Time evolution in the unimolecular master equation at low temperatures: full spectral solution with scalable iterative methods and high precision

A new method is presented to determine an accurate eigendecomposition of difficult low temperature unimolecular master equation problems. Based on a generalisation of the Nesbet method, the new method is capable of achieving complete spectral resolution of the master equation matrix with relative accuracy in the eigenvectors. The method is applied to a test case of the decomposition of ethane at 300 K from a microcanonical initial population with energy transfer modelled by both Ergodic Collision Theory and the exponential-down model. The fact that quadruple precision (16-byte) arithmetic is required irrespective of the eigensolution method used is demonstrated. (C) 2001 Elsevier Science B.V. All rights reserved.

The effects of time delays in adaptive phase measurements

It is not possible to make measurements of the phase of an optical mode using linear optics without introducing an extra phase uncertainty. This extra phase variance is quite large for heterodyne measurements, however it is possible to reduce it to the theoretical limit of log (n) over bar (4 (n) over bar (2)) using adaptive measurements. These measurements are quite sensitive to experimental inaccuracies, especially time delays and inefficient detectors. Here it is shown that the minimum introduced phase variance when there is a time delay of tau is tau/(8 (n) over bar). This result is verified numerically, showing that the phase variance introduced approaches this limit for most of the adaptive schemes using the best final phase estimate. The main exception is the adaptive mark II scheme with simplified feedback, which is extremely sensitive to time delays. The extra phase variance due to time delays is considered for the mark I case with simplified feedback, verifying the tau /2 result obtained by Wiseman and Killip both by a more rigorous analytic technique and numerically.

Mental time travel in animals?

Are humans alone in their ability to reminisce about the past and imagine the future? Recent evidence suggests that food-storing birds (scrub jays) have access to information about what they have stored where and when. This has raised the possibility of mental time travel (MTT) in animals and sparked similar research with other species. Here we caution that such data do not provide convincing evidence for MTT. Examination of characteristics of human MTT (e.g. non-verbal declaration, generativity, developmental prerequisites) points to other avenues as to how a case for animal MTT could be made. In light of the current lack of evidence, however, we maintain that MTT is a uniquely human characteristic.

Real-time PCR in the microbiology laboratory

Use of PCR in the field of molecular diagnostics has increased to the point where it is now accepted as the standard method for detecting nucleic acids from a number of sample and microbial types. However, conventional PCR was already an essential tool in the research laboratory. Real-time PCR has catalysed wider acceptance of PCR because it is more rapid, sensitive and reproducible, while the risk of carryover contamination is minimised. There is an increasing number of chemistries which are used to detect PCR products as they accumulate within a closed reaction vessel during real-time PCR. These include the non-specific DNA-binding fluorophores and the specific, fluorophore-labelled oligonucleotide probes, some of which will be discussed in detail. It is not only the technology that has changed with the introduction of real-time PCR. Accompanying changes have occurred in the traditional terminology of PCR, and these changes will be highlighted as they occur. Factors that have restricted the development of multiplex real-time PCR, as well as the role of real-time PCR in the quantitation and genotyping of the microbial causes of infectious disease, will also be discussed. Because the amplification hardware and the fluorogenic detection chemistries have evolved rapidly, this review aims to update the scientist on the current state of the art. Additionally, the advantages, limitations and general background of real-time PCR technology will be reviewed in the context of the microbiology laboratory.

A theory for execution-time derivation in real-time programs

We provide an abstract command language for real-time programs and outline how a partial correctness semantics can be used to compute execution times. The notions of a timed command, refinement of a timed command, the command traversal condition, and the worst-case and best-case execution time of a command are formally introduced and investigated with the help of an underlying weakest liberal precondition semantics. The central result is a theory for the computation of worst-case and best-case execution times from the underlying semantics based on supremum and infimum calculations. The framework is applied to the analysis of a message transmitter program and its implementation. (c) 2005 Elsevier B.V. All rights reserved.

Using circular statistics to analyse time patterns in crime incidence

A set of techniques referred to as circular statistics has been developed for the analysis of directional and orientational data. The unit of measure for such data is angular (usually in either degrees or radians), and the statistical distributions underlying the techniques are characterised by their cyclic nature-for example, angles of 359.9 degrees are considered close to angles of 0 degrees. In this paper, we assert that such approaches can be easily adapted to analyse time-of-day and time-of-week data, and in particular daily cycles in the numbers of incidents reported to the police. We begin the paper by describing circular statistics. We then discuss how these may be modified, and demonstrate the approach with some examples for reported incidents in the Cardiff area of Wales. (c) 2005 Elsevier Ltd. All rights reserved.

