Showing papers by "Andrey V. Kuznetsov published in 2015"

Numerical investigation of the possibility of macroscopic turbulence in porous media: a direct numerical simulation study

Abstract: When a turbulent flow in a porous medium is determined numerically, the crucial question is whether turbulence models should account only for turbulent structures restricted in size to the pore scale or whether the size of turbulent structures could exceed the pore scale. The latter would mean the existence of macroscopic turbulence in porous media, when turbulent eddies exceed the pore size. In order to determine the real size of turbulent structures in a porous medium, we simulated the turbulent flow by direct numerical simulation (DNS) calculations, thus avoiding turbulence modelling of any kind. With this study, which for the first time uses DNS calculations, we provide benchmark data for turbulent flow in porous media. Since perfect DNS calculations require the resolution of scales down to the Kolmogorov scale, often only approximate DNS solutions can be obtained, especially for high Reynolds numbers. This is accounted for by using and comparing two different DNS approaches, a finite volume method (FVM) with grid refinement towards the wall and a lattice Boltzmann method (LBM) with equal grid distribution. The solid matrix was simulated by a large number of rectangular bars arranged periodically. The number of bars in the solution domain with periodic boundary conditions was reduced systematically until a minimum size was found that does not suppress any large-scale turbulent structures. Two-point correlations, integral length scales and energy spectra were determined in order to answer the question of whether or not macroscopic turbulence can be found in porous media.

A comparison between the diffusion–reaction and slow axonal transport models for predicting tau distribution along an axon

Abstract: This paper developed equations describing steady-state tau distributions for three versions of the diffusion-reaction model of tau transport: a model with constant kinetic rates, a model that additionally accounts for tau diffusion along microtubules (MTs) and a model with a modulated rate of tau attachment to MTs. We demonstrated that, for the model with constant kinetic rates, the concentration of free tau in the cytoplasm was determined by a single dimensionless parameter that represents the ratio of the diffusion time (the time it takes tau to diffuse from the axon hillock to the axon tip) to the half-life of tau. We also developed a model based on the hypothesis that tau is actively transported. Analytical solutions for some special situations were obtained. The model predictions were compared with experimentally measured tau distributions in axons reported in Black et al. (1996, J. Neurosc., 16: , 3601-3619), and based on these comparisons, we discussed the performance of various models. We demonstrated the significance of modulation of the tau attachment rate to MTs in the diffusion-reaction model. On the other hand, the active transport model predictions were consistent with experimental data even with constant kinetic rates. For short axons (up to 600 μm in length) the predicted average transport velocity of tau was in the experimentally reported range for both the diffusion-reaction and active transport models, but for the active transport model the average tau velocity was larger.

The Effect of Vertical Throughflow on Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid: A Revised Model

Abstract: The effect of vertical throughflow on the onset of convection in a horizontal layer of a porous medium saturated by a nanofluid is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The dependences of the critical Rayleigh number for the non-oscillatory and oscillatory modes of instability on the thermophoresis and Brownian motion parameters for the cases with and without throughflow are investigated.

The Effects of Double Diffusion and Local Thermal Non-equilibrium on the Onset of Convection in a Layered Porous Medium: Non-oscillatory Instability

Abstract: The effect of local thermal non-equilibrium on the onset of double-diffusive convection in a porous medium consisting of two horizontal layers is studied analytically. Linear stability theory is applied. Variations of permeability, fluid conductivity, solutal diffusivity, solid conductivity, interphase heat transfer coefficient, and porosity are considered. It is found that with the introduction of double diffusion, the heterogeneity of porosity now has a major effect, comparable to the effects of heterogeneity of permeability and fluid conductivity. The general results are obtained by using a one-term Galerkin approximation. We validate this approximation by comparing these results with those obtained by using a highly accurate numerical solver. We thus established the accuracy of a one-term Galerkin approximation for stability analysis of a complicated convection problem.

A coupled model of fast axonal transport of organelles and slow axonal transport of tau protein.

