Fluidodinamica biomedica computazionale del flusso sanguigno in presenza di affezioni strumentali e/o patologiche

La tesi di Dottorato studia il flusso sanguigno tramite un codice agli elementi finiti (COMSOL Multiphysics). Nell’arteria è presente un catetere Doppler (in posizione concentrica o decentrata rispetto all’asse di simmetria) o di stenosi di varia forma ed estensione. Le arterie sono solidi cilindrici rigidi, elastici o iperelastici. Le arterie hanno diametri di 6 mm, 5 mm, 4 mm e 2 mm. Il flusso ematico è in regime laminare stazionario e transitorio, ed il sangue è un fluido non-Newtoniano di Casson, modificato secondo la formulazione di Gonzales & Moraga. Le analisi numeriche sono realizzate in domini tridimensionali e bidimensionali, in quest’ultimo caso analizzando l’interazione fluido-strutturale. Nei casi tridimensionali, le arterie (simulazioni fluidodinamiche) sono infinitamente rigide: ricavato il campo di pressione si procede quindi all’analisi strutturale, per determinare le variazioni di sezione e la permanenza del disturbo sul flusso. La portata sanguigna è determinata nei casi tridimensionali con catetere individuando tre valori (massimo, minimo e medio); mentre per i casi 2D e tridimensionali con arterie stenotiche la legge di pressione riproduce l’impulso ematico. La mesh è triangolare (2D) o tetraedrica (3D), infittita alla parete ed a valle dell’ostacolo, per catturare le ricircolazioni. Alla tesi sono allegate due appendici, che studiano con codici CFD la trasmissione del calore in microcanali e l’ evaporazione di gocce d’acqua in sistemi non confinati. La fluidodinamica nei microcanali è analoga all’emodinamica nei capillari. Il metodo Euleriano-Lagrangiano (simulazioni dell’evaporazione) schematizza la natura mista del sangue. La parte inerente ai microcanali analizza il transitorio a seguito dell’applicazione di un flusso termico variabile nel tempo, variando velocità in ingresso e dimensioni del microcanale. L’indagine sull’evaporazione di gocce è un’analisi parametrica in 3D, che esamina il peso del singolo parametro (temperatura esterna, diametro iniziale, umidità relativa, velocità iniziale, coefficiente di diffusione) per individuare quello che influenza maggiormente il fenomeno.

Sensitivity analysis of a parabolic-elliptic problem

We consider the heat flux through a domain with subregions in which the thermal capacity approaches zero. In these subregions the parabolic heat equation degenerates to an elliptic one. We show the well-posedness of such parabolic-elliptic differential equations for general non-negative L-infinity-capacities and study the continuity of the solutions with respect to the capacity, thus giving a rigorous justification for modeling a small thermal capacity by setting it to zero. We also characterize weak directional derivatives of the temperature with respect to capacity as solutions of related parabolic-elliptic problems.

Biomedical and industrial applications of atmospheric pressure non-equilibrium plasmas

This dissertation will be focused on the characterization of an atmospheric pressure plasma jet source with an application oriented diagnostic approach and the description of processes supported by this plasma source. The plasma source investigated is a single electrode plasma jet. Schlieren images, optical emission spectra, temperature and heat flux profiles are analyzed to deeply investigate the fluid dynamic, the chemical composition and the thermal output of the plasma generated with a nanosecond-pulsed high voltage generator. The maximum temperature measured is about 45 °C and values close to the room temperature are reached 10 mm down the source outlet, ensuring the possibility to use the plasma jet for the treatment of thermosensitive materials, such as, for example, biological substrate or polymers. Electrospinning of polymeric solution allows the production of nanofibrous non-woven mats and the plasma pre-treatment of the solutions leads to the realization of defect free nanofibers. The use of the plasma jet allows the electrospinnability of a non-spinnable poly(L-lactic acid) (PLLA) solution, suitable for the production of biological scaffold for the wound dressing.

