The equation of state of molybdenum at 1400 °C

Shock compression data to 96 GPa for pure molybdenum, initially heated to 1400 °C, are presented. Finite strain analysis of the data gives a bulk modulus at 1400 °C, K_(0S), of 244 ± 2 GPa and its pressure derivative, K′_(0S), of 4. A fit of shock velocity to particle velocity gives the coefficients of U_S = c_0 + sU_P to be c_0 = 4.77 ± 0.06 km/s and s = 1.43 ± 0.05. From the zero‐pressure sound speed c_0, a bulk modulus of 232 ± 6 GPa is calculated which is consistent with extrapolation of ultrasonic elasticity measurements. The temperature derivative of the bulk modulus at zero pressure, ∂K_(0S)/∂T|_P, is approximately −0.012 GPa/K. A thermodynamic model is used to show that the thermodynamic Grüneisen parameter is proportional to the density and independent of temperature. The Mie–Grüneisen equation of state adequately describes the high‐temperature behavior of molybdenum under the present range of shock loading conditions

Controlling the direction of steady electric fields in liquid using non-antiperiodic potentials

When applying an oscillatory electric potential to an electrolyte solution, it is commonly assumed that the choice of which electrode is grounded or powered does not matter because the time-average of the electric potential is zero. Recent theoretical, numerical, and experimental work, however, has established that certain types of multimodal oscillatory potentials that are "non-antiperodic" can induce a net steady field toward either the grounded or powered electrode [Hashemi et al., Phys. Rev. E 105, 065001 (2022)]. Here, we elaborate on the nature of these steady fields through numerical and theoretical analyses of the asymmetric rectified electric field (AREF) that occurs in electrolytes where the cations and anions have different mobilities. We demonstrate that AREFs induced by a non-antiperiodic electric potential, e.g., by a two-mode waveform with modes at 2 and 3 Hz, invariably yields a steady field that is spatially dissymmetric between two parallel electrodes, such that swapping which electrode is powered changes the direction of the field. Additionally, using a perturbation expansion, we demonstrate that the dissymmetric AREF occurs due to odd nonlinear orders of the applied potential. We further generalize the theory by demonstrating that the dissymmetric field occurs for all classes of zero-time-average (no dc bias) periodic potentials, including triangular and rectangular pulses, and we discuss how these steady fields can tremendously change the interpretation, design, and applications of electrochemical and electrokinetic systems

NMR Chemical Shifts of Trace Impurities: Common Laboratory Solvents, Organics, and Gases in Deuterated Solvents Relevant to the Organometallic Chemist

Tables of ^1H and ^(13)C NMR chemical shifts have been compiled for common organic compounds often used as reagents or found as products or contaminants in deuterated organic solvents. Building upon the work of Gottlieb, Kotlyar, and Nudelman in the Journal of Organic Chemistry, signals for common impurities are now reported in additional NMR solvents (tetrahydrofuran-d_8, toluene-d_8, dichloromethane-d_2, chlorobenzene-d_5, and 2,2,2-trifluoroethanol-d_3) which are frequently used in organometallic laboratories. Chemical shifts for other organics which are often used as reagents or internal standards or are found as products in organometallic chemistry are also reported for all the listed solvents

Effect of mass extractions and injections on the performance of a fixed-size humidification–dehumidification desalination system

The impact of mass extractions and injections as a method for increasing the energetic performance of fixed-size humidification–dehumidification desalination systems is examined. Whereas previous studies of this problem have been restricted to thermodynamic models, the use of a more complete model that includes transport provides the ability to quantify the impact of mass extractions/injections on a realizable, fixed-size system. For a closed air, open water cycle, the results show that a single water extraction from the dehumidifier to the humidifier increases the gained output ratio by up to 10%, with extractions higher in the cycle proving more effective. The sizing problem for the humidifier and dehumidifier under thermodynamically optimized conditions found in literature is also discussed, as is the impact of system size on overall performance of a system without extractions/injections. For a range of sizes, it is shown that a rough doubling of both dehumidifier and humidifier size results in a two- to three-fold increase in gained output ratio, with diminishing returns as the absolute sizes increase.Center for Clean Water and Clean Energy at MIT and KFUPM (Project R4-CW-08)Eni S.p.A. (Firm)MIT Martin Family Society of Fellows for Sustainabilit

