Dissimilarity functions for rank-invariant hierarchical clustering of continuous variables

A theoretical framework is presented for a (copula-based) notion of dissimilarity between continuous random vectors and its main properties are studied. The proposed dissimilarity assigns the smallest value to a pair of random vectors that are comonotonic. Various properties of this dissimilarity are studied, with special attention to those that are prone to the hierarchical agglomerative methods, such as reducibility. Some insights are provided for the use of such a measure in clustering algorithms and a simulation study is presented. Real case studies illustrate the main features of the whole methodology.Comment: 38 pages, 10 figures, 7 table

A novel smoothed particle hydrodynamics formulation for thermo-capillary phase change problems with focus on metal additive manufacturing melt pool modeling

Laser-based metal processing including welding and three dimensional printing, involves localized melting of solid or granular raw material, surface tension-driven melt flow and significant evaporation of melt due to the applied very high energy densities. The present work proposes a weakly compressible smoothed particle hydrodynamics formulation for thermo-capillary phase change problems involving solid, liquid and gaseous phases with special focus on selective laser melting, an emerging metal additive manufacturing technique. Evaporation-induced recoil pressure, temperature-dependent surface tension and wetting forces are considered as mechanical interface fluxes, while a Gaussian laser beam heat source and evaporation-induced heat losses are considered as thermal interface fluxes. A novel interface stabilization scheme is proposed, which is shown to allow for a stable and smooth liquid-gas interface by effectively damping spurious interface flows as typically occurring in continuum surface force approaches. Moreover, discretization strategies for the tangential projection of the temperature gradient, as required for the discrete Marangoni forces, are critically reviewed. The proposed formulation is deemed especially suitable for modeling of the melt pool dynamics in metal additive manufacturing because the full range of relevant interface forces is considered and the explicit resolution of the atmospheric gas phase enables a consistent description of pore formation by gas inclusion. The accuracy and robustness of the individual model and method building blocks is verified by means of several selected examples in the context of the selective laser melting process

Trace metal distributions in sulfide scales of the seawater-dominated Reykjanes geothermal system: Constraints on sub-seafloor hydrothermal mineralizing processes and metal fluxes

Highlights • Predictable trace element enrichments and depletions in the Reykjanes system. • Boiling exerts a major influence on the enrichment of metals. • High concentrations of Au and Ag and Pb indicate accumulation in reservoir fluids. • Three quarters of the metal budget is deposited at depth or in the upflow zone. Abstract Mineral precipitation in the seawater-dominated Reykjanes geothermal system on the Mid-Atlantic Ridge, Iceland is caused by abrupt, artificially induced, pressure and temperature changes as deep high-temperature liquids are drawn from reservoir rocks up through the geothermal wells. Sulfide scales within these wells represent a complete profile of mineral precipitation through a seafloor hydrothermal system, from the deep reservoir to the low-temperature silica-rich surface discharge. Mineral scales have formed under a range of conditions from high pressures and temperatures at depth (>2 km) to boiling conditions in the upflow zone and at the surface. Consistent trace element enrichments, similar to those in black smoker chimneys, are documented: Cu, Zn, Cd, Co, Te, V, Ni, Mo, W, Sn, Fe and S are enriched at higher pressures and temperatures in the deepest scales, Zn and Cu, Bi, Pb, Ag, As, Sb, Ga, Hg, Tl, U, and Th are enriched at lower temperatures and pressures nearer to the surface. A number of elements (e.g., Co, Se, Cd, Zn, Cu, and Au) are deposited in both high- and low-pressure scales, but are hosted by distinctly different minerals. Other trace elements, such as Pb, Ag, and Ga, are strongly partitioned into low-temperature minerals, such as galena (Pb, Ag) and clays (Ga). Boiling and destabilization of metal-bearing aqueous complexes are the dominant control on the deposition of most metals (particularly Au). Other metals (e.g., Cu and Se) may also have been transported in the vapor phase. Very large enrichments of Au, Ag and Pb in the scales (e.g., 948 ppm Au, 23,200 ppm Ag, and 18.8 wt.% Pb) versus average concentrations in black smoker chimneys likely reflect that some elements are preferentially deposited in boiling systems. A mass accumulation of 5.7 t/yr of massive sulfide was calculated for one high-temperature production well, equating to metal fluxes of 1.7 t/yr Zn, 0.3 t/yr Cu, 23 kg/yr Pb, 4.1 kg/yr Ag, and 0.5 kg/yr Au. At least three quarters of the major and trace element load is precipitated within the well before reaching the surface. We suggest that a similar proportion of metals may be deposited below the seafloor in submarine hydrothermal systems where significant boiling has occurred. Mass accumulation estimations over the lifetime of the Reykjanes system may indicate significant enrichment of Zn, Pb, Au, and Ag relative to both modern and ancient mafic-dominated seafloor massive sulfide deposits, and highlights the potential for metal enrichment and accumulation in the deep parts of geothermal systems

