Accessible region

The most general problem should be that of a particle in a nonseparable potential, linearly coupled to an oscillator heat bath, when the dynamics of the particle in the classically accessible region is subject to friction forces due to the bath. However, this multidimensional quantum Kramers problem has not been explored as yet. 

Fig. 3. One-dimensional barrier along the coordinate of an exoergic reaction. Qi(E), Q i(E), QiiE), Q liE) are the turning points, coo and CO initial well and upside-down barrier frequencies, Vo the barrier height, — AE the reaction heat. Classically accessible regions are 1, 3, tunneling region 2.

Mehler EL, Eichele G (1984) Electrostatic effects in water-accessible regions of proteinst. Biochemistry 23 3887-3891. 

For example, on an evenly spaced grid that covers the allowable region in composition space. Or, even better, on a specially adapted grid covering only the accessed region of composition space. 

In other words, a pre-computed lookup table must cover the entire allowable region, while only a small sub-set (the accessed region) is used in a particular simulation. 

In situ adaptive tabulation (IS AT) was proposed by Pope (1997), and it overcomes many of the difficulties associated with pre-computed lookup tables. First, the in situ nature of the method reduces the tabulation to only those points that occur during a particular simulation (i.e., the accessed region). Secondly, an adaptive algorithm is employed to control interpolation errors while minimizing the number of points that must be tabulated. 

Goldfinger, Mark, and Siggia32 oxidized cellulose with sodium periodate in aqueous solution. The observed rates of oxidation were explained on the assumption that the materials consisted of easily accessible and difficulty accessible regions. By extrapolation of the ultimate slow rates,... 

Pump bearing type All Hydrodynamic guide bearing adjacent to accessible region of shaft... 

Each group of experiments should be pre-planned. Perhaps multiple batch experiments, semi-batch or both can be conveniently used. The initial conditions for the batch runs and the steps of the semi-batch runs can be chosen randomly or in a judicious manner. The really important issue is that the mole ratios of any two reagents should never be held constant in a group this constitutes a co-linearity induced by the experimentalist. It can be noted that each perturbation in a semibatch experiment limits the future accessible region of composition space so planning is advisable. 

Because of the dosing technique associated with the vacuum volumetric method there exists a potential source of error which in principle cannot be avoided on samples that are slow to equilibrate. Figure 14.2 represents a plot of the pressure in the sample cell versus time. The pressure up to time tj represents the equilibrium pressure in the sample cell before a new quantity of adsorbate is admitted. At time adsorbate is admitted into the sample cell and is accompanied by a rapid pressure rise. The pressure then gradually decreases to a new equilibrium value at time t2- If the decay to the new equilibrium pressure is slow, it is possible for open or accessible parts of the surface, such as the interior of wide pores, to contain more adsorbate before equilibrium is attained than after equilibrium is established. Less accessible regions, such as the interior of long narrow pores, will adsorb slowly and as the pressure falls because of adsorption in these pores, desorption must occur from the more accessible pores which tend to equilibrate more rapidly. If a porous sample is subjected to... 

A 1 1 relationship can be established between the coefficients of the polynomial jP(rj, rj, r ) in (55) and force constants of the triatomic transfened from the (r, r, oi) to e (j-p Tj, Tj) set. This leaves open the determination of the parameters 7p For H20,7i = 2 taken to be equal to the exponent in the OH diatomic potential of the form (45) and 73 was treated as a variable parameter which as a minimum requirement satisfied the condition that for the whole potential there were no physically accessible regions lower in energy than the equilibrium configuration. 

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