Exact design manifold control of a class of nonlinear singularly perturbed systems

The integral manifold approach captures from a geometric point of view the intrinsic two-time-scale behavior of singularly perturbed systems. An important class of nonlinear singularly perturbed systems considered in this note are fast actuator-type systems. For a class of fast actuator-type systems, which includes many physical systems, an explicit corrected composite control, the sum of a slow control and a fast control, is derived. This corrected control will steer the system exactly to a required design manifold.

Convective quasi–equilibrium

The concept of convective quasi–equilibrium (CQE) is a key ingredient in order to understand the role of deep moist convection in the atmosphere. It has been used as a guiding principle to develop almost all convective parameterizations and provides a basic theoretical framework for large–scale tropical dynamics. The CQE concept as originally proposed by Arakawa and Schubert [1974] is systematically reviewed from wider perspectives. Various interpretations and extensions of Arakawa and Schubert’s CQE are considered in terms of both a thermodynamic analogy and as a dynamical balance. The thermodynamic interpretations can be more emphatically embraced as a homeostasis. The dynamic balance interpretations can be best understood by analogy with the slow manifold. Various criticisms of CQE can be avoided by taking the dynamic balance interpretation. Possible limits of CQE are also discussed, including the importance of triggering in many convective situations, as well as the possible self–organized criticality of tropical convection. However, the most intriguing aspect of the CQE concept is that, in spite of many observational tests supporting and interpreting it in many different senses, it has 1never been established in a robust manner based on a systematic analysis of the cloud–work function budget by observations as was originally defined.

Contact angle of a hemispherical bubble: an analytical approach

We have calculated the equilibrium shape of the axially symmetric Plateau border along which a spherical bubble contacts a flat wall, by analytically integrating Laplace’s equation in the presence of gravity, in the limit of small Plateau border sizes. This method has the advantage that it provides closed-form expressions for the positions and orientations of the Plateau border surfaces. Results are in very good overall agreement with those obtained from a numerical solution procedure, and are consistent with experimental data. In particular we find that the effect of gravity on Plateau border shape is relatively small for typical bubble sizes, leading to a widening of the Plateau border for sessile bubbles and to a narrowing for pendant bubbles. The contact angle of the bubble is found to depend even more weakly on gravity.

Determination of Holocene cave temperatures from Kr and Xe concentrations in stalagmite fluid inclusions

From the concentrations of dissolved atmospheric noble gases in water, a so-called “noble gas temperature” (NGT) can be determined that corresponds to the temperature of the water when it was last in contact with the atmosphere. Here we demonstrate that the NGT concept is applicable to water inclusions in cave stalagmites, and yields NGTs that are in good agreement with the ambient air temperatures in the caves. We analysed samples from two Holocene and one undated stalagmite. The three stalagmites originate from three caves located in different climatic regions having modern mean annual air temperatures of 27 °C, 12 °C and 8 °C, respectively. In about half of the samples analysed Kr and Xe concentrations originated entirely from the two well-defined noble gas components air-saturated water and atmospheric air, which allowed NGTs to be determined successfully from Kr and Xe concentrations. One stalagmite seems to be particularly suitable for NGT determination, as almost all of its samples yielded the modern cave temperature. Notably, this stalagmite contains a high proportion of primary water inclusions, which seem to preserve the temperature-dependent signature well in their Kr and Xe concentrations. In future work on stalagmites detailed microscopic inspection of the fluid inclusions prior to noble gas analysis is therefore likely to be crucial in increasing the number of successful NGT determinations.

Chercher pour or chercher après: arguing the case for contact-induced linguistic innovation in different varieties of French

This paper provides evidence for the claim made in Baetens Beardsmore (1971) that the grammatical collocation "chercher après" «to look for», which is very frequent in Brussels French, is the result of transfer from the contact language, Brussels Dutch. A detailed quantitative analysis of this construction in different varieties of French which have more or less contact with a Germanic language was made to investigate the likelihood of influence from the Germanic substrate. The differences between the meaning of "chercher" and "chercher après" are also analysed in some depth, to find out whether or not the particle is redundant. According to Trudgill (2004) redundant constructions are more often found in contact situations involving long-term, stable contact and child bilingualism. The particle "après" was found to add a particular shade of meaning to "chercher", and is thus not redundant. Therefore no evidence could be obtained from the current data for Trudgill’s (2004) claim.

