PRIORITIZED TASK SCHEDULING IN FOG COMPUTING

Cloud computing is an environment where virtual resources are shared among the many users over network. A user of Cloud services is billed according to pay-per-use model associated with this environment. To keep this bill to a minimum, efficient resource allocation is of great importance. To handle the many requests sent to Cloud by the clients, the tasks need to be processed according to the SLAs defined by the client. The increase in the usage of Cloud services on a daily basis has introduced delays in the transmission of requests. These delays can cause clients to wait for the response of the tasks beyond the deadline assigned. To overcome these concerns, Fog Computing is helpful as it is physically placed closer to the clients. This layer is placed between the client and the Cloud layer, and it reduces the delay in the transmission of the requests, processing and the response sent back to the client greatly. This paper discusses an algorithm which schedules tasks by calculating the priority of a task in the Fog layer. The tasks with higher priority are processed first so that the deadline is met, which makes the algorithm practical and efficient

Graphene with wedge disclination in the presence of intrinsic and Rashba spin orbit couplings

In this article, the modified Kane-Mele Hamiltonian is derived for graphene with wedge disclination and spin orbit couplings (intrinsic and Rashba). The wedge disclination changes the flat lattice into the conical lattice and hence modifies the spin orbit couplings. The Hamiltonian is exactly solved for the intrinsic spin orbit interaction and perturbatively for the Rashba spin orbit interaction. It is shown that there exists the Kramer's degenerate midgap localized spin separated fluxon states around the defect. These zero energy spin separated states occur at the external magnetic flux value $\Phi\pm\Delta\Phi$. The external magnetic flux $\Phi$ is introduced to make the wave-function periodic when the electron circulates around the defect. It is found that this separation occurs due to the effect of the conical curvature on the spin orbit coupling. Further, we find these results are robust to the addition of the Rashba spin orbit interaction which is important for the application to spintronics and nanoelectronics.Comment: 6 pages ,3 figures ,Change in titl

Boundary-layer receptivity due to distributed surface imperfections of a deterministic or random nature

Acoustic receptivity of a Blasius boundary layer in the presence of distributed surface irregularities is investigated analytically. It is shown that, out of the entire spatial spectrum of the surface irregularities, only a small band of Fourier components can lead to an efficient conversion of the acoustic input at any given frequency to an unstable eigenmode of the boundary layer flow. The location, and width, of this most receptive band of wavenumbers corresponds to a relative detuning of O(R sub l.b.(exp -3/8)) with respect to the lower-neutral instability wavenumber at the frequency under consideration, R sub l.b. being the Reynolds number based on a typical boundary-layer thickness at the lower branch of the neutral stability curve. Surface imperfections in the form of discrete mode waviness in this range of wavenumbers lead to initial instability amplitudes which are O(R sub l.b.(exp 3/8)) larger than those caused by a single, isolated roughness element. In contrast, irregularities with a continuous spatial spectrum produce much smaller instability amplitudes, even compared to the isolated case, since the increase due to the resonant nature of the response is more than that compensated for by the asymptotically small band-width of the receptivity process. Analytical expressions for the maximum possible instability amplitudes, as well as their expectation for an ensemble of statistically irregular surfaces with random phase distributions, are also presented

Transition Delay via Vortex Generators in a Hypersonic Boundary Layer at Flight Conditions

The potential of realizable, stationary streaks undergoing non-modal growth to stabilize a hypersonic boundary-layer flow and, subsequently, delay the laminar-turbulent transition onset, is studied via numerical computations. The geometry and flow conditions are selected to match a relevant trajectory location from the ascent phase of the HIFiRE-1 flight experiment, namely, a 7-degree half-angle cone with 2.5 mm nose radius, freestream Mach number of 5.30, freestream unit Reynolds number equal to 13.42 x 10(exp 6)/m, and wall-to-adiabatic temperature ratio of approximately 0.35 over most of the test article. This paper investigates flow modifications induced by wall-mounted vortex generators (VGs), followed by an analysis of the modal instability of the perturbed, streaky boundary-layer flow. Results are presented both for a single array of VGs that was designed on the basis of optimal growth theory and for a VG configuration involving two separate arrays with opposite orientations that ware designed to provide staged control of flow instabilities while simultaneously reducing the amplification of streak instabilities resulting from the control devices. Earlier research had shown that the onset of transition during the HIFiRE-1 flight experiment, which did not include any control devices, correlated with an amplification factor of N = 14.7 for the planar Mack modes. If one assumes that the transition N -factor is not affected by the introduction of the VGs, then the control configurations based on a single array of VGs and two separate arrays would result in a transition delay of 17% and 40%, respectively. These findings suggest a passive flow control s to induce streaks that would delay transition in hypersonic boundary dominated by Mack-mode instabilities

A finite Reynolds number approach for the prediction of boundary layer receptivity in localized regions

