Acceptance rate

Here 6V = V -V and 5V= F-V. The maximum attempted volume change is chosen to give a reasonable acceptance rate, traditionally 35-50% or so there is no fimi reason for this choice. 

In a dense system, the acceptance rate of particle creation and deletion moves will decrease, and the number of attempts must be correspondingly increased eventually, there will come a point at which grand canonical simulations are not practicable, without some tricks to enliance the sampling. 

The idea may be illustrated by considering first a method for increasing the acceptance rate of moves (but at the expense of trying, and discarding, several other possible moves). Having picked an atom to move, calculate the new trial interaction energy for a range of trial positions t = 1.. . k. Pick the actual attempted move from this set, with a probability proportional to the Boltzmann factor. This biases the move selection. 

The main difference between the force-bias and the smart Monte Carlo methods is that the latter does not impose any limit on the displacement that m atom may undergo. The displacement in the force-bias method is limited to a cube of the appropriate size centred on the atom. However, in practice the two methods are very similar and there is often little to choose between them. In suitable cases they can be much more efficient at covering phase space and are better able to avoid bottlenecks in phase space than the conventional Metropolis Monte Carlo algorithm. The methods significantly enhance the acceptance rate of trial moves, thereby enabling Icirger moves to be made as well as simultaneous moves of more than one particle. However, the need to calculate the forces makes the methods much more elaborate, and comparable in complexity to molecular dynamics. 

In this section we discuss the initiation step of free-radical polymerization. This discussion is centered around initiators and their decomposition behavior. The first requirement for an initiator is that it be a source of free radicals. In addition, the radicals must be produced at an acceptable rate at convenient temperatures have the required solubility behavior transfer their activity to... 

Copolymers with butadiene, ie, those containing at least 60 wt % butadiene, are an important family of mbbers. In addition to synthetic mbber, these compositions have extensive uses as paper coatings, water-based paints, and carpet backing. Because of unfavorable reaction kinetics in a mass system, these copolymers are made in an emulsion polymerization system, which favors chain propagation but not termination (199). The result is economically acceptable rates with desirable chain lengths. Usually such processes are mn batchwise in order to achieve satisfactory particle size distribution. 

The lowest temperature for the reaction is 857°C but 1100—1300°C is required for acceptable rates. In this range, the two component reactions proceed at about the same rate and the reduction is diffusion controlled (54). Both reactions are reversible and the overall reaction is endothermic, requiting about 5.5 GJ/t Zn (1.2 X 10 cal/short ton Zn) at 1200 K. 

A standard Metropolis algorithm is used, whereby an attempted move of a randomly selected particle in a random direction Ax e [-1/2,1/2], Ay e [-1/2,1/2], Az G [-1/2,1/2] is accepted according to the standard Metropolis procedure [57] described above. The above displacement widths ensure a reasonably high acceptance rate A of the moves, of the order of... 

If the dynamics of a strongly adsorbed chain can be described by a two-dimensional Rouse model, with a smaller value of W (reflecting the decrease of the acceptance rate of the moves), and using the 2 / value 1 2 = 3/4, from Eqs. (15-21) one predicts... 

The effect of including attractive interactions with the walls is essentially to reduce the acceptance rate of the algorithm as more monomers get adsorbed on the walls. The relaxation times show an Arrhenius behavior, similar to the result on Fig. 9 in Sec. III. 

Both the solvent and ligand were found to play pivotal roles in the reaction. In dioxane the byproduct formation was minimized while acceptable rates and yields were retained. In these studies it was also shown that both n-Bu3P and Ph3P are efficient ligands for the hydrogenolysis, but it is important that the ligand Pd(0) ratio be kept below 1 [158]. 

Transmetalation of lithium enolate 1 a (M = Li ) by treatment with tin(II) chloride at — 42 °C generates the tin enolate that reacts with prostereogenic aldehydes at — 78 °C to preferentially produce the opposite aldol diastereomer 3. Diastereoselectivities of this process may be as high as 97 3. This reaction appears to require less exacting conditions since similar results are obtained if one or two equivalents of tin(ll) chloride arc used. The somewhat less reactive tin enolate requires a temperature of —42 C for the reaction to proceed at an acceptable rate. The steric requirements of the tin chloride counterion are probably less than those of the diethyla-luminum ion (vide supra), which has led to the suggestion26 44 that the chair-like transition state I is preferentially adopted26 44. This is consistent with the observed diastereoselective production of aldol product 3, which is of opposite configuration at the / -carbon to the major product obtained from aluminum enolates. 

