Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems

This series of papers is devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids with more than 90% correlation between their virial W and potential energy U fluctuations in the NVT ensemble. Paper IV [N. Gnan et al., J. Chem. Phys. v131, 234504 (2009)] showed that strongly correlating liquids have "isomorphs", which are curves in the phase diagram along which structure, dynamics, and some thermodynamic properties are invariant in reduced units. In the present paper, using the fact that reduced-unit radial distribution functions are isomorph invariant, we derive an expression for the shapes of isomorphs in the WU phase diagram of generalized Lennard-Jones systems of one or more types of particles. The isomorph shape depends only on the Lennard-Jones exponents; thus all isomorphs of standard Lennard-Jones systems (with exponents 12 and 6) can be scaled onto to a single curve. Two applications are given. One is testing the prediction that the solid-liquid coexistence curve follows an isomorph by comparing to recent simulations by Ahmed and Sadus [J. Chem. Phys. v131, 174504 (2009)]. Excellent agreement is found on the liquid side of the coexistence, whereas the agreement is worse on the solid side. A second application is the derivation of an approximate equation of state for generalized Lennard-Jones systems by combining the isomorph theory with the Rosenfeld-Tarazona expression for the temperature dependence of potential energy on isochores. It is shown that the new equation of state agrees well with simulations.Comment: 12 pages, 14 figures, Section on solid-liquid coexistence expande

Reverse Piercing of the Corporate Veil: A Straightforward Path to Justice

(Excerpt) This Note argues that while outside reverse piercing should not be the norm, there are instances when application of the doctrine is the only way to ensure justice. Because of the competing interests that reverse piercing implicates, this Note proposes that the doctrine be permitted against both legal and equitable owners, but only when traditional, less intrusive remedies are insufficient. Additionally, any innocent shareholders should be permitted a capital exemption prior to payment of the plaintiffs claim when that claim would liquidate the corporation\u27s assets. Finally, dilemmas amongst creditors should be dealt with under preexisting priority laws. Part I discusses both traditional and outside reverse veil piercing. Part II discusses the arguments for and against the various methods of outside reverse piercing through a case law analysis. Finally, Part III advances a solution that safeguards the interests of all involved parties by first identifying the shortcomings of more traditional remedies and then proposing a new approach

Reverse Piercing of the Corporate Veil: A Straightforward Path to Justice

(Excerpt) This Note argues that while outside reverse piercing should not be the norm, there are instances when application of the doctrine is the only way to ensure justice. Because of the competing interests that reverse piercing implicates, this Note proposes that the doctrine be permitted against both legal and equitable owners, but only when traditional, less intrusive remedies are insufficient. Additionally, any innocent shareholders should be permitted a capital exemption prior to payment of the plaintiffs claim when that claim would liquidate the corporation\u27s assets. Finally, dilemmas amongst creditors should be dealt with under preexisting priority laws. Part I discusses both traditional and outside reverse veil piercing. Part II discusses the arguments for and against the various methods of outside reverse piercing through a case law analysis. Finally, Part III advances a solution that safeguards the interests of all involved parties by first identifying the shortcomings of more traditional remedies and then proposing a new approach

Strong pressure-energy correlations in van der Waals liquids

Strong correlations between equilibrium fluctuations of the configurational parts of pressure and energy are found in the Lennard-Jones liquid and other simple liquids, but not in hydrogen-bonding liquids like methanol and water. The correlations, that are present also in the crystal and glass phases, reflect an effective inverse power-law repulsive potential dominating fluctuations, even at zero and slightly negative pressure. In experimental data for supercritical Argon, the correlations are found to be approximately 96%. Consequences for viscous liquid dynamics are discussed.Comment: Phys. Rev. Lett., in pres

Equilibrium Simulation of the Slip Coefficient in Nanoscale Pores

Accurate prediction of interfacial slip in nanoscale channels is required by many microfluidic applications. Existing hydrodynamic solutions based on Maxwellian boundary conditions include an empirical parameter that depends on material properties and pore dimensions. This paper presents a derivation of a new expression for the slip coefficient that is not based on the assumptions concerning the details of solid-fluid collisions and whose parameters are obtainable from \textit{equilibrium} simulation. The results for the slip coefficient and flow rates are in good agreement with non-equilibrium molecular dynamics simulation.Comment: 11 pages, 4 figures, submitted to Phys Rev Let

Olfactory sulcus morphology in patients with current and past major depression

Olfactory deficits have been reported in major depressive disorder (MDD). However, it remains largely unknown whether MDD is associated with abnormalities in olfactory sulcus morphology, a potential marker of olfactory system development. This magnetic resonance imaging study investigated the length and depth of the olfactory sulcus in 29 currently depressed patients, 27 remitted depressed patients, and 33 age- and gender-matched healthy control subjects. Both current and remitted MDD patients had significantly shallower olfactory sulci bilaterally as compared with controls. Only for male subjects, the right olfactory sulcus was significantly shorter in remitted MDD patients than in controls. The right sulcus depth was negatively correlated with number of depressive episodes in the entire MDD group and with residual depressive symptoms in the remitted MDD group. Medication status, presence of melancholia, and comorbidity with anxiety disorders did not affect the sulcus morphology. These findings suggest that abnormality of the olfactory sulcus morphology, especially its depth, may be a trait-related marker of vulnerability to major depression

Strongly correlating liquids and their isomorphs

This paper summarizes the properties of strongly correlating liquids, i.e., liquids with strong correlations between virial and potential energy equilibrium fluctuations at constant volume. We proceed to focus on the experimental predictions for strongly correlating glass-forming liquids. These predictions include i) density scaling, ii) isochronal superposition, iii) that there is a single function from which all frequency-dependent viscoelastic response functions may be calculated, iv) that strongly correlating liquids are approximately single-parameter liquids with close to unity Prigogine-Defay ratio, and v) that the fictive temperature initially decreases for an isobaric temperature up jump. The "isomorph filter", which allows one to test for universality of theories for the non-Arrhenius temperature dependence of the relaxation time, is also briefly discussed