Numerical simulations of MHD flow transition in ducts with conducting Hartmann walls : Limtech Project A3 D4 (TUI) (KIT Scientific Reports ; 7713)

Pressure-driven magnetohydrodynamic duct flows in a transverse, wall-parallel and uniform field have been studied by direct numerical. The conducting Hartmann walls give rise to a laminar velocity distribution with strong jets at the side walls, which are susceptible to flow instability. The onset of time-dependent flow as well as fully developed turbulent flow have been explored in a wide range of parameters

Kombinatorikus Optimalizálás: Algoritmusok, Strukturák, Alkalmazások = Combinatorial optimization: algorithms, structures, applications

Mint azt az OTKA-pályázat munkaterve tartalmazza, a pályázatban résztvevő kutatók alkotják a témavezető irányításával működő Egerváry Jenő Kombinatorikus Optimalizálási Kutatócsoportot. A csoport a kutatási tervben szereplő több témában jelentős eredményeket ért el az elmúlt 4 évben, ezekről a pályázat résztvevőinek több mint 50 folyóiratcikke jelent meg, és számos rangos nemzetközi konferencián ismertetésre kerültek. Néhány kiemelendő eredmény: sikerült polinomiális kombinatorikus algoritmust adni irányított gráf pont-összefüggőségének növelésére; jelentős előrelépés történt a háromdimenziós térben merev gráfok jellemzésével és a molekuláris sejtéssel kapcsolatban; 2 dimenzióban sikerült bizonyítani Hendrickson sejtését; a párosításelméletben egy újdonságnak számító módszerrel számos új algoritmikus eredmény született; több, gráfok élösszefüggőségét jellemző tételt sikerült hipergráfokra általánosítani. | As the research plan indicates, the researchers participating in the project are the members of the Egerváry Research Group, led by the coordinator. The group has made important progress in the past 4 years in the research topics declared in the research plan. The results have been published in more than 50 journal papers, and have been presented at several prestigious international conferences. The most significant results are the following: a polynomial algorithm has been found for the node-connectivity augmentation problem of directed graphs; considerable progress has been made towards the characterization of 3-dimensional rigid graphs and towards the proof of the molecular conjecture; Hendrickson's conjecture has been proved in 2 dimensions; several new algorithmic results were obtained in matching theory using a novel approach; several theorems characterizing connectivity properties of graphs have been generalized to hypergraphs

Ryser Type Conditions for Extending Colorings of Triples

In 1951, Ryser showed that an $n\times n$ array $L$ whose top left $r\times s$ subarray is filled with $n$ different symbols, each occurring at most once in each row and at most once in each column, can be completed to a latin square of order $n$ if and only if the number of occurrences of each symbol in $L$ is at least $r+s-n$. We prove a Ryser type result on extending partial coloring of 3-uniform hypergraphs. Let $X,Y$ be finite sets with $X\subsetneq Y$ and $|Y|\equiv 0 \pmod 3$. When can we extend a (proper) coloring of $\lambda \binom{X}{3}$ (all triples on a ground set $X$, each one being repeated $\lambda$ times) to a coloring of $\lambda \binom{Y}{3}$ using the fewest possible number of colors? It is necessary that the number of triples of each color in $\binom{X}{3}$ is at least $|X|-2|Y|/3$. Using hypergraph detachments (Combin. Probab. Comput. 21 (2012), 483--495), we establish a necessary and sufficient condition in terms of list coloring complete multigraphs. Using H\"aggkvist-Janssen's bound (Combin. Probab. Comput. 6 (1997), 295--313), we show that the number of triples of each color being at least $|X|/2-|Y|/6$ is sufficient. Finally we prove an Evans type result by showing that if $|Y|\geq 3|X|$, then any $q$-coloring of any subset of $\lambda \binom{X}{3}$ can be embedded into a $\lambda\binom{|Y|-1}{2}$-coloring of $\lambda \binom{Y}{3}$ as long as $q\leq \lambda \binom{|Y|-1}{2}-\lambda \binom{|X|}{3}/\lfloor{|X|/3}\rfloor$.Comment: 10 page