Borrowing and shift-induced interference: contrasting patterns in French-Germanic contact in Brussels and Strasbourg

The main aim of the present article is to test hypotheses derived from the model for contact- induced language change as formulated in Thomason and Kaufman (1988 et seq.). As the model correctly predicts the asymmetries between the mutual influences of the Germanic and the Romance varieties in Brussels and Strasbourg it is a very powerful tool for describing the contact patterns in these cities. The analysis shows that the contact patterns are very similar, both from a quantitative and from a qualitative point of view, despite important differences in the sociolinguistic situation of both cities. The striking similarities in the outcome of language contact seem to find a plausible explanation in the fact that the language contact situations in both cities are similar from a typological point of view: in each city a variety of French is in contact with a Germanic variety (Alsatian and Brussels Dutch). Thus, the claim of the present article is that the structure of the languages plays a more prominent role in the outcome of language contact than the sociolinguistic history of the speakers.

The role of transfer in language variation and change: Evidence from contact varieties of French

In this Special Issue, the focus is on contact-induced language variation and change in situations of societal bilingualism that involve long-term contact between French and another language. As is well known, when two or more languages are spoken by groups of speakers in the same geographical area, over time, features from one language can be transferred to the other language, especially when the languages in question are unequal in terms of prestige, institutional support and demographic factors. The process that leads to the adoption of such features in the contact languages is generally known as INTERFERENCE or TRANSFER, and these terms are also used to describe the features in question (i.e. the end product of the process of transfer). In this issue we prefer to use the term TRANSFER over the use of the notion INTERFERENCE, as the former has fewer negative connotations than the latter.

Effect of pH, temperature and surface contact on the elaboration of fimbriae and flagella by Salmonella serotype Enteritidis

Survival of enteric pathogens exposed to various environmental stresses depends upon a number of protective responses, some of which are associated with induction of virulence determinants. Flagella and fimbriae are putative virulence determinants of Salmonella spp, and ELISAs specific for the detection of flagella and SEF21, SEF14 and SEF17 fimbriae were used to assess the effect of temperature and pH upon their elaboration by isolates of Salmonella serotype Enteritidis in planktonic growth and on the surface of two-dimensional gradient agar plates, For three phage type 4 isolates of Enteritidis of comparative clinical provenance, similar phenotypes for the elaboration of these surface antigens were observed. SEF14 fimbriae were elaborated in planktonic growth at 37 degrees C, but not 20 degrees C, at pH 4.77 and above but not at pH 4.04; whereas on agar gradient plates SEF14 fimbriae were elaborated poorly but with best yields at pH 4.04, SEF17 fimbriae were elaborated in planktonic growth at 20 degrees C, but not at 37 degrees C, at pH 6.18 and above but not at pH 5.09 or below; whereas on agar gradient plates SEF17 fimbriae were elaborated well even at pH 4.65, SEF21 fimbriae were expressed very poorly under all conditions tested, Planktonic growth at 37 degrees C induced least flagella whereas growth at 20 degrees C, and particularly surface growth at lower pH values, induced a 'hyper-flagellate' phenotype, Single colonies allowed to form on gradient agar plates were shown to generate different colonial morphologies which were dependent on initial pH. These results demonstrate that the physicochemical environment is an important determinant of bacterial response, especially the induction of putative virulence factors.

Estimating root–soil contact from 3D X-ray microtomographs

Adequate contact with the soil is essential for water and nutrient adsorption by plant roots, but the determination of root–soil contact is a challenging task because it is difficult to visualize roots in situ and quantify their interactions with the soil at the scale of micrometres. A method to determine root–soil contact using X-ray microtomography was developed. Contact areas were determined from 3D volumetric images using segmentation and iso-surface determination tools. The accuracy of the method was tested with physical model systems of contact between two objects (phantoms). Volumes, surface areas and contact areas calculated from the measured phantoms were compared with those estimated from image analysis. The volume was accurate to within 0.3%, the surface area to within 2–4%, and the contact area to within 2.5%. Maize and lupin roots were grown in soil (<2 mm) and vermiculite at matric potentials of −0.03 and −1.6 MPa and in aggregate fractions of 4–2, 2–1, 1–0.5 and < 0.5 mm at a matric potential of −0.03 MPa. The contact of the roots with their growth medium was determined from 3D volumetric images. Macroporosity (>70 µm) of the soil sieved to different aggregate fractions was calculated from binarized data. Root-soil contact was greater in soil than in vermiculite and increased with decreasing aggregate or particle size. The differences in root–soil contact could not be explained solely by the decrease in porosity with decreasing aggregate size but may also result from changes in particle and aggregate packing around the root.