A study of air-sea interaction processes on water mass formation and upwelling in the Mediterranean sea

Air-sea interactions are a key process in the forcing of the ocean circulation and the climate. Water Mass Formation is a phenomenon related to extreme air-sea exchanges and heavy heat losses by the water column, being capable to transfer water properties from the surface to great depth and constituting a fundamental component of the thermohaline circulation of the ocean. Wind-driven Coastal Upwelling, on the other hand, is capable to induce intense heat gain in the water column, making this phenomenon important for climate change; further, it can have a noticeable influence on many biological pelagic ecosystems mechanisms. To study some of the fundamental characteristics of Water Mass Formation and Coastal Upwelling phenomena in the Mediterranean Sea, physical reanalysis obtained from the Mediterranean Forecating System model have been used for the period ranging from 1987 to 2012. The first chapter of this dissertation gives the basic description of the Mediterranean Sea circulation, the MFS model implementation, and the air-sea interaction physics. In the second chapter, the problem of Water Mass Formation in the Mediterranean Sea is approached, also performing ad-hoc numerical simulations to study heat balance components. The third chapter considers the study of Mediterranean Coastal Upwelling in some particular areas (Sicily, Gulf of Lion, Aegean Sea) of the Mediterranean Basin, together with the introduction of a new Upwelling Index to characterize and predict upwelling features using only surface estimates of air-sea fluxes. Our conclusions are that latent heat flux is the driving air-sea heat balance component in the Water Mass Formation phenomenon, while sensible heat exchanges are fundamental in Coastal Upwelling process. It is shown that our upwelling index is capable to reproduce the vertical velocity patterns in Coastal Upwelling areas. Nondimensional Marshall numbers evaluations for the open-ocean convection process in the Gulf of Lion show that it is a fully turbulent, three-dimensional phenomenon.

Dynamics of Bora wind over the Adriatic sea: atmospheric water balance and role of air-sea fluxes and orography

The Bora wind is a mesoscale phenomenon which typically affects the Adriatic Sea basin for several days each year, especially during winter. The Bora wind has been studied for its intense outbreak across the Dinaric Alps. The properties of the Bora wind are widely discussed in the literature and scientific papers usually focus on the eastern Adriatic coast where strong turbulence and severe gust intensity are more pronounced. However, the impact of the Bora wind can be significant also over Italy, not only in terms of wind speed instensity. Depending on the synoptic pressure pattern (cyclonic or anticyclonic Bora) and on the season, heavy snowfall, severe storms, storm surges and floods can occur along the Adriatic coast and on the windward flanks of the Apennines. In the present work five Bora cases that occurred in recent years have been selected and their evolution has been simulated with the BOLAM-MOLOCH model set, developed at ISAC-CNR in Bologna. Each case study has been addressed by a control run and by several sensitivity tests, performed with the purpose of better understanding the role played by air-sea latent and sensible heat fluxes. The tests show that the removal of the fluxes induces modifications in the wind approching the coast and a decrease of the total precipitation amount predicted over Italy. In order to assess the role of heat fluxes, further analysis has been carried out: column integrated water vapour fluxes have been computed along the Italian coastline and an atmospheric water balance has been evaluated inside a box volume over the Adriatic Sea. The balance computation shows that, although latent heat flux produces a significant impact on the precipitation field, its contribution to the balance is relatively minor. The most significant and lasting case study, that of February 2012, has been studied in more detail in order to explain the impressive drop in the total precipitation amount simulated in the sensitivity tests with removed heat fluxes with respect to the CNTRL run. In these experiments relative humidity and potential temperature distribution over different cross-sections have been examined. With respect to the CNTRL run a drier and more stable boundary layer, characterised by a more pronounced wind shear at the lower levels, has been observed to establish above the Adriatic Sea. Finally, in order to demonstrate that also the interaction of the Bora flow with the Apennines plays a crucial role, sensitivity tests varying the orography height have been considered. The results of such sensitivity tests indicate that the propagation of the Bora wind over the Adriatic Sea, and in turn its meteorological impact over Italy, is influenced by both the large air-sea heat fluxes and the interaction with the Apennines that decelerate the upstream flow.

Prokaryotic community structure in ultra-slow spreading Southwest Indian Ridge.

