Tracking space-filling features by two-step optimization

Nowadays, the global increase of energy demand and the necessity to satisfy high safety standards have led engineers and scientists to focus their efforts in order to understand and describe fundamental phenomena that are crucial for a correct design of the new generation nuclear power plants. In this framework, the present thesis aims at providing a first insight of the mechanisms of deposition of aerosol particles inside a closed geometry where relatively strong currents are present due to turbulent natural convective flows. Direct Numerical Simulations were conducted coupling high-order pseudo-spectral code with a Lagrangian particle tracker. Laminar flows were computed in two and three dimensions in order to benchmark the code with published reference data. A parametric study was performed for three different aerosol micro-size particle diameters and two super-critical Rayleigh numbers in a square cavity. An extended analysis of the turbulent flows is provided in terms of first and second order statistics, time-averaged momentum and energy budgets, and moreover, important terms appearing in the transport equations of turbulent kinetic energy and temperature variance are also briefly discussed. Furthermore, the evolution in time of particle concentration for the three different diameters is considered. The text provides information about the deposition velocity, the deposition patterns on the cavity surfaces, the influence of lift and thermophoretic forces and the fractal dimension. The same size dependent parametric study for the three different sets of micro-size particles was carried out in a fully three-dimensional closed cubic cavity for one super-critical Rayleigh number. A detailed investigation of the turbulence was performed by means of statistical quantities, signal processing and conditional averaging, in order to get a general view of the complexity of the flow and its characteristics. Further on, the sedimentation process is studied in the same way as for the two dimensional case. Finally a simple theoretical deposition model is provided in order to interpret the numerical results for the aerosol phase.

Matching is a set of edges in a graph which each of the edge does not share a common vertex. Maximum Matching in a graph is number of maximum matching which a graph can have. Graph that will be used is guaranteed to be a bipartite graph that each of the vertices can be divided into two independent sets and edges in that graph always connect two vertices from different set. Topic in this journal is to find maximum matching in a graph. There are several approaches and optimizations to be done to achieve intended optimal solution. One of those optimization is vertices and edges compression so the algorithm can safely ignore duplicate vertices and edges in the graph. Purpose of this journal is to find accuracy and time complexity of all algorithm used to find maximum matching.

This dataset presents 2D PIV experimental data collected over a range of twelve urban roughnesses with different frontal and plan solidities. These are described in: [1] Placidi, M., Ganapathisubramani, B. (2015). Effects of frontal and plan solidities on aerodynamic parameters and the roughness sublayer in turbulent boundary layers. Journal of Fluid Mechanics, 782, 541–566. http://doi.org/10.1017/jfm.2015.552 [2] Placidi, M., Ganapathisubramani, B. (2018). Turbulent Flow Over Large Roughness Elements: Effect of Frontal and Plan Solidity on Turbulence Statistics and Structure. Boundary-Layer Meteorology, 167, 99–121. http://doi.org/10.1007/s10546-017-0317-3 PLEASE CITE THESE PAPERS AND THIS DATASET DOI WHEN USING THE DATA. Please contact Dr Marco Placidi (m.placidi@surrey.ac.uk) or Prof Bharathram Ganapathisubramani (G.Bharath@soton.ac.uk) for any queries on the dataset. $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Format of the dataset: d = Virtual origin [mm] delta = Boundary layer thickness (delta99 [mm]) deltas = Displacement thickness [mm] dyn_visc_air = Air dynamic viscosity [Kg/(m s)] h = Height of the roughness [mm] K = Acceleration parameter as in [1] rho_air = Air density [kq/m^3] run = Case ID as in [1] and [2] theta = Momentum thickness [mm] U = Mean streamwise velocity [m/s] U_edge = Mean streamwise velocity at the edge of the boundary layer [m/s] utau = Skin friction velocity [m/s] based on drag measurements uu = Streamwise velocity fluctuations uv = Reynolds shear stresses V = Mean wall-normal velocity [m/s] vv = Wall-normal velocity fluctuations X = Streamwise coordinate [mm] Y = Wall-normal coordinate [mm] y0 = Roughness length [mm] Additional notes on the dataset: - The 2D PIV dataset has been averaged across the Field of View in the streamwise direction to obtain 1D profiles. - utau is measured directly by means of a floating-element drag balance as described in [1]. - y0,d, are obtained via best fitting the velocity profiles as in [1]. - The entire dataset has been filtered to match the local resolution for all cases, as discussed in [1]. - The acceleration parameter is defined in [1], and it is calculated from 2D PIV data across the size of the drag balance sensing element (i.e. 200 mm x200 mm). As such, it is affected by a significant experimental uncertainty. Additional verification of ZPG conditions were obtained via Pitot tube measurements between the inlet and outlet of the tunnel test section. The pressure gradient was considered negligible.

