Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

Shifting of the electron-capture-to-the-continuum peak in proton-helium collisions at 10 and 20 keV

A refined theoretical approach has been developed to study the double-differential cross sections (DDCS's) in proton-helium collisions as a function of the ratio of ionized electron velocity to the incident proton velocity. The refinement is done in the present coupled-channel calculation by introducing a continuum distorted wave in the final state coupled with discrete states including direct as well as charge transfer channels. It is confirmed that the electron-capture-to-the-continuum (ECC) peak is slightly shifted to a lower electron velocity than the equivelocity position. Comparing measurements and classical trajectory Monte Carlo (CTMC) calculations at 10 and 20 keV proton energies, excellent agreement of the ECC peak heights is achieved at both energies. However, a minor disagreement in the peak positions between the present calculation and the CTMC results is noted. A smooth behavior of the DDCS is found in the present calculation on both sides of the peak whereas the CTMC results show some oscillatory behavior particularly to the left of the peak, associated with the statistical nature of CTMC calculations.

Trends in the prevalence of cerebral palsy in Northern Ireland, 1981-1997

We describe trends in the prevalence of cerebral palsy (CP) by birth weight group, and in the severity of motor impairments and presence of associated intellectual impairment, in Northern Ireland from 1981 to 1997 (n=909; 510 males, 399 females; total population 415 936 live births) using data from a population-based register of CP. Children with suspected CP or who died before 1 year of age and those with CP of postneonatal origin were excluded. Prevalence of CP was 2.2 per 1000 live births without significant change over time. Among very-low-birthweight (<1500g) live births, prevalence was 44.5 per 1000 (95% confidence interval 32.3–59.8) from 1994 to 1997, with evidence of a statistically significant decline in prevalence since the mid- to late 1980s accompanied by a decrease in the severity of motor impairment and likelihood of intellectual impairment. Among moderately-low-birthweight (1500–2499g) children there was weaker evidence of a peak prevalence in the late 1980s. Prevalence among normal-birthweight infants did not change significantly, but outcome in terms of severity of motor impairment and intellectual impairment improved in the 1990s. Occurrence of bilateral spasticity from 1994 to 1997 was associated with greater severity and likelihood of intellectual impairment for normal-birthweight individuals than for low- or very-low-birth weight individuals.

Reconfiguring Older Bodies in the Prison Time Machine

It is by mapping an area that the geographer comes to understand the contours and formations of a place. The “place” in this case is the prison world. This article serves to map moments in prison demonstrating how “old” female bodies are performed under the prison gaze. In this article I will illustrate how older women subvert, negotiate, or invoke discourse as a means of reinscribing the normalizing discourses that serve to confine and define older women's experiences in prison. Female elders in prison become defined and confined by regimes of femininity and ageism. They have to endure symbolic and actual intrusions of physical privacy, which serve to remind them of what they were, where they are, and what they have become. This article will critically explore the complexity and contradictions of time use in prison and how they impact on embodied identities. By incorporating the voices of elders, I hope to draw out the contradictions and dilemmas which they experience, thereby illustrating the relationship between time, their involvement in doing time, and the performance of time in a total institution (see Goffman, 1961), and the relationship between temporality and existence. The stories of the women show how their identities are caught within the movement and motion of time and space, both in terms of the time of “the real” on the outside and within prison time. This is the in-between space of carceral time within which women live and which they negotiate. It is by being caught in this network of carceral time that they are constantly being “remade” as their body/performance of identities alters within it. While only a small percentage of the female prison population in the United Kingdom are in later life, one has to question why criminological and gerontological literature fail to address the needs of a growing significant minority.

Tracking biological invasions in space and time: elucidating the invasive history of the green alga Codium fragile using old DNA

With the advent of 'ancient DNA' studies on preserved material of extant and extinct species, museums and herbaria now represent an important although still underutilized resource in molecular ecology. The ability to obtain sequence data from archived specimens can reveal the recent history of cryptic species and introductions. We have analysed extant and herbarium samples of the highly invasive green alga Codium fragile, many over 100 years old, to identify cryptic accessions of the invasive strain known as C. fragile ssp. tomentosoides, which can be identified by a unique haplotype. Molecular characterization of specimens previously identified as native in various regions shows that the invasive tomentosoides strain has been colonizing new habitats across the world for longer than records indicate, in some cases nearly 100 years before it was noticed. It can now be found in the ranges of all the other native haplotypes detected, several of which correspond to recognized subspecies. Within regions in the southern hemisphere there was a greater diversity of haplotypes than in the northern hemisphere, probably as a result of dispersal by the Antarctic Circumpolar Current. The findings of this study highlight the importance of herbaria in preserving contemporaneous records of invasions as they occur, especially when invasive taxa are cryptic.

On the origin of the forward peak and backward oscillations in the F + H2(v = 0) to HF(v' = 2) + H reaction

We present a semiclassical complex angular momentum (CAM) analysis of the forward scattering peak which occurs at a translational collision energy around 32 meV in the quantum mechanical calculations for the F + H2(v = 0, j = 0) ? HF(v' = 2, j' = 0) + H reaction on the Stark–Werner potential energy surface. The semiclassical CAM theory is modified to cover the forward and backward scattering angles. The peak is shown to result from constructive/destructive interference of the two Regge states associated with two resonances, one in the transition state region and the other in the exit channel van der Waals well. In addition, we demonstrate that the oscillations in the energy dependence of the backward differential cross section are caused by the interference between the direct backward scattering and the decay of the two resonance complexes returning to the backward direction after one full rotation.