DRASTIC system description

We presented fully self-consistent separable random-phase-approximation (SRPA) method for description of linear dynamics of different finite Fermi-systems. The method is very general, physically transparent, convenient for the analysis and treatment of the results. SRPA drastically simplifies the calculations. It allows to get a high numerical accuracy with a minimal computational effort. The method is especially effective for systems with a number of particles 10 — 10, where quantum-shell effects in the spectra and responses are significant. In such systems, the familiar macroscopic methods are too rough while the full-scale microscopic methods are too expensive. SRPA seems to be here the best compromise between quality of the results and the computational effort. As the most involved methods, SRPA describes the Landau damping, one of the most important characteristics of the collective motion. SRPA results can be obtained in terms of both separate RPA states and the strength function (linear response to external fields). 

Most of the time-resolved emission spectroscopy setups are home made in the sense that they are built from individual devices (laser, detection system,. ..) hence they are not of a plug and press type, so that their exact characteristics may vary from one installation to the other. Some of these differences have no impact on the overall capabilities of the system but some have a drastic influence on the way the collected data are processed and analysed. This aspect will be detailed in the next section, while this section deals with a general description of the apparatus. The most basic type of apparatus will be described, with no reference to sophisticated techniques such as Time Correlated Single Photon Counting or Circularly Polarized Luminescence devices. 

This model of the liquid will be characterized by some macroscopic quantities, to be selected among those considered by classical equilibrium thermodynamics to define a system, such as the temperature T and the density p. This macroscopic characterization should be accompanied by a microscopic description of the collisions. As we are interested in chemical reactions, one is sorely tempted to discard the enormous number of non-reactive collisions. This temptation is strenghtened by the fact that reactive collisions often regard molecules constituting a minor component of the solution, at low-molar ratio, i.e. the solute. The perspective of such a drastic reduction of the complexity of the model is tempered by another naive consideration, namely that reactive collisions may interest several molecular partners, so that for a nominal two body reaction A + B —> products, it may be possible that other molecules, in particular solvent molecules, could play an active role in the reaction. 

The difficulties in searching for viable options to address mathematics-related inadequacies increase considerably for the quantum chemistry course. The inadequacy of students familiarity with the mathematics required by that course is a rather common situation for quantum chemistry courses, also in other contexts. The course contents usually make provision for this, by including the development of familiarity with the needed mathematics (operators etc.) into the course. However, the characteristics of the UNIVEN context drastically reduce the viability of such option, because of the gap between students attained familiarity with mathematics, and what would be needed to cope with the mathematics for quantum chemistry. It is therefore opted to maximise the focus on the conceptual aspects and on the description of systems and behaviours, while only few mathematical procedures (e.g. the solution of the Schrodinger equation for the hydrogen atom) are presented, to provide at least some exposure to the ways of proceeding of quantum chemistry. 

To apply control to a process, one measures the controlled variable and compares it to the setpoint and, based on this comparison, typically uses the actuator to make adjustments to the flow rate of the manipulated variable. The industrial practice of process control is highly dependent upon the performance of the actuator system (final control element) and the sensor system as well as the controller. If either the final control element or the sensor is not performing satisfactorily, it can drastically affect control performance regardless of controller action. Each of these systems (i.e., the actuator, sensor, and controller) is made up of several separate components therefore, the improper design or application of these components, or an electrical or mechanical failure of one of them, can seriously affect the resulting performance of the entire control loop. The present description of these devices focuses on their control-relevant aspects. Later, troubleshooting approaches and control loop component failure modes are discussed. 

For the treatment of large polyatomic systems, computational methodologies deal with a compromise between an overall description of the entire system and a more detailed handling of a properly selected part of it. This situation particularly applies to the transition metal structures that have to be drastically minimized for an adequate ob initio, local density functional, or even semiempirical calculation at a good correlation level. In contrast to this simplification of the system, the improvements of the simpler methods, which are capable of handling the system as a whole, have regained acceptability. This is the case of the EHMO method developed by Hoffman [19], which was initially used for a reasonable description of the structural and electronic properties of the systems at a frozen geometry. Improvements of this method are mainly related to the addition of the (two-body electrostatic correction) term as explained above [20,21],... 