The velocity of probability transport in quantum mechanics

In his study of the 'time of arrival' problem in the nonrelativistic quantum mechanics of a single particle, Allcock [1] noted that the direction of the probability flux vector is not necessarily the same as that of the mean momentum of a wave packet, even when the packet is composed entirely of plane waves with a common direction of momentum. Packets can be constructed, for example for a particle moving under a constant force, in which probability flows for a finite time in the opposite direction to the momentum. A similar phenomenon occurs for the Dirac electron. The maximum amount of probabilitiy backflow which can occur over a given time interval can be calculated in each case.

Large amplitude folding in finely layered viscoelastic rock structures

We analyze folding phenomena in finely layered viscoelastic rock. Fine is meant in the sense that the thickness of each layer is considerably smaller than characteristic structural dimensions. For this purpose we derive constitutive relations and apply a computational simulation scheme (a finite-element based particle advection scheme; see MORESI et al., 2001) suitable for problems involving very large deformations of layered viscous and viscoelastic rocks. An algorithm for the time integration of the governing equations as well as details of the finite-element implementation is also given. We then consider buckling instabilities in a finite, rectangular domain. Embedded within this domain, parallel to the longer dimension we consider a stiff, layered plate. The domain is compressed along the layer axis by prescribing velocities along the sides. First, for the viscous limit we consider the response to a series of harmonic perturbations of the director orientation. The Fourier spectra of the initial folding velocity are compared for different viscosity ratios. Turning to the nonlinear regime we analyze viscoelastic folding histories up to 40% shortening. The effect of layering manifests itself in that appreciable buckling instabilities are obtained at much lower viscosity ratios (1:10) as is required for the buckling of isotropic plates (1:500). The wavelength induced by the initial harmonic perturbation of the director orientation seems to be persistent. In the section of the parameter space considered here elasticity seems to delay or inhibit the occurrence of a second, larger wavelength. Finally, in a linear instability analysis we undertake a brief excursion into the potential role of couple stresses on the folding process. The linear instability analysis also provides insight into the expected modes of deformation at the onset of instability, and the different regimes of behavior one might expect to observe.

Scope for further analytical solutions for constant flux infiltration into a semi-infinite soil profile or redistribution in a finite soil profile

[1] We attempt to generate new solutions for the moisture content form of the one-dimensional Richards' [1931] equation using the Lisle [1992] equivalence mapping. This mapping is used as no more general set of transformations exists for mapping the one-dimensional Richards' equation into itself. Starting from a given solution, the mapping has the potential to generate an infinite number of new solutions for a series of nonlinear diffusivity and hydraulic conductivity functions. We first seek new analytical solutions satisfying Richards' equation subject to a constant flux surface boundary condition for a semi-infinite dry soil, starting with the Burgers model. The first iteration produces an existing solution, while subsequent iterations are shown to endlessly reproduce this same solution. Next, we briefly consider the problem of redistribution in a finite-length soil. In this case, Lisle's equivalence mapping is generalized to account for arbitrary initial conditions. As was the case for infiltration, however, it is found that new analytical solutions are not generated using the equivalence mapping, although existing solutions are recovered.

Caregiver burden, time spent caring and health status in the first 12 months following stroke

Objective: To quantify time caring, burden and health status in carers of stroke patients after discharge from rehabilitation; to identify the potentially modifiable sociodemographic and clinical characteristics associated with these outcomes. Methods: Patients and carers prospectively interviewed 6 (n = 71) and 12 (n = 57) months after discharge. Relationships of carer and patient variables with burden, health status and time analysed by Gaussian and Poisson regression. Results: Carers showed considerable burden at 6 and 12 months. Carers spent 4.6 and 3.6 hours per day assisting patients with daily activities at 6 and 12 months, respectively. Improved patient motor and cognitive function were associated with reductions of up to 20 minutes per day in time spent in daily activities. Better patient mental health and cognitive function were associated with better carer mental health. Conclusions: Potentially modifiable factors such as these may be able to be targeted by caregiver training, support and education programmes and outpatient therapy for patients.