The understanding of prototyping has changed in recent years to an approach that accompanies the product development process. This paper examines whether classic approaches from product development are also suitable for planning prototyping sequences. The stepwise process-oriented and the problem-oriented approach are discussed. A criticality assessment is proposed as a metric for the prioritization of the functional areas and a procedure is derived from this. The procedure is illustrated using an example. The result is discussed and future steps are suggested.

Human health is strongly mediated by the gut microbiota ecosystem, which, in turn, depends not only on its state but also on its dynamics and how it responds to perturbations. Healthy microbiota ecosystems tend to be in criticality and antifragile dynamics corresponding to a maximum complexity configuration, which may be assessed with information and network theory analysis. Under this complex system perspective, we used a new analysis of published data to show that a children’s population with an industrialized urban lifestyle from Mexico City exhibits informational and network characteristics similar to parasitized children from a rural indigenous population in the remote mountainous region of Guerrero, México. We propose then, that in this critical age for gut microbiota maturation, the industrialized urban lifestyle could be thought of as an external perturbation to the gut microbiota ecosystem, and we show that it produces a similar loss in criticality/antifragility as the one observed by internal perturbation due to parasitosis by the helminth A. lumbricoides. Finally, several general complexity-based guidelines to prevent or restore gut ecosystem antifragility are discussed.

We study propagation of avalanches in a certain excitable network. The model is a particular case of the one introduced by Larremore et al. (Phys. Rev. E, 2012) and is mathematically equivalent to an endemic variation of the Reed–Frost epidemic model introduced by Longini (Math. Biosci., 1980). Two types of heuristic approximation are frequently used for models of this type in applications: a branching process for avalanches of a small size at the beginning of the process and a deterministic dynamical system once the avalanche spreads to a significant fraction of a large network. In this paper we prove several results concerning the exact relation between the avalanche model and these limits, including rates of convergence and rigorous bounds for common characteristics of the model.

Critical raw materials (CRMs) are crucial for the transformation towards low carbon mobility. However, their production is often highly concentrated in a few countries, which leads to supply risks. Exemplified by the case of rare earth elements (REEs) and based on in-depth interviews with corporate executives from companies along the automotive supply chain, this contribution provides insights into the strategies of the European automotive industry to cope with these supply risks. Results show a lack of awareness of REE criticality studies and their outcomes in the past, the decisive role of price competitiveness when pursuing mitigation strategies and a lack of willingness or ability to engage in rare earth (RE) projects to get access to production output and secure supply. Overall, affected companies struggle to pursue long-term oriented strategies to secure their need for REEs. These findings are discussed with regard to the new demand for CRMs due to the shift to electric mobility and the specific challenges that the automotive industry faces.

We consider a second-order elliptic operator L in skew product of an ordinary differential operator L1 on an interval (a, b) and an elliptic operator on a domain D2 of a Riemannian manifold such that the associated heat kernel is intrinsically ultracontractive. We give criteria for criticality and subcriticality of L in terms of a positive solution having minimal growth at η (η = a, b) to an associated ordinary differential equation. In the subcritical case, we explicitly determine the Martin compactification and Martin kernel for L on the basis of [24]; in particular, the Martin boundary over η is either one point or a compactification of D2, which depends on whether an associated integral near η diverges or converges. From this structure theorem we show a monotonicity property that the Martin boundary over η does not become smaller as the potential term of L1 becomes larger near η.

In the UK, radioactive wastes currently planned for disposal in a geological disposal facility (GDF) include intermediate level waste, some low level waste and high level waste. Disposal of other materials, including spent fuel, uranium and plutonium is also being evaluated to inform the safety case for a GDF, if such materials were to be classified as wastes in the future. This paper describes the generic safety functions through which waste packages can contribute to the safety case of a GDF in the UK. It describes the engineering approach used or envisaged, in the UK and internationally, to ensure that waste packages retain their safety functions for the required periods of time and summarizes the scientific basis underpinning the current understanding of relevant evolution processes. Where gaps in the knowledge exist, the Nuclear Decommissioning Authority Radioactive Waste Management Directorate has identified specific research activities needed to close out such gaps to a level of maturity sufficient for this stage of the disposal programme (generic). This paper describes the latest results from their R&D programme and presents a summary of the research activities planned to meet the current needs of the disposal programme with specific reference to the topics of package evolution and criticality safety.

In support of the disposal system safety case for a geological disposal facility (GDF) there is a requirement to consider 'what-if' hypothetical scenarios for post-closure nuclear criticality. Although all such scenarios are considered very unlikely, one 'what-if' scenario is the mobilization of fissile material from a number of waste packages and its slow accumulation within the GDF or the immediate surroundings. Should sufficient fissile material accumulate a quasi-steady-state (QSS) transient criticality event could result. A computer model has been developed to understand the evolution and consequences of such an event.

Since a postulated QSS criticality could persist for many millennia, building confidence in the modelling approach is difficult. However, the Oklo natural reactors in Africa operated for similar durations around two billion years ago, providing a natural analogue for comparison. This paper describes the modelling approach, its application to hypothetical criticality events for a GDF, and how the model can be compared to Oklo. The model results are found to be in agreement with the observational evidence from Oklo, building confidence in the use of the QSS model to simulate postulated post-closure criticality events in GDFs.

