Vladan D. Djordjević

Fractional derivatives embody essential features of cell rheological behavior.

AbstractMechanical moduli of cultured airway smooth muscle cells (Fabry, B., et al. Phys. Rev. Lett. 87:148102, 2001) reveal that the frequency dependence of cell rheological behavior conforms to a weak power-law relationship over a wide range of frequency (10-2 -103 Hz).Such a behavior cannot be accounted for by standard viscoelastic models characterized by a discrete number of time constants that have been commonly used in previous studies of cell viscoelasticity. Fractional calculus, by contrast, provides a natural framework for describing weak power-law relationships and requires no assumptions about the type of material, the time constant distribution or the time/frequency interval in which rheological observations are made. In this study, we developed a rheological model of the cell using methods of fractional calculus. We used a least-squares technique to fit the model to data previously obtained from measurements on airway smooth muscle cells. The fit provided an excellent correspondence to the data, and the estimated values of model parameters were physically plausible. The model leads to a novel and unexpected empirical link between dynamic viscoelastic behavior of the cytoskeleton and the static contractile stress that it bears.

On the dissipation of interfacial and internal long gravity waves

The Korteweg-deVries equations modified by viscosity for interfacial and internal long gravity waves between two parallel plates are derived in the paper. A method based on the inverse scattering method developed recently by Karpman and Maslov has been used to confirm the well-known inverse fourth power decay of the amplitude of a solitary wave on the one hand and to find the time evolution of its velocity on the other.ZusammenfassungDie vorliegende Arbeit befasst sich mit der Ableitung der mit der Viskosität modifizierten Korteweg-deVries Gleichungen, die die lange Trennungsflächen- und interne Schwerewellen zwischen zwei parallelen Platten beschreiben. Es wurde eine Methode angewandt, welche auf der inversen Zerstreuungsmethode beruht und neulich von Karpman und Maslov entwickelt worden ist, um den gut bekannten inversen vierten Potenzverfall einer solitären welle einerseits zu bestätigen und anderseits die zeitliche Evolution ihrer Geschwindigkeit zu finden.

Factors affecting the distribution and abundance of orchids in grasslands and herbaceous wetlands

Grasslands, wet meadows, fens, bogs, and marshes represent important ecosystems that host many orchid species. However, research on the joint effect of the multi-scalar abiotic drivers on orchid distribution and abundance in these habitats is limited. In this study, we investigated factors associated with the occurrence and abundance of 42 orchid taxa in grasslands and herbaceous wetlands of 29 mountains and the surrounding low altitude areas in western Serbia (eastern Dinaric Alps, southeastern Europe). Niche analysis of orchids was performed using outlying mean index analysis (OMI). In addition, we used similarity profile analysis (SIMPROF) to classify orchid taxa into ecological groups, multi response permutation procedure (MRPP) to analyse the differences in orchid composition between vegetation types, and indicator species analysis (ISA) to detect orchids with an affinity to a certain type of vegetation and geological bedrock. The most important gradients that separate orchids within the sampled environmental conditions were moisture, temperature, altitude and soil pH. Moreover, this study underlines the importance of certain vegetation types and geological bedrocks in determining the distribution and abundance of orchids. In total, eight ecological groups of orchids were distinguished. The results have shown that 11 orchid taxa are indicators of specific vegetation types, whereas 13 orchid taxa are indicators of specific bedrock types. The study area provides suitable conditions for survival of some rare and endemic orchid species that have southern limits of their distribution in this part of southeastern Europe. The study suggests that the joint effect of ecological factors, especially vegetation communities and bedrock types, is important to consider in the planning and management of orchid species conservation.

Niche analysis of orchids of serpentine and non-serpentine areas: Implications for conservation

Orchids are known for their species richness, intriguing ecology, rarity and the fact that they grow in almost all terrestrial ecosystems. Although numerous studies about their ecology have been carried out concerning calcareous areas, little is known about orchids that occur in serpentine habitats. The aim of this study was to investigate the ecological preferences of orchids in serpentine and non-serpentine areas on the model of the Valjevo Mountain Range (W Serbia). Niche analysis of orchids was performed using outlying mean index analysis. Data concerning geographical coordinates, altitude, habitat type, inclination, bedrock type, light regime, soil moisture, acidity, nitrogen and temperature were used as explanatory variables. Data of 33 orchid taxa from 407 localities were analysed. The most important gradients that govern orchid distribution were geological bedrock, light regime and temperature. The results have shown that only Anacamptis morio and Gymnadenia conopsea have statistically significantly larger populations on serpentine compared with non-serpentine bedrocks. This study highlights the importance of serpentine habitats as orchid habitats, bearing in mind the occurrence of rare species and species which were found exclusively in serpentine habitats.