The Southwest Indian Ridge segment that extends between 10° and 16° E has the slowest spreading rate of any other oceanic ridge (about 8.4 mm/year). In 2013 during the expedition ANTXXIX/8 seismology, geology, microbiology, heat flow analyses were carried out. Here, no hydrothermal plumes or black smoker systems were found but the results of the survey allowed to identify areas with peculiar characteristics: Area 1 with higher heat flux bsf; Area 2 where in 2002 the presence of hydrothermal emissions was hypothesized (Bach et al., 2002); Area 3 with anomalies of methane, ammonium, sulphide and dissolved inorganic carbon in pore water sediment profiles, and recovery of fauna vents. All these aspects suggest the presence of a hydrothermal circulation. Using Illumina 16S gene tag, statistical tools and phylogenetic trees, I provided a biological proof of the presence of hydrothermal circulation in this ridge segment. At Area 3, alpha and beta diversity indexes showed similarities with those described for venting microbial communities and about 40-70% of the dominant microbial community was found phylogenetically related to clones isolated hydrothermal-driven environments. Although the majority of chemosynthetic environment related taxa were not classified like autotrophic prokaryotes, some of them are key taxa in support of the presence of hydrothermal circulation, since they are partners of consortia or mediate specific reaction typically described for hydrothermal and seep environments, or are specialized organisms in exploiting labile organic substrates. Concluding, these results are remarkable because support the importance of ultra slow spreading ridge systems in contributing to global geochemical cycles and larval dispersion of vent fauna.

Use of Land Surface Temperature to Estimate Surface Energy Fluxes: Contributions of Wilfried Brutsaert and Collaborators

Land surface temperature (LST) plays a key role in governing the land surface energy budget, and measurements or estimates of LST are an integral part of many land surface models and methods to estimate land surface sensible heat (H) and latent heat fluxes. In particular, the LST anchors the potential temperature profile in Monin-Obukhov similarity theory, from which H can be derived. Brutsaert has made important contributions to our understanding the nature of surface temperature measurements as well as the practical but theoretically sound use of LST in this framework. His work has coincided with the wide-spread availability of remotely sensed LST measurements. Use of remotely sensed LST estimates inevitably involves complicating factors, such as: varying spatial and temporal scales in measurements, theory, and models; spatial variability of LST and H; the relationship between measurements of LST and the temperature felt by the atmosphere; and the need to correct satellite-based radiometric LST measurements for the radiative effects of the atmosphere. This paper reviews the progress made in research in these areas by tracing and commenting on Brutsaert's contributions.

THERMAL CHARACTERIZATION OF COMBUSTION CHAMBER COMPONENTS IN A GASOLINE TURBOCHARGED DIRECT INJECTION (GTDI) ENGINE

This report is a PhD dissertation proposal to study the in-cylinder temperature and heat flux distributions within a gasoline turbocharged direct injection (GTDI) engine. Recent regulations requiring automotive manufacturers to increase the fuel efficiency of their vehicles has led to great technological achievements in internal combustion engines. These achievements have increased the power density of gasoline engines dramatically in the last two decades. Engine technologies such as variable valve timing (VVT), direct injection (DI), and turbocharging have significantly improved engine power-to-weight and power-to-displacement ratios. A popular trend for increasing vehicle fuel economy in recent years has been to downsize the engine and add VVT, DI, and turbocharging technologies so that a lighter more efficient engine can replace a larger, heavier one. With the added power density, thermal management of the engine becomes a more important issue. Engine components are being pushed to their temperature limits. Therefore it has become increasingly important to have a greater understanding of the parameters that affect in-cylinder temperatures and heat transfer. The proposed research will analyze the effects of engine speed, load, relative air-fuel ratio (AFR), and exhaust gas recirculation (EGR) on both in-cylinder and global temperature and heat transfer distributions. Additionally, the effect of knocking combustion and fuel spray impingement will be investigated. The proposed research will be conducted on a 3.5 L six cylinder GTDI engine. The research engine will be instrumented with a large number of sensors to measure in-cylinder temperatures and pressures, as well as, the temperature, pressure, and flow rates of energy streams into and out of the engine. One of the goals of this research is to create a model that will predict the energy distribution to the crankshaft, exhaust, and cooling system based on normalized values for engine speed, load, AFR, and EGR. The results could be used to aid in the engine design phase for turbocharger and cooling system sizing. Additionally, the data collected can be used for validation of engine simulation models, since in-cylinder temperature and heat flux data is not readily available in the literature..

