Undirected Flow Research Articles

Finding a Closest Point in a Lattice of Voronoi's First Kind

We show that for those lattices of Voronoi's first kind with known obtuse superbasis, a closest lattice point can be computed in $O(n^4)$ operations, where $n$ is the dimension of the lattice. To achieve this a series of relevant lattice vectors that converges to a closest lattice point is found. We show that the series converges after at most $n$ terms. Each vector in the series can be efficiently computed in $O(n^3)$ operations using an algorithm to compute a minimum cut in an undirected flow network.

A practical guide for using proper orthogonal decomposition in engine research

Proper orthogonal decomposition has been utilized for well over a decade to study turbulence and cyclic variation of flow and combustion properties in internal combustion engines. In addition, proper orthogonal decomposition is useful to quantitatively compare multi-cycle in-cylinder measurements with numerical simulations (large-eddy simulations). However, the application can be daunting, and physical interpretation of proper orthogonal decomposition can be ambiguous. In this paper, the mathematical procedure of proper orthogonal decomposition is described conceptually, and a compact MATLAB® code is provided. However, the major purpose is to empirically illustrate the properties of the proper orthogonal decomposition analysis and to propose practical procedures for application to internal combustion engine flows. Two measured velocity data sets from a motored internal combustion engine are employed, one a highly directed flow (each cycle resembles the ensemble average), and the other an undirected flow (no cycle resembles the average). These data are used to illustrate the degree to which proper orthogonal decomposition can quantitatively distinguish between internal combustion engine flows with these two extreme flow properties. In each flow, proper orthogonal decomposition mode 1 is an excellent estimate of ensemble average, and this study illustrates how it is thus possible to unambiguously quantify the cyclic variability of Reynolds-averaged Navier–Stokes ensemble average and turbulence. In addition, this study demonstrates the benefits of comparing two different samples of cycles using a common proper orthogonal decomposition mode set derived by combining the two samples, the effect of spatial resolution, and a method to evaluate the number of snapshots required to achieve convergence.

Laplacians for flow networks

We define a class of Laplacians for multicommodity, undirected flow networks, and bound their smallest nonzero eigenvalues with a generalization of the sparsest cut.

POSI-MODULAR SYSTEMS WITH MODULOTONE REQUIREMENTS UNDER PERMUTATION CONSTRAINTS

Given a system (V, f, r) on a finite set V consisting of a posi-modular function f : 2V → ℝ and a modulotone function r : 2V → ℝ, we consider the problem of finding a minimum set R ⊆ V such that f(X) ≥ r(X) for all X ⊆ V - R. The problem, called the transversal problem, was introduced in [M. Sakashita, K. Makino, H. Nagamochi and S. Fujishige, Minimum transversals in posi-modular systems, SIAM J. Discrete Math.23 (2009) 858–871] as a natural generalization of the source location problem and external network problem with edge-connectivity requirements in undirected graphs and hypergraphs. By generalizing [H. Tamura, H. Sugawara, M. Sengoku and S. Shinoda, Plural cover problem on undirected flow networks, IEICE Trans.J81-A (1998) 863–869] for the source location problem, we show that the transversal problem can be solved by a simple greedy algorithm if r is π-monotone, where a modulotone function r is π-monotone if there exists a permutation π of V such that the function pr: V × 2V → ℝ associated with r satisfies pr(u, W) ≥ pr(v, W) for all W ⊆ V and u, v ∈ V with π(u) ≥ π(v). Here we show that any modulotone function r can be characterized by pr as r(X) = max {pr(v, W) | v ∈ X ⊆ V - W}. We also show the structural properties on the minimal deficient sets [Formula: see text] for the transversal problem for π-monotone function r, i.e., there exists a basic tree T for [Formula: see text] such that π(u) ≤ π(v) for all arcs (u,v) in T, which, as a corollary, gives an alternative proof for the correctness of the greedy algorithm for the source location problem. Furthermore, we show that a fractional version of the transversal problem can be solved by the algorithm similar to the one for the transversal problem.

Inline Concentration Monitoring of Binary Liquid Mixtures in the Presence of a Dispersed Gas Phase with a Modified Speed of Sound Immersion Probe

AbstractA commercial speed of sound (SOS) immersion probe has been modified in order to permit concentration measurements of liquid mixtures in the presence of dispersed gas phases. Experiments were performed in which water was removed from a polymer/water mixture via evaporation and stripping in mixed vessels of different flow patterns. The original and modified SOS immersion probe was used to monitor the water concentration. In the stripping stage, where a persistent gas phase of high volume fraction is generated, the original SOS immersion probe fails to measure the water concentration. This drawback has been successfully eliminated by means of a special SOS probe housing. The modified SOS immersion probe showed reliable inline water concentration monitoring for directed (draft tube reactor) and undirected flow pattern (ordinary stirred reactor) under boiling and stripping conditions.

