A treatment of atomic mean square displacement in higher order perturbation theory

A general derivation of the anharmonic coefficients for a periodic lattice invoking the special case of the central force interaction is presented. All of the contributions to mean square displacement (MSD) to order 14 perturbation theory are enumerated. A direct correspondance is found between the high temperature limit MSD and high temperature limit free energy contributions up to and including 0(14). This correspondance follows from the detailed derivation of some of the contributions to MSD. Numerical results are obtained for all the MSD contributions to 0(14) using the Lennard-Jones potential for the lattice constants and temperatures for which the Monte Carlo results were calculated by Heiser, Shukla and Cowley. The Peierls approximation is also employed in order to simplify the numerical evaluation of the MSD contributions. The numerical results indicate the convergence of the perturbation expansion up to 75% of the melting temperature of the solid (TM) for the exact calculation; however, a better agreement with the Monte Carlo results is not obtained when the total of all 14 contributions is added to the 12 perturbation theory results. Using Peierls approximation the expansion converges up to 45% of TM• The MSD contributions arising in the Green's function method of Shukla and Hubschle are derived and enumerated up to and including 0(18). The total MSD from these selected contributions is in excellent agreement with their results at all temperatures. Theoretical values of the recoilless fraction for krypton are calculated from the MSD contributions for both the Lennard-Jones and Aziz potentials. The agreement with experimental values is quite good.

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.

Phonon dispersion curves and atomic mean square displacement for several fcc and bcc materials

The atomic mean square displacement (MSD) and the phonon dispersion curves (PDC's) of a number of face-centred cubic (fcc) and body-centred cubic (bcc) materials have been calclllated from the quasiharmonic (QH) theory, the lowest order (A2 ) perturbation theory (PT) and a recently proposed Green's function (GF) method by Shukla and Hiibschle. The latter method includes certain anharmonic effects to all orders of anharmonicity. In order to determine the effect of the range of the interatomic interaction upon the anharmonic contributions to the MSD we have carried out our calculations for a Lennard-Jones (L-J) solid in the nearest-neighbour (NN) and next-nearest neighbour (NNN) approximations. These results can be presented in dimensionless units but if the NN and NNN results are to be compared with each other they must be converted to that of a real solid. When this is done for Xe, the QH MSD for the NN and NNN approximations are found to differ from each other by about 2%. For the A2 and GF results this difference amounts to 8% and 7% respectively. For the NN case we have also compared our PT results, which have been calculated exactly, with PT results calculated using a frequency-shift approximation. We conclude that this frequency-shift approximation is a poor approximation. We have calculated the MSD of five alkali metals, five bcc transition metals and seven fcc transition metals. The model potentials we have used include the Morse, modified Morse, and Rydberg potentials. In general the results obtained from the Green's function method are in the best agreement with experiment. However, this improvement is mostly qualitative and the values of MSD calculated from the Green's function method are not in much better agreement with the experimental data than those calculated from the QH theory. We have calculated the phonon dispersion curves (PDC's) of Na and Cu, using the 4 parameter modified Morse potential. In the case of Na, our results for the PDC's are in poor agreement with experiment. In the case of eu, the agreement between the tlleory and experiment is much better and in addition the results for the PDC's calclliated from the GF method are in better agreement with experiment that those obtained from the QH theory.

Relative transition probability and pressure broadening parameters of copper atomic lines /

Inserted Report documentation page designates D. W. Boyer ... [et al.] as "authors."

Investigation on parameters used in warning systems for rain-induced embankment instability

A number of instrumented laboratory-scale soil embankment slopes were subjected to artificial rainfall until they failed. The factor of safety of the slope based on real-time measurements of pore-water pressure (suction) and laboratory measured soil properties were calculated as the rainfall progressed. Based on the experiment measurements and slope stability analysis, it was observed that slope displacement measurements can be used to warn the slope failure more accurately. Further, moisture content/pore-water pressure measurements near the toe of the slope and the real-time factor of safety can also be used for prediction of rainfall-induced embankment failures with adequate accuracy.

Using Fiber Bragg Grating (FBG) sensors for vertical displacement measurement of bridges

In many bridges, vertical displacements are one of the most relevant parameters for structural health monitoring in both the short and long terms. Bridge managers around the globe are always looking for a simple way to measure vertical displacements of bridges. However, it is difficult to carry out such measurements. On the other hand, in recent years, with the advancement of fiber-optic technologies, fiber Bragg grating (FBG) sensors are more commonly used in structural health monitoring due to their outstanding advantages including multiplexing capability, immunity of electromagnetic interference as well as high resolution and accuracy. For these reasons, using FBG sensors is proposed to develop a simple, inexpensive and practical method to measure vertical displacements of bridges. A curvature approach for vertical displacement measurement using curvature measurements is proposed. In addition, with the successful development of a FBG tilt sensors, an inclination approach is also proposed using inclination measurements. A series of simulation tests of a full-scale bridge was conducted. It shows that both the approaches can be implemented to determine vertical displacements for bridges with various support conditions, varying stiffness (EI) along the spans and without any prior known loading. These approaches can thus measure vertical displacements for most of slab-on-girder and box-girder bridges. Moreover, with the advantages of FBG sensors, they can be implemented to monitor bridge behavior remotely and in real time. Further recommendations of these approaches for developments will also be discussed at the end of the paper.

