Compressional Regime Research Articles

Investigation of Geological Structures between Acıpınar-Hanobası-Altınkaya (Aksaray-Türkiye) About Satellite-Based Tectonic Lineaments

The region between Aksaray, Central Anatolia, and Altınkaya (Turkey) is included in the study area. The area's basement comprises ophiolites, igneous rocks from the Late Cretaceous period, and metamorphic rocks from the Palaeozoic to Mesozoic ages. Late Cretaceous-Quaternary sedimentary units were formed in the area called Tuzgolü Basin. The Late Cretaceous-Mio-Pliocene sedimentary rocks in the study area have undergone polyphase deformation under compressive and extensional tectonic regimes. As a result of these deformations, the rocks in the area have developed folded, faulted and fractured structures. These structures have formed lineations. In this study, the relationship between the tectonic lineaments identified in the field and those obtained by computer processing of Landsat 8 images was evaluated. It was found that the lineaments belonging to the Tuzgölü fault and the structural geological structures determined in the field are in significant agreement.

Active tectonics in Quaternary marine formations in the Tangier region (North West Rif, Morocco): Persistent Scatterer (PSInSAR) contribution

This study investigates recent tectonic activity in Tangier, Morocco, using PSInSAR data and microtectonic field observations. The exploration of marine deposits in the Achakar basin during the Plio-Quaternary period holds significance for tracking the recent geodynamic changes in the study area. Microtectonic analysis revealed a shift from a NE-SW compressive regime in the Late Pliocene to a Quaternary regime dominated by a NE-SW extension regime and a NW-SE compressive regime. PSInSAR detected ground displacement rates ranging from subsidence (-4.9 mm/yr) to uplift (4.9 mm/yr) during the study period (2018 2021).

Simulating the onset of damage in DCDC tests using a novel gradient‐extended damage model for tension‐compression asymmetry

AbstractIn the present work, an existing framework for gradient‐extended damage is extended to simulate the damage onset in double cleavage drilled compression (DCDC) tests. The main idea is to consider the different evolution of the damage variable under tensile and compressive loading. More specifically, the star‐convex decomposition is exploited to split the strain energy into an active part and an inactive part, and only the active part drives the evolution of the damage variable in the compressive regime. A parameter adopted in the star‐convex decomposition is applied to calibrate the compressive strength independently from the tensile strength, such that the current model can simulate different types of the damage onset. Furthermore, the strengthening effect induced by damage hardening is discussed in this work.

The effect of working fluid and compressibility on the optimal solidity of axial turbine cascades

The blade solidity, namely the blade chord-to-pitch ratio, largely affects the fluid-dynamic performance of turbomachinery and its cost. For turbo-machines operating with air or steam, the optimal value of the solidity which maximizes the efficiency is estimated with empirical correlations such as the ones proposed by <xref ref-type="bibr" rid="fn19">Zweifel (1945)</xref> and <xref ref-type="bibr" rid="fn17">Traupel (1966)</xref>. However, if the turbomachine operates with unconventional fluids, the accuracy of these correlations is questionable. Examples of such fluids are the organic compounds (e.g., hydrocarbons, siloxanes) used in organic Rankine cycle (ORC) power systems. This study concerns an investigation on how the working fluid, its thermodynamic state, and flow compressibility influence the optimum pitch-to-chord ratio of turbine stages. A first principle reduced-order model (ROM) for the computation of profile losses was developed for this purpose. The ROM results are compared with those obtained from numerical simulations of the flow over two axial turbine cascade geometries. The influence of both the working fluid, the flow compressibility, and the solidity value on both the boundary layer state at the blade trailing edge and the base pressure are evaluated. Models to compute mixing and passage losses in the compressible regime as a function of the axial solidity are proposed and discussed. Results show that the value of the optimal solidity of turbine cascades significantly increases with the flow compressibility, and mildly increases if the fluid is in the dense vapor state. Moreover, the optimal solidity value is strongly affected by the mixing process occurring downstream of the blade trailing edge. Therefore, currently available models for its estimation, which are solely based on the minimization of the profile losses, are inaccurate.

