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All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Aerodynamic properties of turbulent combustion fields

Flow fields involving turbulent flames in premixed gases under a variety of conditions are modeled by the use of a numerical technique based on the random vortex method to solve the Navier-Stokes equations and a flame propagation algorithm to trace the motion of the front and implement the Huygens principle, both due to Chorin. A successive over-relaxation hybrid method is applied to solve the Euler equation for flows in an arbitrarily shaped domain. The method of images, conformal transformation, and the integral-equation technique are also used to treat flows in special cases, according to their particular requirements. Salient features of turbulent flame propagation in premixed gases are interpreted by relating them to the aerodynamic properties of the flow field. Included among them is the well-known cellular structure of flames stabilized by bluff bodies, as well as the formation of the characteristic tulip shape of flames propagating in ducts. In its rudimentary form, the mechanism of propagation of a turbulent flame is shown to consist of: (1) rotary motion of eddies at the flame front, (2) self-advancement of the front at an appropriate normal burning speed, and (3) dynamic effects of expansion due to exothermicity of the combustion reaction. An idealized model is used to illustrate these fundamental mechanisms and to investigate basic aerodynamic features of flames in premixed gases. The case of a confined flame stabilized behind a rearward-facing step is given particular care and attention. Solutions are shown to be in satisfactory agreement with experimental results, especially with respect to global properties such as the average velocity profiles and reattachment length.

Hsiao, C. C.↗
NASA NTRS2012

Investigation of Freeze and Thaw Cycles of a Gas-Charged Heat Pipe

The traditional constant conductance heat pipes (CCHPs) currently used on most spacecraft run the risk of bursting the pipe when the working fluid is frozen and later thawed. One method to avoid pipe bursting is to use a gas-charged heat pipe (GCHP) that can sustain repeated freeze/thaw cycles. The construction of the GCHP is similar to that of the traditional CCHP except that a small amount of non-condensable gas (NCG) is introduced and a small length is added to the CCHP condenser to serve as the NCG reservoir. During the normal operation, the NCG is mostly confined to the reservoir, and the GCHP functions as a passive variable conductance heat pipe (VCHP). When the liquid begins to freeze in the condenser section, the NCG will expand to fill the central core of the heat pipe, and ice will be formed only in the grooves located on the inner surface of the heat pipe in a controlled fashion. The ice will not bridge the diameter of the heat pipe, thus avoiding the risk of pipe bursting during freeze/thaw cycles. A GCHP using ammonia as the working fluid was fabricated and then tested inside a thermal vacuum chamber. The GCHP demonstrated a heat transport capability of more than 200W at 298K as designed. Twenty-seven freeze/thaw cycles were conducted under various conditions where the evaporator temperature ranged from 163K to 253K and the condenser/reservoir temperatures ranged from 123K to 173K. In all tests, the GCHP restarted without any problem with heat loads between 10W and 100W. No performance degradation was noticed after 27 freeze/thaw cycles. The ability of the GCHP to sustain repeated freeze/thaw cycles was thus successfully demonstrated.

Ku, Jentung↗
NASA NTRS2014

Ground Testing of the EMCS Seed Cassette for Biocompatibility with the Cellular Slime Mold, Dictyostelium Discoideum

The European Modular Cultivation System, EMCS, was developed by ESA for plant experiments. To expand the use of flight verified hardware for various model organisms, we performed ground experiments to determine whether ARC EMCS Seed Cassettes could be adapted for use with cellular slime mold for future space flight experiments. Dictyostelium is a cellular slime mold that can exist both as a single-celled independent organism and as a part of a multicellular colony which functions as a unit (pseudoplasmodium). Under certain stress conditions, individual amoebae will aggregate to form multicellular structures. Developmental pathways are very similar to those found in Eukaryotic organisms, making this a uniquely interesting organism for use in genetic studies. Dictyostelium has been used as a genetic model organism for prior space flight experiments. Due to the formation of spores that are resistant to unfavorable conditions such as desiccation, Dictyostelium is also a good candidate for use in the EMCS Seed Cassettes. The growth substratum in the cassettes is a gridded polyether sulfone (PES) membrane. A blotter beneath the PES membranes contains dried growth medium. The goals of this study were to (1) verify that Dictyostelium are capable of normal growth and development on PES membranes, (2) develop a method for dehydration of Dictyostelium spores with successful recovery and development after rehydration, and (3) successful mock rehydration experiments in cassettes. Our results show normal developmental progression in two strains of Dictyostelium discoideum on PES membranes with a bacterial food source. We have successfully performed a mock rehydration of spores with developmental progression from aggregation to slug formation, and production of morphologically normal spores within 9 days of rehydration. Our results indicate that experiments on the ISS using the slime mold, Dictyostelium discoideum could potentially be performed in the flight verified hardware of the EMCS ARC Seed Cassettes.

