A non-regular Groebner fan

The Groebner fan of an ideal $I\subset k[x_1,...,x_n]$, defined by Mora and Robbiano, is a complex of polyhedral cones in $R^n$. The maximal cones of the fan are in bijection with the distinct monomial initial ideals of $I$ as the term order varies. If $I$ is homogeneous the Groebner fan is complete and is the normal fan of the state polytope of $I$. In general the Groebner fan is not complete and therefore not the normal fan of a polytope. We may ask if the restricted Groebner fan, a subdivision of $R_{>=0}^n$, is regular i.e. the normal fan of a polyhedron. The main result of this paper is an example of an ideal in $Q[x_1,...,x_4]$ whose restricted Groebner fan is not regular.Comment: 11 page

On the Recognition of Fan-Planar and Maximal Outer-Fan-Planar Graphs

Fan-planar graphs were recently introduced as a generalization of 1-planar graphs. A graph is fan-planar if it can be embedded in the plane, such that each edge that is crossed more than once, is crossed by a bundle of two or more edges incident to a common vertex. A graph is outer-fan-planar if it has a fan-planar embedding in which every vertex is on the outer face. If, in addition, the insertion of an edge destroys its outer-fan-planarity, then it is maximal outer-fan-planar. In this paper, we present a polynomial-time algorithm to test whether a given graph is maximal outer-fan-planar. The algorithm can also be employed to produce an outer-fan-planar embedding, if one exists. On the negative side, we show that testing fan-planarity of a graph is NP-hard, for the case where the rotation system (i.e., the cyclic order of the edges around each vertex) is given

Electronics Cooling Fan Noise Prediction

Using the finite volume CFD software FLUENT, one fan was studied at a given flow rate (1.5m3/min) for three different operational rotating speeds : 2,000, 2,350 and 2,700 rpm. The turbulent air flow analysis predicts the acoustic behavior of the fan. The best fan operating window, i.e. the one giving the best ratio between noise emissions and cooling performance, can then be determined. The broadband noise acoustic model is used. As the computation is steady state, a simple Multiple Reference Frame model (MRF, also known as stationary rotor approach) is used to represent the fan. This approach is able to capture the effects of the flow non-uniformity at the fan inlet together with their impact on the fan performance. Furthermore, it is not requiring a fan curve as an input to the model. When compared to the available catalog data the simulation results show promising qualitative agreement that may be used for fan design and selection purposes.Comment: Submitted on behalf of TIMA Editions (http://irevues.inist.fr/tima-editions

Experimental study of blade thickness effects on the global and local performances of a Controlled Vortex Designed axial-flow fan

The purpose of this work is to study the effects of blade thickness on the performances of an axial-flow fan. Two fans that differ only in the thickness of their blades were studied. The first fan was designed to be part of the cooling system of an automotive vehicle power unit and has very thin blades. The second fan has much thicker blades compatible with the rotomoulding conception process. The global performances of the fans were measured in a test bench designed according to the ISO-5801 standard. The curve of aerodynamics characteristics (pressure head versus ow-rate) is slightly steeper for the fan with thick blades, and the nominal point is shifted towards lower flow-rates. The efficiency of the thick blades fan is lower than the efficiency of the fan with thin blades but remains high on a wider flow-rate range. The mean velocity field downstream of the rotors are very similar at nominal points with less centrifugation for the thick blades fan. The thick blades fan moreover maintains an axial exit-flow on a wider range of flow-rates. The main dierences concern local properties of the flow: Phase-averaged velocities and wall pressure fluctuations strongly differ at the nominal flow-rates. The total level of fluctuations is lower for the thick blades fan that for the thin blades fan and the spectral decomposition of the wall fluctuations and velocity signals reveal more harmonics for the thick blades fan, with less correlation between the different signals. For this kind of turbomachinery, the use of thick blades could lead to a good compromise between aerodynamic and acoustic performances, on a wider operating range

Quantifying slope-channel coupling in an active gully and fan complex at Tarndale, Waipaoa catchment, New Zealand

Two RIEGL LMS‐Z420i scanner surveys (November 2007 and November 2008) of the Tarndale Gully complex and its associated fan were used to generate a digital elevation model (DEM) of difference in order to quantify gully‐fan‐channel connectivity. The Te Weraroa Stream, into which the first order Tarndale system feeds, is buffered from sediment generated by the gully complex by a fan. Sediment yields and the role of the fan in buffering Te Weraroa Stream are inferred from the TLS of the entire complex. DEM analysis suggests that c.25% of material derived from the gully is buffered from the stream by being stored in the fan. This figure was applied to fan behaviour since December 2004, mapped on nine successive occasions using detailed GPS surveys to get a longer‐term picture of sediment supply within the system and appraise a qualitative assessment of connectivity constructed on the basis of fan behaviour alone