Southeastern extension of Singhbhum Shear Zone, Eastern Indian Shield: A detailed appraisal

Trans-crustal, northerly dipping, arcuate Singhbhum Shear Zone (SSZ) constituting the interface of Proterozoic North Singhbhum Mobile Belt (NSMB) and Singhbhum Craton (SC) is established over a strike length of about ∼200 km from Baharagorato Chakradharpur in the west beyond which it bifurcates around the wedge shaped Chakradharpur granite. Based on geological mapping and meso to micro scale structural analysis, present work examines the SSZ’s southeastern extension beyond Baharagora, indicating its southward continuation for about 50 km to Dubukidihi within the NSMB lithopackage. Bangriposi Shear Zone (BSZ) which defines the terrane boundary between the SC and NSMB in this sector, splays towards north as Bangriposi West Shear Zone (BWSZ) and both transects the Dhanjori Basin longitudinally. BSZ and BWSZ are interpreted to be cogenetic with SSZ. NSMB in this area comprises of pelitic and psamopelitic rocks intruded by mafic–ultramafic magmatism and granitoids. Considering a north to south compression regime during accretion of NSMB with SC, the study area, which forms the interface between the craton and mobile belt, is at an acute to obtuse angle with the direction of overall stress field. It is marked by several high strain zones characterized by N-S shear band cleavages with moderate easterly dips, and northerly pitching stretching/mineral lineation. Consistent westerly vergent folds on mylonitic plane and orientation of stretching lineation indicates top to WSW movement in the shear zones. Tectonically interleaved mafic–ultramafic schist within the Romapahari granite are sites of copper mineralization with enhanced nickel concentration pointing towards future exploration sites for epigenetic copper, uranium mineralization which is so characteristic of SSZ.

Physics-informed neural networks for weakly compressible flows using Galerkin–Boltzmann formulation

In this work, we study the Galerkin–Boltzmann formulation within a physics-informed neural network (PINN) framework to solve flow problems in weakly compressible regimes. The Galerkin–Boltzmann equations are discretized with second-order Hermite polynomials in microscopic velocity space, which leads to a first-order conservation law with six equations. Reducing the output dimension makes this equation system particularly well suited for PINNs compared with the widely used D2Q9 lattice Boltzmann velocity space discretizations. We created two distinct neural networks to overcome the scale disparity between the equilibrium and non-equilibrium states in collision terms of the equations. We test the accuracy and performance of the formulation with benchmark problems and solutions for forward and inverse problems with limited data. We compared our approach with the incompressible Navier–Stokes equation and the D2Q9 formulation. We show that the Galerkin–Boltzmann formulation results in similar L2 errors in velocity predictions in a comparable training time with the Navier–Stokes equation and lower training time than the D2Q9 formulation. We also solve forward and inverse problems for a flow over a square, try to capture an accurate boundary layer, and infer the relaxation time parameter using available data from a high-fidelity solver. Our findings show the potential of utilizing the Galerkin–Boltzmann formulation in PINN for weakly compressible flow problems.

An asymptotic-preserving and exactly mass-conservative semi-implicit scheme for weakly compressible flows based on compatible finite elements

We present a novel asymptotic-preserving semi-implicit finite element method for weakly compressible and incompressible flows based on compatible finite element spaces. The momentum is sought in an H(div)-conforming space, ensuring exact pointwise mass conservation at the discrete level. We use an explicit discontinuous Galerkin-based discretization for the nonlinear convective terms, while treating the pressure and viscous terms implicitly, so that the CFL condition depends only on the fluid velocity. To handle shocks and damp spurious oscillations in the compressible regime, we incorporate an a posteriori limiter that employs artificial viscosity and is based on a discrete maximum principle. By using hybridization, the final algorithm requires solving only symmetric positive definite linear systems. As the Mach number approaches zero and the density remains constant, the method naturally converges to an H(div)-based discretization of the incompressible Navier-Stokes equations in the vorticity-velocity-pressure formulation. Several numerical tests validate the proposed method.

