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.

Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

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.

The effects of postural threat on cognitive strategies used to maintain upright stance

It is well established that postural threat modifies postural control, although little is known regarding the underlying mechanism(s) responsible. It is possible that changes in postural control under conditions of elevated postural threat result from alterations in cognitive strategies. The purpose of this study was to determine the influence of elevated postural threat on cognitive strategies and to determine the relationship between postural control, psychological, and cognitive measures. It was hypothesized that elevated postural threat would cause a shift to more conscious control of posture. It was also expected that a relationship between fear of falling and postural control would exist that could be explained by changes in conscious control of posture. Forty-eight healthy young adults stood on a force plate at two different surface heights: ground level (LOW) and 3.2m above ground level (HIGH). Center of pressure (COP) summary measures calculated to quantify postural control were the mean position (AP-COP MP), root mean square (AP-COP RMS) and mean power frequency (AP-COP MPF) in the anteriorposterior direction. Trunk sway measures calculated in the pitch direction were trunk angle and trunk velocity. Psychological measures including perceived balance confidence, perceived fear of falling, perceived anxiety, and perceived stability were self reported. As a physiological indicator of anxiety, electrodermal activity was collected. The cognitive strategies assessed were movement reinvestment and attention focus. A modified state-sp-ecific version of the Movement Specific Reinvestment Scale was used to measure conscious motor processing (CMP) and movement self-consciousness (MSC). An attention focus questionnaire was developed to assess the amount of attention directed to internal and external sources. An effect of postural threat on cognitive strategies was observed as participants reported more conscious control and a greater concern or worry about their posture at the HIGH postural threat condition as well as an increased internal and external focus of attention. In addition changes in postural control, psychological, and physiological measures were found. The participants leaned away from the edge of the platform, the frequency of their postural adjustments increased, and the velocity of their trunk movements increased. Participants felt less confident, more fearful, more anxious, and less stable with an accompanying increase in physiological anxiety. Significant correlations between perceived anxiety, AP-COP MP, and cognitive measures revealed a possible relationship that could be mediated by cognitive measures. It was found that with greater conscious motor processing, more movement self-consciousness, and a greater amount of attention focused externally there was a larger shift of the mean position away from the edge of the platform. This thesis provides evidence that postural threat can influence cognitive strategies causing a shift to more conscious control of movement which is associated with leaning away from the edge of the platform. Shifting the position of the body away from the direction of the postural threat may reflect a cognitive strategy to ensure safety in this situation due to the inability to employ a stepping strategy when standing on an elevated platform.

Phonon spectra and temperature variation of thermodynamic properties of fcc metals via Finnis-Sinclair type many body potentials: Sutton-Chen and improved Sutton-Chen models

Volume(density)-independent pair-potentials cannot describe metallic cohesion adequately as the presence of the free electron gas renders the total energy strongly dependent on the electron density. The embedded atom method (EAM) addresses this issue by replacing part of the total energy with an explicitly density-dependent term called the embedding function. Finnis and Sinclair proposed a model where the embedding function is taken to be proportional to the square root of the electron density. Models of this type are known as Finnis-Sinclair many body potentials. In this work we study a particular parametrization of the Finnis-Sinclair type potential, called the "Sutton-Chen" model, and a later version, called the "Quantum Sutton-Chen" model, to study the phonon spectra and the temperature variation thermodynamic properties of fcc metals. Both models give poor results for thermal expansion, which can be traced to rapid softening of transverse phonon frequencies with increasing lattice parameter. We identify the power law decay of the electron density with distance assumed by the model as the main cause of this behaviour and show that an exponentially decaying form of charge density improves the results significantly. Results for Sutton-Chen and our improved version of Sutton-Chen models are compared for four fcc metals: Cu, Ag, Au and Pt. The calculated properties are the phonon spectra, thermal expansion coefficient, isobaric heat capacity, adiabatic and isothermal bulk moduli, atomic root-mean-square displacement and Gr\"{u}neisen parameter. For the sake of comparison we have also considered two other models where the distance-dependence of the charge density is an exponential multiplied by polynomials. None of these models exhibits the instability against thermal expansion (premature melting) as shown by the Sutton-Chen model. We also present results obtained via pure pair potential models, in order to identify advantages and disadvantages of methods used to obtain the parameters of these potentials.