Analysis of in-cylinder pressure transducer data quality utilizing a SIDI turbocharged engine

In-cylinder pressure transducers have been used for decades to record combustion pressure inside a running engine. However, due to the extreme operating environment, transducer design and installation must be considered in order to minimize measurement error. One such error is caused by thermal shock, where the pressure transducer experiences a high heat flux that can distort the pressure transducer diaphragm and also change the crystal sensitivity. This research focused on investigating the effects of thermal shock on in-cylinder pressure transducer data quality using a 2.0L, four-cylinder, spark-ignited, direct-injected, turbo-charged GM engine. Cylinder four was modified with five ports to accommodate pressure transducers of different manufacturers. They included an AVL GH14D, an AVL GH15D, a Kistler 6125C, and a Kistler 6054AR. The GH14D, GH15D, and 6054AR were M5 size transducers. The 6125C was a larger, 6.2mm transducer. Note that both of the AVL pressure transducers utilized a PH03 flame arrestor. Sweeps of ignition timing (spark sweep), engine speed, and engine load were performed to study the effects of thermal shock on each pressure transducer. The project consisted of two distinct phases which included experimental engine testing as well as simulation using a commercially available software package. A comparison was performed to characterize the quality of the data between the actual cylinder pressure and the simulated results. This comparison was valuable because the simulation results did not include thermal shock effects. All three sets of tests showed the peak cylinder pressure was basically unaffected by thermal shock. Comparison of the experimental data with the simulated results showed very good correlation. The spark sweep was performed at 1300 RPM and 3.3 bar NMEP and showed that the differences between the simulated results (no thermal shock) and the experimental data for the indicated mean effective pressure (IMEP) and the pumping mean effective pressure (PMEP) were significantly less than the published accuracies. All transducers had an IMEP percent difference less than 0.038% and less than 0.32% for PMEP. Kistler and AVL publish that the accuracy of their pressure transducers are within plus or minus 1% for the IMEP (AVL 2011; Kistler 2011). In addition, the difference in average exhaust absolute pressure between the simulated results and experimental data was the greatest for the two Kistler pressure transducers. The location and lack of flame arrestor are believed to be the cause of the increased error. For the engine speed sweep, the torque output was held constant at 203 Nm (150 ft-lbf) from 1500 to 4000 RPM. The difference in IMEP was less than 0.01% and the PMEP was less than 1%, except for the AVL GH14D which was 5% and the AVL GH15DK which was 2.25%. A noticeable error in PMEP appeared as the load increased during the engine speed sweeps, as expected. The load sweep was conducted at 2000 RPM over a range of NMEP from 1.1 to 14 bar. The difference in IMEP values were less 0.08% while the PMEP values were below 1% except for the AVL GH14D which was 1.8% and the AVL GH15DK which was at 1.25%. In-cylinder pressure transducer data quality was effectively analyzed using a combination of experimental data and simulation results. Several criteria can be used to investigate the impact of thermal shock on data quality as well as determine the best location and thermal protection for various transducers.

Numerical investigation of effects of addition of ethanol to gasoline on Laminar Flame Speed (LFS), autoignition, and wall quenching

Since the advent of automobiles, alcohol has been considered a possible engine fuel1,2. With the recent increased concern about the high price of crude oil due to fluctuating supply and demand and environmental issues, interest in alcohol based fuels has increased2,3. However, using pure alcohols or blends with conventional fuels in high percentages requires changes to the engine and fuel system design2. This leads to the need for a simple and accurate conventional fuels-alcohol blends combustion models that can be used in developing parametric burn rate and knock combustion models for designing more efficient Spark Ignited (SI) engines. To contribute to this understanding, numerical simulations were performed to obtain detailed characteristics of Gasoline-Ethanol blends with respect to Laminar Flame Speed (LFS), autoignition and Flame-Wall interactions. The one-dimensional premixed flame code CHEMKIN® was applied to simulate the burning velocity and autoignition characteristics using the freely propagating model and closed homogeneous reactor model respectively. Computational Fluid Dynamics (CFD) was used to obtain detailed flow, temperature, and species fields for Flame-wall interactions. A semi-detailed validated chemical kinetic model for a gasoline surrogate fuel developed by Andrae and Head4 was used for the study of LFS and Autoignition. For the quenching study, a skeletal chemical kinetic mechanism of gasoline surrogate, having 50 species and 174 reactions was used. The surrogate fuel was defined as a mixture of pure n-heptane, isooctane, and toluene. For LFS study, the ethanol volume fraction was varied from 0 to 85%, initial pressure from 4 to 8 bar, initial temperature from 300 to 900K, and dilution from 0 to 32%. Whereas for Autoignition study, the ethanol volume fraction was varied between 0 to 85%, initial pressure was varied between 20 to 60 bar, initial temperature was varied between 800 to 1200K, and the dilution was varied between 0 to 32% at equivalence ratios of 0.5, 1.0 and 1.5 to represent the in-cylinder conditions of a SI engine. For quenching study three Ethanol blends, namely E0, E25 and E85 are described in detail at an initial pressure of 8 atm and 17 atm. Initial wall temperature was taken to be 400 K. Quenching thicknesses and heat fluxes to the wall were computed. The laminar flame speed was found to increase with ethanol concentration and temperature but decrease with pressure and dilution. The autoignition time was found to increase with ethanol concentration at lower temperatures but was found to decrease marginally at higher temperatures. The autoignition time was also found to decrease with pressure and equivalence ratio but increase with dilution. The average quenching thickness was found to decrease with an increase in Ethanol concentration in the blend. Heat flux to the wall increased with increase in ethanol percentage in the blend and at higher initial pressures. Whereas the wall heat flux decreased with an increase in dilution. Unburned Hydrocarbon (UHC) and CO % was also found to decrease with ethanol concentration in the blend.

