Dynamic algorithms for multicast with intra-session network coding

The problem of multiple multicast sessions with intra-session network coding in time-varying networks is considered. The network-layer capacity region of input rates that can be stably supported is established. Dynamic algorithms for multicast routing, network coding, power allocation, session scheduling, and rate allocation across correlated sources, which achieve stability for rates within the capacity region, are presented. This work builds on the back-pressure approach introduced by Tassiulas et al., extending it to network coding and correlated sources. In the proposed algorithms, decisions on routing, network coding, and scheduling between different sessions at a node are made locally at each node based on virtual queues for different sinks. For correlated sources, the sinks locally determine and control transmission rates across the sources. The proposed approach yields a completely distributed algorithm for wired networks. In the wireless case, power control among different transmitters is centralized while routing, network coding, and scheduling between different sessions at a given node are distributed

An Aerodynamic Assessment of Vehicle-Side Wall Interaction using Numerical Simulation

The effects of induced pressure loads from a realistic vehicle onto the surface of a road-side wall are numerically investigated. Parameters such as vehicle speeds, vehicle-wall separation distances and the effects of inclined walls are examined to numerically characterise the vehicle-wall interactions. Aerodynamic characteristics such as the drag, lift, side forces and pressure co-efficients are analysed on the vehicle to provide a basis for comparison between each of the aforementioned variations. Our results demonstrate that a smaller separation distance between vehicle and wall enhances the pressure induced on both the wall and car which is found to be consistent with the experimental data published previously. We find that the presence of a wall in close proximity to the passing vehicle unfavourably influences the induced pressure on the side-wall and abruptly increases the drag, lift and side forces experienced by the vehicle. For a vertical side-wall, from a wall separation point of view, a separation distance of 1.35 normalised by the height of the vehicle tends to retrieve the cars’ original drag and lift value. In addition, our results demonstrate that a wall inclined to the ground favourably influences the aerodynamic characteristics of the vehicle compared to its vertical counterpart

Breakup and coalescence of drops during transition from dripping to jetting in a Newtonian fluid

We present numerical simulations of dripping to jetting transitions that occur during the flow of a Newtonian liquid. An axi-symmetric, Volume of Fluid (VOF) model along with Continuum Surface Force (CSF) representation is developed to capture various regimes of drop formation. By numerically studying different nozzle diameters subjected to various flow rates, we examine the critical conditions under which the dripping to jetting transition takes place. At every stage of dripping and jetting, we assess the accuracy of the present simulations through a number of comparisons with previously published experimental data and empirical correlation and find reasonable agreements. Our numerical simulations show different responses that characterize the dripping and the dripping faucet regimes leading to chaotic dripping patterns. Within the chaotic regime, we identify four unique modes of satellite formation and their merging patterns which have not been reported earlier. Finally, we observe that as soon as the flow rate approaches a threshold the jetting regime begins where, subsequent disintegration of drops and coalescence patterns are observed downstream. Detailed flow patterns, pressure distributions and drop shapes are provided for various dimensionless numbers alongside the spatial-temporal resolutions of both jetting and coalescence of primary drops. Of the many complex dynamics that influence the primary droplet coalescence, we find that the oscillatory motion of drops during their travel downstream, which is dampened normally due to viscous effects, can be influential and can aid both coalescence and breakup of droplets

Formation and merging of satellite droplets disintegrated from laminar liquid jets

Numerical simulations of the break-up of laminar liquid jets are presented that reveal the formation of satellite droplets resulting from (i) the non-linear disintegration of jet liquid core and (ii) coalescence of two primary droplets. For the case(i), when satellites disintegrate from the jet liquid core, they tend to show forward, rear and simultaneous merging responses on both the aft side as well as the foreside of the primary droplets that are present downstream that were evidenced experimentally by Vassallo and Ashgriz (1991). However, for the case (ii) the satellites that are formed show similarities with that observed by Zhang et al. (2009) for two stationary droplets at the onset of coalescence. However,our numerical results predict that when two primary drops disintegrated from a liquid jet, that undergoes surface oscillations coalesce, satellites can pinch-off from both the fore-side and the aft-side of the coalesced droplet with effective diameter ratios as small as d1/d2-1.15, 1.97 �respectively. Effect of pressure waves during binary droplet coalescence and the subsequent pinch-off dynamics for satellite formation is presented

Oscillatory motion and merging responses of primary and satellite droplets from Newtonian liquid jets

Numerical simulations of laminar Newtonian liquid jets are presented that divulge several breakup and merging responses for both primary and satellite droplets. Using an axisymmetric VOF model, we predict the presence of surface oscillations of droplets disintegrated from jets, which at times lead to merging of droplets when travelling downstream. Our simulations indicate that when primary droplets undergo merging, they exhibit characteristics such as i) permanent and ii) partial coalescence. We find that the partial coalescence of droplets can lead to a reflexive-like separation and then show re-merge responses. The formation of an air-bubble during the merging of binary droplets is predicted. Characteristics such as forward, rear, and simultaneous merging patterns of satellites with primary droplets are captured in our numerical simulations. Furthermore, a new merging pattern is reported wherein, satellites formed from the swellings of the jet can be absorbed back into the moving core of the liquid jet