Stability of Motion of a Nonholonomic System

Perturbation differential equations of motion of a general nonholonomic system subjected to the ideal nonholonomic constraints of Chetaev＇s type are established, and the equation of variation of energy is deduced by using the perturbation equations of the system. A criterion of the stability is obtained and an example is given to illustrate the application of the result.     

A multi-scale Monte Carlo study of oxide structures on the Cu(1 0 0) surface

We present a multi-scale Monte Carlo study of the oxidation of the Cu(1 0 0) surface based on the Bortz-Kalos-Lebowitz model with the equilibrium energetics obtained from ab initio calculations. The radial and island size distribution functions are examined and Cu-O structures are analyzed at different temperatures and coverages. We concentrate on the coverages of 0.3 monolayer O or less, with variable sub-monolayer coverages of Cu. The results show that even though the ab initio calculations yield a higher barrier for O than for Cu adatom diffusion on Cu(1 0 0), the stability of Cu structures causes the O adatoms to be more mobile on the Cu(1 0 0) surface than the Cu adatoms. We are able to reproduce the c(2 × 2)-O domains seen in the experiments. However, we give an alternative explanation based on the repulsive interactions of O that, on one hand, cause the local ordering and, on the other hand, prohibits large well-ordered domains. We also give interpretation on the formation of the R45°-O reconstruction of Cu(1 0 0) above the O coverages of 0.3 monolayer based on the ab initio energetics.     

Thermal behaviour of two anti-inflammatory drugs (celecoxib and rofecoxib) and slow relaxation dynamics in their amorphous solid state. Comparison between the dynamic fragility obtained by dielectric spectroscopy and by thermostimulated currents

This study of the thermal behaviour of two glass formers showed that rofecoxib has a good ability to vitrify while celecoxib displays a moderate glass forming ability. On the other hand, celecoxib forms an instable glass while rofecoxib displays moderate glass stability. The α-relaxation of the two amorphous drugs was studied by differential scanning calorimetry (DSC) and thermally stimulated depolarization currents (TSDC). The values of the dynamic fragility obtained by the two techniques are in good mutual agreement and suggest that both drugs are moderately fragile glass formers. These values are however considerably lower than those obtained by dielectric relaxation spectroscopy (DRS) and published in the literature. In the present work we will compare the values of the dynamic fragility obtained by TSDC and DRS for a set of ~30 glass-forming liquids, in order to evaluate their relative suitability for the determination of the m-index. The observed differences are discussed and interpreted. Finally, secondary mobility modes were detected by TSDC in both celecoxib and rofecoxib. The kinetic parameters are identical in both cases and similar to those found by DRS for the slow-b relaxation of celecoxib. These secondary relaxations, that are precursors of the main relaxation on its lower temperature side, are believed to be Johari-Goldstein relaxations.     

The Asymmetric One-Dimensional Constrained Ising Model: Rigorous Results

We study a one-dimensional spin (interacting particle) system, with product Bernoulli (p) stationary distribution, in which a site can flip only when its left neighbor is in state +1. Such models have been studied in physics as simple exemplars of systems exhibiting slow relaxation. In our East model the natural conjecture is that the relaxation time (p), that is 1/(spectral gap), satisfies log (p) as p0. We prove this up to a factor of 2. The upper bound uses the Poincaré comparison argument applied to a wave (long-range) comparison process, which we analyze by probabilistic techniques. Such comparison arguments go back to Holley (1984, 1985). The lower bound, which atypically is not easy, involves construction and analysis of a certain coalescing random jumps process.     

