Dynamic task distribution

The load imbalance resulting from a dynamic distribution of tasks is very difficult to model because the times required for the individual computational tasks are not known in advance. Provided that the number of tasks is much larger than the number of processes, however, it is reasonable to assume that the dynamic task distribution will enable an essentially even distribution of the load. For this to remain true as the number of processes increases, the number of tasks, umn, must increase proportionally to p. Although this is the same growth rate as obtained for a static work distribution, the actual value for umn needed for high efficiency for a given process count is much smaller for the dynamic distribution, and the assumption of perfect load balance is therefore adequate for our purposes. 

Processes request tasks (atom quartets) by calling the function get quartet, which has been implemented in both a dynamic and a static version. The dynamic work distribution uses a manager-worker model with a manager process dedicated to distributing tasks to the other processes, whereas the static version employs a round-robin distribution of tasks. When the number of processes is small, fhe sfafic scheme achieves the best parallel performance because the dynamic scheme, when run on p processes, uses only p - 1 processes for compulation. As the number of processes increases, however, the parallel performance for the dynamic task distribution surpasses that of the static scheme, whose efficiency is reduced by load imbalance. Wifh fhe entire Fock and density matrix available to every process, no communication is required during the computation of the Fock matrix other than the fetching of tasks in the dynamic scheme. After all ABCD tasks have been processed, a global summation is required to add the contributions to the Fock matrix from all processes and send the result to every process. 

Outline of a parallel algorithm for Fock matrix formation using replicated Fock and density matrices. A, B, C, and D represent atoms M, N, R, and S denote shells of basis functions. The full integral permutational symmetry is utilized. Each process computes the integrals and the associated Fock matrix elements for a subset of the atom quartets, and processes request work (in the form of atom quartets) by caUing the function get quartet. Communication is required only for the final summation of the contributions to F, or, when dynamic task distribution is used, in get quartet. 

As discussed in section 7.3, it is advantageous from a load balancing perspective, when using a dynamic task distribution, to process computationally expensive blocks first however, if we are otherwise careless about the order in which tasks are processed, it is possible for all of the tasks to simultaneously request the same density block, resulting in a communication bottleneck for the process holding that block. Thus, even when dynamic task distribution is used, some degree of randomization is employed in the task ordering. 

BR assumptions by age and level of exercise are taken from the ICRP Committee 2 report by the Lung Dynamics Task Group (ICRP, 1960). These data are also used in ICRP 66 as the basis for BR estimates. ICRP 2 data were used to derive a distribution of annual BRs using a simple Monte Carlo technique to simulate assumed activity levels (Hamby, 1993). BR distributions are determined by two different methods for adults and children. Adult males and females, 15-year-old males and females, and 10-year-old children are handled in a similar manner. The methodology is similar for 5-year-old children, 1-year-old children and 3-month-old infants, but distinct from the method employed for more mature age groups. 

Outline of a dynamic manager-worker task distribution scheme. The number of tasks and processes are designated ntask and p, respectively. One process is assigned to be the manager, and the remaining p — 1 processes are the workers. 

For direct reactions, the calculation of Fim(T) is a complicated dynamical task. However, it has often been found that the results of both dynamic calculations and of experiments can be described by the distribution Fim(T) which is in turn relatively simply expressed via Ff (T) (the so-called surprisal plot) [39, 270]... 

The calculation of the time evolution operator in multidimensional systems is a fomiidable task and some results will be discussed in this section. An alternative approach is the calculation of semi-classical dynamics as demonstrated, among others, by Heller [86, 87 and 88], Marcus [89, 90], Taylor [91, 92], Metiu [93, 94] and coworkers (see also [83] as well as the review by Miller [95] for more general aspects of semiclassical dynamics). This method basically consists of replacing the 5-fimction distribution in the true classical calculation by a Gaussian distribution in coordinate space. It allows for a simulation of the vibrational... 

The study of dynamics of a real polymer chain of finite length and containing some conformational defects represents a very difficult task. Due to the lack of symmetry and selection mles, the number of vibrational modes is enormous. In this case, instead of calculating the frequency of each mode, it is more convenient to determine the density of vibrational modes, that is, the number of frequencies that occur in a given spectral interval. The density diagram matches, apart from an intensity factor, the experimental spectmm. Conformational defects can produce resonance frequencies when the proper frequency of the defect is resonating with those of the perfect lattice (the ideal chain), or quasi-localized frequencies when the vibrational mode of the defect cannot be transmitted by the lattice. The number and distribution of the defects may be such... 

The Okhotsk Sea aquatory is divided into zones having specific ecological features (Suzuki, 1992). The spatial distribution of the fish biomass depends on seasonal conditions and to a great extent correlates with the layers outlined above. The use of sea biological resources is a function of this distribution. Fishing intensity essentially depends on knowledge of the biomass distribution in zones with specific environmental conditions. Many authors (Plotnikov, 1996 Aota et al., 1992) have tried to solve this task by means of models simulating ecosystem dynamics. However,... 

One reason to use micro structured reaction chambers is certainly the possibility of describing the fluid dynamic behavior in these structures due to the laminar flow regime. With the following calculations the reactive gas flow in a square micro structure with coated catalytically active walls will be studied in detail. The task was to find a channel arrangement and to calculate the residence time distribution of this arrangement numerically (Figure 4.93). 

Recall that in Section 10.3 we worked out a detailed theory for the equilibrium distribution for the reaction A + 11 C. Here the task is to determine the governing differential equation (chemical master equation) for the dynamics of the state probabilities in Equation (11.5). 

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