Effects of isometric elbow flexion on electromyographic spike analysis

The main objective of this research was to examine the relationship between surface electromyographic (SEMG) spike activity and force. The secondary objective was to determine to what extent subcutaneous tissue impacts the high frequency component of the signal, as well as, examining the relationship between measures of SEMG spike shape and their traditional time and frequency analogues. A total of96 participants (46 males and 50 females) ranging in age (18-35 years), generated three 5-second isometric step contractions at each force level of 40, 60, 80, and 100 percent of maximal voluntary contraction (MVC). The presentation of the contractions was balanced across subjects. The right arm of the subject was positioned in the sagittal plane, with the shoulder and elbow flexed to 90 degrees. The elbow rested on a support in a neutral position (mid pronation/mid supination) and placed within a wrist cuff, fastened below the styloid process. The wrist cuff was attached to a load cell (JR3 Inc., Woodland, CA) recording the force produced. Biceps brachii activity was monitored with a pair of Ag/AgCI recording electrodes (Grass F-E9, Astro-Med Inc., West Warwick, RI) placed in a bipolar configuration, with an interelectrode distance (lED) of 2cm distal to the motor point. Data analysis was performed on a I second window of data in the middle of the 5-second contraction. The results indicated that all spike shape measures exhibited significant (p < 0.01) differences as force increase~ from 40 to 100% MVC. The spike shape measures suggest that increased motor unit (MU) recruitment was responsible for increasing force up to 80% MVC. The results suggested that further increases in force relied on MU III synchronization. The results also revealed that the subcutaneous tissue (skin fold thickness) had no relationship (r = 0.02; P > 0.05) with the mean number of peaks per spike (MNPPS), which was the high frequency component of the signal. Mean spike amplitude (MSA) and mean spike frequency (MSF) were highly correlated with their traditional measures root mean square (RMS) and mean power frequency (MPF), respectively (r = 0.99; r = 0.97; P < 0.01).

The surface electromyography-force relationship during isometric dorsiflexion in males and females

This study evaluated sex-related differences in the tibialis anterior (TA) surface electromyography (EMG) to force relationship. One-hundred participants (50 males and 50 females) performed three isometric contractions at 20, 40, 60, 80, and 100% of maximal voluntary contraction (MVC) in an apparatus designed to isolate the action of the dorsiflexors. The surface EMG signal was amplified (lOOOx), band-pass filtered (10-500Hz), and sampled at 2048 Hz. The load cell signal was low-passed filtered at 100 Hz and sampled at the same rate. Males were stronger than females {P <0.05). However, there was no significant difference in root-mean-square (RMS) values between sexes {P <0.05). Both sexes exhibited a quadratic increase in RMS across force levels (P <0.05). The mean power frequency (MNF) for males was greater than for females {P <0.05). Males and females exhibited a linear increase in both frequency measures up to 80% of MVC (P <0.05). Between 80 and 100% MVC, the frequency values for the females plateaued while males showed a decrease {P <0.05). The magnitude of the difference in MNF between males and females was consistent with sex-specific TA physiology. In general, the pattern of means for RMS and MNF between males and females revealed no sex-related differences in the surface EMG/force relationship. We therefore conclude that there are no sex-related differences in the gradation of muscle force.

Training distribution and the acquisition of maximal isometric elbow flexion strength

Twenty-six sedentary, college-aged females were matched and randomly assigned to one of two groups. The massed group (n=13) completed 15 maximal isometric elbow flexion strength trials in one session, while the distributed group (n=13) performed five such contractions on three successive days. After a two-week and three month rest interval, both groups returned to perfonn another five maximal isometric elbow flexion strength trials to assess retention of any potential strength gains. Elbow flexion torque and surface electromyography (SEMG) of the biceps and triceps were monitored concurrently. There was a significant (P < 0.05) increase in strength in both groups from block one (first five contractions) to block four (first retest) and from block one to block five (second retest). Both groups exhibited a similar linear increasing (P < 0.05) trend in biceps root-mean-square (RMS) SEMG amplitude. A significant (P < 0.05) decrease in triceps RMS SEMG amplitude was found between block one and block four for the distributed group. However, a significant (P < 0.05) increase was then found between block one and five for the massed group, and between blocks four and five for distributed group. These results suggest that there is flexibility in resistive exercise schedules. An increase in neural drive to the agonist muscle continued throughout testing. This was accompanied by a reduction in antagonist co activation that was a short-tenn (two weeks) training effect, dissipated over the longer rest interval (three months).

