Probability backflow for a Dirac particle

The phenomenon of probability backflow, previously quantified for a free nonrelativistic particle, is considered for a free particle obeying Dirac's equation. It is known that probability backflow can occur in the opposite direction to the momentum; that is to say, there exist positive-energy states in which the particle certainly has a positive momentum in a given direction, but for which the component of the probability flux vector in that direction is negative. It is shown thar the maximum possible amount of probability that can flow backwards, over a given time interval of duration T, depends on the dimensionless parameter epsilon = root 4h/mc(2)T, where m is the mass of the particle and c is the speed of light. At epsilon = 0, the nonrelativistic value of approximately 0.039 for this maximum is recovered. Numerical studies suggest that the maximum decreases monotonically as epsilon increases from 0, and show that it depends on the size of m, h, and T, unlike the nonrelativistic case.

Repeated flood events and fossil forests at Curio Bay (Middle Jurassic), New Zealand

During the Middle Jurassic, the regional environment of Curio Bay, southeast South Island, New Zealand, was a fluvial plain marginal to volcanic uplands. Intermittent flashy, poorly-confined flood events buried successive conifer forests. With the termination of each flood, soils developed and vegetation was reestablished. In most cases, this developed into coniferous forest. In approximately 40 m of vertical section, 10 fossil forest horizons can be distinguished, highlighting a type of fluvial architecture which is poorly documented. Flood-basin material is minimal, but a short-Lived floodbasin lake is inferred to have developed within the interval of study. Paleocurrent indicators suggest enclosure of the basin on more than one side. Sedimentation style suggests a relatively dry (less than humid but not arid) climate with seasonal rainfall. (C) 2001 Elsevier Science B.V. All rights reserved.

The 'muscle-bone unit' during the pubertal growth spurt

Mechanostat theory postulates that developmental changes in bone strength are secondary to the increasing loads imposed by larger muscle forces. Therefore, the increase in muscle strength should precede the increase in bone strength. We tested this prediction using densitometric surrogate measures of muscle force (lean body mass, LBM) and bone strength (bone mineral content, BMC) in a study on 70 boys and 68 girls who were longitudinally examined during pubertal development. On the level of the total body, the peak in LBM accrual preceded the peak in BMC accretion by an average of 0.51 years in girls and by 0.36 years in boys. In the arms, the maximal increase in LBM was followed by arm peak BMC accrual after an interval of 0.71 years in girls and 0.63 years in boys. In the lower extremities, the maximal increase in LBM was followed by peak BMC accrual after an interval of 0.22 years in girls and 0.48 years in boys. A multiple regression model revealed that total body peak LBM velocity, but not peak height velocity and sex, was independently associated with total body peak BMC velocity (r(2) = 0.50; P < 0.001). Similarly, arm and leg peak LBM velocity, but not peak height velocity and sex, were independently associated with arm and leg peak BMC velocity, respectively (r(2) = 0.61 for arms, r(2) = 0.41 for legs; P < 0.001 in both cases). These results are compatible with the view that bone development is driven by muscle development, although the data do not exclude the hypothesis that the two processes are independently determined by genetic mechanisms. (C) 2004 Elsevier Inc. All rights reserved.

Covariation and interference between physiological reflexes: Eye-blink startle cardiac defense, and skin conductance

Comparative studies of autonomic and somatic reflexes, such as cardiac defense and motor startle, are rare. However, examination of the pattern of covariation, independence, or interference among physiological reflexes may help to clarify their functional significance and elucidate their complex modulation by psychological factors. Here we report the results of a study that examined the pattern of interference of eye-blink startle on subsequent cardiac defense. Participants were 63 students (31 women) distributed into three groups according to the sensory modality of the eliciting stimulus during the startle trials: acoustic high intensity (105 dB), acoustic low intensity (65 dB), and visual modality. Startle trials consisted of 12 presentations of the eliciting stimulus with a duration of 50 ms, instantaneous risetime, and a variable inter-stimulus interval of 16 – 20 s.Defense trials began 20 s after the last startle trial and consisted, for all groups, of 3 presentations of the high intensity acoustic stimulus with a duration of 500 ms and an inter-stimulus interval of 215 s. Results showed a clear interference of the startle trials on the subsequent defense trials when both types of trials shared identical sensory modality (acoustic) independently of intensity: the expected pattern of cardiac defense in the first trial only appeared in the visual modality. Similar interference effects were observed in the skin conductance response. Subjective reactivity to the defense stimulus did not detect differences between conditions.