EQUATION OF STATE FOR POLYMER SOLIDS

A new equation of state for polymer solids is given by P = B0/4 98[(V0/V)7.14 - (V0/V)2.16 + T/T0] comparison of the equation of state with experimental data is made for six kinds of polymers at different temperatures and pressures. The results obtained shown that the equation is suitable to describe the compression behavior of solid polymers in the region without transition.

A NEW ISOTHERMAL EQUATION OF STATE FOR POLYMERS

A new isothermal equation of state for polymers in the solid and the liquid is given by P = B(T, 0)/(n - m){[V(T, 0)/V(T, P)]n + 1 - [V(T, 0)/V(T, P)]m + 1} where n = 6.14 and m = 1.16 are general constant's for polymer systems. Comparison of the equation with experimental data is made for six polymers at different temperatures and pressures. The results predict that the equation of state describes the isothermal compression behaviour of polymers in the glass and the melt states, except at the transition temperature.

EQUATION OF STATE FOR POLYMERS

In the theoretical study on equation of state for polymers, much attention has been paid to the polymer in liquid state, but less to that in solid state. Therefore, some empirical and semi-empirical equations of state have been used to describe its pressure-volume-temperature (P-V-T) relations.

Resting energy expenditure in non-ventilated, non-sedated patients recovering from serious traumatic brain injury: Comparison of prediction equations with indirect calorimetry values

Background & aims: Little is known about energy requirements in brain injured (TBI) patients, despite evidence suggesting adequate nutritional support can improve clinical outcomes. The study aim was to compare predicted energy requirements with measured resting energy expenditure (REE) values, in patients recovering from TBI.

Methods: Indirect calorimetry (IC) was used to measure REE in 45 patients with TBI. Predicted energy requirements were determined using FAO/WHO/UNU and Harris–Benedict (HB) equations. Bland– Altman and regression analysis were used for analysis.

Results: One-hundred and sixty-seven successful measurements were recorded in patients with TBI. At an individual level, both equations predicted REE poorly. The mean of the differences of standardised areas of measured REE and FAO/WHO/UNU was near zero (9 kcal) but the variation in both directions was substantial (range 591 to þ573 kcal). Similarly, the differences of areas of measured REE and HB demonstrated a mean of 1.9 kcal and range 568 to þ571 kcal. Glasgow coma score, patient status, weight and body temperature were signi?cant predictors of measured REE (p < 0.001; R²⁼ 0.47).

Conclusions: Clinical equations are poor predictors of measured REE in patients with TBI. The variability in REE is substantial. Clinicians should be aware of the limitations of prediction equations when estimating energy requirements in TBI patients.

An experimental evaluation of prediction models for the mechanical behavior of unreinforced, lime-mortar masonry under compression

This paper contributes to the understanding of lime-mortar masonry strength and deformation (which determine durability and allowable stresses/stiffness in design codes) by measuring the mechanical properties of brick bound with lime and lime-cement mortars. Based on the regression analysis of experimental results, models to estimate lime-mortar masonry compressive strength are proposed (less accurate for hydrated lime (CL90s) masonry due to the disparity between mortar and brick strengths). Also, three relationships between masonry elastic modulus and its compressive strength are proposed for cement-lime; hydraulic lime (NHL3.5 and 5); and hydrated/feebly hydraulic lime masonries respectively.

Disagreement between the experimental results and former mathematical prediction models (proposed primarily for cement masonry) is caused by a lack of provision for the significant deformation of lime masonry and the relative changes in strength and stiffness between mortar and brick over time (at 6 months and 1 year, the NHL 3.5 and 5 mortars are often stronger than the brick). Eurocode 6 provided the best predictions for the compressive strength of lime and cement-lime masonry based on the strength of their components. All models vastly overestimated the strength of CL90s masonry at 28 days however, Eurocode 6 became an accurate predictor after 6 months, when the mortar had acquired most of its final strength and stiffness.

