331,624 research outputs found

    Joint Cache Partition and Job Assignment on Multi-Core Processors

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    Multicore shared cache processors pose a challenge for designers of embedded systems who try to achieve minimal and predictable execution time of workloads consisting of several jobs. To address this challenge the cache is statically partitioned among the cores and the jobs are assigned to the cores so as to minimize the makespan. Several heuristic algorithms have been proposed that jointly decide how to partition the cache among the cores and assign the jobs. We initiate a theoretical study of this problem which we call the joint cache partition and job assignment problem. By a careful analysis of the possible cache partitions we obtain a constant approximation algorithm for this problem. For some practical special cases we obtain a 2-approximation algorithm, and show how to improve the approximation factor even further by allowing the algorithm to use additional cache. We also study possible improvements that can be obtained by allowing dynamic cache partitions and dynamic job assignments. We define a natural special case of the well known scheduling problem on unrelated machines in which machines are ordered by "strength". Our joint cache partition and job assignment problem generalizes this scheduling problem which we think is of independent interest. We give a polynomial time algorithm for this scheduling problem for instances obtained by fixing the cache partition in a practical case of the joint cache partition and job assignment problem where job loads are step functions

    An advanced meshless method for time fractional diffusion equation

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    Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations

    Flow Induced by the Impulsive Motion of an Infinite Flat Plate in a Dusty Gas

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    Flow Induced by the Impulsive Motion of an Immite Flat Plate in a Dusty Gas. The problem of flow induced by an infinite flat plate suddenly set into motion parallel to its own plane in an incompressible dusty gas is of considerable physical interest in its own right as well as because of its close relation to the non-linear, steady (constant-pressure) laminar boundary layer. Its solution provides complete and exact information about modifications of the boundary layer growth and skin friction due to particle-fluid interaction. Moreover, it provides a basis for judging the accuracy of approximations which have been employed in more complex problems of viscous fluid-particle motion. The uncoupled thermal Rayleigh problem for small relative temperature differences is directly inferred and this answers questions about the modifications of the surface heat transfer rate and about the possibility of similarity with the velocity boundary layer. Similarity is possible when, in addition to a Prandtl number of unity, the streamwise relaxation processes are also similar

    Revisiting the hot matter in the center of gamma-ray bursts and supernova

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    Hot matter with nucleons can be produced in the inner region of the neutrino-dominated accretion flow in gamma-ray bursts or during the proto-neutron star birth in successful supernova. The composition and equation of state of the matter depend on the dynamic β\beta equilibrium under various neutrino opacities. The strong interaction between nucleons may also play an important role. We plan to extend the previous studies by incorporating these two aspects in our model. The modification of the β\beta-equilibrium condition from neutrino optically thin to thick has been modeled by an equilibrium factor χ\chi ranging between the neutrino-freely-escaping case and the neutrino-trapped case. We employ the microscopic Brueckner-Hartree-Fock approach extended to the finite temperature regime to study the interacting nucleons. We show that the composition and chemical potentials of the hot nuclear matter for different densities and temperatures at each stage of β\beta equilibrium. We also compare our realistic equation of states with those of the free gas model. We find the neutrino opacity and the strong interaction between nucleons are important for the description and should be taken into account in model calculations.Comment: accepted Astronomy & Astrophysics (2013