Interacting constraints of defensive pressure and ball displacement trajectories shape locomotor pointing behaviours in association football

Performance of locomotor pointing tasks (goal-directed locomotion) in sport is typically constrained by dynamic factors, such as positioning of opponents and objects for interception. In the team sport of association football, performers have to coordinate their gait with ball displacement when dribbling and when trying to prevent opponent interception when running to kick a ball. This thesis comprises two studies analysing the movement patterns during locomotor pointing of eight experienced youth football players under static and dynamic constraints by manipulating levels of ball displacement (ball stationary or moving) and defensive pressure (defenders absent, or positioned near or far during performance). ANOVA with repeated measures was used to analyse effects of these task constraints on gait parameters during the run-up and cross performance sub-phase. Experiment 1 revealed outcomes consistent with previous research on locomotor pointing. When under defensive pressure, participants performed the run-up more quickly, concurrently modifying footfall placements relative to the ball location over trials. In experiment 2 players coordinated their gait relative to a moving ball significantly differently when under defensive pressure. Despite no specific task instructions being provided beforehand, context dependent constraints interacted to influence footfall placements over trials and running velocity of participants in different conditions. Data suggest that coaches need to manipulate task constraints carefully to facilitate emergent movement behaviours during practice in team games like football.

Static vertical displacement measurement of bridges using Fiber Bragg Grating (FBG) sensors

Vertical displacements are one of the most relevant parameters for structural health monitoring of bridges in both the short and long terms. Bridge managers around the globe are always looking for a simple way to measure vertical displacements of bridges. However, it is difficult to carry out such measurements. On the other hand, in recent years, with the advancement of fiber-optic technologies, fiber Bragg grating (FBG) sensors are more commonly used in structural health monitoring due to their outstanding advantages including multiplexing capability, immunity of electromagnetic interference as well as high resolution and accuracy. For these reasons, using FBG sensors is proposed to develop a simple, inexpensive and practical method to measure vertical displacements of bridges. A curvature approach for vertical displacement measurements using curvature measurements is proposed. In addition, with the successful development of FBG tilt sensors, an inclination approach is also proposed using inclination measurements. A series of simulation tests of a full- scale bridge was conducted. It shows that both of the approaches can be implemented to determine vertical displacements for bridges with various support conditions, varying stiffness (EI) along the spans and without any prior known loading. These approaches can thus measure vertical displacements for most of slab-on-girder and box-girder bridges. Besides, the approaches are feasible to implement for bridges under various loading. Moreover, with the advantages of FBG sensors, they can be implemented to monitor bridge behavior remotely and in real time. A beam loading test was conducted to determine vertical displacements using FBG strain sensors and tilt sensors. The discrepancies as compared with dial gauges reading using the curvature and inclination approaches are 0.14mm (1.1%) and 0.41mm (3.2%), respectively. Further recommendations of these approaches for developments will also be discussed at the end of the paper.

Sensitivity of peak positions to flight-path parameters in a deep-inelastic scattering neutron TOF spectrometer

The effects of small changes in flight-path parameters (primary and secondary flight paths, detector angles), and of displacement of the sample along the beam axis away from its ideal position, are examined for an inelastic time-of-flight (TOF) neutron spectrometer, emphasising the deep-inelastic regime. The aim was to develop a rational basis for deciding what measured shifts in the positions of spectral peaks could be regarded as reliable in the light of the uncertainties in the calibrated flight-path parameters. Uncertainty in the length of the primary or secondary flight path has the least effect on the positions of the peaks of H, D and He, which are dominated by the accuracy of the calibration of the detector angles. This aspect of the calibration of a TOF spectrometer therefore demands close attention to achieve reliable outcomes where the position of the peaks is of significant scientific interest and is discussed in detail. The corresponding sensitivities of the position of peak of the Compton profile, J(y), to flight-path parameters and sample position are also examined, focusing on the comparability across experiments of results for H, D and He. We show that positioning the sample to within a few mm of the ideal position is required to ensure good comparability between experiments if data from detectors at high forward angles are to be reliably interpreted.

Monotonous trend estimation of deck displacement for automatic landing of rotorcraft UAVs

This paper presents a novel and practical procedure for estimating the mean deck height to assist in automatic landing operations of a Rotorcraft Unmanned Aerial Vehicle (RUAV) in harsh sea environments. A modified Prony Analysis (PA) procedure is outlined to deal with real-time observations of deck displacement, which involves developing an appropriate dynamic model to approach real deck motion with parameters identified through implementing the Forgetting Factor Recursive Least Square (FFRLS) method. The model order is specified using a proper order-selection criterion based on minimizing the summation of accumulated estimation errors. In addition, a feasible threshold criterion is proposed to separate the dominant components of deck displacement, which results in an accurate instantaneous estimation of the mean deck position. Simulation results demonstrate that the proposed recursive procedure exhibits satisfactory estimation performance when applied to real-time deck displacement measurements, making it well suited for integration into ship-RUAV approach and landing guidance systems.

