Flux-Across-Surfaces Theorem for a Dirac Particle

We consider the asymptotic evolution of a relativistic spin-1/2-particle. i.e. a particle whose wavefunction satisfies the Dirac equation with external static potential. We prove that the probability for the particle crossing a (detector) surface converges to the probability, that the direction of the momentum of the particle lies within the solid angle defined by the (detector) surface, as the distance of the surface goes to infinity. This generalizes earlier non relativistic results, known as flux across surfaces theorems, to the relativistic regime

On the quantum probability flux through surfaces

We remark that the often ignored quantum probability current is fundamental for a genuine understanding of scattering phenomena and, in particular, for the statistics of the time and position of the first exit of a quantum particle from a given region, which may be simply expressed in terms of the current. This simple formula for these statistics does not appear as such in the literature. It is proposed that the formula, which is very different from the usual quantum mechanical measurement formulas, be verified experimentally. A full understanding of the quantum current and the associated formula is provided by Bohmian mechanics.Comment: 15 pages, 3 figures, revised and more detailed version, to be published in Journal of Statistical Physics, August 9

The Message of the Quantum?

We criticize speculations to the effect that quantum mechanics is fundamentally about information. We do this by pointing out how unfounded such speculations in fact are. Our analysis focuses on the dubious claims of this kind recently made by Anton Zeilinger

Optimization of struvite precipitation in synthetic biologically treated swine wastewater - Determination of the optimal process parameters

A sustainable way to recover phosphorus (P) in swine wastewater involves a preliminary step of P dissolution followed by the separation of particulate organic matter. The next two steps are firstly the precipitation of struvite crystals done by adding a crystallization reagent (magnesia) and secondly the filtration of the crystals. A design of experiments with five process parameters was set up to optimize the size of the struvite crystals in a synthetic swine wastewater. More than 90% of P was recovered as large crystals of struvite in optimal conditions which were: low Mg:Ca ratio (2.25:1), the leading parameter, high N:P ratio (3:1), moderate stirring rate (between 45 and 90 rpm) and low temperature (below 20°C). These results were obtained despite the presence of a large amount of calcium and using a cheap reactant (MgO). The composition of the precipitates was identified by Raman analysis and solid dissolution. Results showed that amorphous calcium phosphate (ACP) co-precipitated with struvite and that carbonates were incorporated with solid fractions

Naive Realism about Operators

A source of much difficulty and confusion in the interpretation of quantum mechanics is a ``naive realism about operators.'' By this we refer to various ways of taking too seriously the notion of operator-as-observable, and in particular to the all too casual talk about ``measuring operators'' that occurs when the subject is quantum mechanics. Without a specification of what should be meant by ``measuring'' a quantum observable, such an expression can have no clear meaning. A definite specification is provided by Bohmian mechanics, a theory that emerges from Sch\"rodinger's equation for a system of particles when we merely insist that ``particles'' means particles. Bohmian mechanics clarifies the status and the role of operators as observables in quantum mechanics by providing the operational details absent from standard quantum mechanics. It thereby allows us to readily dismiss all the radical claims traditionally enveloping the transition from the classical to the quantum realm---for example, that we must abandon classical logic or classical probability. The moral is rather simple: Beware naive realism, especially about operators!Comment: 18 pages, LaTex2e with AMS-LaTeX, to appear in Erkenntnis, 1996 (the proceedings of the international conference ``Probability, Dynamics and Causality,'' Luino, Italy, 15-17 June 1995, a special issue edited by D. Costantini and M.C. Gallavotti and dedicated to Prof. R. Jeffrey

Time of Arrival from Bohmian Flow

We develop a new conception for the quantum mechanical arrival time distribution from the perspective of Bohmian mechanics. A detection probability for detectors sensitive to quite arbitrary spacetime domains is formulated. Basic positivity and monotonicity properties are established. We show that our detection probability improves and generalises earlier proposals by Leavens and McKinnon. The difference between the two notions is illustrated through application to a free wave packet.Comment: 18 pages, 8 figures, to appear in Journ. Phys. A; representation of ref. 5 improved (thanks to Rick Leavens

A Review on Joint Models in Biometrical Research

In some fields of biometrical research joint modelling of longitudinal measures and event time data has become very popular. This article reviews the work in that area of recent fruitful research by classifying approaches on joint models in three categories: approaches with focus on serial trends, approaches with focus on event time data and approaches with equal focus on both outcomes. Typically longitudinal measures and event time data are modelled jointly by introducing shared random effects or by considering conditional distributions together with marginal distributions. We present the approaches in an uniform nomenclature, comment on sub-models applied to longitudinal measures and event time data outcomes individually and exemplify applications in biometrical research

Average Run Length and Mean Delay for Changepoint Detection: Robust Estimates for Threshold Alarms

Online Monitoring is a rapidly expanding field in different areas such as quality control, finance and navigation. The automated detection of so-called changepoints is playing a prominent role in all these fields, be it the detection of sudden shifts of the mean of a continuously monitored quantity, the variance of stock quotes or the change of some characteristic features indicating the malfunctioning of one of the detectors used for navigation (the ``faulty sensor problem''). A prominent example for the application of advanced statistical methods for the detection of changepoints in biomedical time series is the multi-process Kalman filter used by Smith and West [Smith 1983] to monitor renal transplants. However, despite the fact that the algorithm could be tuned in such a way that the computer could predict dangerous situations on the average one day before the human experts it has nevertheless become superfluous as soon as new diagnosic tools became available. Many of the automated monitoring systems which are widely used in practice are based on simple threshold alarms. Some upper and lower limits are chosen at the beginning of the monitoring session and an alarm is triggered whenever the measured values exceed the upper limit or fall below the lower limit. This is e.g. common practice for the monitoring of patients during surgery, where such thresholds are chosen for heart rate, blood pressure etc. by the anaesthesist. The fate of the multi-process Kalman filter for monitoring renal transplants teaches two lessons: first, there is considerable power in statistical methods to improve conventional biomedical monitoring techniques. Second, if the statistical model and the methods are too refined they may never be used in practice. We shall suggest a stochastic model for changepoints which we have found to have the capacity to be very useful in practice, i.e. which is sufficiently complex to cover the important features of a changepoint system but simple enough to be understandable and adaptible. We focus our attention on the properties of the threshold alarm for different values of the parameters of the threshold alarm and the model. This will give us practically relevant estimates for this important class of alarm systems and moreover a benchmark for the evaluation of competing alternative algorithms. Note that virtually every algorithm designed to detect changepoints is based on a threshold alarm, the only difference being that the threshold alarm is not fed with the original data but by a transformation thereof, usually called ``residuum'' [Basseville 1993]. As a general measure for quality, we look on the one hand at the mean delay time $\tau$ between a changepoint and its detection and on the other hand at the mean waiting time for a false alarm, the so-called average run length ARL

Scattering theory from microscopic first principles

We sketch a derivation of abstract scattering theory from the microscopic first principles defined by Bohmian mechanics. We emphasize the importance of the flux-across-surfaces theorem for the derivation, and of randomness in the impact parameter of the initial wave function---even for an, inevitably inadequate, orthodox derivation.Comment: To appear in Physica A, May 200