Experimental investigation and numerical simulation of injection molding with micro‐features

AbstractInjection molding of thin plates of micro sized features was studied in order to manufacture micro‐fluidic devices for bioMEMS applications. Various types of mold inserts—CNC‐machined steel, epoxy photoresist, and photolithography and electroplating produced nickel molds—were fabricated and tested in injection molding. The feature size covers a range of 5 microns to several hundred microns. Issues such as surface roughness and sidewall draft angle of the mold insert were considered. Two optically clear thermoplastics, PMMA and optical quality polycarbonate, were processed at different mold and melt temperatures, injection speeds, shot sizes, and holding pressures. It was found that the injection speed and mold temperature in injection molding greatly affect the replication accuracy of microstructures on the metal mold inserts. The UV‐LIGA produced nickel mold with positive draft angles enabled successful demolding. Numerical simulation based on the 2D software C‐MOLD was performed on two types of cavity fillings: the radial flow and the undirectional flow. The simulation and experimental data were compared, showing correct qualitative predictions but discrepancies in the flow front profile and filled depth.

Solving the undirected multicommodity flow problem using a shortest path-based pricing algorithm

Solving the undirected multicommodity flow problem using a shortest path-based pricing algorithm

On a realization problem from non‐terminal capacity matrices on undirected flow networks

AbstractThe problem of realizing a given matrix on an undirected flow network has been studied and various results have been obtained. Most of these results consist of necessary and sufficient conditions for methods of realization in which the maximum good flow between the two points and the matrix components coincide. However, there are cases in which coincidence is not required as long as they are close to each other. In this paper, we consider the realization under certain conditions when values not necessarily realizable as maximum good flows of the flow network are given between two points. First, the upper and lower bounds of the maximum good flow are given. The problem of realization between these two extremes is studied and the necessary and sufficient condition is given. Next, by means of this result, we consider the problem of minimizing the difference between the given value and the maximum good flow in the undirected flow network. A realization method is studied. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(12): 28–39, 2001

Multiple cover problem on undirected flow networks

Multiple cover problem on undirected flow networks

Multiple cover problem on undirected flow networks

Multiple cover problem on undirected flow networks

Two‐route flows in an undirected flow network

AbstractThis paper defines anew the maximum two‐route flow as a measure to represent the relation between two vertices in the flow network. The maximum two‐route flow corresponds to the maximum number of communication channels that are composed of two‐route paths between two terminals in a communication network. The ℱ‐rings that can be composed simultaneously, containing the considered two vertices, is defined as the maximum two‐route flow between those two vertices.It is shown in this paper that a theorem exists for the maximum two‐route flow similar to the max‐flow min‐cut theorem for the ordinary flow.

Synthesis of flow networks minimizing the sum of edge capacities

AbstractSeveral synthesis methods to construct a flow network with the minimum sum of edge capacities for a given terminal capacity matrix have already been presented. However, there are networks that cannot be constructed by the known method.For the case where the given terminal capacity matrix is called elementary terminal capacity matrix, a synthesis method is presented that can construct any undirected flow network with the minimum sum of edge capacities. This paper is based on that synthesis method and presents a synthesis method that can construct any undirected flow network with the minimum sum of edge capacities for a given terminal capacity matrix with that matrix as the terminal capacity matrix.

Synthesis of a flow network with a given centrality on each vertex

AbstractThis paper considers the problem of constructing a flow network when the centrality at each vertex is given. Here, attention is given to a centrality function such that the centrality at a vertex under consideration is the sum of maximum flow values between it and all other vertices. It is a representative centrality function among those representing the centrality of each vertex in an undirected flow network in which edges have capacity. First, we introduce a necessary and sufficient condition wherein a given sequence is a centrality sequence for a flow network. Next, we present a procedure for determining a terminal capacity matrix of a flow network with a given centrality sequence. Furthermore, we determine a terminal capacity matrix of a flow network with a given centrality sequence such that the sum of edge capacity is minimum. From these discussions we can see that the problem of constructing a flow network when a centrality is given, can be reduced to the previously known problem of constructing a flow network when a terminal capacity matrix is given.

"Architextured" fluid management of biological liquids.

Novel "architextured" liquid-spreading and capillary flow systems are described as an adjunct to diagnostic procedures that range from the fully automated to techniques requiring no instrumentation. These systems were developed because of the observation that local features of macroscopic surfaces--roughness and chemical heterogeneity--influence both the spreading rate and equilibrium shape of liquid drops on solid surfaces. By use of organized patterns of surface structure complemented by surface chemical modification, this uncontrolled and undirected capillary flow is recast into flow behavior that is remarkably reproducible. Flow fronts are engineered to have prescribed shapes, and flow rates that are insensitive to the rheological properties of the biological liquids are obtained. To demonstrate the utility of fluid-management principles, we describe the implementation of architextured capillary configurations in microvolume liquid dispensers and potentiometric analytical systems.