Enthalpy Relaxation Study of Poly(Vinyl Chloride) Films Based on the Time-Temperature Superposition Principle

Abstract

In the enthalpy relaxation of poly(vinyl chloride), a decrease in enthalpy upon the isothermal ageing was measured using the differential scanning calorimetry method as a function of ageing time (t_A) and ageing temperature. The range of the ageing temperature was from 56?°C (T_g ? 25?°C) to 72?°C (T_g ? 9?°C) where T_g denotes the glass transition temperature. The limiting value of the decrease in enthalpy was determined by applying a stretched exponential function to the measured enthalpy data. The relaxation function (?) was derived from the measured enthalpy and the construction of a master curve was tried by shifting the ? ? t_A curves of the respective ageing temperatures horizontally. Although there was no agreement between the shift factors (a_T) and the relaxation times of the ? ? t_A curves, the superposition was successfully constructed and the a_T values obtained for the poly(vinyl chloride) sample were found to be comparable to those reported for viscoelastic experiments over a broad temperature range above and below T_g carried out for different polymers. The origin of the decrease in enthalpy was briefly discussed in terms of the chain dynamics in the isothermal condition.     

Change in motor cortex activation for muscle release by motor learning

For central nervous system disorders'' rehabilitation, it is important to accurately understand motor control and implement an appropriate motor learning process to induce neuroplastic changes. The neurophysiological studies have revealed that neural control mechanisms are crucial during both the onset of muscular activities and muscle release after contraction. When performing various movements during daily activities, muscle relaxation control enables precise force output and timing control. Moreover, surround inhibition is a functional mechanism in the motor system. Surround inhibition of the motor system may be involved in the selective execution of desired movements. This review demonstrates cortical excitability resulting from motor learning, movement control mechanisms including muscle relaxation and the suppression of nontarget muscle groups, and the voluntary drive''s importance that is required for movement.     

Oxygen relaxation and phase transition in GdBaCo2O5 + δ oxide

Electrical conductivity, internal friction techniques and dilatometer have been used to investigate the oxygen relaxation, phase transition and thermal expansion behavior of GdBaCo₂O_5 + δ. The main electronic charge carriers in GdBaCo₂O_5 + δ are electronic holes, which could be assigned to the formation of Co⁴⁺. The oxygen exchange kinetics intensely depends on oxygen partial pressure and is also closely related to temperature. Both electrical conductivity and internal friction give rise to an abnormal at about 75 °C, which are related to the insulator-metal transition occurring in GdBaCo₂O_5 + δ. One large relaxation internal friction peak, due to the motion of oxygen within Gd-O plane, is also found in the oxide. The average thermal expansion coefficient (TEC) of GdBaCo₂O_5 + δ is about 21.4 × 10⁻⁶ K⁻¹ between 500 °C and 900 °C.     

Long-Time Dynamical Behaviour of Alternative-Current Stark Effect

We report the long time dynamical behaviour of ac Stark effect in a simple quantum model in which two level atoms interact with quantized coherent radiation field. A new phenomenon of periodic quantum collapse and revival of the ac Stark shift of energy level due to ac Stark effect is expressed accurately by analysing the phase of transition probability amplitude. The analytic prediction is confirmed by the numerical results.     

Side-hole to anti-hole conversion in time-resolved spectral hole burning of ruby: Long-lived spectral holes due to ground state level population storage

We report time-resolved transient spectral hole burning of Verneuil-grown 20 ppm and ca. 0.6 ppm ruby (Al₂O₃:Cr³⁺) in zero field and low magnetic fields B∥c at 4 K. The hole-burning spectroscopy of the 20 ppm sample implies relatively rapid cross relaxation in the ⁴A₂ ground state on the ∼1 ms timescale both in zero field and in low magnetic fields, B∥c, up to 0.2 T. In the 0.6 ppm sample, side-hole to anti-hole conversion is observed both in zero field and in low magnetic fields. This conversion is caused by population storage in ⁴A₂ ground state levels. Spin-lattice relaxation, on the 200 ms timescale, is directly observed from the time dependence of the resonant hole and anti holes in B∥c, consistent with a very low cross-relaxation rate. However, in zero field cross relaxation in the ⁴A₂ ground state is still a significant relaxation mechanism for the 0.6 ppm sample resulting in hole decay in ∼50 ms.