Development of an In Situ Measurement Device for Obtaining Material Thermal Properties

This thesis presents a methodology for measuring thermal properties in situ, with a special focus on obtaining properties of layered stack-ups commonly used in armored vehicle components. The technique involves attaching a thermal source to the surface of a component, measuring the heat flux transferred between the source and the component, and measuring the surface temperature response. The material properties of the component can subsequently be determined from measurement of the transient heat flux and temperature response at the surface alone. Experiments involving multilayered specimens show that the surface temperature response to a sinusoidal heat flux forcing function is also sinusoidal. A frequency domain analysis shows that sinusoidal thermal excitation produces a gain and phase shift behavior typical of linear systems. Additionally, this analysis shows that the material properties of sub-surface layers affect the frequency response function at the surface of a particular stack-up. The methodology involves coupling a thermal simulation tool with an optimization algorithm to determine the material properties from temperature and heat flux measurement data. Use of a sinusoidal forcing function not only provides a mechanism to perform the frequency domain analysis described above, but sinusoids also have the practical benefit of reducing the need for instrumentation of the backside of the component. Heat losses can be minimized by alternately injecting and extracting heat on the front surface, as long as sufficiently high frequencies are used.

Amplified inception of European Little Ice Age by sea ice-ocean-atmosphere feedbacks

The inception of the Little Ice Age (~1400–1700 AD) is believed to have been driven by an interplay of external forcing and climate system internal variability. While the hemispheric signal seems to have been dominated by solar irradiance and volcanic eruptions, the understanding of mechanisms shaping the climate on a continental scale is less robust. In an ensemble of transient model simulations and a new type of sensitivity experiments with artificial sea ice growth, the authors identify a sea ice–ocean–atmosphere feedback mechanism that amplifies the Little Ice Age cooling in the North Atlantic–European region and produces the temperature pattern suggested by paleoclimatic reconstructions. Initiated by increasing negative forcing, the Arctic sea ice substantially expands at the beginning of the Little Ice Age. The excess of sea ice is exported to the subpolar North Atlantic, where it melts, thereby weakening convection of the ocean. Consequently, northward ocean heat transport is reduced, reinforcing the expansion of the sea ice and the cooling of the Northern Hemisphere. In the Nordic Seas, sea surface height anomalies cause the oceanic recirculation to strengthen at the expense of the warm Barents Sea inflow, thereby further reinforcing sea ice growth. The absent ocean–atmosphere heat flux in the Barents Sea results in an amplified cooling over Northern Europe. The positive nature of this feedback mechanism enables sea ice to remain in an expanded state for decades up to a century, favoring sustained cold periods over Europe such as the Little Ice Age. Support for the feedback mechanism comes from recent proxy reconstructions around the Nordic Seas.

