Lattice model theory of the equation of state covering the gas, liquid, and solid phases

The three stable states of matter and the corresponding phase transitions were obtained with a single model. Patterned after Lennard-Jones and Devonshires's theory, a simple cubic lattice model containing two fcc sublattices (alpha and beta) is adopted. The interatomic potential is taken to be the Lennard-Jones (6-12) potential. Employing the cluster variation method, the Weiss and the pair approximations on the lattice gas failed to give the correct phase diagrams. Hybrid approximations were devised to describe the lattice term in the free energy. A lattice vibration term corresponding to a free volume correction is included semi-phenomenologically. The combinations of the lattice part and the free volume part yield the three states and the proper phase diagrams. To determine the coexistence regions, the equalities of the pressure and Gibbs free energy per molecule of the coexisting phases were utilized. The ordered branch of the free energy gives rise to the solid phase while the disordered branch yields the gas and liquid phases. It is observed that the triple point and the critical point quantities, the phase diagrams and the coexistence regions plotted are in good agreement with the experimental values and graphs for argon

Reflection of light and heavy holes from a linear potential barrier

In this paper we study reflection of holes in direct-band semiconductors from the linear potential barrier. It is shown that light-heavy hole transformation matrix is universal. It depends only on a dimensionless product of the light hole longitudinal momentum and the characteristic length determined by the slope of the potential and doesn't depend on the ratio of light and heavy hole masses, provided this ratio is small. It is shown that the transformation coefficient goes to zero both in the limit of small and large longitudinal momenta, however the phase of a reflected hole is different in these limits. An approximate analytical expression for the light-heavy hole transformation coefficient is found.Comment: 6 pages, 2 figure

First-principles envelope-function theory for lattice-matched semiconductor heterostructures

In this paper a multi-band envelope-function Hamiltonian for lattice-matched semiconductor heterostructures is derived from first-principles norm-conserving pseudopotentials. The theory is applicable to isovalent or heterovalent heterostructures with macroscopically neutral interfaces and no spontaneous bulk polarization. The key assumption -- proved in earlier numerical studies -- is that the heterostructure can be treated as a weak perturbation with respect to some periodic reference crystal, with the nonlinear response small in comparison to the linear response. Quadratic response theory is then used in conjunction with k.p perturbation theory to develop a multi-band effective-mass Hamiltonian (for slowly varying envelope functions) in which all interface band-mixing effects are determined by the linear response. To within terms of the same order as the position dependence of the effective mass, the quadratic response contributes only a bulk band offset term and an interface dipole term, both of which are diagonal in the effective-mass Hamiltonian. Long-range multipole Coulomb fields arise in quantum wires or dots, but have no qualitative effect in two-dimensional systems beyond a dipole contribution to the band offsets.Comment: 25 pages, no figures, RevTeX4; v3: final published versio

Influence of molecular weight on the phase behavior and structure formation of branched side-chain hairy-rod polyfluorene in bulk phase.

We report on an experimental study of the self-organization and phase behavior of hairy-rod π -conjugated branched side-chain polyfluorene, poly[9,9-bis(2-ethylhexyl)-fluorene-2,7-diyl]—i.e., poly[2,7–(9,9–bis(2–ethylhexyl)fluorene] (PF2∕6) —as a function of molecular weight (Mn) . The results have been compared to those of phenomenological theory. Samples for which Mn=3–147 kg∕mol were used. First, the stiffness of PF2∕6 , the assumption of the theory, has been probed by small-angle neutron scattering in solution. Thermogravimetry has been used to show that PF2∕6 is thermally stable over the conditions studied. Second, the existence of nematic and hexagonal phases has been phenomenologically identified for lower and higher Mn (LMW, Mn<Mn* and HMW, Mn>Mn* ) regimes, respectively, based on free-energy argument of nematic and hexagonal hairy rods and found to correspond to the experimental x-ray diffraction (XRD) results for PF2∕6 . By using the lattice parameters of PF2∕6 as an experimental input, the nematic-hexagonal transition has been predicted in the vicinity of glassification temperature (Tg) of PF2∕6 . Then, by taking the orientation parts of the free energies into account the nematic-hexagonal transition has been calculated as a function of temperature and Mn and a phase diagram has been formed. Below Tg of 80 °C only (frozen) nematic phase is observed for Mn<Mn*=104 g∕mol and crystalline hexagonal phase for Mn>Mn* . The nematic-hexagonal transition upon heating is observed for the HMW regime depending weakly on Mn , being at 140–165 °C for Mn>Mn* . Third, the phase behavior and structure formation as a function of Mn have been probed using powder and fiber XRD and differential scanning calorimetry and reasonable semiquantitative agreement with theory has been found for Mn≥3 kg∕mol . Fourth, structural characteristics are widely discussed. The nematic phase of LMW materials has been observed to be denser than high-temperature nematic phase of HMW compounds. The hexagonal phase has been found to be paracrystalline in the (ab0) plane but a genuine crystal meridionally. We also find that all these materials including the shortest 10-mer possess the formerly observed rigid five-helix hairy-rod molecular structure

Quadratic response theory for spin-orbit coupling in semiconductor heterostructures

