1,085,456 research outputs found
A note on nowhere-zero 3-flow and Z_3-connectivity
There are many major open problems in integer flow theory, such as Tutte's
3-flow conjecture that every 4-edge-connected graph admits a nowhere-zero
3-flow, Jaeger et al.'s conjecture that every 5-edge-connected graph is
-connected and Kochol's conjecture that every bridgeless graph with at
most three 3-edge-cuts admits a nowhere-zero 3-flow (an equivalent version of
3-flow conjecture). Thomassen proved that every 8-edge-connected graph is
-connected and therefore admits a nowhere-zero 3-flow. Furthermore,
Lovsz, Thomassen, Wu and Zhang improved Thomassen's result to
6-edge-connected graphs. In this paper, we prove that: (1) Every
4-edge-connected graph with at most seven 5-edge-cuts admits a nowhere-zero
3-flow. (2) Every bridgeless graph containing no 5-edge-cuts but at most three
3-edge-cuts admits a nowhere-zero 3-flow. (3) Every 5-edge-connected graph with
at most five 5-edge-cuts is -connected. Our main theorems are partial
results to Tutte's 3-flow conjecture, Kochol's conjecture and Jaeger et al.'s
conjecture, respectively.Comment: 10 pages. Typos correcte
Shortest path and maximum flow problems in planar flow networks with additive gains and losses
In contrast to traditional flow networks, in additive flow networks, to every
edge e is assigned a gain factor g(e) which represents the loss or gain of the
flow while using edge e. Hence, if a flow f(e) enters the edge e and f(e) is
less than the designated capacity of e, then f(e) + g(e) = 0 units of flow
reach the end point of e, provided e is used, i.e., provided f(e) != 0. In this
report we study the maximum flow problem in additive flow networks, which we
prove to be NP-hard even when the underlying graphs of additive flow networks
are planar. We also investigate the shortest path problem, when to every edge e
is assigned a cost value for every unit flow entering edge e, which we show to
be NP-hard in the strong sense even when the additive flow networks are planar
Bulk-edge correspondence, spectral flow and Atiyah-Patodi-Singer theorem for the Z2-invariant in topological insulators
We study the bulk-edge correspondence in topological insulators by taking
Fu-Kane spin pumping model as an example. We show that the Kane-Mele invariant
in this model is Z2 invariant modulo the spectral flow of a single-parameter
family of 1+1-dimensional Dirac operators with a global boundary condition
induced by the Kramers degeneracy of the system. This spectral flow is defined
as an integer which counts the difference between the number of eigenvalues of
the Dirac operator family that flow from negative to non-negative and the
number of eigenvalues that flow from non-negative to negative. Since the bulk
states of the insulator are completely gapped and the ground state is assumed
being no more degenerate except the Kramers, they do not contribute to the
spectral flow and only edge states contribute to. The parity of the number of
the Kramers pairs of gapless edge states is exactly the same as that of the
spectral flow. This reveals the origin of the edge-bulk correspondence, i.e.,
why the edge states can be used to characterize the topological insulators.
Furthermore, the spectral flow is related to the reduced eta-invariant and thus
counts both the discrete ground state degeneracy and the continuous gapless
excitations, which distinguishes the topological insulator from the
conventional band insulator even if the edge states open a gap due to a strong
interaction between edge modes. We emphasize that these results are also valid
even for a weak disordered and/or weak interacting system. The higher spectral
flow to categorize the higher-dimensional topological insulators are expected.Comment: 9 page, accepted for publication in Nucl Phys
Vortex-lift roll-control device
A wing is described for aircraft of cropped, arrow-type planform with thin leading and side edges. The wing has a pivotable tip to alter the crop angle of the wing during flight. Increasing the crop angle causes the wing side edge to become a trailing edge which reduces the strength of the side edge vortex flow. Decreasing the crop angle causes opposite results, in particular the side edge is now a leading edge and can generate a leading edge vortex flow. The wing constitutes a roll control device for aircraft of the stated design particularly effective at higher angles of attack
Low-speed aerodynamic characteristics of a highly swept arrow wing configuration with several deflected leading edge concepts
The effectiveness of leading edge concepts for minimizing or controlling leading edge flow separation was studied. Emphasis was placed on low speed performance, stability, and control characteristics of configurations with highly swept wings. Simple deflection of the leading edge, a variable camber leading edge system, and a leading edge vortex flow system were among the concepts studied. The data are presented without analysis
Pressure Bifurcation Phenomenon on Supersonic Blowing Trailing Edges
Turbine blades operating in transonic-supersonic regime develop a complex
shock wave system at the trailing edge, a phenomenon that leads to unfavorable
pressure perturbations downstream and can interact with other turbine stages.
Understanding the fluid behavior of the area adjacent to the trailing edge is
essential in order to determine the parameters that have influence on these
pressure fluctuations. Colder flow, bled from the high-pressure compressor, is
often purged at the trailing edge to cool the thin blade edges, affecting the
flow behavior and modulating the intensity and angle of the shock waves system.
However, this purge flow can sometimes generate non-symmetrical configurations
due to a pressure difference that is provoked by the injected flow. In this
work, a combination of RANS simulations and global stability analysis is
employed to explain the physical reasons of this flow bifurcation. Analyzing
the features that naturally appear in the flow and become dominant for some
value of the parameters involved in the problem, an anti-symmetrical global
mode, related to the sudden geometrical expansion of the trailing edge slot, is
identified as the main mechanism that forces the changes in the flow topology.Comment: Submitted to AIAA Journa
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