Shock-wave viscosity measurement

The problem of measuring the viscosity of fluids under shock-loading conditions is discussed. The authors examine in detail the method of Sakharov et al. (1965) and Zaidel' (1967) for measuring shear viscosity from the decay of perturbations on a corrugated shock front. The relevance of initial conditions, finite shock amplitude, bulk viscosity, and the sensitivity of the measurements to the shock boundary conditions are discussed. The validity of the viscous perturbation approach is examined by numerically solving the second-order Navier-Stokes equations. These numerical experiments indicate that shock instabilities may occur even when the Kontorovich-D'yakov stability criteria are satisfied. The corrugated shock front induces mixing of the shocked sample. This mixing is particularly vigorous in viscous materials and may be responsible for the rapid rate of some shock-induced chemical reactions. The experimental results for water at 15 GPa are discussed, and several possibilities are considered to explain why the viscosity obtained by these experiments is so different from those obtained by other methods. Two possible reasons are favored: (1) the analytic method may be inappropriate because it ignores possible complications at the onset of the shock perturbations, and (2) the large effective viscosity determined by this method may reflect the existence of ice VII on the Rayleigh path of the Hugoniot. The latter interpretation reconciles the experimental results with estimates and measurements obtained by other means and is consistent with pressure-volume-temperature Hugoniot data and the phase diagram of H2O

Founder effects and species introductions: A host versus parasite perspective

Species colonizations (both natural and anthropogenic) can be associated with genetic founder effects, where founding populations demonstrate significant genetic bottlenecks compared to native populations. Yet, many successfully established free�living species exhibit little reduction in genetic diversity—possibly due to multiple founding events and/or high propagule pressure during introductions. Less clear, however, is whether parasites may show differential signatures to their free�living hosts. Parasites with indirect life cycles may particularly be more prone to founder effects (i.e., more genetically depauperate) because of inherently smaller founding populations and complex life cycles. We investigated this question in native (east coast) and introduced (west coast) North American populations of a host snail Tritia obsoleta (formerly Ilyanassa obsoleta, the eastern mudsnail) and four trematode parasite species that obligately infect it. We examined genetic diversity, gene flow, and population structure using two molecular markers (mitochondrial and nuclear) for the host and the parasites. In the host snail, we found little to no evidence of genetic founder effects, while the trematode parasites showed significantly lower genetic diversity in the introduced versus native ranges. Moreover, the parasite's final host influenced infection prevalence and genetic diversity: Trematode species that utilized fish as final hosts demonstrated lower parasite diversity and heightened founder effects in the introduced range than those trematodes using birds as final hosts. In addition, inter�regional gene flow was strongest for comparisons that included the putative historical source region (mid�Atlantic populations of the US east coast). Overall, our results broaden understanding of the role that colonization events (including recent anthropogenic introductions) have on genetic diversity in non�native organisms by also evaluating less studied groups like parasites

A multiphysics coupling framework for exascale simulation of fracture evolution in subsurface energy applications

Predicting the evolution of fractured media is challenging due to coupled thermal, hydrological, chemical and mechanical processes that occur over a broad range of spatial scales, from the microscopic pore scale to field scale. We present a software framework and scientific workflow that couples the pore scale flow and reactive transport simulator Chombo-Crunch with the field scale geomechanics solver in GEOS to simulate fracture evolution in subsurface fluid-rock systems. This new multiphysics coupling capability comprises several novel features. An HDF5 data schema for coupling fracture positions between the two codes is employed and leverages the coarse resolution of the GEOS mechanics solver which limits the size of data coupled, and is, thus, not taxed by data resulting from the high resolution pore scale Chombo-Crunch solver. The coupling framework requires tracking of both before and after coarse nodal positions in GEOS as well as the resolved embedded boundary in Chombo-Crunch. We accomplished this by developing an approach to geometry generation that tracks the fracture interface between the two different methodologies. The GEOS quadrilateral mesh is converted to triangles which are organized into bins and an accessible tree structure; the nodes are then mapped to the Chombo representation using a continuous signed distance function that determines locations inside, on and outside of the fracture boundary. The GEOS positions are retained in memory on the Chombo-Crunch side of the coupling. The time stepping cadence for coupled multiphysics processes of flow, transport, reactions and mechanics is stable and demonstrates temporal reach to experimental time scales. The approach is validated by demonstration of 9 days of simulated time of a core flood experiment with fracture aperture evolution due to invasion of carbonated brine in wellbore-cement and sandstone. We also demonstrate usage of exascale computing resources by simulating a high resolution version of the validation problem on OLCF Frontier

