Numbers random

A random number (between 0 and 1) is picked, and the associated value of gross reservoir thickness (T) is read from within the range described by the above distribution. The value of T close to the mean will be randomly sampled more frequently than those values away from the mean. The same process is repeated (using a different random number) for the net-to-gross ratio (N/G). The two values are multiplied to obtain one value of net sand thickness. This is repeated some 1,000-10,000 times, with each outcome being equally likely. The outcomes are used to generate a distribution of values of net sand thickness. This can be performed simultaneously for more than two variables. 

The vector of errors at time t is e t). The essential assumption which we made is that e t) is a Gaussian random number, and that the errors are not correlated in time. 

The network is initialized, and all the weights of the neurons obtain numerical values, in most cases random numbers. 

IlyperChem can either use initial velocilies gen eraled in a previous simulation or assign a Gaussian distribution of initial velocities derived from a random n iim her generator. Random numbers avoid introducing correlated motion at the beginn ing of a sim illation. ... 

One option is to first generate two random numbers and 2 between 0 and 1. T1 corresponding two numbers from the normal distribution are then calculated using... 

An alternative approach is to generate twelve random numbers, ..., 2 and then calculal... 

These two methods generate random numbers in the normal distribution with zero me< and unit variance. A number (x) generated from this distribution can be related to i counterpart (x ) from another Gaussian distribution with mean (x ) and variance cr using... 

Qj is a random number with zero mean and unit variance, chosen independently for each pair of particles and at each time step in the integration. 

Fig. 8.2 Simple Monte Carlo integration, (a) The shaded area under the irregular curve equals the ratio of the number of random points under the curve to the total number of points, multiplied by the area of the bounding area, (b) An estimate of tt can be obtained by generating random numbers within the square, v then equals the number of points within the circle divided by the total number of points within the square, multiplied by 4.

As an alternative to the random selection of particles it is possible to move the atom sequentially (this requires one fewer call to the random number generator per iteration) Alternatively, several atoms can be moved at once if an appropriate value for the maximun displacement is chosen then this may enable phase space to he covered more efficiently. 

If AH is negative then the move is accepted otherwise, exp —AH/k T) is compared to random number between 0 and 1 and the move accepted according to ... 

Having generated a trial conformation it must be decided whether to accept it or not. To d this a random number is generated in the range 0-1 and compared with the ratio of tf Rosenbluth weights for the trial conformation (W trial) and the old conformation (W/oid The new chain is then accepted using the following criterion ... 

The second generator is an arithmetic sequence method that generates random number using the following mathematical operation ... 

Marsaglia G, A Zaman and W W Tsang 1990. Towards a Universal Random Number Generate Statistics and Probability Letters 8 35-39. 

Sharp W E and C Bays 1992. A Review of Portable Random Number Generators. Computers at Geosciences 18 79-87. 

The energies may be random within some fixed range. Random-number generators use this property intentionally. 

Here, y is the friction coefficient of the solvent, in units of ps and Rj is the random force imparted to the solute atoms by the solvent. The friction coefficient is related to the diffusion constant D of the solvent by Einstein s relation y = kgT/mD. The random force is calculated as a random number, taken from a Gaussian distribu-... 

If Restart is not checked then the velocities are randomly assigned in a way that leads to a Maxwell-Boltzmann distribution of velocities. That is, a random number generator assigns velocities according to a Gaussian probability distribution. The velocities are then scaled so that the total kinetic energy is exactly 12 kT where T is the specified starting temperature. After a short period of simulation the velocities evolve into a Maxwell-Boltzmann distribution. 

To analyze the properties of a 100 cm X 100 cm polymer sheet, ten 1 cm X 1 cm samples are to be selected at random and removed for analysis. Explain how a random number table can be used to ensure that samples are drawn at random. 

A shipment of 100 barrels of an organic solvent is to be evaluated by collecting and analyzing single samples from 10 of the barrels. A random number table is used to determine the barrels to be sampled. From which barrels should the samples be drawn if the first barrel is given by the twelfth entry in the random number table in Appendix IE, with subsequent barrels given by every third entry ... 

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