String Field Theory Projectors for Fermions of Integral Weight

The interaction vertex for a fermionic first order system of weights (1,0) such as the twisted bc-system, the fermionic part of N=2 string field theory and the auxiliary \eta\xi system of N=1 strings is formulated in the Moyal basis. In this basis, the Neumann matrices are diagonal; as usual, the eigenvectors are labeled by \kappa\in\R. Oscillators constructed from these eigenvectors make up two Clifford algebras for each nonzero value of \kappa. Using a generalization of the Moyal-Weyl map to the fermionic case, we classify all projectors of the star-algebra which factorize into projectors for each \kappa-subspace. At least for the case of squeezed states we recover the full set of bosonic projectors with this property. Among the subclass of ghost number-homogeneous squeezed state projectors, we find a single class of BPZ-real states parametrized by one (nearly) arbitrary function of \kappa. This class is shown to contain the generalized butterfly states. Furthermore, we elaborate on sufficient and necessary conditions which have to be fulfilled by our projectors in order to constitute surface states. As a byproduct we find that the full star product of N=2 string field theory translates into a canonically normalized continuous tensor product of Moyal-Weyl products up to an overall normalization. The divergent factors arising from the translation to the continuous basis cancel between bosons and fermions in any even dimension.Comment: LaTeX, 1+23 pages, minor improvements, references adde

Towards Additively Manufactured Metamaterials with Powder Inclusions for Controllable Dissipation: The Critical Influence of Packing Density

Particle dampers represent a simple yet effective means to reduce unwanted oscillations when attached to structural components. Powder bed fusion additive manufacturing of metals allows to integrate particle inclusions of arbitrary shape, size and spatial distribution directly into bulk material, giving rise to novel metamaterials with controllable dissipation without the need for additional external damping devices. At present, however, it is not well understood how the degree of dissipation is influenced by the properties of the enclosed powder packing. In the present work, a two-way coupled discrete element - finite element model is proposed allowing for the first time to consistently describe the interaction between oscillating deformable structures and enclosed powder packings. As fundamental test case, the free oscillations of a hollow cantilever beam filled with various powder packings differing in packing density, particle size, and surface properties are considered to systematically study these factors of influence. Critically, it is found that the damping characteristics strongly depend on the packing density of the enclosed powder and that an optimal packing density exists at which the dissipation is maximized. Moreover, it is found that the influence of (absolute) particle size on dissipation is rather small. First-order analytical models for different deformation modes of such powder cavities are derived to shed light on this observation

Constraints on the behavior of trace elements in the actively-forming TAG deposit, Mid-Atlantic Ridge, based on LA-ICP-MS analyses of pyrite

The distribution of trace ore elements in different paragenetic stages of pyrite has been documented for the first time in the sub-seafloor of the actively-forming TAG massive sulfide deposit. Trace element distributions have been determined by in-situ laser ablation inductively-coupled plasma mass spectrometry (LA-ICP-MS) of pyrite formed at different stages of mineralization, and at different temperatures constrained by previously published fluid inclusion analyses. The data reveal a strong dependence on paragenetic stage, with distinct low- and high-temperature enrichments. Porous pyrite (and marcasite) formed at low temperatures (350 °C) at the base of the hydrothermal mound and in the stockwork zone is enriched in Co, Se, Bi, Cu, Ni, and Sn. A number of different sub-types of pyrite also have characteristic trace element signatures; e.g., the earliest pyrite formed at the highest temperatures is always enriched in Co and Se compared to later stages. Ablation profiles for Co, Se, and Ni are smooth and indicate that these elements are present mainly in lattice substitutions rather than as inclusions of other sulfides. Profiles for As, Sb, Tl, and Cu can be either irregular or smooth, indicating both lattice substitutions and inclusions. Lead and Ag have mostly smooth profiles, but because Pb cannot substitute directly into the pyrite lattice, it is interpreted to be present as homogeneously distributed micro- or nano-scale particles. The behavior of the different trace elements mainly reflects their aqueous speciation in the hydrothermal fluids at different temperatures, and for some elements like Co and Se, strong partitioning into the pyrite lattice at elevated temperatures. Adsorption onto pyrite surfaces controls the distribution of a number of redox-sensitive elements (i.e., Mo, V, Ni, U), particularly in the upper part of the mound which is infiltrated by cold seawater. Where micro- or nano-scale inclusions of chalcopyrite, sphalerite, galena, or sulfosalts are present, there is still a strong temperature dependence on the inclusion population (e.g., more abundant chalcopyrite in the highest-temperature pyrite), suggesting that the inclusions were co-precipitated with pyrite rather than overgrown. However, at the deposit scale, the trace element distributions are also strongly controlled by remobilization and chemical zone refining, as previously documented in bulk geochemical profiles. The results show that pyrite chemistry is a remarkably good model of the chemistry of the entire hydrothermal system. For many trace elements, the concentrations in pyrite are highly predictive in terms of the conditions of mineral formation over a wide range of temperatures, from the stockwork zone to the cooler outer margins of the deposit. Calculated minimum concentrations of the trace elements in the fluids needed to account for the observed concentrations in pyrite show good agreement with measured vent fluid concentrations, particularly Pb, As, Mo, Ag, and Tl. However, significantly higher concentrations are indicated for Co (and Se) than have been measured in sampled fluids, confirming the strong partitioning of these elements into high-temperature pyrite