The accurate description of a chemical reaction requires detailed knowledge of its potential energy surface (PES). In principle Bom-Oppenheimer PESs can be theoretically obtained using a grid of PES points, but in practice it is not possible because of the drastic increase in computer resources, even for small systems. The alternative way is to find stationary points (minima, maxima and saddle points) and to estimate characteristics of the PES along the reaction path. 

Another option that reduces the number of functions, particularly when heavy atoms are involved, is the replacement of inner shell electrons by effective (or pseudo) potentials. Such procedures have been incorporated into many ab initio program systems including ACES II. Since the core electrons are not explicitly considered, effective potentials can drastically reduce the computational effort demanded by the integral evaluation. However, because the step is an inexpensive part of a correlated calculation, the role of effective potentials in correlated calculations is less important, due to the fact that dropping orbitals is tantamount to excluding them via effective potentials. An exception occurs when relativistic effects are important, as they would be in a description of heavy atom systems. Most such chemically relevant effects are due to inner shell elearons their important physical effects, like expanding the Pt valence shell, can be introduced via effective potentials that are extracted from Dirac-Fock or other relativistic calculations on atoms. ° Similarly, some effeaive potentials introduce some spin-orbital effects as well. Thus, besides simplifying the computation, effective potential calculations could include important physical effects absent from the ordinary nonrelativistic methods routinely applied. 

As molecular systems become larger the less rigorous are the methods used to describe their chemical and physical properties. As moleeular stractures containing many hundreds or thousands of atoms are far beyond the reach of even the fastest super-eomputers, drastic simplifications are needed for a reasonable description of chemicals such as oligopeptides and proteins. 

The two-component system—crystal lamellae or blocks alternating with amorphous layers which are reinforced by tie molecules— results in a mechanism of mechanical properties which is drastically different from that of low molecular weight solids. In the latter case it is based on crystal defects and grain boundaries. In the former case it depends primarily on the properties and defects of the supercrystalline lattice of lamellae alternating with amorphous surface layers (in spherulitic, transcrystalline or cylindritic structure) or of microfibrils in fibrous structure, and on the presence, number, conformation and spatial distribution of tie molecules. It matters how taut they are, how well they are fixed in the crystal core of the lamellae or in the crystalline blocks of the microfibrils and how easily they can be pulled out of them. In oriented material the orientation of the amorphous component (/,) is a good indicator of the amount of taut tie molecules present and hence an excellent parameter for the description of mechanical properties. In fibrous structure it directly measures the fraction and strength of microfibrils present and therefore turns out to be almost proportional to elastic modulus and strength in the fibre direction. 

Only when polymer chains form part of a crystal lattice can a precise structure be specified for the sample. In such a case the system can be defined by copying the contents of the unit cell along directions parallel to the lattice vectors. But polymers by their nature depart drastically from this ideal. Motions in noncrystalline media are subject to so many random or indeterminable factors that they cannot be treated by methods that require specifying a precise structure. Nevertheless we include a brief account of how randomness can be introduced into the simulation of polymer systems, since results have been shown to produce useful descriptions of noncrystalline polymer states. For more details about the methods, we refer the reader to books and specialist review articles " and descriptions of polymer simulation codes. " " ... 

Quantum chemical calculations allow an assessment of possible intermediates during the racemization process, since the results can be correlated with experimental observables. Starting from model system 4, it is possible to locate transition state TS-4 for the inversion at the silicon center (Fig. 1). The calculated barrier (159 kJ/mol for the inversion) is decreased drastically if the methyl groups at the silicon center are exchanged by phenyl groups, because these substituents can stabilize the transition state. These results prove once more the importance of the presence of solvated molecules in calculations in order to obtain the sufficient description of inversion processes and barriers, which can be compared with experimental results (inversion barrier for MesSi 199 kJ/mol). Nevertheless, when calculations are considered in the present literature, free silyl anions and unsolvated silyllithium compounds are still discussed as appropriate model systems [14]. 

Another approach for data processing involves simulation of pure spectra. These model spectra are then taken for a quantitative description of the mixture spectra. This procedure is referred to as indirect hard modelling (IHM). Obviously, changes in line shape, line width, and chemical shift may occur as function of concentration and due to system imperfections which are taken into account by IHM. The peaks are modelled by Voigt-functions with variable Gaussian to exponential ratio. The main advantage of IHM is that it allows a limited physical interpretation of the models. Further, unlike PLS based methods, IHM only requires reference spectra of the pure compounds, reducing the calibration effort drastically. 

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