A matrix-algebraic formulation of distributed-memory maximal cardinality matching algorithms in bipartite graphs

This paper addresses the critical problem of global wire optimization for nanometer scale very large scale integration technologies, and elucidates the impact of such optimization on power dissipation, bandwidth, and performance. Specifically, this paper introduces a novel methodology for optimizing global interconnect width, which maximizes a novel figure of merit (FOM) that is a user-defined function of bandwidth per unit width of chip edge and latency. This methodology is used to develop analytical expressions for optimum interconnect widths for typical FOMs for two extreme scenarios regarding line spacing: 1) spacing kept constant at its minimum value and 2) spacing kept the same as line width. These expressions have been used to compute the optimal global interconnect width and quantify the effect of increasing the line width on various performance metrics such as delay per unit length, total repeater area and power dissipation, and bandwidth for various International Technology Roadmap for Semiconductors technology nodes.

Part I. Values of the total conductivity for air in turbulent flow were originally reported without regard to effects of viscous dissipation. The reported values were corrected for such effects by utilizing measurements taken at the time of the original investigation. The total conductivity obtained by taking into account dissipation effects was found to be independent of the average temperature gradient with which measurements were made. Part II. The heat transfer characteristics from a 0.001-inch diameter platinum wire in the boundary flow about a 1-inch copper cylinder were measured at Reynolds numbers, based on the cylinder diameter of about 1750, 3500 and 7100. The results are presented in terms of the Nusselt number for the wire as a function of position for the three Reynolds numbers investigated. Comparison of the measured Nusselt numbers with values predicted from calculated velocity distributions indicate that, in the vicinity of the cylinder wall, the Nusselt number is not a unique function of the Reynolds number based on the wire diameter.

Summary form only given. Many materials in the nature or fabricated in laboratories exhibit nonlinear behavior where the permittivity and/or permeability is a function of the magnitude of the electric or magnetic field intensity. Such nonlinearity results in a nonlinear system of Maxwell's equations, which are more challenging to solve. Generally speaking, there are two kinds of methods commonly adopted to solve nonlinear problems. The first kind of methods solves the linearized versions of the original problems, while the second kind of methods deals with the nonlinear problems directly. Although more difficult to solve with a high efficiency, the second kind of methods is more desirable in order to capture the nonlinear phenomenon more accurately. Among various nonlinear solvers developed in the applied mathematics community, the Newton-Raphson method is widely used due to its second-order convergence, if started from an initial guess sufficiently close to the true solution. However, in a real application, there is no straightforward way to choose a good initial guess. As a result, the Newton-Raphson method could be unstable or divergent in solving complicated problems. Another difficulty of applying the Newton-Raphson method is that the Jacobian matrix needs to be updated and solved in every Newton iteration, which could be very time consuming for solving large problems. When the nonlinear electromagnetic problems are formulated and solved with the finite element method in time domain (J. M. Jin, The Finite Element Method in Electromagnetics, Second Edition. New York: Wiley, 2002), the numerical solution at a previous time step can be used as a natural choice for the initial guess of the Newton iteration at the successive time step. The convergent of the Newton-Raphson method can be achieved if the time step is small enough such that the solutions of two successive time steps are sufficiently close. In this presentation, we employ the time-domain finite element method (TDFEM) combined with the Newton-Raphson method and its variations to solve nonlinear electromagnetic problems. We first study the TDFEM formulation of nonlinear problems, and then show how it can be solved with Newton(-like) methods. We demonstrate and compare the performance of different nonlinear solvers including the basic Newton-Raphson method and its variations through a number of numerical examples.

