Collective variables choice

Let us discuss the physical meaning of this formal result. The form of Eq. (300) suggests that 8 is a control parameter generating cooperative and noncooperative properties. We see that the choice 8=1 corresponds to creating a collective motion that is totally insensitive to the frequencies of the bath oscillators and, consequently, yields no cooperation. The collective variable i becomes equivalent to white noise. 

In this chapter we provide a general introduction to metadynamics without entering into the details of the choice of the collective variables, which is, as we already underlined, a system-specific issue. In Sect. 1 we describe the... 

We define the center of the tube with the help of (1) a guiding trajectory, (2) a steepest descent path (SDP) calculation, (3) and a flexible choice of collective variables. 

Of course, the assumption of one dovish and one hawkish attitude only is an oversimplification. Returning to the general case described by (6.1-3) it can be shown that there exists a plausible choice of individual transition probabilities between the elements of a set of gradually varying attitudes leading to exactly the same equation of motion (6.12) for the collective variable Pj, even though the socio-configuration considered is much more complicated. 

In general, the expression on the rhs of (6.16) not only depends on the collective variables P, E, and Q but, due to the presence of the factors S and C, also on the whole socio-configuration. To obtain the equivalence of (6.16) with the simple dove/hawk model equation (6.12), choices for the open parameters/,f and/ i have to be made, which yield... 

The choice (6.26) is plausible in itself. It means that, as far as the parameters /are concerned, the transition to higher levels of the attitude a is less probable than the transition to lower levels if one starts from a positive attitude a > 0, and vice versa for attitudes starting with a < 0. The above considerations show that the reasonable assumptions of (6.13) for the transition probabilities together with the choice (6.23) lead to the simple equation of motion (6.12) for the collective variable P, as defined by (6.2), even if the underlying socioconfigurations have a complex structure with a sequence of many intermediate attitudes between dovishness and hawkishness. It will be assumed, therefore, that the equations of motion for P, (t) are of the form (6.12). 

The coordination number collective variable is a good choice for modeling solvent thermodynamics of ions in solution. The coordination number of species A with respect to species B is defined using a Fermi-Dirac function as... 

It is important to realize that in general the reaction coordinate q r), like the collective variables we use for free energy calculations, is a function we define with some arbitrariness on the basis of what we already know about the process we would like to study (we will discuss procedures that can be employed to facilitate the search for a good reaction coordinate later). Our particular choice of q r) may or may not be suitable to describe the reaction of interest. From a good reaction coordinate we expect to be able to teU how far a reaction has proceeded and what will most likely happen next. The reaction coordinate q r) should, for instance, tell us whether a particular configuration r is a transition state, i.e., a configuration from which both states A and B are equally accessible. By looking at the reaction coordinate q r) only, we should also be able to teU whether a reaction has just started or is about to be completed. 

Under controlled conditions (e.g., in the laboratory), the inherent collection efficiency of fabric filters approaches 100 per cent. In actual operation, it is determined by several variables, in particular the properties of the dust to be removed, choice of filter fabric, gas velocity, method of cleaning, and cleaning cycle. Inefficiency usually results from bags that are poorly installed, torn, or stretched from excessive dust loading and excessive pressure drop. 

The instrument variables Rs, RB, and Rs + 2RB are used in instrument optimization for example, an improved matching of the laser bandwidth to the HO absorption could increase Rs, a reduction in illumination of walls near the detection zone by ambient light or scattered or diffracted laser light could decrease RB, and an increase in photon collection efficiency could increase (Rs + 2RB). The remaining quantities fav, MAT, SNR, and MDC may be traded off during data processing, but the choice of their values is restricted by the instrument variables. 

The large majority of skeletal remains from prehistoric Sardinia come from collective burials where skeletal elements were not articulated nor associated in any way deemed significant by the excavators. It was therefore necessary to select one skeletal element in order to insure that the same individuals were not being sampled more than once. Crania were found to be the best choice, since they hold the highest potential to identify the individual s sex, age and pathologies. While we know of different turnover rates in different skeletal elements and within the same element, the specific times have not been documented. Growth speed is believed to affect intra-bone variability mostly in... 

The extracted compounds are collected into a vial that usually has in it a small volume of an organic collection solvent. The choice of collection solvent is important to ensure good recovery. Although there are many variables to consider when developing an extraction method by SFE, manufacturers of SFE instruments will provide information on the most appropriate conditions for a particular compound from a given matrix. Applications range from the extraction of fats and oils from foodstuffs to the... 

The limitations of these methods should be understood. Their application requires the determination of the empirical parameters in eqns (5.2) and (5.3), as well as the partial atomic charges in the coulombic term. The former are usually parameterized from experimental solid state data such as vibrational frequencies or sublimation enthalpies, which in themselves contain some experimental uncertainties and variability from system to system. The partial atomic charges can and do vary with the choice of basis set for the calculations from which they are derived. The function chosen and the complete set of parameters are often collectively termed a force field . Ideally, one would like to develop a universal force field, but given the diversity... 

Data on biological variability are used to assist in the selection of the most appropriate test in a given situation. For example, creatinine clearance and urine creatinme have less intraindividual variation than serum creatinine so that creatinine clearance is a better choice than serum creatinine for initial assessment of renal function in an individual but the lower RCV for serum creatinine make this test better for monitoring individuals. However, the need for a urine collection reduces the practicality of using clearance in the initial assessment of renal function. Studies to determine whether the GFR calculated from the serum creatinine concentration might enhance the utility of the serum measurement still have to be performed. 

NCCLS. Ionized calcium determinations precollection variables, specimen choice, collection, and han-dhng approved guideline, 2nd ed, C31-A2. Wayne,... 

The second reason to introduce the derivation (6 -9) is to note that all that is required to evaluate the absorption and emission probability F A (t, r) of (9) are matrix elements of the evolution operator exp(-i//r/h). (These matrix elements are the conventional probability amplitudes When considering a situation in which many different kinds of decay processes are involved, e.g. radiative and nonradiative decay, it is not always convenient to deal directly with the matrix elements of exp(-itfr/h), the af(t). Rather, it is simpler to introduce (imaginary) Laplace transforms 16) in the same manner that electrical engineers use them to solve ac circuit equations 33L Thus, if E is the transform variable conjugate to t, the transforms of af(t) are gf(E). The quantities gf (E) can also be labeled by the initial state k and are denoded by Gjk(E). It is customary in quantum mechanics to collect all these Gjk(E) into a matrix G(E). Since matrix methods in quantum mechanics imply some choice of basis set and all physical observables are independent of the chosen basis set, it is convenient to employ operator formulations. If G (E) is the operator whose matrix elements are Gjk(E), then it is well known that G(E) is the Green s function i6.3o.34) or resolvent operator... 

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