biocompatibility↗
NASA NTRS1978

Strainrange partitioning behavior of the nickel-base superalloys, Rene 80 and IN-100

A study was made to assess the ability of the method of strainrange partitioning (SRP) to both correlate and predict high temperature, low cycle fatigue lives of nickel-base superalloys for gas turbine applications. Baseline data from strain-controlled, low cycle fatigue tests were expressed in terms of the PP, PC, CP, and CC partitioned inelastic strainrange versus life relationships for coated and uncoated Rene' 80 at 1000 C, Gatorized (creep-formed)IN 100 at 760 C, and cast IN 100 at 925 C. The SRP is shown to correlate the cyclic lives of the baseline tests to within factors of nearly two. The partitioned strainrange versus life relationships for uncoated Rene' 80 and cast IN 100 were also determined from the ductility normalized-strainrange partitioning equations. These were used to predict the cyclic lives of the baseline tests. Predicted and observed cyclic lives agreed to within factors of nearly three.

Halford, G. R.↗
NASA NTRS2009

Cambium

The Cambium investigation is one in a pair of investigations which utilizes the Advanced Biological Research System (ABRS). Cambium seeks definitive evidence that gravity has a direct effect on cambial cells (cells located under the inner bark where secondary growth occurs) in willow, Salix babylonica. The Cambium investigation uses willow plants flown on the International Space Station to better understand the fundamental processes by which plants produce cellulose and lignin, the two main structural materials found in plant matter. On Earth, the nature of wood within tree stems varies depending on position, and that within-tree variation includes differences in cell types and chemistry including lignin and cellulose, two major components of wood influencing wood strength, usefulness and carbon content. Reaction wood is an extreme example of such variation, and it is believed that reaction wood develops as a reaction to the influence of gravity. For the Cambium experiment, young willow plants will be launched to the ISS where their stems will be looped in an attempt to induce reaction wood formation. After on-orbit growth, the plants will be preserved and returned to Earth for analysis. Understanding the role of gravity in wood formation is expected to enable wiser management of forests for carbon sequestration as well as better utilization of trees for wood products. Detailed Research Description: The Cambium experiment will provide an understanding of physiological processes such as gene expression, metabolism and general plant development that are affected in plant systems exposed to space flight. Cambium seeks definitive evidence that gravity has a direct effect on the cambial cells (cells located under the inner bark where secondary growth occurs) that contribute to xylogenesis (reaction wood formation) in willow plants, Salix babylonica. Tension wood fibers differentiate on the upper sides of stems when the stem is altered from its normal (vertical) growth position by looping. This reaction wood response does not occur if the orientation of the plant stem with respect to gravity is not altered. If a localized zone of tension wood should be formed in looped stems under microgravity conditions, this would be the first conclusive evidence that gravity is not required. On the other hand, if a zone of tension wood is not produced in looped stems (subjected to tension on one side, compression on the other) in microgravity, this would be the first definitive evidence that gravity has a direct effect on the cambial cells which contribute to reaction wood formation. Following return to Earth the plants will be analyzed by microscopy and chemical methods.

Savidge, Rodney↗
NASA NTRS1972

Calculation of heat transfer on shuttle type configurations including the effects of variable entropy at boundary layer edge

A relatively simple method is presented for including the effect of variable entropy at the boundary-layer edge in a heat transfer method developed previously. For each inviscid surface streamline an approximate shockwave shape is calculated using a modified form of Maslen's method for inviscid axisymmetric flows. The entropy for the streamline at the edge of the boundary layer is determined by equating the mass flux through the shock wave to that inside the boundary layer. Approximations used in this technique allow the heating rates along each inviscid surface streamline to be calculated independent of the other streamlines. The shock standoff distances computed by the present method are found to compare well with those computed by Maslen's asymmetric method. Heating rates are presented for blunted circular and elliptical cones and a typical space shuttle orbiter at angles of attack. Variable entropy effects are found to increase heating rates downstream of the nose significantly higher than those computed using normal-shock entropy, and turbulent heating rates increased more than laminar rates. Effects of Reynolds number and angles of attack are also shown.