The induction of mental and contact contamination

Background: Extreme fear of contamination within Obsessive Compulsive Disorder is traditionally conceptualised as a physical phenomenon. More recent research has supported the notion of ‘mental’ contamination, in which people feel contaminated in the absence of physical contact. The current research sought to determine whether feelings of contact and mental contamination could be induced within a non-clinical sample, whether the impact of mental and contact contamination was comparable in terms of associated feelings and behaviour and whether related psychopathology related to the impact of the tasks. Methods: Undergraduate students (n=60) completed OCD relevant measures and were randomly assigned to either a contact contamination condition (CC: moving a bucket of fake vomit) or a mental contamination condition (MC: thinking about a bucket of vomit). Results: Both manipulations induced feelings of contamination. Participants in the contact condition had significantly greater urges to wash than those in the mental condition. Neutralising behaviour did not differ across conditions. Conclusions: Feelings of contamination can be induced in the absence of physical contact and for those in the MC group, some aspects of OCD-relevant psychopathology were related to the impact of the manipulation. These findings have implications for the understanding and treatment of contamination-related fears in OCD.

On Hamiltonian balanced dynamics and the slowest invariant manifold

The concept of a slowest invariant manifold is investigated for the five-component model of Lorenz under conservative dynamics. It is shown that Lorenz's model is a two-degree-of-freedom canonical Hamiltonian system, consisting of a nonlinear vorticity-triad oscillator coupled to a linear gravity wave oscillator, whose solutions consist of regular and chaotic orbits. When either the Rossby number or the rotational Froude number is small, there is a formal separation of timescales, and one can speak of fast and slow motion. In the same regime, the coupling is weak, and the Kolmogorov–Arnold-Moser theorem is shown to apply. The chaotic orbits are inherently unbalanced and are confined to regions sandwiched between invariant tori consisting of quasi-periodic regular orbits. The regular orbits generally contain free fast motion, but a slowest invariant manifold may be geometrically defined as the set of all slow cores of invariant tori (defined by zero fast action) that are smoothly related to such cores in the uncoupled system. This slowest invariant manifold is not global; in fact, its structure is fractal; but it is of nearly full measure in the limit of weak coupling. It is also nonlinearly stable. As the coupling increases, the slowest invariant manifold shrinks until it disappears altogether. The results clarify previous definitions of a slowest invariant manifold and highlight the ambiguity in the definition of “slowness.” An asymptotic procedure, analogous to standard initialization techniques, is found to yield nonzero free fast motion even when the core solutions contain none. A hierarchy of Hamiltonian balanced models preserving the symmetries in the original low-order model is formulated; these models are compared with classic balanced models, asymptotically initialized solutions of the full system and the slowest invariant manifold defined by the core solutions. The analysis suggests that for sufficiently small Rossby or rotational Froude numbers, a stable slowest invariant manifold can be defined for this system, which has zero free gravity wave activity, but it cannot be defined everywhere. The implications of the results for more complex systems are discussed.

Effect of disease-selective predation on prey infected by contact and external sources

We propose and analyze a simple mathematical model for susceptible prey (S)–infected prey (I)–predator (P) interaction, where the susceptible prey population (S) is infected directly from external sources as well as through contact with infected class (I) and the predator completely avoids consuming the infected prey. The model is analyzed to obtain different thresholds of the key parameters under which the system exhibits stability around the biologically feasible equilibria. Through numerical simulations we display the effects of external infection and the infection through contact on the system dynamics in the absence as well as in the presence of the predator. We compare the system dynamics when infection occurs only through contact, with that when it occurs through contact and external sources. Our analysis demonstrates that under a disease-selective predation, stability and oscillations of the system is determined by two key parameters: the external infection rate and the force of infection through contact. Due to the introduction of external infection, the predator and the prey population show limit-cycle oscillations over a range parametric values. We suggest that while predicting the dynamics of such an eco-epidemiological system, the modes of infection and the infection rates might be carefully investigated.

Relaxation of surface tension in the liquid-solid interfaces of Lennard-Jones liquids

We have established the surface tension relaxation time in the liquid-solid interfaces of Lennard-Jones (LJ) liquids by means of direct measurements in molecular dynamics (MD) simulations. The main result is that the relaxation time is found to be almost independent of the molecular structures and viscosity of the liquids (at seventy-fold change) used in our study and lies in such a range that in slow hydrodynamic motion the interfaces are expected to be at equilibrium. The implications of our results for the modelling of dynamic wetting processes and interpretation of dynamic contact angle data are discussed.