Three-dimensional eigensolutions of the unsteady compressible boundary-region equations

A previous paper of the authors (Duck & Stephen, J. Fluid Mech., vol. 917, 2021, A56) considered the effect of three-dimensional, temporally periodic, linear and incompressible disturbances on a Blasius boundary layer, in particular when the disturbance wavelength is both comparable to and longer than the boundary-layer thickness. This previous study revealed that, unlike the two-dimensional counterpart, a mode exists that exhibits regimes of downstream spatial growth. In this paper we extend the analysis to the compressible regime, based on the boundary-region equations methodology. The aforementioned unstable mode is seen to persist into the compressible regime, and is studied using a combination of numerical and asymptotic methods. The paper adopts several approaches. First is a numerical approach in which the spatial development of the disturbances is assessed. This then leads to a consideration of the far-downstream behaviour, using (several) asymptotic limits. Of some note, in addition to unstable modes found in the incompressible case, is the existence of a further class of instability, not found in the incompressible case (which is also analysed asymptotically), corresponding to what amounts to an inviscid instability. The far-downstream analysis enables a (sub-)classification into entropy and non-entropy modes. The former, according to this analysis, are spatially damped, with one caveat, as revealed by our marching procedure, which highlights how spatial development of disturbances can be important.

Spatially varying stress regime in the southern Junggar Basin, NW China

The southern Junggar Basin in NW China is an important tectonic unit in the region of the Tibetan Plateau and has been the focus of considerable research into its tectonic processes and geodynamic setting. However, the relationship between deep structural deformation and stress in this region remains unclear. This study investigates the Gaoquan and Hutubi anticlines in the southern Junggar Basin using three-dimensional geophysical data and a finite-element numerical simulation to examine the crustal stress distribution and stress regime at depths of up to 7 km. Numerical simulation results indicate that the stress regime in the southern Junggar Basin changes from west to east. In the western part of the region, including the Gaoquan anticline at depths of 4900–6100 m, the maximum horizontal principal stress shows a peak of 140–200 MPa, the minimum horizontal principal stress is 110–170 MPa, and the vertical principal stress is 115–175 MPa, indicating a mixed stress regime incorporating both compression and strike-slip components. In the eastern part of the region, including the Hutubi anticline at depths of 5400–7800 m, the maximum horizontal principal stress shows a peak of 160–280 MPa, the minimum horizontal principal stress is 155–250 MPa, and the vertical principal stress is 125–215 MPa, indicating a compressive stress regime. The stress magnitude and orientation are affected by the presence of faults and depth in the crust. Combining these results with the regional tectonic setting, it is considered that the geometrical relationship between pre-existing faults and the current stress field is the main control on the west–east differentiation in the stress regime, with spatial variations in the mechanical parameters of the crust and the pressure coefficient being secondary factors. These results provide insights into the relationship between stress and deformation, and support the updated version of the World Stress Map database.

Deep‐Focus Earthquake Mechanisms at the Subducting Nazca Plate (Peru‐Brazil Border): Cold Slab Behavior in a Warm Plate

