Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion

We present a new a-priori estimate for discrete coagulation fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a-priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case.

Diffusion in spatially and temporarily inhomogeneous media: Effects of turbulent mixing

We consider diffusion of a passive substance C in a phase-separating nonmiscible binary alloy under turbulent mixing. The substance is assumed to have different diffusion coefficients in the pure phases A and B, leading to a spatially and temporarily dependent diffusion ¿coefficient¿ in the diffusion equation plus convective term. In this paper we consider especially the effects of a turbulent flow field coupled to both the Cahn-Hilliard type evolution equation of the medium and the diffusion equation (both, therefore, supplemented by a convective term). It is shown that the formerly observed prolonged anomalous diffusion [H. Lehr, F. Sagués, and J.M. Sancho, Phys. Rev. E 54, 5028 (1996)] is no longer seen if a flow of sufficient intensity is supplied.

Diffusion in spatially and temporarily inhomogeneous media

In this paper we consider diffusion of a passive substance C in a temporarily and spatially inhomogeneous two-dimensional medium. As a realization for the latter we choose a phase-separating medium consisting of two substances A and B, whose dynamics is determined by the Cahn-Hilliard equation. Assuming different diffusion coefficients of C in A and B, we find that the variance of the distribution function of the said substance grows less than linearly in time. We derive a simple identity for the variance using a probabilistic ansatz and are then able to identify the interface between A and B as the main cause for this nonlinear dependence. We argue that, finally, for very large times the here temporarily dependent diffusion "constant" goes like t-1/3 to a constant asymptotic value D¿. The latter is calculated approximately by employing the effective-medium approximation and by fitting the simulation data to the said time dependence.

Diffusion in spatially and temporarily inhomogeneous media: Effects of turbulent mixing

We consider diffusion of a passive substance C in a phase-separating nonmiscible binary alloy under turbulent mixing. The substance is assumed to have different diffusion coefficients in the pure phases A and B, leading to a spatially and temporarily dependent diffusion ¿coefficient¿ in the diffusion equation plus convective term. In this paper we consider especially the effects of a turbulent flow field coupled to both the Cahn-Hilliard type evolution equation of the medium and the diffusion equation (both, therefore, supplemented by a convective term). It is shown that the formerly observed prolonged anomalous diffusion [H. Lehr, F. Sagués, and J.M. Sancho, Phys. Rev. E 54, 5028 (1996)] is no longer seen if a flow of sufficient intensity is supplied.

Diffusion in spatially and temporarily inhomogeneous media

In this paper we consider diffusion of a passive substance C in a temporarily and spatially inhomogeneous two-dimensional medium. As a realization for the latter we choose a phase-separating medium consisting of two substances A and B, whose dynamics is determined by the Cahn-Hilliard equation. Assuming different diffusion coefficients of C in A and B, we find that the variance of the distribution function of the said substance grows less than linearly in time. We derive a simple identity for the variance using a probabilistic ansatz and are then able to identify the interface between A and B as the main cause for this nonlinear dependence. We argue that, finally, for very large times the here temporarily dependent diffusion "constant" goes like t-1/3 to a constant asymptotic value D¿. The latter is calculated approximately by employing the effective-medium approximation and by fitting the simulation data to the said time dependence.

Precision and scaling in morphogen gradient read-out.

Morphogen gradients infer cell fate as a function of cellular position. Experiments in Drosophila embryos have shown that the Bicoid (Bcd) gradient is precise and exhibits some degree of scaling. We present experimental results on the precision of Bcd target genes for embryos with a single, double or quadruple dose of bicoid demonstrating that precision is highest at mid-embryo and position dependent, rather than gene dependent. This confirms that the major contribution to precision is achieved already at the Bcd gradient formation. Modeling this dynamic process, we investigate precision for inter-embryo fluctuations in different parameters affecting gradient formation. Within our modeling framework, the observed precision can only be achieved by a transient Bcd profile. Studying different extensions of our modeling framework reveals that scaling is generally position dependent and decreases toward the posterior pole. Our measurements confirm this trend, indicating almost perfect scaling except for anterior most expression domains, which overcompensate fluctuations in embryo length.