Decreased motor unit firing rate in the potentiated tibialis anterior in humans

With repeated activity, force production, rate of force production, and relaxation time are impaired. These are characteristics ofa fatigued muscle (Vandenboom, 2004). However, brief bouts of near maximal to maximal activity results in the increased ability of the muscle to generate force, termed post activation potentiation (P AP)(V andervoort et aI., 1983). The purpose of the present study was to characterize motor unit firing rate (MUFR) in the unfatigued, potentiated tibialis anterior (TA). Using a quadrifilar needle electrode, MUFR was measured during a 5s 50% MVC in which the TA was either potentiated or unpotentiated; monopolar electrodes measured surface parameters. A lOs MVC was used to potentiate the muscle. Firing rate decreased significantly from 20.15±2.9Opps to 18.27±2.99pps, while mean power frequency decreased significantly from 60. 13±7.75 Hz to 53.62±8.56 Hz. No change in root mean square (RMS) was observed. Therefore, in the present study, MUFR decreases in response to a potentiated TA.

Neuromotor Mechanisms Involved in the Recovery from Local Muscular Fatigue

The phenomenon of over-recovery consists of a participant’s maximal force levels returning to values above initial levels. The present study examined the presence and causes of over-recovery following local muscular fatigue. Fourteen males completed two fatigue protocols consisting of maximal isometric dorsiflexion contractions. Upon completion of the fatigue protocol participants’ force was monitored over a 15 minute recovery period. Dorsiflexion force and surface electromyography (sEMG) from the tibialis anterior and soleus were monitored concurrently. Following the two fatigue conditions (10 and 20% force decrement) force recovered to 100.5 and 99.5% of initial levels for each condition, respectively. Surface EMG root-mean-square amplitude and MPF exhibited changes consistent with a warm-up effect. It was concluded that over-recovery was not present in the tibialis anterior following a local muscular fatigue. However, the return in force to initial values, rather than a persistent decrement as normally observed, was mediated by the warm-up effect.

The electromyographic threshold in boys and men

Abstract Background Children have been shown to have higher lactate (LaTh) and ventilatory (VeTh) thresholds than adults, which might be explained by lower levels of type-II motor-unit (MU) recruitment. However, the electromyographic threshold (EMGTh), regarded as indicating the onset of accelerated type-II MU recruitment, has been investigated only in adults. Purpose To compare the relative exercise intensity at which the EMGTh occurs in boys versus men. Methods Participants were 21 men (23.4 ± 4.1 years) and 23 boys (11.1 ± 1.1 years), with similar habitual physical activity and peak oxygen consumption (VO2pk) (49.7 ± 5.5 vs. 50.1 ± 7.4 ml kg−1 min−1, respectively). Ramped cycle ergometry was conducted to volitional exhaustion with surface EMG recorded from the right and left vastus lateralis muscles throughout the test (~10 min). The composite right–left EMG root mean square (EMGRMS) was then calculated per pedal revolution. The EMGTh was then determined as the exercise intensity at the point of least residual sum of squares for any two regression line divisions of the EMGRMS plot. Results EMGTh was detected in 20/21 of the men (95.2 %) and only in 18/23 of the boys (78.3 %). The boys’ EMGTh was significantly higher than the men’s (86.4 ± 9.6 vs. 79.7 ± 10.0 % of peak power output at exhaustion; p < 0.05). The pattern was similar when EMGTh was expressed as percentage of VO2pk. Conclusions The boys’ higher EMGTh suggests delayed and hence lesser utilization of type-II MUs in progressive exercise, compared with men. The boys–men EMGTh differences were of similar magnitude as those shown for LaTh and VeTh, further suggesting a common underlying factor.