The experimental results agreed with former stress-strain curves. It was evidenced that mortar strongly impacts masonry deformation, and that the masonry stress/strain relationship becomes increasingly non-linear as mortar strength lowers. It was also noted that, the influence of masonry stiffness on its compressive strength becomes smaller as the mortar hydraulicity increases.

Exploring the use of prediction and summarization to increase students' listening and reading comprehension /

This study examined the effect of expHcitly instructing students to use a repertoire of reading comprehension strategies. Specifically, this study examined whether providing students with a "predictive story-frame" which combined the use of prediction and summarization strategies improved their reading comprehension relative to providing students with generic instruction on prediction and summarization. Results were examined in terms of instructional condition and reading ability. Students from 2 grade 4 classes participated in this study. The reading component of the Canadian Achievement Tests, Second Edition (CAT/2) was used to identify students as either "average or above average" or "below average" readers. Students received either strategic predication and summarization instruction (story-frame) or generic prediction and summarization instruction (notepad). Students were provided with new but comparable stories for each session. For both groups, the researcher modelled the strategic tools and provided guided practice, independent practice, and independent reading sessions. Comprehension was measured with an immediate and 1-week delayed comprehension test for each of the 4 stories, hi addition, students participated in a 1- week delayed interview, where they were asked to retell the story and to answer questions about the central elements (character, setting, problem, solution, beginning, middle, and ending events) of each story. There were significant differences, with medium to large effect sizes, in comprehension and recall scores as a fimction of both instructional condition and reading ability. Students in the story-frame condition outperformed students in the notepad condition, and average to above average readers performed better than below average readers. Students in the story-frame condition outperformed students in the notepad condition on the comprehension tests and on the oral retellings when teacher modelling and guidance were present. In the cued recall sessions, students in the story-frame instructional condition recalled more correct information and generated fewer errors than students in the notepad condition. Average to above average readers performed better than below average readers across comprehension and retelling measures. The majority of students in both instructional conditions reported that they would use their strategic tool again.

An analysis of decoupling procedures in generating thermal Green's functions of O([lambda]â ´) by the Zubarev equation of motion method

The Zubarev equation of motion method has been applied to an anharmonic crystal of O( ,,4). All possible decoupling schemes have been interpreted in order to determine finite temperature expressions for the one phonon Green's function (and self energy) to 0()\4) for a crystal in which every atom is on a site of inversion symmetry. In order to provide a check of these results, the Helmholtz free energy expressions derived from the self energy expressions, have been shown to agree in the high temperature limit with the results obtained from the diagrammatic method. Expressions for the correlation functions that are related to the mean square displacement have been derived to 0(1\4) in the high temperature limit.

Application of [Lambda] to the fourth perturbation theory in calculating the equation of state of rare gas solids and fcc metals

We have calculated the thermodynamic properties of monatomic fcc crystals from the high temperature limit of the Helmholtz free energy. This equation of state included the static and vibrational energy components. The latter contribution was calculated to order A4 of perturbation theory, for a range of crystal volumes, in which a nearest neighbour central force model was used. We have calculated the lattice constant, the coefficient of volume expansion, the specific heat at constant volume and at constant pressure, the adiabatic and the isothermal bulk modulus, and the Gruneisen parameter, for two of the rare gas solids, Xe and Kr, and for the fcc metals Cu, Ag, Au, Al, and Pb. The LennardJones and the Morse potential were each used to represent the atomic interactions for the rare gas solids, and only the Morse potential was used for the fcc metals. The thermodynamic properties obtained from the A4 equation of state with the Lennard-Jones potential, seem to be in reasonable agreement with experiment for temperatures up to about threequarters of the melting temperature. However, for the higher temperatures, the results are less than satisfactory. For Xe and Kr, the thermodynamic properties calculated from the A2 equation of state with the Morse potential, are qualitatively similar to the A 2 results obtained with the Lennard-Jones potential, however, the properties obtained from the A4 equation of state are in good agreement with experiment, since the contribution from the A4 terms seem to be small. The lattice contribution to the thermal properties of the fcc metals was calculated from the A4 equation of state, and these results produced a slight improvement over the properties calculated from the A2 equation of state. In order to compare the calculated specific heats and bulk moduli results with experiment~ the electronic contribution to thermal properties was taken into account~ by using the free electron model. We found that the results varied significantly with the value chosen for the number of free electrons per atom.