Filling a White Spot on the Yedoma Map: the Baldwin Peninsula, West Alaska

Vast regions of Arctic Siberia, Alaska and the Yukon are covered with ice-rich silts penetrated by large ice wedges, resulting from syngenetic sedimentation and freezing during the Pleistocene. These deposits are termed yedoma permafrost. Because of rapid incorporation of organic material into permafrost during sedimentation, yedoma deposits are expected to store poorly degraded organic matter. The total amount of organic carbon in the yedoma region is estimated to be approx. 400 gigatons. As a consequence of the high ground ice content, yedoma deposits are especially prone to degradation triggered by climate changes and/or human activity. When yedoma deposits degrade, large amounts of previously sequestered carbon as well as nutrients will be released which is of global significance for the climate system. Following on the tracks of permafrost pioneer David M. Hopkins, who studied this region during his conceptualization of the Bering Land Bridge in the 1950/60s (Hopkins et al. 1959, 1962), we conducted a field campaign to the Baldwin Peninsula in West Alaska. Based at the town of Kotzebue, one of the aims of this expedition was to describe yedoma landscapes and start a carbon inventory of this previously undocumented part of yedoma. The intention was to search for and characterize yedoma deposits whose presence was inferred from landscape morphometrics typical for yedoma (deep thermokarst lake basins, multiple overlapping lake basin generations, rolling hills with uplands where small deep thermokarst ponds are found, steep erosion margins along lake and coastal shores) on the neighboring Seward Peninsula and in Siberia as identified in remote sensing imagery. We were able to identify several yedoma upland exposures eroded by the Chukchi Sea on the western shore of the Baldwin Peninsula. We found clear evidence of yedoma permafrost occurrence at Cape Blossom, 20 km south of Kotzebue. We used a cryostratigraphical approach to sample yedoma and drained thaw lake basin exposures at this site. Moreover, different generations of drained lake basins in the hinterland of the cape were sampled with a SIPRE permafrost auger. For landscape scale estimation we used Landsat and high resolution WorldView imagery, airborne IfSAR digital elevation datasets as well as aerial survey flights during the expedition. The yedoma layer at Cape Blossom was characterized by a height of approx. 12 m including massive syngenetic ice wedges. The mean carbon content of the 7.8-m high sampled profile was 2.0 wt%. The average ice content for the sediment, not including ice wedges, was 45.2 wt%. Another bluff close by exposing sediments of a drained thermokarst basin contains 6.8 wt% carbon and 41.1 wt% pore ice. We were able to detect a chaotic layer at the bottom of the sediment sequence indicating lake initiation. This study gives evidence for the occurrence of ice-rich late Pleistocene yedoma deposits in Western Alaska. This yedoma is of importance because of its paleoenvironmental implications for the widespread occurrence of yedoma in the Bering Land Bridge region (e.g. mammoth steppe conditions), as well as for the future vulnerability of the landscape to thaw because of its high excess ground ice content. Permafrost thaw will affect these yedoma areas first, as its location is close to the continuous/discontinuous permafrost zone border, with the result that a considerable amount of carbon becomes available for microbial activity. References: Hopkins, D.M., 1959. Cenozoic History of the Bering Land Bridge. Science 129, 1519-1528. Hopkins, D.M., McCulloch, D.S., and Janda, R.J., 1962, Pleistocene stratigraphy and structure of Baldwin Peninsula, Kotzebue Sound, Alaska: 12th Alaskan Science Conference, p. 150-151