AbstractWe calculate focal mechanisms and centroid depths for deep‐focus earthquakes (DFEs) along the Peru‐Brazil border. We obtained a total of 28 focal solutions for events with magnitudes between 4.2 and 7.5 Mw and occurring between 2014 and 2022. Focal mechanisms indicate predominance of normal faulting, demonstrating a rather uniform down‐dip compression (DDC) regime within the plate. The orientations of the nodal planes suggest that earthquakes tend to occur along faults parallel to the local slab strike, although other fault types are documented. Stress orientations derived from the focal mechanisms agree with patterns expected if faulting were initiated by transformational faulting on a metastable olivine wedge (MOW) under DDC. Centroid depths range between 557 and 659 km, defining a narrow seismic zone within the lower portion of the subducting plate and an aseismic upper portion. We suggest that DFEs nucleate through transformational faulting within a narrow MOW preserved at a colder slab segment right above the lower mantle and juxtaposed to a shallower, warmer segment at around 500 km depth. This thermal complexity was possibly produced through flat subduction initiated by the subduction of the Nazca Ridge. We speculate that subduction of other aseismic ridges is possibly controlling the thermal state of the Nazca slab as a whole and, consequently, the depth distribution of DFEs along the South America subduction front.

Turbulence effects in the topology optimization of compressible subsonic flow

AbstractTurbulence significantly influences fluid flow topology optimization, and this has already been verified under the incompressible flow regime. However, the same cannot be said about the compressible flow regime, in which the density field now affects and couples all of the fluid flow and turbulence equations and makes obtaining the adjoint model, which is necessary for topology optimization, extremely difficult. Up to now, the turbulence phenomenon has still not been considered in compressible flow topology optimization, which is what is being proposed and analyzed here. Rather than being based in the Reynolds‐Averaged Navier–Stokes (RANS) equations which are defined only for incompressible flow, the equations are now based on the Favre‐Averaged Navier–Stokes (FANS) equations, which are the counterpart of the RANS equations for compressible flow and feature different dependencies and terms. The compressible turbulence model being considered is the compressible version of the Spalart–Allmaras model, which differs from the usual Spalart–Allmaras model, since now there are some new spatially varying density and specific heat terms that depend on the primal variables and that act over some of the turbulence terms of the overall model. The adjoint equations are obtained by using an automatic differentiation scheme through a coupled software platform. The optimization algorithm is IPOPT, and some examples are presented to show the effect of turbulence in the compressible flow topology optimization.

Modified Zweifel Coefficient and Lift Coefficient Definition Considering Compressible Effect

The accurate prediction of blade loading is crucial to designing efficient turbomachinery, but traditional methods often neglect the impact of compressibility, leading to inaccuracies at high speeds. This study investigates the effect of compressibility on the blade loading parameters, particularly the Zweifel coefficient (Zw) and lift coefficient (CL), in turbine cascades. A novel intermediate method (IM), with averaged flow properties derived from both inlet and outlet conditions, is proposed to enhance the accuracy of Zw and CL calculations in compressible flow regimes. This method is based on the extended Kutta–Joukowski theorem for compressible flow and incorporates the Mach number directly into the modified definitions of Zw and CL. The analysis reveals that the averaged flow angle (αm), calculated by using a velocity-weighted approach, serves as a crucial parameter for blade similarity studies. The proposed correction method is applied and validated based on CFD simulations of the VKI-RG turbine cascade. The IM and modified definitions provide a robust framework for accurately predicting blade loading at high speeds, enabling improved design and analysis of turbomachinery.

Anomalous Landau Level Gaps Near Magnetic Transitions in Monolayer WSe2

First-order phase transitions produce abrupt changes to the character of both ground and excited electronic states. Here we conduct electronic compressibility measurements to map the spin phase diagram and Landau level (LL) energies of monolayer WSe2 in a magnetic field. We resolve a sequence of first-order phase transitions between completely spin-polarized LLs and states with LLs of both spins. Unexpectedly, the LL gaps are roughly constant over a wide range of magnetic fields below the transitions, which we show reflects spin-polarized ground states with opposite spin excitations. These transitions also extend into compressible regimes, with a sawtooth boundary between full and partial spin polarization. We link these observations to the important influence of LL filling on the exchange energy beyond a smooth density-dependent contribution. Our results show that WSe2 realizes a unique hierarchy of energy scales where such effects induce reentrant magnetic phase transitions tuned by density and magnetic field. Published by the American Physical Society 2024