The factor of 2 appears in the rate law because two N02 molecules are formed from each N202 molecule consumed. This expression is not yet an acceptable rate law for the overall reaction because it includes the concentration of an intermediate, N202, and intermediates do not appear in the overall rate law for a reaction. 

The effectiveness of catheter-based intra-arterial therapy to remove residual thrombus after IV rt-PA treatment is being tested in the Interventional Management of Stroke study (IMS-Ill). This study will randomize patients to 0.6 mg/kg IV rt-PA, followed by angiography with additional intra-arterial therapy as indicated, or IV full-dose rt-PA (0.9 mg/kg). A nonrandomized safety study suggested that intraarterial therapy, after 0.6 mg/kg IV rt-PA, could be accomphshed with acceptable rates of sICH. ° ... 

It appeared that, we needed to limit or omit the ethyl iodide if we were going to operate the ethylene carbonylation in ionic liquids. Unfortunately, the previous literature indicated that EtI or HI (which are interconvertible) represented a critical catalyst component. Therefore, it was surprising when we found that, in iodide based ionic liquids, the Rh catalyzed carbonylation of ethylene to propionic acid was still operable at acceptable rates in the absence of ethyl iodide, as shown in Table 37.2. Further, we not only achieved acceptable rates when omitting the ethyl iodide, we also achieved the desired reduction in the levels of ethyl propionate. More importantly, when the reaction products were analyzed, there was no detectable ethyl iodide formed in situ. However, we should note that we now observed traces of ethanol which were normally undetectable in the earlier Ed containing experiments. 

The method based on the orientation of pairs of vectors of length L produces slower dynamics than the method based on next-nearest neighbor distances. Since the acceptance rates for single-bead moves differ very little in the two methods, it appears that the probability for immediate reversal of a successful move is higher in the method based on the orientation of the pairs of vectors, such that the chain shivers rapidly, but moves its center of mass slowly. This problem is more severe in PP melts than in PE melts. Significant diffusion of the center of mass of the chains in PP melts is achieved when reptation, as well as single-bead moves, is allowed [158, 158A]. 

Avoidance of the intramolecular collapses in PE can be achieved by selection of a relationship between the 2nnd lattice and its underlying diamond lattice at the outset of the simulation, and then prohibition of occupation by three beads of that half of the equilateral triangles with area L2/2 that form the local collapse. Implementation of this restriction did not decrease the acceptance rate significantly (the decrease is less than 1%) in our simulations of amorphous PE at bulk density. The acceptance rate is scarcely affected because the moves that would have created the intramolecular collapse were already of low probability, due to their weighting by oj, which is much less than one. There was, however, a reduction in the mean square displacement of the center of mass per MC step, as discussed in Sect. 4.3.1.3. 

A trial move of an atom consisted of a small displacement in its position and momentum simultaneously. Step lengths of 0.9 in velocity and 0.09 in position gave an acceptance rate of about 50%. A cycle consisted of one trial move of all the atoms. 

What can be considered as an acceptable rate of attack will depend on the cost of the material the duty, particularly as regards to safety and the economic life of the plant. For... 

In the standard HMC method two ingredients are combined to sample states from a canonical distribution efficiently. One is molecular dynamics propagation with a large time step and the other is a Metropolis-like acceptance criterion [76] based on the change of the total energy. Typically, the best sampling of the configuration space of molecular systems is achieved with a time step of about 4 fs, which corresponds to an acceptance rate of about 70% (in comparison with 40-50% for Metropolis MC of pure molecular liquids). 

Initially, the as-received pump could not pass a 13.8-bar (200 psig) static pressure test at ambient temperature. Consequently, the pump was returned to the manufacturer for extensive seal modifications. Upon receiving the modified pump, the unit was placed into service for a hot shakedown test with C30 oil at 175 psig pressure under the present experimental setup. The modified seal continued to leak at a small but acceptable rate on the order of 1 g/min. However, leak problems were encountered in the threaded seal of the stator and the pump housing. The stator was resealed with a thick Teflon tape and a high-temperature pipe sealant that initially slowed the total system leaks to less than 50 g/h. 

Your minimum acceptable rate of return (MARR) is 18%, the project life is 10 years, and no alternatives have a salvage value. The following mutually exclusive alternatives have been proposed. Rank them, and recommend the best alternative. 

---