus test particle method, Fluid Phase Equil. 1995,112, 173-197... 

The data analysis in Table 9.3 summarizes the crystallographic information of the Co-Mo-S phase active for hydrodesulfurization. The Co-S distance in Co-Mo-S is 0.22 nm, with a high sulfur coordination of 6.2 1.3. Each cobalt has on average 1.7 0.35 molybdenum neighbors at a distance of 0.28 nm. Based on these distances and coordination numbers one can test structure models for the CoMoS phase. The data are in full agreement with a structure in which cobalt is on the edge of a MoS2 particle, in the same plane as molybdenum. 

In order to test this model, we measured the quantum yield of the electron transfer to methylviologen as a function of the particle radius of CdS nanoparticle.13) The dependence of the electron transfer yield on the particle size well proved the applicability of the 2D ladder model to this system. For a low excitation limit of gV< 1, the quantum yield is independent of the light intensity, as expressed by... 

Small-angle neutron scattering (SANS) can be applied to food systems to obtain information on intra- and inter-particle structure, on a length scale of typically 10-1000 A. The systems studied are usually disordered, and so only a limited number of parameters can be determined. Some model systems (e.g., certain microemulsions) are characterized by only a limited number of parameters, and so SANS can describe them fully without complementary techniques. Food systems, however, are often disordered, polydisperse and complex. For these systems, SANS is rarely used alone. Instead, it is used to study systems that have already been well characterized by other methods, viz., light scattering, electron microscopy, NMR, fluorescence, etc. SANS data can then be used to test alternative models, or to derive quantitative parameters for an existing qualitative model. 

Figure 3. The photon as a rotating doublet (a) composite photon model—extended electron-positron pair rotating in x-y plane (b) electrostatic field of doublet—electrostatic force on a test particle at rest.

The second part of Eq. (101) is based on the 4D model of Section IV. The electron is an isotropic 3D source that emits a momentum flow q+c at time te. The preonic fluid14 propagates in straight line with constant speed c from the point of emission to a spatially separated point P located at distance de at the moment of emission. The preonic fluid carries momentum, which materializes as force during interaction with an obstacle, say, a test charge. To be specific, let the test particle be an electron of effective radius re, then Atest = nr1. From... 

Section IV reviews our more recently developed 4D ether model [102-104], which is based on the premise of the existence of E. Rest mass is associated to a flow of primordial fluid (preons). This novel dynamic concept of mass solves at once several longstanding difficulties two of them are (1) the infinities associated with electric and gravitational fields and (2) the stability of orbits under Coulomb attraction. Indeed, there is a permanent flow of momentum across a particle (source) the momentum flux is occasionally tapped by interaction with a (test) particle. Such process does not change the total momentum flux available at the source hence, there is no loss of potential energy as in the conventional interpretation. The total momentum that crosses a source is, of course, infinite in an infinite time, but the source is always finite. 

Finally, because models such as the IBM consider only valence particles—those beyond the nearest closed shell or, in some instances, subshell—researchers are interested in mapping, experimentally, the locations of shells and subshells into regions far from stability. An improved knowledge of shell and subshell gaps at the extremes of nuclear stability will provide important benchmarks for testing nuclear models. 

Our analysis gave strong support to the Zeldovich pancake scenario. This model was based essentially on the neutrino dominated dark matter model. However, some important differences between the model and observations were detected. First of all, there exists a rarefied population of test particles in voids absent in real data. This was the first indication for the presence of biasing in galaxy formation - there is primordial gas and dark matter in voids,... 

To examine further the fate of particle-reactive radionuclides we will use a simple one-dimensional model that, in the case of 234Th, would supply 234Th to the seabed from a source of 238U in the water column. To test this model, a sedimentary inventory (I) of 234Th would have to be calculated based on the excess 234Th profiles in cores using the following equation described by McKee et al. (1984) ... 

In order to test the model used here, calculated values of the limiting free polymer concentration 0 at which phase separation occurs are compared with the experimental data [6] on the aqueous dispersions of polystyrene latex particles with adsorbed polyethylene oxide and with polyethylene oxide as the free polymer. Since no information is available regarding the thickness of the adsorbed layer, the values used by Vincent et al. [6] in their theoretical calculations are adopted. Table 1 compares the experimental values of the limiting volume fraction of the free polymer with our calculated values for two different molecular weights of the free polymer. The simple model used here gives reasonably good agreement with the experimental values. 

Activity Tests with Model Compounds. Activity tests with model compounds were also carried out for the fresh, regenerated, and aged catalysts in a fixed bed reactor under a vapor phase condition at 5.0 MPa. 3 cm of crushed catalyst (0.35 - 0.5mm) was diluted with 9 cm of inactive alumina particles. Catalyst activities, such as hydrodesulfurization (HDS), hydrodenitrogenation (HDN), and hydrogenation (HG), were measured, feeding a mixture of 1 wt% carbon dioxide, lwt% dibenzothiophene, 1 wt% indole, and 1 wt% naphthalene in n-heptane. The catalysts were presulfided with a 5% H2S/H2 mixture at 400 °C for two hours and aged with a liquid feed at a reaction condition for 24 hours. Tests for HDS and HDN reactions were conducted at 275 °C, while those for a HG reaction were done at 325 °C. Condensed liquid products were analyzed with gas chromatography. Since all the reactions took place with the crashed catalysts in the vapor phase, we assumed that effectiveness factors were unity (9). 

FIGURE 1 Hard sphere model of a molecular surface (a) and contact surface (b). The contact surface is generated by rolling a test particle (sphere) over the hard sphere model. 

---