In the present work we develop a Monte Carlo algorithm of the carbon chains ordered into 2D hexagonal array.The chemical bond of the chained carbon is computed from 1K to 1300K. Our model confirms that the beta phase is more energetic preferable at low temperatures but the system prefers the alpha phase at high temperatures. Based on the thermal effect on the bond distributions and 3D atomic vibrations in the carbon chains, the bond softening temperature is observed at 500K. The bond softening temperature is higher in the presence of interstitial doping but it does not change with the length of nanowire. The elastic modulus of the carbon chains is 1.7TPa at 5K and the thermal expansion is +7 x 10 -5 K -1 at 300K via monitoring the collective atomic vibrations and bond distributions. Thermal fluctuation in terms of heat capacity as a function of temperatures is computed in order to study the phase transition across melting point. The heat capacity anomaly initiates around 3800K.

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In this paper we present a new data partitioning algorithm to improve the performance of parallel matrix multiplication of dense square matrices on heterogeneous clusters. Existing algorithms either use single speed performance models which are too simplistic or they do not attempt to minimise the total volume of communication. The functional performance model (FPM) is more realistic then single speed models because it integrates many important features of heterogeneous processors such as the processor heterogeneity, the heterogeneity of memory structure, and the effects of paging. To load balance the computations the new algorithm uses FPMs to compute the area of the rectangle that is assigned to each processor. The total volume of communication is then minimised by choosing a shape and ordering so that the sum of the halfperimeters is minimised. Experimental results demonstrate that this new algorithm can reduce the total execution time of parallel matrix multiplication in comparison to existing algorithms.

Heterogeneous multiprocessor systems, which are composed of a mix of processing elements, such as commodity multicore processors, graphics processing units (GPUs), and others, have been widely used in scientific computing community. Software applications incorporate the code designed and optimized for different types of processing elements in order to exploit the computing power of such heterogeneous computing systems. In this paper, we consider the problem of optimal distribution of the workload of data-parallel scientific applications between processing elements of such heterogeneous computing systems. We present a solution that uses functional performance models (FPMs) of processing elements and FPM-based data partitioning algorithms. Efficiency of this approach is demonstrated by experiments with parallel matrix multiplication and numerical simulation of lid-driven cavity flow on hybrid servers and clusters.