Triviality of the 2D stochastic Allen-Cahn equation

We consider the stochastic Allen-Cahn equation driven by mollified space-time white noise. We show that, as the mollifier is removed, the solutions converge weakly to 0, independently of the initial condition. If the intensity of the noise simultaneously converges to 0 at a sufficiently fast rate, then the solutions converge to those of the deterministic equation. At the critical rate, the limiting solution is still deterministic, but it exhibits an additional damping term

A Scenario-Based Approach to Validating and Testing Software Systems Using Statecharts

Scenarios (Use cases) are used to describe the functionality and behavior of a (software) system in a user-centered perspective. As scenarios form a kind of abstract level test cases for the system under development, the idea to use them to derive test cases for system test is quite intriguing. Yet in practice scenarios from the analysis phase are seldom used to create concrete system test cases. In this paper we present a procedure to create scenarios in the analysis phase and use those scenarios in system test to systematically determine test cases. This is done by formalization of scenarios into statecharts, annotation of statecharts with helpful information for test case creation/generation and by path traversal in the statecharts to determine concrete test cases

Spatio-temporal structure of cell distribution in cortical Bone Multicellular Units: a mathematical model

Bone remodelling maintains the functionality of skeletal tissue by locally coordinating bone-resorbing cells (osteoclasts) and bone-forming cells (osteoblasts) in the form of Bone Multicellular Units (BMUs). Understanding the emergence of such structured units out of the complex network of biochemical interactions between bone cells is essential to extend our fundamental knowledge of normal bone physiology and its disorders. To this end, we propose a spatio-temporal continuum model that integrates some of the most important interaction pathways currently known to exist between cells of the osteoblastic and osteoclastic lineage. This mathematical model allows us to test the significance and completeness of these pathways based on their ability to reproduce the spatio-temporal dynamics of individual BMUs. We show that under suitable conditions, the experimentally-observed structured cell distribution of cortical BMUs is retrieved. The proposed model admits travelling-wave-like solutions for the cell densities with tightly organised profiles, corresponding to the progression of a single remodelling BMU. The shapes of these spatial profiles within the travelling structure can be linked to the intrinsic parameters of the model such as differentiation and apoptosis rates for bone cells. In addition to the cell distribution, the spatial distribution of regulatory factors can also be calculated. This provides new insights on how different regulatory factors exert their action on bone cells leading to cellular spatial and temporal segregation, and functional coordination.Comment: 14 pages, 5 figures; v2: Completed model description after Eq. (16), clarified discussion/description after Eq. (23), between Eqs. (29)-(31), and in 2nd bullet point in conclusion

A quantitative interspecies comparison of the respiratory mucociliary clearance mechanism

Collectively coordinated ciliary activity propels the airway mucus, which lines the luminal surface of the vertebrate respiratory system, in cranial direction. Our contemporary understanding on how the quantitative characteristics of the metachronal wave field determines the resulting mucociliary transport is still limited, partly due to the sparse availability of quantitative observational data. We employed high-speed video reflection microscopy to image and quantitatively characterize the metachronal wave field as well as the mucociliary transport in excised bovine, porcine, ovine, lapine, turkey and ostrich samples. Image processing techniques were used to determine the ciliary beating frequency (CBF), the velocity and wavelength of the metachronal wave and the mucociliary transport velocity. The transport direction was found to strongly correlate with the mean wave propagation direction in all six species. The CBF yielded similar values (10–15 Hz) for all six species. Birds were found to exhibit higher transport speeds (130–260 [Formula: see text] m/s) than mammals (20–80 [Formula: see text] m/s). While the average transport direction significantly deviates from the tracheal long axis in mammals, no significant deviation was found in birds. The metachronal waves were found to propagate at about 4–8 times the speed of mucociliary transport in mammals, whereas in birds they propagate at about the transport speed. The mucociliary transport in birds is fast and roughly follows the TLA, whereas the transport is slower and proceeds along a left-handed spiral in mammals. The longer wavelengths and the lower ratio between the metachronal wave speed and the mucociliary transport speed provide evidence that the mucociliary clearance mechanism operates differently in birds than in mammals. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s00249-021-01584-8