Abstract: We have developed a model that accounts for the effect of a non-uniform distribution of tau protein along the axon length on fast axonal transport of intracellular organelles. The tau distribution is simulated by using a slow axonal transport model; the numerically predicted tau distributions along the axon length were validated by comparing them with experimentally measured tau distributions reported in the literature. We then developed a fast axonal transport model for organelles that accounts for the reduction of kinesin attachment rate to microtubules by tau. We investigated organelle transport for two situations: (1) a uniform tau distribution and (2) a non-uniform tau distribution predicted by the slow axonal transport model. We found that non-uniform tau distributions observed in healthy axons (an increase in tau concentration towards the axon tip) result in a significant enhancement of organelle transport towards the synapse compared with the uniform tau distribution with the same average amount of tau. This suggests that tau may play the role of being an enhancer of organelle transport.

Local Thermal Non-equilibrium and Heterogeneity Effects on the Onset of Double-Diffusive Convection in an Internally Heated and Soluted Porous Medium

Abstract: The effect of local thermal non-equilibrium on the onset of double-diffusive convection in a porous medium consisting of two horizontal layers, each internally heated, is studied analytically. Linear stability theory is applied. Variations of permeability, fluid thermal conductivity, solid thermal conductivity, heat source strength in the solid and fluid phases, concentration source strength, interphase heat transfer coefficient and porosity are considered. In addition to the major effects from heterogeneity of permeability, fluid thermal conductivity and heat source strength in the fluid phase as with single-diffusive convection, it is now found that major effects arise from heterogeneity of solutal source strength and porosity. We used two different methods to obtain our results. Analytical results that readily show the effects of parameter variations were obtained by using a low-term Galerkin approximation, which was validated by using a highly accurate numerical solver. Since for a problem with large number of parameters simple analytical results are highly desirable, the quantification of the accuracy of a low-term Galerkin approximation presented in our paper is quite important.

Modeling neuropeptide transport in various types of nerve terminals containing en passant boutons.

Abstract: We developed a mathematical model for simulating neuropeptide transport inside dense core vesicles (DCVs) in axon terminals containing en passant boutons. The motivation for this research is a recent experimental study by Levitan and colleagues (Bulgari et al., 2014) which described DCV transport in nerve terminals of type Ib and type III as well as in nerve terminals of type Ib with the transcription factor DIMM. The goal of our modeling is validating the proposition put forward by Levitan and colleagues that the dramatic difference in DCV number in type Ib and type III terminals can be explained by the difference in DCV capture in type Ib and type III boutons rather than by differences in DCV anterograde transport and half-life of resident DCVs. The developed model provides a tool for studying the dynamics of DCV transport in various types of nerve terminals. The model is also an important step in gaining a better mechanistic understanding of transport processes in axons and identifying directions for the development of new models in this area.

Thismia puberula (Thismiaceae), a new species from Southern Vietnam

Abstract: Thismia puberula , a new species of Thismiaceae, is described and illustrated. The species was discovered in 2014 during botanical survey of Chu Yang Sin national park (Dak Lak province, Southern Vietnam). Thismia puberula possesses vermiform roots and mitriform inner tepals. It is most similar to T. angustimitra , T. mirabilis , T. mucronata and T. okhaensis . The new species differs from related species mainly by dome-shaped annulus with delimited vertical and horizontal parts covered by hairs, broad mitre with foveae, inner mitre surface covered by papillate trichomes, and presence of interstaminal glands. An updated key to Vietnamese species of Thismia is provided.

Can an increase in neuropeptide production in the soma lead to DCV circulation in axon terminals with type III en passant boutons

Abstract: Neuropeptides are synthesized in the neuron soma; they are packaged in dense core vesicles (DCVs) which undergo axonal transport toward nerve terminals. Published experimental results suggest that in terminals with type Ib boutons DCVs circulate in the terminal, undergoing repeated anterograde and retrograde transport, while in type III terminals DCVs do not circulate in the terminal. In this paper we developed a mathematical model that allowed us to investigate the effects of an increased rate of DCV production in the soma. We demonstrated that our model reproduces some important experimental results, in particular those concerning DCV circulation in type Ib and type III terminals. Our model makes testable predictions. Probably the most important prediction concerns the effect of an increased DCV production rate in the soma, which we anticipate leads to increased DCV circulation in type Ib boutons and to the appearance of DCV circulation in type III boutons. Other predictions concern various stages of development of DCV circulation in the terminals after they were depleted of DCVs due to neuropeptide release.