Dejarnette, F. R.↗
NASA NTRS1995

Report on twisted nematic and supertwisted nematic device characterization program

In this study we measured the optical characteristics of normally white twisted nematic (NWTN) and super twisted nematic (STN ) cells. Though no dynamic computer model was available, the static observations were compared with computer simulated behavior. The measurements were taken as a function of both viewing angle and applied voltage and included in the static case not only luminance but also contrast ratio and chromaticity . We employed the computer model Twist Cell Optics, developed at Kent State in conjunction with this study, and whose optical modeling foundation, Iike the ViDEOS program, is the 4 x 4 matrix method of Berreman. In order to resolve discrepancies between the experimental and modeled data the optical parameters of the individual cell components, where not known, were determined using refractometry, profilometry, and various forms of ellipsometry. The resulting agreement between experiment and model is quite good due primarily to a better understanding of the structure and optics of dichroic sheet polarizers. A description of the model and test cells employed are given in section 2. Section 3 contains the experimental data gathered and section 4 gives examples of the fit between model and experiment. Also included with this report are a pair of papers which resulted from the research and which detail the polarizer properties and some of the cell characterization methods.

Source record↗
NASA NTRS2006

Difficulties in Laboratory Studies and Astronomical Observations of Organic Molecules: Hydroxyacetone and Lactic Acid

For the past 35 years, radio astronomy has revealed a rich organic chemistry in the interstellar gas, which is exceptionally complex towards active star-forming regions. New solar systems condense out of this gas and may influence the evolution of life on newly formed planets. Much of the biologically important functionality is present among the some 130 gas-phase molecules found to date, including alcohols, aldehydes, ketones, acids, amines, amides and even the simplest sugar - glycolaldehyde. Still, many unidentified interstellar radio signals remain, and their identification relies on further laboratory study. The molecules hydroxyacetone and lactic acid are relatively small organic molecules, but possess rather complex rotational spectra owing to their high asymmetry. Hydroxyacetone is particularly problematic because it possess a very low barrier to internal rotation, and exhibits strong coupling of the free-rotor states with the overall rotation of the molecule. As in the case of acetamide, a full decomposition method was employed to order the resultant eigenstates onto normal asymmetric top eigenvectors.

Apponi, A. J.↗
NASA NTRS1998

Profile Evolution Simulation in Etching Systems Using Level Set Methods

Semiconductor device profiles are determined by the characteristics of both etching and deposition processes. In particular, a highly anisotropic etch is required to achieve vertical sidewalls. However, etching is comprised of both anisotropic and isotropic components, due to ion and neutral fluxes, respectively. In Ar/Cl2 plasmas, for example, neutral chlorine reacts with the Si surfaces to form silicon chlorides. These compounds are then removed by the impinging ion fluxes. Hence the directionality of the ions (and thus the ion angular distribution function, or IAD), as well as the relative fluxes of neutrals and ions determines the amount of undercutting. One method of modeling device profile evolution is to simulate the moving solid-gas interface between the semiconductor and the plasma as a string of nodes. The velocity of each node is calculated and then the nodes are advanced accordingly. Although this technique appears to be relatively straightforward, extensive looping schemes are required at the profile corners. An alternate method is to use level set theory, which involves embedding the location of the interface in a field variable. The normal speed is calculated at each mesh point, and the field variable is updated. The profile comers are more accurately modeled as the need for looping algorithms is eliminated. The model we have developed is a 2-D Level Set Profile Evolution Simulation (LSPES). The LSPES calculates etch rates of a substrate in low pressure plasmas due to the incident ion and neutral fluxes. For a Si substrate in an Ar/C12 gas mixture, for example, the predictions of the LSPES are identical to those from a string evolution model for high neutral fluxes and two different ion angular distributions.(2) In the figure shown, the relative neutral to ion flux in the bulk plasma is 100 to 1. For a moderately isotropic ion angular distribution function as shown in the cases in the left hand column, both the LSPES (top row) and rude's string method (bottom row) predict tapered profiles. The LSPES uses an AD with a FWHM = 13.5 degrees, and rude's model uses a ratio of sheath voltage to ion temperature of 50. The more anisotropic IADs produce profiles with more vertical sidewalls and a wider bottom surface, as shown in the right hand column. Here, the LSPES has an AD with a FWHM = 2 degrees, and rude's model uses a ratio of 500 of sheath voltage to ion temperature. The agreement between the LSPES and rude's model is excellent in both cases. We will present etching profiles generated by the LSPES, including calculations of the re-emitted fluxes of both neutrals and ions off of the profile walls. In addition, we will show the effect of geometric structures (overhangs, etc.) on the etching profiles. Other physical aspects, such as surface diffusion, will also be included in the model.