A route for tunable C-VO doped perovskite SrTiO3 functionalities through epitaxial strain engineering

Using density functional theory calculations, the interaction between oxygen vacancies and carbon in bi-axially strained SrTiO3 has been investigated. CTi-Vo binding energy and reorientation of CTi have been examined for ±1%, ±2%, ±3% and ±4% compressive and tensile strains. The results show that compressive strain is an effective route to restrict the diffusion of electrically active Vo in the presence of CTi dopants. According to our results the reorientation barrier volumetric and bi-axial strain dependences differ in the compression and tension regimes and is expected to affect dielectric characteristics of SrTiO3 under an alternating electric field.

Nonclassical wave propagation measurements in the high temperature vapor of D6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {D}_{6}$$\\end{document} with the asymmetric shock tube for experiments in rarefaction waves (ASTER)

A novel test setup called the asymmetric shock tube for experiments on nonideal rarefaction waves (ASTER) has been commissioned at Delft University of Technology. The ASTER, which works according to the principle of Ludwieg tubes, is designed to generate and measure the speed of small and finite amplitude waves propagating in the dense vapors of fluids formed by complex organic molecules, therefore in the nonideal compressible fluid dynamics regime. The ultimate goal of the associated research is to prove the existence of nonclassical gasdynamics. The setup consists of a high-pressure charge tube and a vacuum tank separated by a glass disk equipped with a breaking mechanism for rarefaction waves experiments. When the glass disk is broken, an expansion wave propagates into the tube in the direction opposite to the fluid flow. The propagation speed of this wave is measured using a time-of-flight method with the help of four fast-response pressure sensors placed equidistantly in the middle of the tube. The charge tube can withstand pressures and temperatures of up to 15 bar and 400∘C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\circ }\\mathrm{C}$$\\end{document}. Preliminary rarefaction experiments were successfully conducted using dodecamethylcyclohexasiloxane, D6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {D}_{6}$$\\end{document}, as the working fluid and at pressures and temperatures of up to 9.4 bar and 372∘C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\circ }\\mathrm{C}$$\\end{document} , respectively. The results of an experiment featuring the initial state for which a theoretical model predicts the nonclassical acceleration of rarefaction waves show that the propagation is qualitatively different from that put into evidence by experiments for which the propagation is classic. Upcoming setup improvements and experimental campaigns are planned with the objective of experimentally verifying the existence of nonclassical gasdynamics.Graphical abstract

An all Mach number scheme for visco-resistive magnetically-dominated MHD flows

In this work we present a novel conservative, semi-implicit, finite-volume scheme, designed for the numerical simulation of magnetically-dominated plasma rapidly evolving from a near-equilibrium state into a time-dependent compressible regime. The proposed scheme utilises a well-studied flux vector splitting approach, where the ideal magnetohydrodynamic (MHD) system is partitioned into two sub-systems, one containing all the advective terms and the other containing the rest of the terms, including not only the gas pressure but also magnetic pressure terms. The former is discretised explicitly as part of a standard finite-volume update, while the latter is treated implicitly by means of a nested Picard algorithm. As a result, the algorithm is constrained only by a mild velocity CFL stability condition, rendering it highly suitable for low Mach number flows in both gas and magnetic pressure dominated conditions, and for the incompressible limit of the MHD equations. The visco-resistive dissipative terms are also treated implicitly so that the numerical stability of the algorithm remains dependent only on the fluid velocity, maintaining its efficiency even for visco-resistive dominated problems. The divergence constraint of the magnetic field is handled through either staggered or unstaggered adaptations of the constrained transport methodology, which are both shown to preserve the divergence error up to machine precision levels. The algorithm is validated thoroughly by means of several benchmark problems for high and low Mach number flows, as well as multiple visco-resistive test cases. The scheme is found to perform well for both regimes, providing accurate and computationally efficient results in low Mach number flows in both gas and magnetic pressure dominated scenarios, while also demonstrating excellent shock-capturing capacity. A novel test case is finally introduced to truly demonstrate the all Mach number capabilities of the proposed scheme.