A detachment algorithm for inferring a graph from path frequency

Abstract: Inferring graphs from path frequency has been studied as an important problem which has a potential application to drug design and elucidation of chemical structures. Given a multiple set g of strings of labels with length at most K, the problem asks to find a vertex-labeled graph G that attains a one-to-one correspondence between g and the occurrences of labels along all paths of length at most K in G. In this paper, we prove that the problem with K = 1 can be formulated as a problem of finding a loopless and connected detachment, based on which an efficient algorithm for solving the problem is derived. Our algorithm also solves the problem with an additional constraint such that every vertex in an inferred graph is required to have a specified degree

Direct Numerical Simulation of Transition and Turbulence in Magnetohydrodynamic Flows in Rectangular Ducts

In this work, a flow of an electrically conducting fluid is driven through a rectangular duct by a constant pressure gradient in the presence of a transverse, externally applied magnetic field: the flow is studied using the method of Direct Numerical Simulation (DNS). This particular Magnetohydrodynamic (MHD) flow investigation is important in the development of liquid metal blankets design, which is the proposed cooling system within nuclear fusion reactors. The duct walls parallel to the magnetic field are ideally electrically insulating, while the walls perpendicular to the magnetic field are ideally electrically conducting. This flow is referred to as a Hunt’s flow. In this work the emergence of time dependent flow and its transition to a fully developed turbulent regime is explored. By fixing the strength of the magnetic field and increasing the fluid velocity, a number of time-dependent flow regimes have been observed in the side layers, which includes Ting-Walker vortices, elongated vortical structures, fully turbulent side-wall jets, as well as singular and multiple side-wall jet detachments. It has been found that at low velocities, the time-dependant flow takes the form of TingWalker vortices, which develop in the side layers of the duct. For all but the lowest magnetic fields studied, the Ting-Walkers vortices completely disappear after a short initial transient time, being replaced by new, higher energy, complex, anisotropic vortical structures. Additionally, a number of new flow regimes involving jet detachment have been identified. This study also demonstrates that Hunt’s flow exhibits hysteresis behaviour, where different unsteady states are possible for the same flow parameters

On the uniqueness of the Laplacian spectra of coalescence of complete graphs

Acknowledgments: I would like to thank Nicole Snashall for her encouragement, comments and support. I also would like to thank Jozef Siran for his comments on amalgamations, which led to more thinking about defining my graphs. This project started with an application to social networks; however, it developed into a much more general study. I would like to dedicate this paper to the memory of Alto Zeitler (1945-2022), my mathematics teacher.Peer reviewedPublisher PD

Characterising fracture systems within upfaulted basement highs in the Hebridean Islands: an onshore analogue for the Clair Field