Hwang, Helen H.↗
NASA NTRS1984

Impact of LANDSAT MSS Sensor Differences on Change Detection Analysis

Change detection techniques were used to pinpoint differences in the multispectral band scanners on LANDSAT 2, 3, and 4 satellites. The method of analysis was to co-register 512 by 512 pixel subwindows for all data pairs followed by scattergram generation and analysis. In all cases, the LANDSAT-4 data were used as the base to which other images were registered. There appear to be no major problems preventing use of LANDSAT-4 MSS with previous MSS sensors for charge detection, provided the interference noise can be removed or minimized. This noise may result in detection of spurious changes, as well as affect other uses of the data, including image classification. Analysis of dark (water and forests), rather than light features will be most impacted because the noise will form a higher percentage of the total response at low DN values. Any data normalizations for change detection should be based upon the data, rather than solely upon calibration information. While the observed relative radiometric transfer function between LANDSAT 3 and 4 was approximately as predicted, there were still significant deviations. Normalizing based upon data content also can have the advantage of allowing simultaneous normalization of the atmosphere as well as the radiometry.

Likens, W. C.↗
NASA NTRS1991

Use of T7 RNA polymerase to direct expression of outer Surface Protein A (OspA) from the Lyme disease Spirochete, Borrelia burgdorferi

The OspA gene from a North American strain of the Lyme disease Spirochete, Borrelia burgdorferi, was cloned under the control of transciption and translation signals from bacteriophage T7. Full-length OspA protein, a 273 amino acid (31kD) lipoprotein, is expressed poorly in Escherichia coli and is associated with the insoluble membrane fraction. In contrast, a truncated form of OspA lacking the amino-terminal signal sequence which normally would direct localization of the protein to the outer membrane is expressed at very high levels (less than or equal to 100 mg/liter) and is soluble. The truncated protein was purified to homogeneity and is being tested to see if it will be useful as an immunogen in a vaccine against Lyme disease. Circular dichroism and fluorescence spectroscopy was used to characterize the secondary structure and study conformational changes in the protein. Studies underway with other surface proteins from B burgdorferi and a related spirochete, B. hermsii, which causes relapsing fever, leads us to conclude that a strategy similar to that used to express the truncated OspA can provide a facile method for producing variations of Borrelia lipoproteins which are highly expressed in E. coli and soluble without exposure to detergents.

Dunn, John J.↗
NASA NTRS2009

90 GHz and 150 GHz Observations of the Orion M42 Region. A Submillimeter to Radio Analysis

We have used the new 90GHz MUSTANG camera on the Robert C. Green Bank Telescope (GBT)to map the bright Huygens region of the star-forming region M42 with a resolution of 9" and a sensitivity of 2.8 mJy/beam. Ninety GHz is an interesting transition frequency, as MUSTANG detects both the free-free emission characteristic of the H II region created by the Trapezium stars, normally seen at lower frequencies, and thermal dust emission from the background OMCI molecular cloud, normally mapped at higher frequencies. We also present similar data from the 150 GHz GISMO camera taken on the IRAM 30 m telescope. This map has 15" resolution. By combining the MUSTANG data with 1.4, 8. and 31 GHz radio data from the VLA and GBT, we derive a new estimate of the emission measure averaged electron temperature of T(sub e) = 11376+/-1050 K by an original method relating free-free emission intensities at optically thin and optically thick frequencies. Combining Infrared Space Observatory-long wavelength spectrometer (ISO-LWS) data with our data, we derive a new estimate of the dust temperature and spectral emissivity index within the 80" ISO-LWS beam toward Orion KL/BN, T(sub d) = 42+/-3 K and Beta(sub d) = 1.3+/-0.1. We show that both T(sub d) and Beta(sub d) decrease when going from the H II region and excited OMCI interface to the denser UV shielded part OMCI (Orion KL/BN, Orion S). With a model consisting of only free-free and thermal dust emission, we are able to fit data taken at frequencies from 1.5 GHz to 854 GHz (350 micrometers).