Stress regimes in the Himalaya–Karakoram–Tibet, the western part of India–Eurasia collision: stress field implications based on focal mechanism solution data

SUMMARY The stress regime patterns of high-seismically active regions within the western part of the India–Eurasia collision, spanning from 67° E to 83° E and 27° N to 39° N, are elucidated through analysis of 684 Focal Mechanism Solutions from 1962 to 2021. Eighteen seismically active zones used for the stress tensor inversion, are defined based on the spatial extent of the seismicity, the depth distribution of seismic events, focal mechanism studies, and seismotectonics of the region. The defined regimes are: (1) Sulaiman Ranges and Lobe Region, (2) Hindukush, (3) Pamir, (4) Nanga Parbat Syntaxis, (5) Hazara Syntaxis, (6) Kashmir–Zanskar region, (7) Kangra–Chamba, (8) Kinnaur and Kaurik–Chango fault zone (KCFZ), (9) Garhwal, (10) Kumaon, (11) Karakoram fault zone, and (12) Gozha–Ashikule fault zone. Seismicity is reported only in the crust or up to mid-crust in most of the regions, except for the Pamir and Hindukush, where the seismicity can be observed down to 160 and 280 km, respectively. We report a clockwise rotation of the maximum horizontal stress (SHmax) of about 42° and 21° in the Hindukush and Pamir regions, respectively. with increasing focal depths from north west to north. The region where major and strong earthquakes occur indicates pure compressive regimes. Most of the zones support transpressive and transtensional tectonics with a few zones by normal and strike-slip fault regimes. Regions like Nanga Parbat syntaxis, Kinnaur, KCFZ, and Zanskar are exceptions, where extensional and transformational tectonic features dominate. Plate convergence force has less effect on defining the stress regime in the Karakoram fault zone and Gozha–Ashikule regions, which display transtensional and pure extensional regimes, respectively. Underthrusting of the Indian plate through complex tectonics is indicated by dominant compression stresses with evidences of normal, strike-slip, and oblique fault mechanisms.

An explicit primitive conservative solver for the Euler equations with arbitrary equation of state

This work presents a procedure to solve the Euler equations by explicitly updating, in a conservative manner, a generic thermodynamic variable such as temperature, pressure or entropy instead of the total energy. The presented procedure is valid for any equation of state and spatial discretization. When using complex equations of state such as Span–Wagner, choosing the temperature as the generic thermodynamic variable yields great reductions in the computational costs associated to thermodynamic evaluations. Results computed with a state of the art thermodynamic model are presented, and computational times are analyzed. Particular attention is dedicated to the conservation of total energy, the propagation speed of shock waves and jump conditions. The procedure is thoroughly tested using the Span–Wagner equation of state through the CoolProp thermodynamic library and the Van der Waals equation of state, both in the ideal and non-ideal compressible fluid-dynamics regimes, by comparing it to the standard total energy update and analytical solutions where available.

The Intraplate Stress Field of West Africa

AbstractWest Africa continues to host a growing number of low and intermediate‐magnitude earthquakes (M2‐5) along its passive margins, and its continental interior. Earthquake activity in these regions raises the need to comprehend the causes and the tectonic controls of the seismicity. Unfortunately, such studies are rare. Here, we apply single‐station inversion techniques to constrain fourteen focal mechanisms, computed after compiling a set of high‐quality waveforms. We describe the connection between seismicity, the contemporary stress field, anthropogenic activity and Holocene fault scarps in the region. Our results indicate transpressive stresses acting on the inherited brittle structures in the passive margins. We also observe a compressive regime in the intracontinental failed rifts. We attribute the seismicity to the reactivation of “weak” faults in the Neoproterozoic and Mesozoic failed rifts, the passive transform structures, and the intracratonic Precambrian brittle shear zones.