Hummocky cross‐stratification, tropical hurricanes and intense winter storms

ABSTRACTDuke (1985b) argues that ‘most examples (of hummocky cross‐stratification) were formed by tropical hurricanes.’ His statement is based on the assumption that ‘hurricane‐generated surface gravity waves form powerful oscillating or multidirectional flows at the water‐sediment interface which do not possess a significant unidirectional component.’ It is true, as one of us has previously stated, that hurricanes are rapidly‐moving, short‐lived, localized, and infrequent systems as compared with mid‐latitude storms; midlatitude storms are consequently more efficient in coupling with the shelf water‐column than are hurricanes. However, Duke's argument that hummocky cross‐stratification may be the result of purely oscillatory flow is untenable. His reasoning contradicts established theory about oscillatory bedforms, and his numerous examples of hummocky cross‐stratification come largely from continental shelf settings where the storms (tropical or otherwise) would have created concurrent alongshelf undirectional flow as well as wave oscillatory motion. There is no theoretical or observational basis for the belief that water movement on the sea‐floor during hurricanes is qualitatively different from water movement during mid‐latitude storms. Consequently, hummocks are no more liable to form beneath hurricanes than they are beneath mid‐latitude storms.

Subaerial storm deposits formed on barrier flats by wind-driven currents

Coastal storm deposits produced by moderate- to high-velocity wind-driven currents are documented on aerial photographs of Texas Gulf Coast barriers following Hurricanes Carla, Beulah, and Celia. Sedimentary features on back-barrier flats that serve as criteria for inferring wind-driven currents include: (1) counterclockwise curvature of washover channels, (2) flame-shaped fans emerging from deeply incised channels, (3) closely spaced, slightly curved striations, (4) transverse sand waves along bay shorelines, and in some cases, (5) rhomboid bed forms. Flame-shaped and striated fans composed of sand and shell fragments also form on higher ground between washover channels. These fans coalesce laterally to form thin sediment wedges with crenulated landward and seaward margins; sediment by-pass areas separate these wedges from storm berms. The preserved storm features were formed after storm landfall by undirectional flow. Surface drift velocities, which lack precision because of underlying assumptions, were estimated by (1) small-wave theory applied to rhomboid bed forms, (2) ratios of surface drift velocity to wind velocity (3–5%), and (3) calculations based on drag coefficients. These estimates suggest that average wind-driven currents were between 1.3 and 2.9 m/sec.

Gravitational field of a radiating rotating body

A nonstationary solution of the Einstein field equations, corresponding to the field of a radiating rotating body, is presented. The solution is algebraically special of Petrov type II with a twisting, shear-free, null congruence identical to that of the Kerr metric. The new metric bears the same relation to the Kerr metric as does Vaidya's metric to the Schwarzschild metric, in the sense that in both cases the radiating solution is generated from the nonradiating one by replacing the mass parameter by an arbitrary function of a retarded time coordinate. The energy-momentum tensor in the present case, however, has two terms, a Vaidya type radiative one and an additional nonradiative residual term. Due to the presence of the nonradiative term in this case, however, the energy-momentum tensor becomes Vaidya-like asymptotically only, thus allowing for a geometrical optics interpretation. Asymptotically, part of the radiation field is purely electromagnetic with a Maxwell tensor which admits only one principal null direction corresponding to the undirectional flow of radiation.

Methods and conclusions in functional analysis: a reply

This paper is a reply to criticism presented by C. R. C. Paul and R. Cowen in immediately preceding articles in Lethaia. Contrary to the assertion by Paul, the present author did not reject the paradigmatic method but (1) criticized it for its limitations and seemingly erroneous results, (2) applied it to the richthofeniacean and lyttoniacean brachiopods by use of the pump as paradigm, and (3) extended it to include anatomic, metabolic, and phylogenetic considerations that go beyond the structural and mechanistic constraints of the original formulation. The rhythmic flow mechanism was rejected primarily on the basis of evidence for a ptycholophous lophophore in the Productidina. and the relative inefficiency of ‘valve flapping’ in contrast to ciliary action in pumping nutrient-bearing fluid into the shell. A Chinese blast furnace was claimed by Cowen to employ a single oscillating panel as a pump, but instead this panel must act as a valve that admits air in surges while the draft in the furnace maintains unidirectional flow through the system. This is analogous to ciliary feeding in brachiopods, where undirectional flow is maintained by ciliary pumping, and the valve opens to admit water. A richthofeniid with a Composita entrapped beneath the apertural meshwork is introduced as additional evidence against the likelihood of ‘valve flapping’.

On the relationship between the cut-tree and the fundamental cut set of multi-terminal flow networks

We are concerned with undirected flow networks in which any two nodes, generically designated by s and t, can serve as source and terminal, respectively. Let G be any linear network of N notes and A arcs with every arc aEA possessing a finite capacity c(a). Let R be the cut-tree of G obtained by the Gomory-Hu construction (1), and denote its links (which are, in fact, cut sets of G) by ra, r2, • . . , r~l . Let arc a = (i , j)eA be the are joining the two nodes i and j in G. Then we have

Sensitivity Analysis of Multiterminal Flow Networks

Given an undirected flow network with finite arc capacities, an algorithm is developed for the determination of the effect of a reduction (or increase) in the capacity of any arc on the maximum flow between any two nodes of the network. The algorithm is based on the Gomory-Hu construction of “cut-trees.”