Study of the diffusion in polymer solutions and hydrogels by NMR spectroscopy and NMR imaging

Afin d'étudier la diffusion et la libération de molécules de tailles inférieures dans un gel polymère, les coefficients d'auto-diffusion d'une série de polymères en étoile avec un noyau d'acide cholique et quatre branches de poly(éthylène glycol) (PEG) ont été déterminés par spectroscopie RMN à gradient de champ pulsé dans des solutions aqueuses et des gels de poly(alcool vinylique). Les coefficients de diffusion obtenus ont été comparés avec ceux des PEGs linéaires et dendritiques pour étudier l'effet de l'architecture des polymères. Les polymères en étoile amphiphiles ont des profils de diffusion en fonction de la concentration similaires à leurs homologues linéaires dans le régime dilué. Ils diffusent plus lentement dans le régime semi-dilué en raison de leur noyau hydrophobe. Leurs conformations en solution ont été étudiées par des mesures de temps de relaxation spin-réseau T1 du noyau et des branches. L'imagerie RMN a été utilisée pour étudier le gonflement des comprimés polymères et la diffusion dans la matrice polymère. Les comprimés étaient constitués d'amidon à haute teneur en amylose et chargés avec de l'acétaminophène (de 10 à 40% en poids). Le gonflement des comprimés, ainsi que l'absorption et la diffusion de l'eau, augmentent avec la teneur en médicament, tandis que le pourcentage de libération du médicament est similaire pour tous les comprimés. Le gonflement in vitro des comprimés d'un complexe polyélectrolyte à base d'amidon carboxyméthylé et de chitosane a également été étudié par imagerie RMN. Ces comprimés sont sensibles au pH : ils gonflent beaucoup plus dans les milieux acides que dans les milieux neutres en raison de la dissociation des deux composants et de la protonation des chaînes du chitosane. La comparaison des résultats avec ceux d'amidon à haute teneur en amylose indique que les deux matrices ont des gonflements et des profils de libération du médicament semblables dans les milieux neutres, alors que les comprimés complexes gonflent plus dans les milieux acides en raison de la dissociation du chitosane et de l'amidon.

Population persistence in weakly-coupled sinks

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Proton diffusion tensor spectroscopy of metabolites in human muscle in vivo

PURPOSE To study the apparent diffusivity and its directionality for metabolites of skeletal muscle in humans in vivo by (1) H magnetic resonance spectroscopy. METHODS The diffusion tensors were determined on a 3 Tesla MR system using optimized acquisition and processing methods including an adapted STEAM sequence with orientation-dependent diffusion weighting, pulse-triggering with individually adapted delays, eddy-current correction schemes, median filtering, and simultaneous prior-knowledge fitting of all related spectra. RESULTS The average apparent diffusivities, as well as the fractional anisotropies of taurine (ADCav  = 0.74 × 10(-3) s/mm(2) , FA = 0.46), creatine (ADCav  = 0.41 × 10(-3)  s/mm(2) , FA = 0.33), trimethylammonium compounds (ADCav  = 0.48 × 10(-3)  s/mm(2) , FA = 0.34), carnosine (ADCav  = 0.46 × 10(-3)  s/mm(2) , FA = 0.47), and water (ADCav  = 1.5 × 10(-3)  s/mm(2) , FA = 0.36) were estimated. The diffusivities of most metabolites and water were significantly different from each other. Diffusion was found to be anisotropic and the diffusion tensors showed tensor correlation coefficients close to 1 and were hence found to be essentially coaligned. The magnitudes of apparent metabolite diffusivities were largely ordered according to molecular weight, with taurine as the smallest molecule diffusing fastest, both along and across the fiber direction. CONCLUSION Diffusivities, directional dependence of diffusion and fractional anisotropies of (1) H MRS-visible muscle metabolites were presented. It was shown that metabolites share diffusion directionality with water and have similar fractional anisotropies, hinting at similar diffusion barriers. Magn Reson Med, 2014. © 2014 Wiley Periodicals, Inc.