Dicker, S. R.↗
NASA NTRS2002

Influence of Turbulence on the Restraint of Liquid Jets by Surface Tension in Microgravity Investigated

Microgravity poses many challenges to the designer of spacecraft tanks. Chief among these are the lack of phase separation and the need to supply vapor-free liquid or liquidfree vapor to the spacecraft processes that require fluid. One of the principal problems of phase separation is the creation of liquid jets. A jet can be created by liquid filling, settling of the fluid to one end of the tank, or even closing a valve to stop the liquid flow. Anyone who has seen a fountain knows that jets occur in normal gravity also. However, in normal gravity, the gravity controls and restricts the jet flow. In microgravity, with gravity largely absent, surface tension forces must contain jets. To model this phenomenon, a numerical method that tracks the fluid motion and the surface tension forces is required. Jacqmin has developed a phase model that converts the discrete surface tension force into a barrier function that peaks at the free surface and decays rapidly away. Previous attempts at this formulation were criticized for smearing the interface. This can be overcome by sharpening the phase function, double gridding the fluid function, and using a higher order solution for the fluid function. The solution of this equation can be rewritten as two coupled Poisson equations that also include the velocity. After the code was implemented in axisymmetric form and verified by several test cases at the NASA Glenn Research Center, the drop tower runs of Aydelott were modeled. Work last year with a laminar model was found to overpredict Aydelott's results, except at the lowest Reynolds number conditions of 400. This year, a simple turbulence model was implemented by adding a turbulent viscosity based on the mixing-length hypothesis and empirical measurements of previous works. Predictions made after this change was implemented have been much closer to experimentally observed flow patterns and geyser heights. Two model runs is shown. The first, without any turbulence correction, breaks through the free surface and strikes the far end of the tank. In the second, the turbulence spreads the jet momentum over more of the free surface, enabling the surface tension forces to turn the jet back into the bulk liquid. The model geyser height with the second model is 1.1 cm. This is quite close to the 1.5-cm geyser height measured by Aydelott.

Chato, David J.↗
NASA NTRS2012

Disentangling AGN and Star Formation in Soft X-Rays

We have explored the interplay of star formation and active galactic nucleus (AGN) activity in soft X-rays (0.5-2 keV) in two samples of Seyfert 2 galaxies (Sy2s). Using a combination of low-resolution CCD spectra from Chandra and XMM-Newton, we modeled the soft emission of 34 Sy2s using power-law and thermal models. For the 11 sources with high signal-to-noise Chandra imaging of the diffuse host galaxy emission, we estimate the luminosity due to star formation by removing the AGN, fitting the residual emission. The AGN and star formation contributions to the soft X-ray luminosity (i.e., L(sub x,AGN) and L(sub x,SF)) for the remaining 24 Sy2s were estimated from the power-law and thermal luminosities derived from spectral fitting. These luminosities were scaled based on a template derived from XSINGS analysis of normal star-forming galaxies. To account for errors in the luminosities derived from spectral fitting and the spread in the scaling factor, we estimated L(sub x,AGN) and L(sub x,SF))from Monte Carlo simulations. These simulated luminosities agree with L(sub x,AGN) and L(sub x,SF) derived from Chandra imaging analysis within a 3sigma confidence level. Using the infrared [Ne ii]12.8 micron and [O iv]26 micron lines as a proxy of star formation and AGN activity, respectively, we independently disentangle the contributions of these two processes to the total soft X-ray emission. This decomposition generally agrees with L(sub x,SF) and L(sub x,AGN) at the 3 sigma level. In the absence of resolvable nuclear emission, our decomposition method provides a reasonable estimate of emission due to star formation in galaxies hosting type 2 AGNs.

Disentangling↗
NASA NTRS1974

Method and apparatus for stable silicon dioxide layers on silicon grown in silicon nitride ambient

A method and apparatus for thermally growing stable silicon dioxide layers on silicon is disclosed. A previously etched and baked silicon nitride tube placed in a furnace is used to grow the silicon dioxide. First, pure oxygen is allowed to flow through the tube to initially coat the inside surface of the tube with a thin layer of silicon dioxide. After the tube is coated with the thin layer of silicon dioxide, the silicon is oxidized thermally in a normal fashion. If the tube becomes contaminated, the silicon dioxide is etched off thereby exposing clean silicon nitride and then the inside of the tube is recoated with silicon dioxide. As is disclosed, the silicon nitride tube can also be used as the ambient for the pyrolytic decomposition of silane and ammonia to form thin layers of clean silicon nitride.