Modelling organelle transport after traumatic axonal injury.

Abstract: This paper is motivated by recent experimental research (Tang-Schomer et al. 2012) on the formation of periodic varicosities in axons after traumatic brain injury (TBI). TBI leads to the formation of undulated distortions in the axons due to their dynamic deformation. These distortions result in the breakage of some microtubules (MTs) near the peaks of undulations. The breakage is followed by catastrophic MT depolymerisation around the broken ends. Although after relaxation axons regain their straight geometry, the structure of the axon after TBI is characterised by the presence of periodic regions where the density of MTs has been decreased due to depolymerisation. We modelled organelle transport in an axon segment with such a damaged MT structure and investigated how this structure affects the distributions of organelle concentrations and fluxes. The modelling results suggest that organelles accumulate at the boundaries of the region where the density of MTs has been decreased by depolymerisation. Accor...

A Critical Review of Experimental and Modeling Research on the Leftward Flow Leading to Left-Right Symmetry Breaking in the Embryonic Node

Abstract: In this chapter, we present a critical review of experimental and numerical work on the leftward flow in a mouse ventral node. This flow is generated by rotating primary cilia located in the floor of the node and is believed to play a pivotal role in breaking the left-right symmetry during the mouse embryo development. We also review two hypotheses concerning how the leftward flow is sensed, mechanosensing and chemosensing. Finally, we review a recently suggested simplified method of modeling flow and morphogen transport in the node, which is based on assuming a given vorticity distribution at the edge of the ciliated surface.

Can a death signal half-life be used to sense the distance to a lesion site in axons?

Abstract: Neuron response to injury depends on the distance to the lesion site, which means that neurons are capable of sensing this distance. Several mechanisms explaining how neurons can do this have been proposed and it is possible that neurons use a combination of several mechanisms to make such measurements. In this paper we investigate the feasibility of the simplest mechanism, which is based on the hypothesis that death signals, produced at the lesion site, propagate toward the neuron soma. The signals are propelled by dynein motors. If signals have a finite half-life, they decay as they propagate. By measuring the concentration of death signals arriving to the soma, neurons should thus be able to determine the distance to the injury site. We develop and solve a transport equation based on the above model. We investigate how a death signal distribution depends on the dynein velocity distribution. We evaluate the efficiency of such a mechanism by investigating the sensitivity of death signal concentration at the soma to the distance to the injury site. By using the hypothesis that system performance is optimized by evolution, we evaluate death signal half-lives that would maximize this sensitivity.

◾ Modeling Convection in Nanofluids: From Clear Fluids to Porous Media

Abstract: In this chapter, we discuss the mathematical modeling of convection in nanofluids, with emphasis on two problems that are paradigmatic for confined convection and external convection, respectively. The first problem is the onset of convection in a fluid layer heated uniformly from below and the second problem involves a thermal boundary layer adjacent to a vertical wall. We also consider forced convection in a channel.

Turbulent flow in the micro structures of porous media

Abstract: Some fundamental issues with respect to turbulent flows through a porous matrix are addressed by analyzing DNS results (DNS: direct numerical simulation, i.e. no turbulence modeling). In a porous matrix with pore sizes of micro or even nano dimensions turbulent flow may occur when the (local) Reynolds number is sufficiently large. An open question, however, is whether turbulence structures are restricted in size by the pore size dimensions or not. This is an important aspect that immediately affects the way turbulence has to be modelled. In order to find out which influence the solid matrix has on the turbulence a generic matrix built from a large number of bars with square cross sections is investigated. Two different DNS approaches are used, a finite volume one and a Lattice-Boltzmann approach. From both DNS calculations detailed flow field information about the influence of the solid matrix on the turbulence structure are obtained. Finally the extension of Darcy’s friction law by the Forchheimer term is investigated with respect to the question whether this extended law may be used in the fully turbulent flow regime.Copyright © 2015 by ASME