Where to find 1.5 million yr old ice for the IPICS "Oldest-Ice" ice core

The recovery of a 1.5 million yr long ice core from Antarctica represents a keystone of our understanding of Quaternary climate, the progression of glaciation over this time period and the role of greenhouse gas cycles in this progression. Here we tackle the question of where such ice may still be found in the Antarctic ice sheet. We can show that such old ice is most likely to exist in the plateau area of the East Antarctic ice sheet (EAIS) without stratigraphic disturbance and should be able to be recovered after careful pre-site selection studies. Based on a simple ice and heat flow model and glaciological observations, we conclude that positions in the vicinity of major domes and saddle position on the East Antarctic Plateau will most likely have such old ice in store and represent the best study areas for dedicated reconnaissance studies in the near future. In contrast to previous ice core drill site selections, however, we strongly suggest significantly reduced ice thickness to avoid bottom melting. For example for the geothermal heat flux and accumulation conditions at Dome C, an ice thickness lower than but close to about 2500 m would be required to find 1.5 Myr old ice (i.e., more than 700 m less than at the current EPICA Dome C drill site). Within this constraint, the resolution of an Oldest-Ice record and the distance of such old ice to the bedrock should be maximized to avoid ice flow disturbances, for example, by finding locations with minimum geothermal heat flux. As the geothermal heat flux is largely unknown for the EAIS, this parameter has to be carefully determined beforehand. In addition, detailed bedrock topography and ice flow history has to be reconstructed for candidates of an Oldest-Ice ice coring site. Finally, we argue strongly for rapid access drilling before any full, deep ice coring activity commences to bring datable samples to the surface and to allow an age check of the oldest ice.

Three-dimensional Vortex Structures on Heated Micro-lattice in a Gas

This paper addresses the microscale heat transfer problem from heated lattice to the gas. A micro-device for enhanced heat transfer is presented and numerically investigated. Thermal creep induces 3-D vortex structures in the vicinity of the lattice. The gas flow is in the slip flow regime (Knudsen number Kn⩽0.1Kn⩽0.1). The simulations are performed using slip flow Navier–Stokes equations with boundary condition formulations proposed by Maxwell and Smoluchowski. In this study the wire thicknesses and distances of the heated lattice are varied. The surface geometrical properties alter significantly heat flux through the surface.

Ar-40/Ar-39 Evidence for Middle Proterozoic (1300-1500 Ma) Slow Cooling of the Southern Black Hills, South Dakota, Midcontinent, North America: Implications for Early Proterozoic P-T Evolution and Posttectonic Magmatism

Ar-40/Ar-39 total gas and plateau dates from muscovite and biotite in the southern Black Hills, South Dakota, provide evidence for a period of Middle Proterozoic slow cooling. Early Proterozoic (1600-1650 Ma) mica dates were obtained from metasedimentary rocks located in a synformal structure between the Harney Peak and Bear Mountain domes and also south of Bear Mountain. Metamorphic rocks from the dome areas and undeformed samples of the similar to 1710 Ma Harney Peak Granite (HPG) yield Middle Proterozoic mica dates (similar to 1270-1500 Ma). Two samples collected between the synform and Bear Mountain dome yield intermediate total gas mica dates of similar to 1550 Ma. We suggest two end-member interpretations to explain the map pattern of cooling ages: (1) subhorizontal slow cooling of an area which exhibits variation in mica Ar retention intervals or (2) mild folding of a Middle Proterozoic (similar to 1500 Ma) similar to 300 degrees C isotherm. According to the second interpretation, the preservation of older dates between the domes may reflect reactivation of a preexisting synformal structure (and downwarping of relatively cold rocks) during a period of approximately east-west contraction and slow uplift during the Middle Proterozoic. The mica data, together with hornblende data from the Black Hills published elsewhere, indicate that the ambient country-rock temperature at the 3-4 kbar depth of emplacement of the HPG was between 350 degrees C and 500 degrees C, suggesting that the average upper crustal geothermal gradient was 25 degrees-40 degrees C/km prior to intrusion. The thermochronologic data suggest HPG emplacement was followed by a similar to 200 m.y. period of stability and tectonic quiescence with little uplift. We propose that crust thickened during the Early Proterozoic was uplifted and erosionally(?) thinned prior to similar to 1710 Ma and that the HPG magma was emplaced into isostatically stable crust of relatively normal thickness. We speculate that uplift and crustal thinning prior to HPG intrusion was the result of differential thinning of the subcrustal lithosphere beneath the Black Hills. If so, this process would have also caused an increase in mantle heat flux across the Moho and triggered vapor-absent melting of biotite to produce the HPG magma. This scenario for posttectonic granite generation is supported, in part, by the fact that in the whole of the Black Hills, the HPG is spatially associated with the deepest exposed Early Proterozoic country rock.