Center-of-gravity principle

The split of the final slurry between crystals and mother liquor can be found by what is called the center-of-gravity principle, which says that the masses of the two phases, in a two-phase mixture, are inversely proportional to the differences between their concentrations and that of the overall mixture. This principle is applied to the 70°F isotherm in either Fig. 27.3 or 27.4. The concentration of the mother liquor is 0.259, and that of the crystals is 0.488. Then, the crystals are... 

The fundamental principle of separation by SEC was described by Benoit and coworkers in 1967. They found an excellent correlation between the elution volume and a dynamically based molecular size, the hydrodynamic volume Vjj for a wide range of species and large-scale molecular architectures [9]. Their theory assumed a thermodynamic separation principle considering that the elution volume is independent of the flow rates. Recently, it has been proved that the radius of gyration is more appropriate than the hydrodynamic volume [10]. The radius of gyration is defined as the mean square distance away from the center of gravity [11]. Its mathematical definition is ... 

The microstmctural representation requires an initial conhguration of the particles, which can be, in principle, arbitrary (e.g., amorphous, granular, single crystalline, or molecular). Usually their mass is concentrated in their center of gravity, and its coordinates determine the position of the particle in space and their distance relative to each other (cf. Fig. 1). 

There is a part of the truth in this idealized picture. For most cases, it is sufficient to limit oneself (by concentration on optical excitations and photo-electron ionization, obeying the principle of Franck and Condon or by resignation) to scrutinize the electronic density determined by fixed nuclear positions. The really great success of quantum mechanics was the application to monatomic entities (but some restraining comments are made in section 4.8) where the nucleus is firmly put at the origin (unless below 10 amu, in which case perfectionists start worrying about the center of gravity shifted a trifle by the electrons). 

Note that here individual blobs with a size of f is defined as portions of the confined chain whose center of gravity undergoes the Brownian motion under the agitation of the thermal energy. Such a dependence (Eq. 5.8) was supported by the recent first principle calculation [36, 37]. 

Forklifts have a narrower wheelbase than a car and a much higher center of gravity this is why forklifts can easily be tipped over. Forklifts operate on a teeter-totter principle. A counterweight on the rear helps balance the load on the front. Forklifts that are empty are still potentially dangerous. A car handles and carries its load on the inside of the vehicle a forklift carries its load on the outside. This load can be unstable because of its height, weight, width, shape, or the load not being properly secured. 

In principle, every dipole has several types of oscillations, which affect the energy of its interaction with an ion (rotation in various planes, displacement of the center of gravity, etc.). The value of the induced moment is also subjected to thermal oscillations, in particular because of the anisotropy in molecular polarizability polarization of any covalent bond depends on the angle between the bond and the direction of the field. As mentioned above, a more rigorous analysis should consider a set of effective oscillators instead of the simple picture of oscillating dipoles. 

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