The Equation of State of a Molten Komatiite. 1. Shock Wave Compression to 36 GPa

The equation of state (EOS) of an initially molten (1550°C) komatiite (27 wt % MgO) was determined in the 5–36 GPa pressure range via shock wave compression. Shock wave velocity U_s and particle velocity U_p (kilometers/second) follow the linear relationship U_s = 3.13(±0.03) + 1.47(±0.03) U_p . Based on a calculated density at 1550°C, 0 bar of 2.745±0.005 g/cm^3, this U_s -U_p relationship gives the isentropic bulk modulus K_s = 27.0 ± 0.6 GPa, and its first and second isentropic pressure derivatives, K′_s = 4.9 ±0.1 and K″_s = −0.109 ± 0.003 GPa^(−1). The calculated liquidus compression curve agrees within error with the static compression results of Agee and Walker (1988) to 6 GPa but is less dense than their extrapolated values at higher pressures. We determine that olivine (FO_(94)) will be neutrally buoyant in komatiitic melt of the composition that we studied near 8.2 GPa. Clinopyroxene would also be neutrally buoyant near this pressure. Liquidus garnet-majorite may be less dense than this komatiitic liquid in the 20–24 GPa interval; however, pyropic-garnet and perovskite phases are denser than this komatiitic liquid in their respective liquidus pressure intervals to 36 GPa. Liquidus perovskite may be neutrally buoyant near 70 GPa. At 40 GPa, the density of shock-compressed molten komatiite would be approximately equal to the calculated density of an equivalent mixture of dense solid oxide components. This observation supports the model of Rigden et al. (1989) for compressibilities of liquid oxide components. Using their theoretical EOS for liquid forsterite and fayalite, we calculate the densities of a spectrum of melts from basaltic through peridotitic that are related to the experimentally studied komatiitic liquid by addition or subtraction of olivine. At low pressure, olivine fractionation lowers the density of basic magmas, but above 13–14 GPa this trend is reversed. All of these basic to ultrabasic liquids are predicted to have similar densities at 13–14 GPa, and this density is approximately equal to the density of the bulk (preliminary reference Earth model) mantle in this pressure range. This suggests that melts derived from a peridotitic mantle may be inhibited from ascending from depths greater than 400 km

A lower bound for nodal count on discrete and metric graphs

According to a well-know theorem by Sturm, a vibrating string is divided into exactly N nodal intervals by zeros of its N-th eigenfunction. Courant showed that one half of Sturm's theorem for the strings applies to the theory of membranes: N-th eigenfunction cannot have more than N domains. He also gave an example of a eigenfunction high in the spectrum with a minimal number of nodal domains, thus excluding the existence of a non-trivial lower bound. An analogue of Sturm's result for discretizations of the interval was discussed by Gantmacher and Krein. The discretization of an interval is a graph of a simple form, a chain-graph. But what can be said about more complicated graphs? It has been known since the early 90s that the nodal count for a generic eigenfunction of the Schrodinger operator on quantum trees (where each edge is identified with an interval of the real line and some matching conditions are enforced on the vertices) is exact too: zeros of the N-th eigenfunction divide the tree into exactly N subtrees. We discuss two extensions of this result in two directions. One deals with the same continuous Schrodinger operator but on general graphs (i.e. non-trees) and another deals with discrete Schrodinger operator on combinatorial graphs (both trees and non-trees). The result that we derive applies to both types of graphs: the number of nodal domains of the N-th eigenfunction is bounded below by N-L, where L is the number of links that distinguish the graph from a tree (defined as the dimension of the cycle space or the rank of the fundamental group of the graph). We also show that if it the genericity condition is dropped, the nodal count can fall arbitrarily far below the number of the corresponding eigenfunction.Comment: 15 pages, 4 figures; Minor corrections: added 2 important reference