The Environment Agency Guidance on Requirements for Authorisation (GRA) of a geological disposal facility (GDF) requires a demonstration that "the possibility of a local accumulation of fissile material such as to produce a neutron chain reaction is not a significant concern." A neutron chain reaction that is just self-sustaining is also known as critical.

Waste packages can be designed to ensure that criticality is impossible during the transport and operational phases of a GDF, and for a significant period post-closure. Over longer times, however, packages may degrade, and groundwater flows could lead to a localized accumulation of fissile material. Hence, even though the initial distribution of materials would need to change substantially, criticality cannot be ruled out completely.

This paper describes how an accumulation of fissile material could, hypothetically, lead to a critical configuration; how such a system could evolve; what the local consequences could be; and how the engineered and geological barriers could be affected. The conclusion from studies to date is that, even for large (and very unlikely) fissile accumulations, the consequences of a post-closure criticality event are not a significant concern.

In support of the Radioactive Waste Management (RWM) safety case for a geological disposal facility (GDF) in the UK, there is a regulatory requirement to consider the likelihood and consequences of nuclear criticality. Waste packages are designed to ensure that criticality is not possible during the transport and operational phases of a GDF and for a significant period post-closure. However, over longer post-closure timescales, conditions in the GDF will evolve.

For waste packages containing spent fuel, it can be shown that, under certain conditions, package flooding could result in a type of criticality event referred to as 'quasi-steady-state' (QSS). Although unlikely, this defines a 'what-if' scenario for understanding the potential consequences of post-closure criticality. This paper provides an overview of a methodology to understand QSS criticality and its application to a spent fuel waste package.

The power of such a hypothetical criticality event is typically estimated to be a few kilowatts: comparable with international studies of similar systems and the decay heat for which waste packages are designed. This work has built confidence in the methodology and supports RWM's demonstration that post-closure criticality is not a significant concern.

Nous étudions l'écoulement dans le plan de sortie d'un jet tournant à grand nombre deReynolds généré à l'aide d'un nid d'abeilles tournantsuivi d'une tuyère convergente. Des mesures fil chaud réalisées en sortie de deux tuyères de taux de contraction différents montrent l'apparition progressive de turbulencepour des valeurs identiques du taux de rotation de l'écoulementen amont des tuyères. Afin d'expliquer ce phénomène, nous étudions donc la dynamique de l'écoulement de conduite compris entre le nid d'abeilles et le plan de sortie des convergents. Un modèle stationnaire simple d'écoulement est d'abord introduit. Il montre la possibilité d'unerecirculation à la paroi de la tuyère lorsque les conditions amont sont proches de la criticité,définie au sens des ondes inertielles pouvant se propager dans l'écoulement. Nous trouvons ensuiteque cessolutions sont globalement stables à des perturbations axisymétriques, mais sontsusceptibles d'amplifier fortement des perturbations de petite échelle initiées à l'amontde l'écoulement et suivies le long de leur trajectoire jusqu'en sortie.

In this article, we present a self-contained review of recent work on complex biological systems which exhibit no characteristic scale. This property can manifest itself with fractals (spatial scale invariance), flicker noise or 1/f-noise where f denotes the frequency of a signal (temporal scale invariance) and power laws (scale invariance in the size and duration of events in the dynamics of the system). A hypothesis recently put forward to explain these scale-free phenomomena is criticality, a notion introduced by physicists while studying phase transitions in materials, where systems spontaneously arrange themselves in an unstable manner similar, for instance, to a row of dominoes. Here, we review in a critical manner work which investigates to what extent this idea can be generalized to biology. More precisely, we start with a brief introduction to the concepts of absence of characteristic scale (power-law distributions, fractals and 1/f- noise) and of critical phenomena. We then review typical mathematical models exhibiting such properties: edge of chaos, cellular automata and self-organized critical models. These notions are then brought together to see to what extent they can account for the scale invariance observed in ecology, evolution of species, type III epidemics and some aspects of the central nervous system. This article also discusses how the notion of scale invariance can give important insights into the workings of biological systems.

The multitype discrete time indecomposable branching process with immigration is considered. Using a martingale approach a limit theorem is proved for such processes when the totality of immigrating individuals at a given time depends on evolution of the processes generating by previously immigrated individuals. Corollaries of the limit theorem are obtained for the cases of finite and infinite second moments of offspring distribution in critical processes.

Sufficient conditions for survival and extinction of multitype population-size-dependent branching processes in discrete time are obtained. Growth rates are determined on the set of divergence to infinity. The limiting distribution of a properly normalized process can be generalized gamma, normal or degenerate.

We consider a multitype population-size-dependent branching process in discrete time. A process is considered to be near-critical if the mean matrices of offspring distributions approach the mean matrix of a critical process as the population size increases. We show that if the second moments of offspring distributions stabilize as the population size increases, and the limiting variances are not too large in comparison with the deviation of the means from criticality, then the extinction probability is less than 1 and the process grows arithmetically fast, in the sense that any linear combination which is not orthogonal to the left eigenvector of the limiting mean matrix grows linearly to a limit distribution. We identify cases when the limiting distribution is gamma. A result on transience of multidimensional Markov chains is also given.