One-parameter Equation Of State Research Articles

Equation of state of PEG/PEO in good solvent. Comparison between a one-parameter EOS and experiments

We investigate, through osmotic pressure measurements, the validity of the single-parameter equation of state (EOS) for solutions of polyethylene glycols in water, by Cohen et al.1,2 We show that it is physically meaningful and that a reasonable good correspondence between the osmotic pressures for PEG35 in large range of concentrations is obtained. We also take the chain length dependence into account in our analysis, as suggested by Cohen et al. By recalculating the experimental pressures in the paper by Jönsson et al.3 applying the new calibration curve, which is based on the experimental results obtained in this study and the EOS obtained by Cohen et al., there is almost a perfect correspondence between the simulations and the experiments. These results have implications for correctly probing macromolecular interactions in wide range of systems when applying the osmotic stress method.

Pressure–volume data for epsilon iron and platinum to earth-core pressures and above from one-parameter equation of state: Implication on platinum pressure scale

The one-parameter equation of state (EoS), wherein the bulk modulus at ambient pressure is the only unknown parameter and the pressure derivative of the bulk modulus is fixed by requiring that the state of matter approaches Thomas–Fermi state under strong compression, has been used to compute the pressure, bulk modulus, and pressure derivative of bulk modulus as functions of volume compression for epsilon iron. To earth-core pressures (∼363 GPa), these data are in excellent agreement with the 300 K data obtained from the analysis of the PREM tabulation using K-primed equation. Even to ∼2300 GPa, the two sets of data show excellent agreement. This agreement suggests that compression behavior of the core alloy deduced at 300 K is close to that of pure epsilon iron. The pressure–volume data for platinum to ∼650 GPa computed from one-parameter EoS are in excellent agreement with those obtained from the first-principle calculations and shock-wave experiments. This agreement does not strengthen the suggestion in the literature that the platinum pressure scale contains large systematic errors. The breakdown of the fundamental assumption made in high-pressure X-ray diffraction experiments that the pressure on the sample equals that on the pressure standard is shown to cause the discrepancy between the compression data on epsilon iron from laboratory source and those predicted from one-parameter EoS.

Rotational modes of relativistic stars: Analytic results

We study the r-modes and rotational ``hybrid'' modes of relativistic stars. As in Newtonian gravity, the spectrum of low-frequency rotational modes is highly sensitive to the stellar equation of state. If the star and its perturbations obey the same one-parameter equation of state (as with isentropic stars), there exist {\it no pure r-modes at all} - no modes whose limit, for a star with zero angular velocity, is an axial-parity perturbation. Rotating stars of this kind similarly have no pure g-modes, no modes whose spherical limit is a perturbation with polar parity and vanishing perturbed pressure and density. We compute the post-Newtonian corrections to the $l=m$ r-modes of isentropic and non-isentropic uniform density stars.

Where are ther‐Modes of Isentropic Stars?

Almost none of the r-modes ordinarily found in rotating stars exist, if the star and its perturbations obey the same one-parameter equation of state; and rotating relativistic stars with one-parameter equations of state have no pure r-modes at all, no modes whose limit, for a star with zero angular velocity, is a perturbation with axial parity. Similarly (as we show here) rotating stars of this kind have no pure g-modes, no modes whose spherical limit is a perturbation with polar parity and vanishing perturbed pressure and density. Where have these modes gone? In spherical stars of this kind, r-modes and g-modes form a degenerate zero-frequency subspace. We find that rotation splits the degeneracy to zeroth order in the star's angular velocity $\Omega$, and the resulting modes are generically hybrids, whose limit as $\Omega\to 0$ is a stationary current with axial and polar parts. Because each mode has definite parity, its axial and polar parts have alternating values of $l$. We show that each mode belongs to one of two classes, axial-led or polar-led, depending on whether the spherical harmonic with lowest value of $l$ that contributes to its velocity field is axial or polar. We numerically compute these modes for slowly rotating polytropes and for Maclaurin spheroids, using a straightforward method that appears to be novel and robust. Timescales for the gravitational-wave driven instability and for viscous damping are computed using assumptions appropriate to neutron stars.

Approximate equations of state for a finite lattice system with two-, three-, and four-body potentials: Models for the binding of oxygen to hemoglobin.

Biochemical binding systems present many-body problems, even after integrating over solvent and polymer configurational degrees of freedom, because biological molecules are dense in cellular compartments. Furthermore, the resulting effective potentials are likely to include substantial n-body contributions with n>2. The binding of oxygen to hemoglobin is studied as a prototype problem of this kind. (i) The Hill coefficient (simply related to the change in the fractional binding with a change in the ligand chemical potential) has proven to be a useful, model-independent descriptor of ligand binding behavior. An obvious generalization of this approach is given and the resulting coefficients are shown to describe stably the binding of oxygen to hemoglobin over a broad range of free-ligand concentrations. (ii) An expansion of the standard Helmholtz free energy in the local binding density is used to find the excess standard Helmholtz free energy for saturation of hemoglobin with oxygen. This requires equations to change from local potential field variables to density variables that are equivalent to the two-, three-, and four-point Ornstein-Zernike equations. The method permits exact inclusion of two-, three-, and four-body potentials in the limit of weak interaction potentials, but is very poor for strong interactions. (iii) An expansion of the two-body direct correlation function with r\ensuremath{\ne}0 and the core condition are used in the compressibility equation to find the excess pressure as a function of the fractional saturation, and thus also to find the standard free-energy change upon saturating the protein with ligand.At first order, this procedure provides a model for the binding of oxygen to hemoglobin that does not require the assumption of pair decomposability of the interaction potentials or explicit calculation of a partition function, and yet is competitive with models that require both. The model is accurate for a wide range of interaction potentials. The result is a one-parameter equation of state that does not exhibit a phase transition for a finite system, but may exhibit a phase transition in the limit of infinite system size (depending on the magnitude of the cooperativeness parameter).

Variations in ductility produced by strain rate changes in tensile testing

A simplified analysis has been developed to describe the plastic behaviour of metallic materials over a limited range of strain rates. The stress-strain relations at a constant strain rate, and after a change in strain rate, are expressed using the concept of the mechanical equation of state proposed by Hart. The implications with respect to the stability of plastic flow are also investigated. The analytical predictions are then compared with the results obtained from a careful examination of the tensile behaviour of aluminium under varying strain rates. The experimental observations (excluding the transient following a change in strain rate) are in agreement with a one-parameter equation of state, associated with a Voce form of the work-hardening law. In particular, the model gives a reasonable account of the variations in ductility produced by rate changes.