The effects of body position on distortion-product Otoacoustic emission testing

Otoacoustic emissions are frequently acquired from patients in a variety of body positions aside from the standard, seated orientation. Yet little knowledge is available regarding whether these deviations will produce nonpathological changes to the clinical results obtained. The present study aimed to describe the effects of body position on the distortion-product otoacoustic emissions of 60 normal-hearing adults. With particular attention given to common clinical practice, the Otodynamics ILO292, and the measurement parameters of amplitude, signal-to-noise ratio, and noise were utilized. Significant position-related effects and interactions were revealed for all parameters. Specifically, stronger emissions in the mid frequencies and higher noise levels at the extreme low and high frequencies were produced by testing subjects while lying on their side compared with the seated position. Further analysis of body position effects on emissions is warranted, in order to determine the need for clinical application of position-dependent normative data.

Position information but not force information is used in adapting to changes in environmental dynamics

This study investigated how movement error is evaluated and used to change feedforward commands following a change in the environmental dynamics. In particular, we addressed the question of whether only position-error information is used or whether information about the force-field direction can also be used for rapid adaptation to changes in the environmental dynamics. Subjects learned to move in a position-dependent force field (PF) with a parabolic profile and the dynamics of a negative spring, which produced lateral force to the left of the target hand path. They adapted very rapidly, dramatically reducing lateral error after a single trial. Several times during training, the strength of the PF was unexpectedly doubled (PF2) for two trials. This again created a large leftward deviation, which was greatly reduced on the second PF2 trial, and an aftereffect when the force field subsequently returned to its original strength. The aftereffect was abolished if the second PF2 trial was replaced by an oppositely directed velocity-dependent force field (VF). During subsequent training in the VF, immediately after having adapted to the PF, subjects applied a force that assisted the force field for similar to 15 trials, indicating that they did not use information about the force-field direction. We concluded that the CNS uses only the position error for updating the internal model of the environmental dynamics and modifying feedforward commands. Although this strategy is not necessarily optimal, it may be the most reliable strategy for iterative improvement in performance.

The European Community and innovation policy : reorienting towards diffusion

This study aims to explore the position of diffusion oriented support mechanisms in European Community (EC) innovation policy. With the shift from the traditional linear model towards an integrative approach to innovation, the role of diffusion of technologies and knowledge, achieved greater weight. This shift in both the thinking of academic experts, and of national policy makers, induced EC policy makers to appeal for similar changes in Community innovation policy. From the mid-1980s, the Commission of the European Communities, the key actor in EC policy making, thought to move its innovation policy away from the traditional science push approach. This study shows that in the implementation of programmes for research, technology and innovation, the traditional linear model is still dominant. The core research and technological development programmes still operate from a science push concept of innovation, mainly due to their pre-competitive nature. The case of SPRINT illustrates that policy programmes with an integrated innovation perspective can be successful at Community level. However the programme operates in a relatively isolated position from overall research and technological development policy. The case of BRITE-EURAM illustrates the difficulties of collaborative research programmes, the bulk of EC support mechanisms, to move away from the traditional model. The study shows how conflicting policy objectives arising from the different policy networks that shape EC policy making, in combination with a lack of co-ordination in those policy domains, hinder the emergence of the integrated approach. Consequently EC diffusion policy, implemented from the perspective of the linear model, will have a sub-optimal impact on the competitiveness of European industries.

The shape of soap films and Plateau borders

We have calculated the shapes of flat liquid films, and of the transition region to the associated Plateau borders (PBs), by integrating the Laplace equation with a position-dependent surface tension γ(x), where 2x is the local film thickness. We discuss films in either zero or non-zero gravity, using standard γ(x) potentials for the interaction between the two bounding surfaces. We have investigated the effects of the film flatness, liquid underpressure, and gravity on the shape of films and their PBs. Films may exhibit 'humps' and/or 'dips' associated with inflection points and minima of the film thickness. Finally, we propose an asymptotic analytical solution for the film width profile.

Domain growth in binary mixtures at low temperatures

We have studied domain growth during spinodal decomposition at low temperatures. We have performed a numerical integration of the deterministic time-dependent Ginzburg-Landau equation with a variable, concentration-dependent diffusion coefficient. The form of the pair-correlation function and the structure function are independent of temperature but the dynamics is slower at low temperature. A crossover between interfacial diffusion and bulk diffusion mechanisms is observed in the behavior of the characteristic domain size. This effect is explained theoretically in terms of an equation of motion for the interface.