A micro-level investigation of the solid displacement method for porosity determination of dried food

Porosity is one of the key parameters of the macroscopic structure of porous media, generally defined as the ratio of the free spaces occupied (by the volume of air) within the material to the total volume of the material. Porosity is determined by measuring skeletal volume and the envelope volume. Solid displacement method is one of the inexpensive and easy methods to determine the envelope volume of a sample with an irregular shape. In this method, generally glass beads are used as a solid due to their uniform size, compactness and fluidity properties. The smaller size of the glass beads means that they enter into the open pores which have a larger diameter than the glass beads. Although extensive research has been carried out on porosity determination using displacement method, no study exists which adequately reports micro-level observation of the sample during measurement. This study set out with the aim of assessing the accuracy of solid displacement method of bulk density measurement of dried foods by micro-level observation. Solid displacement method of porosity determination was conducted using a cylindrical vial (cylindrical plastic container) and 57 µm glass beads in order to measure the bulk density of apple slices at different moisture contents. A scanning electron microscope (SEM), a profilometer and ImageJ software were used to investigate the penetration of glass beads into the surface pores during the determination of the porosity of dried food. A helium pycnometer was used to measure the particle density of the sample. Results show that a significant number of pores were large enough to allow the glass beads to enter into the pores, thereby causing some erroneous results. It was also found that coating the dried sample with appropriate coating material prior to measurement can resolve this problem.

Nitrogen-doped graphene films from chemical vapor deposition of pyridine: Influence of process parameters on the electrical and optical properties

Graphene films were produced by chemical vapor deposition (CVD) of pyridine on copper substrates. Pyridine-CVD is expected to lead to doped graphene by the insertion of nitrogen atoms in the growing sp2 carbon lattice, possibly improving the properties of graphene as a transparent conductive film. We here report on the influence that the CVD parameters (i.e., temperature and gas flow) have on the morphology, transmittance, and electrical conductivity of the graphene films grown with pyridine. A temperature range between 930 and 1070 °C was explored and the results were compared to those of pristine graphene grown by ethanol-CVD under the same process conditions. The films were characterized by atomic force microscopy, Raman and X-ray photoemission spectroscopy. The optical transmittance and electrical conductivity of the films were measured to evaluate their performance as transparent conductive electrodes. Graphene films grown by pyridine reached an electrical conductivity of 14.3 × 105 S/m. Such a high conductivity seems to be associated with the electronic doping induced by substitutional nitrogen atoms. In particular, at 930 °C the nitrogen/carbon ratio of pyridine-grown graphene reaches 3%, and its electrical conductivity is 40% higher than that of pristine graphene grown from ethanol-CVD.

Direct shear testing on unsaturated silty soils to investigate the effects of drying and wetting on shear strength parameters at low suction

A modified conventional direct shear device was used to measure unsaturated shear strength of two silty soils at low suction values (0 ~ 50 kPa) that were achieved by following drying and wetting paths of soil water characteristic curves (SWCCs). The results revealed that the internal friction angle of the soils was not significantly affected by either the suction or the drying wetting SWCCs. The apparent cohesion of soil increased with a decreasing rate as suction increased. Shear stress-shear displacement curves obtained from soil specimens subjected to the same net normal stress and different suction values showed a higher initial stiffness and a greater peak stress as suction increased. A soil in wetting exhibited slightly higher peak shear stress and more contractive volume change behavior than that of soil in drying at the same net normal stress and suction.

Combined Atomic Force Microscopy and Modeling Study of The Evolution of Octadecylamine Films on a Mica Surface

The time evolution of the film thickness and domain formation of octadecylamine molecules adsorbed oil a mica surface is investigated Using atomic force microscopy. The adsorbed Film thickness is determined by measuring the height profile across the mica-amine interface of a mica surface partially immersed in a 15 mM solution of octadecylamine in chloroform. Using this novel procedure, adsorption of amine on mica is found to occur in three distinct stages, with morphologically distinct domain Formation and growth occurring during each stage. In the first stage, where adsorption is primarily in the thin-film regime, all average Film thickness of 0.2 (+/- 0.3) nm is formed for exposure times below 30 s and 0.8 (+/- 0.2) nm for 60 s of immersion time. During this stage, large sample spanning domains are observed. The second stage, which occurs between 60-300 s, is associated with it regime of rapid film growth, and the film thickness increases from about 0.8 to 25 nm during this stage. Once the thick-film regime is established, further exposure to the amine solution results in all increase in the domain area, and it regime of lateral domain growth is observed. In this stage, the domain area coverage grows from 38 to 75%, and the FTIR spectra reveal an increased level of crystallinity in the film. Using it diffusion-controlled model and it two-step Langmuir isotherm, the time evolution of the film growth is quantitatively captured. The model predicts the time at which the thin to thick film transition occurs as well its the time required for complete film growth at longer times. The Ward-Tordai equation is also solved to determine the model parameters in the monolayer (thin-film) regime, which occurs during the initial stages of film growth.