The Chain of Processes Forming Porphyry Copper Deposits—An Invited Paper

Abstract Porphyry-related mineral deposits are giant geochemical anomalies in the Earth’s crust with orders-of-magnitude differences in the content and proportion of the three main ore metals Cu, Au, and Mo. Deposit formation a few kilometers below surface is the product of a chain of geologic processes operating at different scales in space and time. This paper explores each process in this chain with regard to optimizing the chances of forming these rare anomalies. On the lithosphere scale, deposits with distinct metal ratios occur in provinces that formed during brief times of change in plate motions. Similar metal ratios of several deposits in such provinces compared with global rock reservoirs suggest preceding enrichment of Au or Mo in lithospheric regions giving rise to distinct ore provinces. The largest Cu-dominated deposits and provinces are traditionally explained by selective removal of Au during generation or subsequent evolution of mantle magmas, but the possibility of selective Cu pre-enrichment of lithosphere regions by long-term subduction cannot be dismissed, even though its mechanism remains speculative. Evolution of hydrous basaltic melts to fertile magmas forming porphyry Cu deposits requires fractionation toward more H2O-rich magmas in the lower crust, as shown by their adakite-like trace element composition. The prevailing interpretation that this fractionation leads to significant loss of chalcophile ore metals by saturation and removal of magmatic sulfide might be inverted to a metal enrichment step, if the saturating sulfides are physically entrained with the melt fraction of rapidly ascending magmas. Ascent of fertile magma delivers a large mass of H2O-rich ore fluid to the upper crust, along points of weakness in an overall compressive stress regime, within a limited duration as required by mass and heat balance constraints. Two mechanisms of rapid magma ascent are in debate: (1) wholesale emplacement of highly fractionated and volatile-rich granitic melt into a massive transcrustal channelway, from which fluids are exsolved by decompression starting in the lower crust, or (2) partly fractionated magmas filling a large upper crustal magma chamber, from which fluids are expelled by cooling and crystallization. Transfer of ore-forming components to a hydrothermal ore fluid is optimized if the first saturating fluid is dense and Cl rich. This can be achieved by fluid saturation at high pressure, or after a moderately H2O rich intermediate-composition melt further crystallizes in an upper crustal reservoir before reaching fluid saturation. In either case, metals and S (needed for later hydrothermal sulfide precipitation) are transferred to the fluid together, no matter whether ore components are extracted from the silicate melt or liberated to the ore fluid by decomposition of magmatic sulfides. Production and physical focusing of fluids in a crystallizing upper crustal magma chamber are controlled by the rate of heat loss to surrounding rocks. Fluid focusing, requiring large-scale lateral flow, spontaneously occurs in mushy magma because high water content and intermediate melt/crystal ratio support a network of interconnected tubes at the scale of mineral grains. Calculated cooling times of such fluid-producing magma reservoirs agree with the duration of hydrothermal ore formation measured by high-precision zircon geochronology, and both relate to the size of ore deposits. Ore mineral precipitation requires controlled flow of S- and metal-rich fluids through a vein network, as shown by fluid inclusion studies. The degree of hydrothermal metal enrichment is optimized by the balance between fluid advection and the efficiency of cooling of the magmatic fluid plume by heat loss to convecting meteoric water. The depth of fluid production below surface controls the pressure-temperature (P-T) evolution along the upflow path of magmatic fluids. Different evolution paths controlling density, salinity, and phase state of fluids contribute to selective metal precipitation: porphyry Au deposits can form at shallow subvolcanic levels from extremely saline brine or salt melt; high-grade Au-Cu coprecipitation from coexisting and possibly rehomogenizing brine and vapor is most efficient at a depth of a few kilometers; whereas fluids cooling at greater depth tend to precipitate Cu ± Mo but transport Au selectively to shallower epithermal levels. Exhumation and secondary oxidation and enrichment by groundwater finally determine the economics of a deposit, as well as the global potential of undiscovered metal resources available for future mining.