Cohen, R. A.↗
NASA NTRS1990

VIPER project

The VIPER project has so far produced a formal specification of a 32 bit RISC microprocessor, an implementation of that chip in radiation-hard SOS technology, a partial proof of correctness of the implementation which is still being extended, and a large body of supporting software. The time has now come to consider what has been achieved and what directions should be pursued in the future. The most obvious lesson from the VIPER project was the time and effort needed to use formal methods properly. Most of the problems arose in the interfaces between different formalisms, e.g., between the (informal) English description and the HOL spec, between the block-level spec in HOL and the equivalent in ELLA needed by the low-level CAD tools. These interfaces need to be made rigorous or (better) eliminated. VIPER 1A (the latest chip) is designed to operate in pairs, to give protection against breakdowns in service as well as design faults. We have come to regard redundancy and formal design methods as complementary, the one to guard against normal component failures and the other to provide insurance against the risk of the common-cause failures which bedevil reliability predictions. Any future VIPER chips will certainly need improved performance to keep up with increasingly demanding applications. We have a prototype design (not yet specified formally) which includes 32 and 64 bit multiply, instruction pre-fetch, more efficient interface timing, and a new instruction to allow a quick response to peripheral requests. Work is under way to specify this device in MIRANDA, and then to refine the spec into a block-level design by top-down transformations. When the refinement is complete, a relatively simple proof checker should be able to demonstrate its correctness. This paper is presented in viewgraph form.

Kershaw, John↗
NASA NTRS1943

On a new method for calculating the potential flow past a body of revolution

A new method is presented for obtaining the velocity potential of the flow about a body of revolution moving uniformly in the direction of its axis of symmetry in a fluid otherwise at rest. This method is based essentially on the fact that the form of the differential equation for the velocity potential is invariant with regard to conformal transformation of the meridian plane. By means of the conformal transformation of the meridian profile into a circle a system of orthogonal curvilinear coordinates is obtained, the main feature of which is that one of the coordinate lines is the meridian profile itself. The use of this type of coordinate system yields a simple expression of the boundary condition at the surface of the solid and leads to a rational process of iteration for the solution of the differential equation for the velocity potential. It is shown that the velocity potential for an arbitrary body of revolution may be expressed in terms of universal functions which, although not normal, are obtainable by means of simple quadratures. The general results are applied to a body of revolution obtained by revolving a symmetrical Joukowski profile about its axis of symmetry. A numerical example further serves to illustrate the theory.

Kaplan, Carl↗
NASA NTRS1993

Thermophysical properties of simple liquid metals: A brief review of theory

In this paper, we review the current theory of the thermophysical properties of simple liquid metals. The emphasis is on thermodynamic properties, but we also briefly discuss the nonequilibrium properties of liquid metals. We begin by defining a 'simple liquid metal' as one in which the valence electrons interact only weakly with the ionic cores, so that the interaction can be treated by perturbation theory. We then write down the equilibrium Hamiltonian of a liquid metal as a sum of five terms: the bare ion-ion interaction, the electron-electron interaction, the bare electron-ion interaction, and the kinetic energies of electrons and ions. Since the electron-ion interaction can be treated by perturbation, the electronic part contributes in two ways to the Helmholtz free energy: it gives a density-dependent term which is independent of the arrangement of ions, and it acts to screen the ion-ion interaction, giving rise to effective ion-ion pair potentials which are density-dependent, in general. After sketching the form of a typical pair potential, we briefly enumerate some methods for calculating the ionic distribution function and hence the Helmholtz free energy of the liquid: monte Carlo simulations, molecular dynamics simulations, and thermodynamic perturbation theory. The final result is a general expression for the Helmholtz free energy of the liquid metal. It can be used to calculate a wide range of thermodynamic properties of simple metal liquids, which we enumerate. They include not only a range of thermodynamic coefficients of both metals and alloys, but also many aspects of the phase diagram, including freezing curves of pure elements and phase diagrams of liquid alloys (including liquidus and solidus curves). We briefly mention some key discoveries resulting from previous applications of this method, and point out that the same methods work for other materials not normally considered to be liquid metals (such as colloidal suspensions, in which the suspended microspheres behave like ions screened by the salt solution in which they are suspended). We conclude with a brief discussion of some non-equilibrium (i.e., transport) properties which can be treated by an extension of these methods. These include electrical resistivity, thermal conductivity, viscosity, atomic self-diffusion coefficients, concentration diffusion coefficients in alloys, surface tension and thermal emissivity. Finally, we briefly mention two methods by which the theory might be extended to non-simple liquid metals: these are empirical techniques (i.e., empirical two- and three-body potentials), and numerical many-body approaches. Both may be potentially applicable to extremely complex systems, such as nonstoichiometric liquid semiconductor alloys.

Stroud, David↗