In situ fiber-optical monitoring of cytosolic calcium in tissue explant cultures

We present a fluorescence-lifetime based method for monitoring cell and tissue activity in situ, during cell culturing and in the presence of a strong autofluorescence background. The miniature fiber-optic probes are easily incorporated in the tight space of a cell culture chamber or in an endoscope. As a first application we monitored the cytosolic calcium levels in porcine tracheal explant cultures using the Calcium Green-5N (CG5N) indicator. Despite the simplicity of the optical setup we are able to detect changes of calcium concentration as small as 2.5 nM, with a monitoring time resolution of less than 1 s.Comment: 26 pages, 6 figures Article first published online: 11 SEP 2013. appears in J. Biophoton. (2013

Thermal quantum electrodynamics of nonrelativistic charged fluids

The theory relevant to the study of matter in equilibrium with the radiation field is thermal quantum electrodynamics (TQED). We present a formulation of the theory, suitable for non relativistic fluids, based on a joint functional integral representation of matter and field variables. In this formalism cluster expansion techniques of classical statistical mechanics become operative. They provide an alternative to the usual Feynman diagrammatics in many-body problems which is not perturbative with respect to the coupling constant. As an application we show that the effective Coulomb interaction between quantum charges is partially screened by thermalized photons at large distances. More precisely one observes an exact cancellation of the dipolar electric part of the interaction, so that the asymptotic particle density correlation is now determined by relativistic effects. It has still the $r^{-6}$ decay typical for quantum charges, but with an amplitude strongly reduced by a relativistic factor.Comment: 32 pages, 0 figures. 2nd versio

Emergence, transition, and continuity: Resource Commodity Production Pathways in Northeastern British Columbia, Canada

The purpose of this paper is to reflect upon the processes of emergence, transition, and continuity in global economic geography for one rural, and relatively remote, region in northeastern British Columbia (BC), Canada. Guided by a theoretical framework comprised of staples theory, evolutionary economic geography, and institutionalism, we reflect back on the path of the resource sector and identify recent trends that are fundamentally reshaping the economic geography of the region and province. Many of these changes are similar, albeit guided by new technical and managerial processes, to historical patterns of resource exploitation that defined the provincial and Canadian economy. Issues of dependence, vulnerability, and truncated regional development would resonate with readers in the 1970s. Other issues, like the geographic orientation of capital and the scale and rapidity of resource fluctuations bring new challenges to local and provincial actors seeking to mitigate impacts and retain a greater share of benefits from resource developments. The reflective synergy between emergence, transition, and continuity seen in the case study is also noted in the theoretical framework as evolutionary economic geography and institutionalism not only link to one another but also help to inform some of the ideas at the core of staples theory. The paper contributes to an international discourse that is seeking to document and compare cases associated with the new rural regional economies emerging out of the rapid and far-reaching transformations of the global economy

Sustained High Basal Motion of the Greenland Ice Sheet Revealed by Borehole Deformation

Ice deformation and basal motion characterize the dynamical behavior of the Greenland ice sheet (GrIS). We evaluate the contribution of basal motion from ice deformation measurements in boreholes drilled to the bed at two sites in the western marginal zone of the GrIS. We find a sustained high amount of basal motion contribution to surface velocity of 44–73% in winter, and up to 90% in summer. Measured ice deformation rates show an unexpected variation with depth that can be explained with the help of an ice-flow model as a consequence of stress transfer from slippery to sticky areas. This effect necessitates the use of high-order ice-flow models, not only in regions of fast-flowing ice streams but in all temperate-based areas of the GrIS. The agreement between modeled and measured deformation rates confirms that the recommended values of the temperature-dependent flow rate factor A are a good choice for ice-sheet models