Clustering and domination in perfect graphs

Consider a complete weighted bipartite graph G in which each left vertex u has two real numbers intercept and slope, each right vertex v has a real number quality, and the weight of any edge (u, v) is defined as the intercept of u plus the slope of u times the quality of v. Let m (resp., n) denote the number of left (resp., right) vertices, and assume that m geq n. We develop a fast algorithm for computing a maximum weight matching (MWM) of such a graph. Our algorithm begins by computing an MWM of the subgraph induced by the n right vertices and an arbitrary subset of n left vertices; this step is straightforward to perform in O(n log n) time. The remaining m - n left vertices are then inserted into the graph one at a time, in arbitrary order. As each left vertex is inserted, the MWM is updated. It is relatively straightforward to process each such insertion in O(n) time; our main technical contribution is to improve this time bound to O(sqrt{n} log^2 n). This result has an application related to unit-demand auctions. It is well known that the VCG mechanism yields a suitable solution (allocation and prices) for any unit-demand auction. The graph G may be viewed as encoding a special kind of unit-demand auction in which each left vertex u represents a unit-demand bid, each right vertex v represents an item, and the weight of an edge (u, v) represents the offer of bid u on item v. In this context, our fast insertion algorithm immediately provides an O(sqrt{n} log^2 n)-time algorithm for updating a VCG allocation when a new bid is received. We show how to generalize the insertion algorithm to update (an efficient representation of) the VCG prices within the same time bound.

Turbulent flow is a complicated physical phenomenon, and a daunting subject for students of engineering. Turbulent flow is disordered, with random and unsteady velocity fluctuations. This description by itself suggests that exact predictions cannot be determined, and that analysis of turbulent flows will not be easy. However intimidating turbulence may be, its importance is clear: turbulent flows are found in many industrial and natural processes, and affect quantities of great practical importance to engineers, like the local velocity distribution, drag force, and heat transfer. Moreover, a better understanding of this flow allows engineers to make design decisions that could either reduce the effects of turbulence or enhance them, in order to improve the performance of their devices.

Twelve Countings with Rooted Plane Trees

Shuffled complex evolution approach for effective and efficient surface wave analysis

Motivated by an application in controllability we consider maximum matchings in random bipartite graphs G = (A, B). First we analyse Karp–Sipser's algorithm to determine the asymptotic size of maximum matchings in random bipartite graphs with a fixed degree distribution. We then allow an adversary to delete one edge adjacent to every vertex in A in the more restricted model where each vertex in A chooses d neighbours uniformly at random from B.

In this paper, we consider the following distributed bipartite matching problems: Let G=(L, R; E) be a bipartite graph in which boys are part L (left nodes), and girls are part R (right nodes.) There is an edge (li, rj) ∈ E iff boy li is interested in girl rj. Every boy li will propose to a girl rj among all those he is interested in, i.e., his adjacent right nodes in the bipartite graph G. If several boys propose to the same girl, only one of them will be accepted by the girl. We assume that none of the boys communicate with others. This matching problem is typical of distributed computing under incomplete information: Each boy only knows his own preference but none of the others. We first study the one-round matching problem: each boy proposes to at most one girl, so that the total number of girls receiving a proposal is maximized. If the maximum matching is M, then no deterministic algorithm can produce a matching of size not bounded by a constant, but a randomized algorithm achieves √M—and this is shown optimal by an adversary argument. If we allow many rounds in matching, with the senders learning from their failures, then the ratio is unbounded when the number of rounds is smaller than Δ, and becomes bounded (two) at the Δ-th round. In contrast, an extension of the one-round randomized algorithm establishes that there is no such discontinuity in the randomized case. This randomized result is also matched by an upper bound of asymptotically the same order.

A set S ⊆ V is a dominating set in G if for every u ∈ V \ S, there exists v ∈ S such that (u, v) ∈ E, i.e., N[S] = V . A dominating set S is an isolate dominating set (IDS) if the induced subgraph G[S] has at least one isolated vertex. It is known that Isolate Domination Decision problem (IDOM) is NP-complete for bipartite graphs. In this paper, we extend this by showing that the IDOM is NP-complete for split graphs and perfect elimination bipartite graphs, a subclass of bipartite graphs. A set S ⊆ V is an independent set if G[S] has no edge. A set S ⊆ V is a secure dominating set of G if, for each vertex u ∈ V \ S, there exists a vertex v ∈ S such that (u, v) ∈ E and (S \ {v}) ∪ {u} is a dominating set of G. In addition, we initiate the study of a new domination parameter called, independent secure domination. A set S ⊆ V is an independent secure dominating set (InSDS) if S is an independent set and a secure dominating set of G. The minimum size of an InSDS in G is called the independent secure domination number of G and is denoted by γ is (G). Given a graph G and a positive integer k, the InSDM problem is to check whether G has an independent secure dominating set of size at most k. We prove that InSDM is NP-complete for bipartite graphs and linear time solvable for bounded tree-width graphs and threshold graphs, a subclass of split graphs. The MInSDS problem is to find an independent secure dominating set of minimum size, in the input graph. Finally, we show that the MInSDS problem is APX-hard for graphs with maximum degree 5.