Similarity and cotenability

In this paper I present some difficulties for Lewis’s and similar theories of counterfactuals, and suggest that the problem lies in the notion of absolute similarity. In order to explain the problem, I discuss the relation between Lewis’s and Goodman’s theory, and show that the two theories are not related in the way Lewis thought they were.

A Higher-Order Asymptotic Theory for Fully Developed Turbulent Flow in Smooth Pipes

A complete second-order asymptotic theory for fully developed turbulent flow in smooth pipes at high turbulent Reynolds numbers is presented in the paper. The theory is based on Prandtls mixing-length hypothesis involving a fourth-order polynomial representation for the mixing length and taking into account its dependence on the Reynolds number. Two main contributions with respect to the existing literature have been achieved:(a) the friction law is obtained by asymptotic evaluation of an integral, completely independently of the velocity field, and(b) an axis layer (in addition to the wall layer and the outer layer) has to be included in the analysis in order to remove a nonuniformity appearing in the second-order solution for the velocity fieldClosed-form analytic expressions for all constants and wake functions appearing up to the second-order solution in both the friction law and the velocity field are obtained. The results are in a very good agreement with experiments.

On the simultaneous effect of viscosity and variable depth on the propagation of solitary waves

Abstract The Korteweg-de Vries equation modified by both the effect of viscosity and the effect of variable depth is derived and the evolution of a solitary wave in the presence of both of them is discussed by the method of multiple scales. The analysis has been focused on the eventual balance between both effects, which might allow a solitary wave to preserve its initial shape. It has been shown that cither the amplitude or the length or the speed of the wave can only be preserved and the corresponding forms of the channel have been found.

Instationäre Grenzschichten an langsam bewegten Körpern in einer rotierenden Flüssigkeit

SummaryIn this work equations of boundary layers on arbitrary smooth surfaces are derived which are moving relatively slowly through a rotating fluid. For the case of the impulsive start of the motion from rest, the equations are solved exactly for arbitrary velocities at the outer edge of the boundary layer. The results are applied to the case of the motion of a sphere in the direction of the axis of revolution using Stewartsons velocity at the outer edge. The boundary layer calculated in such a way does not separate from the sphere surface; this makes it possible to calculate the total drag. The formula reduces for the case of non-viscous fluid to the known result given by Stewartson.

Goodman’s Only World

An incorrect interpretation of Goodman’s theory of counterfactuals is persistently being offered in the literature. I find that strange. Even more so since the incorrectness is rather obvious. In this paper I try to figure out why is that happening. First I try to explain what Goodman did say, which of his claims are ignored, and what he did not say but is sometimes ascribed to him. I emphasize one of the bad features of the interpretation: it gives counterfactuals some formal properties that neither Goodman nor (usually) the interpreter would accept. The usual interpretation (UI), which I claim should not be ascribed to Goodman, considers a counterfactual \(\mathrm{A}\rightarrow \mathrm{C}\) true iff A, together with natural laws and all contingent truths cotenable with it, entails C. (UI) makes valid the law of conditional excluded middle, which Goodman clearly rejected. Among possible reasons for which the interpreters might find (UI) adequate is that (UI), as I argue, smuggles in the idea of minimal change, which is otherwise attractive, natural to many, but not to be found anywhere in Goodman’s paper. At the end I stress the significance of Goodman’s theory by arguing that we still need some of his notions to test the adequacy of our modern theories.

On the Rarefied Gas Flow in Pipes

Rarefied gas flow in a pipe is treated in the paper by modeling the slip boundary condition by means of a fractional derivative. At that the order of the derivative is conveniently chosen to be a function of the average value of the Knudsen number so that the entire Knudsen number range, from continuum flow to free molecular flow, is covered. Very good agreement with the solutions of linearized Boltzmann equation is achieved. The paper represents a natural extension of the work of the same author on the rarefied micro channel flow, published earlier.Copyright