Previous theoretical work on the boundary layer receptivity problem has utilized large Reynolds number asymptotic theories, thus being limited to a narrow part of the frequency - Reynolds number domain. An alternative approach is presented for the prediction of localized instability generation which has a general applicability, and also accounts for finite Reynolds number effects. This approach is illustrated for the case of Tollmien-Schlichting wave generation in a Blasius boundary layer due to the interaction of a free stream acoustic wave with a region of short scale variation in the surface boundary condition. The specific types of wall inhomogeneities studied are: regions of short scale variations in wall suction, wall admittance, and wall geometry (roughness). Extensive comparison is made between the results of the finite Reynolds number approach and previous asymptotic predictions, which also suggests an alternative way of using the latter at Reynolds numbers of interest in practice

Nonlinear Grtler Vortices and Their Secondary Instability in a Hypersonic Boundary Layer

Nonlinear development of the Grtler instability over a concave surface gives rise to a highly distorted inflectional flow field in the boundary layer that leads to both wall-normal and spanwise gradients in the flow. Such nonlinear structures are susceptible to strong, high-frequency secondary instabilities that may lead to the onset of laminar-turbulent transition. The present numerical study uses direct numerical simulations and linear secondary instability theory to investigate finite amplitude Grtler vortices and their secondary instability characteristics, respectively, in the hypersonic flow over an axisymmetric cone with a concave aft body. To complement previous studies in the literature wherein the Grtler instability was usually studied for a flat plate and initiated at some upstream location by imposing an eigenfunction as the inflow condition or by blowing and suction at the wall, the present investigation is focused on fully realizable Grtler instability that is excited by an azimuthally periodic array of surface protuberances. Furthermore, while the previous work had mostly focused on the secondary instability of Grtler vortices with cross-plane velocity contours that resembled bell-shaped structures, the present results confirm that fully developed mushroom structures also exist in the hypersonic regime when the Grtler vortex amplitude is sufficiently large. Computations further reveal that the dominant modes of secondary instability in these mushroom-shaped structures correspond to an antisymmetic (i.e., sinuous) stem mode that concentrates within the strong, nearly wall-normal internal shear layers surrounding the stem regions underneath the caps of the mushroom structures. Additionally, there exist a multitude of other significantly unstable secondary instability modes of both symmetric and antisymmetric types. Analogous to the secondary instability of crossflow vortices in hypersonic flows, secondary instability modes of both symmetric and antisymmetric types. Analogous to the secondary instability of crossflow vortices in hypersonic flows, secondary instability modes originating from the Mack mode instability play an important role during the nonlinear breakdown process

Instability WaveStreak Interactions in a High Mach Number Boundary Layer at Flight Conditions

The interaction of stationary streaks undergoing nonmodal growth with modally unstable instability waves in a hypersonic boundary-layer flow is studied using numerical computations. The geometry and flow conditions are selected to match a relevant trajectory location from the ascent phase of the HIFiRE-1 ight experiment; namely, a 7 degree half-angle, circular cone with 2:5 mm nose radius, freestream Mach number equal to 5:30, unit Reynolds number equal to 13:42 m-1, and wall-to-adiabatic temperature ratio of approximately 0:35 over most of the vehicle. This paper investigates the nonlinear evolution of initially linear optimal disturbances that evolve into finite-amplitude streaks, followed by an analysis of the modal instability characteristics of the perturbed, streaky boundary-layer flow. The investigation is performed with stationary direct numerical simulations (DNS) and plane-marching parabolized stability equations (PSE), in conjunction with partial-differential-equation-based planar eigenvalue analysis. The overall effect of streaks is to reduce the peak amplification factors of instability waves, indicating a possible downstream shift in the onset of laminar-turbulent transition. The present study conforms previous findings that the mean flow distorsion of the nonlinear streak perturbation reduces the amplification rates of the Mack-mode instability. More importantly, however, the present results demonstrate that the spanwise varying component of the streak can produce a larger effect on the Mack-mode amplification. The study with selected azimuthal wavenumbers for the stationary streaks reveals that a wavenumber of approximately 1:4 times larger than the optimal wavenumber is more effective in stabilizing the planar Mack-mode instabilities. In the absence of unstable first-mode waves for the present cold-wall condition, transition onset is expected to be delayed until the peak streak amplitude increases to nearly 35 percent of the freestream velocity, when intrinsic instabilities of the boundary-layer streaks begin to dominate the transition process. For streak amplitudes below that limit a significant net stabilization is achieved, yielding a potential transition delay that can exceed 100 percent of the length of the laminar region in the uncontrolled case

DNS of Laminar to Turbulent Transition on NACA 0012 Airfoil with Sand Grain Roughness

The Lattice-Boltzmann-based solver PowerFLOW is used to perform direct numerical simulations of the transitional flow over an airfoil at Reynolds number equal to 0.657 million. The leading edge of the airfoil is covered with sand particles, represented by polyhedra, to mimic the grit used in experiments. The sensitivity of the laminar to turbulent transition to the size of these particles, grid resolution, spanwise length is evaluated and rectangular trips are also tested