This paper examines the properties of the self-energy operator in lattice-matched semiconductor heterostructures, focusing on nonanalytic behavior at small values of the crystal momentum, which gives rise to long-range Coulomb potentials. A nonlinear response theory is developed for nonlocal spin-dependent perturbing potentials. The ionic pseudopotential of the heterostructure is treated as a perturbation of a bulk reference crystal, and the self-energy is derived to second order in the perturbation. If spin-orbit coupling is neglected outside the atomic cores, the problem can be analyzed as if the perturbation were a local spin scalar, since the nonlocal spin-dependent part of the pseudopotential merely renormalizes the results obtained from a local perturbation. The spin-dependent terms in the self-energy therefore fall into two classes: short-range potentials that are analytic in momentum space, and long-range nonanalytic terms that arise from the screened Coulomb potential multiplied by a spin-dependent vertex function. For an insulator at zero temperature, it is shown that the electronic charge induced by a given perturbation is exactly linearly proportional to the charge of the perturbing potential. These results are used in a subsequent paper to develop a first-principles effective-mass theory with generalized Rashba spin-orbit coupling.Comment: 20 pages, no figures, RevTeX4; v2: final published versio

Balance differences in people with Parkinson disease with and without freezing of gait

Published in final edited form as: Gait Posture. 2015 September ; 42(3): 306–309. doi:10.1016/j.gaitpost.2015.06.007.BACKGROUND: Freezing of gait (FOG) is a relatively common and remarkably disabling impairment associated with Parkinson disease (PD). Laboratory-based measures indicate that individuals with FOG (PD+FOG) have greater balance deficits than those without FOG (PD-FOG). Whether such differences also can be detected using clinical balance tests has not been investigated. We sought to determine if balance and specific aspects of balance, measured using Balance Evaluation Systems Test (BESTest), differs between PD+FOG and PD-FOG. Furthermore, we aimed to determine if time-efficient clinical balance measures (i.e. Mini-BESTest, Berg Balance Scale (BBS)) could detect balance differences between PD+FOG and PD-FOG. METHODS: Balance of 78 individuals with PD, grouped as either PD+FOG (n=32) or PD-FOG (n=46), was measured using the BESTest, Mini-BESTest, and BBS. Between-groups comparisons were conducted for these measures and for the six sections of the BESTest using analysis of covariance. A PD composite score was used as a covariate. RESULTS: Controlling for motor sign severity, PD duration, and age, PD+FOG had worse balance than PD-FOG when measured using the BESTest (p=0.008, F=7.35) and Mini-BESTest (p=0.002, F=10.37), but not the BBS (p=0.27, F=1.26). BESTest section differences were noted between PD+FOG and PD-FOG for reactive postural responses (p<0.001, F=14.42) and stability in gait (p=0.003, F=9.18). CONCLUSIONS: The BESTest and Mini-BESTest, which specifically assessed reactive postural responses and stability in gait, were more likely than the BBS to detect differences in balance between PD+FOG and PD-FOG. Because it is more time efficient to administer, the Mini-BESTest may be the preferred tool for assessing balance deficits associated with FOG.This study was conducted with funding from the Davis Phinney Foundation, Parkinson's Disease Foundation, NIH R01 NS077959, NIH UL1 TR000448, Greater St. Louis American Parkinson Disease Association (APDA), APDA Center for Advanced PD Research at Washington University in St. Louis. The funding sources had no role in the study design, in the collection, analysis and interpretation of data; in the writing of the manuscript; or in the decision to submit the manuscript for publication. (Davis Phinney Foundation; Parkinson's Disease Foundation; R01 NS077959 - NIH; UL1 TR000448 - NIH; Greater St. Louis American Parkinson Disease Association (APDA); APDA Center for Advanced PD Research at Washington University in St. Louis

Systematic study of the 87^{87}Sr clock transition in an optical lattice

With ultracold $^{87}$Sr confined in a magic wavelength optical lattice, we present the most precise study (2.8 Hz statistical uncertainty) to-date of the $^1S_0$ - $^3P_0$ optical clock transition with a detailed analysis of systematic shifts (20 Hz uncertainty) in the absolute frequency measurement of 429 228 004 229 867 Hz. The high resolution permits an investigation of the optical lattice motional sideband structure. The local oscillator for this optical atomic clock is a stable diode laser with its Hz-level linewidth characterized across the optical spectrum using a femtosecond frequency comb.Comment: 4 pages, 4 figures, 1 tabl

Neuroimaging of Prayer: Questions of Validity

Studies investigating the brain in relation to religious experiences via neuroimaging tools have increased considerably. Most assume without verification that religious experience (e.g., prayer) while inside an imaging machine is the same as in normal settings. Addressing the validity of this assumption, we utilized a mock fMRI to compare self-reported typical prayer experience and 3 experimental conditions (silent room, initial fMRI, and acclimated fMRI). Forty-two individuals participated. In multiple aspects the “typical” and silent room conditions were indistinguishable; however, typical and fMRI conditions differed significantly. In sum, it was not clear what previous studies measured. These findings highlight the need for imaging research exploring religious experiences to include thorough debriefing protocols to disambiguate interpretations and facilitate meta-analytic efforts

High elevation of the ‘Nevadaplano’ during the Late Cretaceous

During the Late Cretaceous, central Nevada may have been a high elevation plateau, the Nevadaplano; some geodynamic models of the western US require thickened crust and high elevations during the Mesozoic to drive the subsequent tectonic events of the Cenozoic while other models do not. To test the hypothesis of high elevations during the late Mesozoic, we used carbonate clumped isotope thermometry to determine the temperature contrast between Late Cretaceous to Paleocene carbonates atop the putative plateau in Nevada versus carbonates from relatively low paleoelevation central Utah site. Lacustrine carbonates from the Nevada site preserve summer temperatures ∼13 °C cooler than summer temperatures from paleosol carbonates from the Utah site, after correcting for ∼1.2 °C of secular climatic cooling between the times of carbonate deposition at the two sites. This ∼13 °C temperature difference implies an elevation difference between the two sites of ∼2.2–3.1 km; including uncertainties from age estimation and climate change broadens this estimate to ⩾2 km. Our findings support crustal thickness estimates and Cenozoic tectonic models that imply thickened crust and high elevation in Nevada during the Mesozoic