Equal-weight, rule

The location of phase coexistence can be accurately estimated by the equal-weight rule [63] Two phases coexist if the weights of the two corresponding peaks in the distribution function of the order parameter are equal. It is important for the system to tunnel often between the two phases in... 

Thus the equal weight-rule rephrases the macroscopic definition of phase coexistence Two phases coexists if they have equal pressure at equal chemical potential. 

Figure 14 exemplifies two computational methods to determine the probability distribution of composition for binary polymer blends described by the bond fluctuation model [67]. Phase coexistence can be extracted from these data via the equal-weight rule. For the specific example of a symmetric blend, the coexistence value of the exchange chemical potential, A/u, is dictated by the S3munetry. One can simply simulate at A oex = 0 and monitor the composition. Nevertheless, the probability distribution contains additional information, as discussed in Sect. 3.5. 

The techniques (e.g., weighted histogram analysis, equal weight rule, etc.) utilized for one-component systems or incompressible binary mixtures can be readily carried over to compressible systems. Since the system is described by two order parameters one monitors the joint probability distribution of... 

Ideally, the bimodal line in density and nematic order as a functionof temperature and chemical potential would be determined by applying the equal weight rule to the probability distributions of density and ne-... 

The equal valence rule translates into sums around circuits on the connectivity matrix. There are three four-circuits yielding three equations, of which only two eire independent. These are given here without weights for simplicity ... 

The rules proposed by Wein are not easy to compute for general multiclass M/G/ queues, and hence, their applicability in practice may be limited. Wein derives these rules for a special case with only two classes of jobs, exponential processing times and equal weights for each class. To test the performance... 

Ether Soap,—Another form of medicated soap made by a few firms is a liquid ether soap containing mercuric iodide, and intended for surgeons use. This, as a rule, consists of a soap made from olive oil and potash, dissolved in alcohol and mixed with ether, the mercuric iodide being dissolved in a few drops of water containing an equal weight of potassium iodide, and this solution added to the alcohol-ether soap. ... 

This ensemble is a weighted superposition of NVT ensembles with different values, of N. As a rule of tiuiinb, a typical MC sweep consists of N attempted moves, each of which is chosen randomly to be (i) a displacement (liandled exactly as in constant-AfTMC) (ii) the creation of a new particle at a randomly selected position (iii) the destruction of a randomly selected particle from the system. The probabilities for attempting creation and destniction must be equal (for consistency with what follows), but they need not be equal to the probability for attempting displacement (although they often are). 

Several arbitrary rules of thumb have been suggested to account for the reduction in efficiency when moisture particles are present. One is to multiply the efficiency by the mean vapor content, by weight. For example, if expansion is started in the superheated region and ends with 6% by weight of liquid, the mean vapor content is 97%. If the design efficiency is 78%, the adjusted value of efficiency is 0.78 (0.97) = 0.757 or 75.7%. Some designers prefer to assume a loss equal to twice the value used in the example. 

There is a fundamental relationship between d-dimensional PCA and d + 1)-dimensional Ising spin models. The simplest way to make the connection is to think of the successive temporal layers of the PCA as successive hyper-planes of the next higher-dimensional spatial lattice. Because the PCA rules (at least the set of PCA rules that we will be dealing with) are (1) Markovian (i.e. the probability of a state at time t + T depends only on a set of states at time t, and (2) local, one can always define a Hamiltonian on the higher-dimensioned spatial lattice such that the thermodynamic weight of a configuration 5j,( is equal to the probability of a corresponding space-time history Si t). ... 

As we shall see in the next section, the output of a node is computed from its total input the bias provides a threshold in this computation. Suppose that a node follows a rule that instructs it to output a signal of +1 if its input is greater than or equal to zero, but to output zero otherwise. If the input signal from the bias node, after multiplication by the connection weight, was +0.1, the remaining inputs to the node would together have to sum to a value no smaller than -0.1 in order to trigger a... 

Compton rule phys chem An empirical law stating that the heat of fusion of an element times its atomic weight divided by its melting point in degrees Kelvin equals approximately 2. kam-ton, rul ... 

Stoichiometry. The measurement of reactants and products of a chemical reaction. Fundamentals, rule that the combined weights of reactants will equal combined weights of products in reactions going to completion. 

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