On the equation of state and atomic mean square displacement of crystals

We have presented a Green's function method for the calculation of the atomic mean square displacement (MSD) for an anharmonic Hamil toni an . This method effectively sums a whole class of anharmonic contributions to MSD in the perturbation expansion in the high temperature limit. Using this formalism we have calculated the MSD for a nearest neighbour fcc Lennard Jones solid. The results show an improvement over the lowest order perturbation theory results, the difference with Monte Carlo calculations at temperatures close to melting is reduced from 11% to 3%. We also calculated the MSD for the Alkali metals Nat K/ Cs where a sixth neighbour interaction potential derived from the pseudopotential theory was employed in the calculations. The MSD by this method increases by 2.5% to 3.5% over the respective perturbation theory results. The MSD was calculated for Aluminum where different pseudopotential functions and a phenomenological Morse potential were used. The results show that the pseudopotentials provide better agreement with experimental data than the Morse potential. An excellent agreement with experiment over the whole temperature range is achieved with the Harrison modified point-ion pseudopotential with Hubbard-Sham screening function. We have calculated the thermodynamic properties of solid Kr by minimizing the total energy consisting of static and vibrational components, employing different schemes: The quasiharmonic theory (QH), ).2 and).4 perturbation theory, all terms up to 0 ().4) of the improved self consistent phonon theory (ISC), the ring diagrams up to o ().4) (RING), the iteration scheme (ITER) derived from the Greens's function method and a scheme consisting of ITER plus the remaining contributions of 0 ().4) which are not included in ITER which we call E(FULL). We have calculated the lattice constant, the volume expansion, the isothermal and adiabatic bulk modulus, the specific heat at constant volume and at constant pressure, and the Gruneisen parameter from two different potential functions: Lennard-Jones and Aziz. The Aziz potential gives generally a better agreement with experimental data than the LJ potential for the QH, ).2, ).4 and E(FULL) schemes. When only a partial sum of the).4 diagrams is used in the calculations (e.g. RING and ISC) the LJ results are in better agreement with experiment. The iteration scheme brings a definitive improvement over the).2 PT for both potentials.

A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.

Understanding mixing efficiency in the oceans. Do the nonlinearities of the equation of state matter?

There exist two central measures of turbulent mixing in turbulent stratified fluids that are both caused by molecular diffusion: 1) the dissipation rate D(APE) of available potential energy APE; 2) the turbulent rate of change Wr, turbulent of background gravitational potential energy GPEr. So far, these two quantities have often been regarded as the same energy conversion, namely the irreversible conversion of APE into GPEr, owing to the well known exact equality D(APE)=Wr, turbulent for a Boussinesq fluid with a linear equation of state. Recently, however, Tailleux (2009) pointed out that the above equality no longer holds for a thermally-stratified compressible, with the ratio ξ=Wr, turbulent/D(APE) being generally lower than unity and sometimes even negative for water or seawater, and argued that D(APE) and Wr, turbulent actually represent two distinct types of energy conversion, respectively the dissipation of APE into one particular subcomponent of internal energy called the "dead" internal energy IE0, and the conversion between GPEr and a different subcomponent of internal energy called "exergy" IEexergy. In this paper, the behaviour of the ratio ξ is examined for different stratifications having all the same buoyancy frequency N vertical profile, but different vertical profiles of the parameter Υ=α P/(ρCp), where α is the thermal expansion coefficient, P the hydrostatic pressure, ρ the density, and Cp the specific heat capacity at constant pressure, the equation of state being that for seawater for different particular constant values of salinity. It is found that ξ and Wr, turbulent depend critically on the sign and magnitude of dΥ/dz, in contrast with D(APE), which appears largely unaffected by the latter. These results have important consequences for how the mixing efficiency should be defined and measured in practice, which are discussed.