The Outer Hebrides are a structurally complex area, comprised predominantly of crystalline basement rocks of the Lewisian Gneiss Complex with the multiply reactivated Outer Hebrides Fault Zone following eastern portions of the islands for over 200 km along strike. In Eastern Lewis, the Permo-Triassic Stornoway Formation unconformably overlies Lewisian basement rocks of the OHFZ in a half-graben. This structural setting is analogous to the major offshore Clair oil field, where oil is found within Devonian-Carboniferous red beds of the Clair Group directly overlying Lewisian Gneiss Complex rocks of the Rona Ridge, which was upfaulted in the Mesozoic. Oil connection and flow has been proven in the basement rocks at Clair, however, little is known about the nature of fracturing and faulting within the basement and how these faults link to the cover sequence. Here, the cover and basement rocks of the Outer Hebridean Islands of Lewis and Harris are studied as an analogue. Faults, fault rocks and deformation are characterised within the Stornoway Formation, and at the basement-cover interface, allowing recognition of Mesozoic and younger faults within the Lewisian and their separation from older structures. Three fault sets are distinguished within the Stornoway Formation: a NNW-SSE striking normal fault set (Set 1); a N-S and E-W quadrimodal normal fault set (Set 2); and a less numerous late E-W strike-slip set (Set 3). Tertiary dolerite dyke intrusion occurred along Set 1 and Set 2 faults prior to the formation of Set 3. Palaeostress analyses reveal that Set 1 and 2 result from E-W and ENE-WSW directed extension vectors, followed by E-W directed contraction associated with Set 3. These orientations are interpreted to be representative of Mesozoic extension related to the opening of the Atlantic, followed by Cenozoic contraction. Faults in the Stornoway Formation are accompanied by development of authigenic clay-bearing gouges and cataclasites, ± calcite cement and late zeolite. Zeolite is often associated with secondary porosity, produced through dissolution of calcite. Mesozoic and younger faults are readily identified in Lewisian Gneiss rocks of the Stornoway region based on fault rock characterisation, and these faults also display an ENE-WSW directed extension vector. The major bounding faults of the Stornoway Formation are sub-parallel with the local foliation and the reactivation of the basement foliation by Mesozoic faults is proven. Fault trends identified within the Stornoway Formation are also sub-parallel with the local foliation. Conjugate faulting apparent in the Stornoway Formation is not present within the Lewisian, possibly indicating a degree of structural detachment between faulting in the basement and faulting in the cover, probably linked to the development of low-angle faults within the Stornoway Formation within metres of and parallel with the basement-cover unconformity. The basement-cover interface displays abundant evidence of fluid overpressure, potentially linked with dewatering during lithification and local fault movements. Mesozoic and younger-age brittle fault rocks post-date pre-existing extensive ductile and brittle deformation that are most intense within the OHFZ. Brittle fault rocks of pre-Mesozoic age are associated with pseudotachylites, fine grained cataclasites, epidote-bearing cataclasites and pumpellyite-bearing cataclasites. Mesozoic fault rocks contain authigenic clay-bearing gouges and cataclasites often associated with zeolite and adularia mineralisation that often accompanies the development of secondary porosity within the fault rocks. This chronological fault rock assemblage represents the continued exhumation of the islands after the successively lower temperature and pressures conditions experienced since the initial development of the basement gneiss complex. Across Lewis, fault rock characterisation allows identification of major Mesozoic and younger structures that cross the islands, with a km-scale offset postulated across the major Seaforth Fault that may link the major NE-SW striking Minch Fault to a NE-SW striking fault lying offshore western Lewis/Harris. On Lewis, the predominant orientation of Mesozoic structures is NNW-SSE, becoming NW-SE on Harris, south of the Seaforth Fault and where foliation becomes pervasively NW-SE. It seems highly likely that, as identified in the Stornoway Region, the foliation orientation plays a significant role in the development of later structures. At Clair, fault rock development within the Devonian-Carboniferous Clair Group is dependent on the host lithology, with gouges formed in mudstones, and granulation seams found in porous, oil-bearing sandstones. Calcite-cemented breccias are present in zones of calcite cemented host rock. Pyrite and calcite vein mineralisation are associated with oil influx, and a late phase of dissolution was accompanied by faulting that produced uncemented brittle fault rocks (gouge). In the basement, oil is seen along open fractures and in vug-like secondary porosity associated with adularia mineralisation, of which two forms are present. Euhedral adularia is often altered to green clay and partially to wholly infills tensile fractures that may predate the emplacement of the Clair Group. Later adularia occurs as ‘speckled’ veins, with haematite, clay, calcite, pyrite, minor zeolite and oil, and appears to be contemporaneous with calcite-pyrite veining (i.e. Mesozoic in age). Porosity in both adularia-bearing fractures is associated with oil staining. The basement displays little evidence of extensive mylonites or phyllonites that are obvious in the OHFZ of the Outer Hebrides. Scalability studies show that it is difficult to assign power-law spacing distributions to fractures within the basement rocks of the Hebrides. Fractures parallel with Mesozoic structures do however tend to display a greater degree of organisation with more clustering of fractures as the faults are approached. Mesozoic fault-perpendicular fracture sets display more strongly random fracture spacing distributions consistent with a jointing origin. At Clair, fracture spacing studies in the cover show a low fracture density compared to basement, with fracture spacing that is clustered and may be well represented by power-laws. Dissolution has locally produced a randomly spaced fracture network. Although fracture spacings in the Hebridean Lewisian are generally random, fracture apertures define a clear power law relationship over ~5 orders of magnitude. Similarly, results from the Clair group also display equivalent power law relationships