Formation and stability of dissipative structures

The nonlinear interaction of the disturbed wave packet modes has been analysed within nonlinear parabolic equation. There has also been designed the approach to a limit cycle regime of an isolated mode, the analytical stability criterion of the obtained solutions having separated the existance spheres of isolated and multimode regimes. Stochastization and self-organization processes taking place during the formation of dissipative structures have been studied by methods of random function theory.     

Changes in shear wave propagation within skeletal muscle during active and passive force generation

Muscle force can be generated actively through changes in neural excitation, and passively through externally imposed changes in muscle length. Disease and injury can disrupt force generation, but it can be challenging to separate passive from active contributions to these changes. Ultrasound elastography is a promising tool for characterizing the mechanical properties of muscles and the forces that they generate. Most prior work using ultrasound elastography in muscle has focused on the group velocity of shear waves, which increases with increasing muscle force. Few studies have quantified the phase velocity, which depends on the viscoelastic properties of muscle. Since passive and active forces within muscle involve different structures for force transmission, we hypothesized that measures of phase velocity could detect changes in shear wave propagation during active and passive conditions that cannot be detected when considering only group velocity. We measured phase and group velocity in the human biceps brachii during active and passive force generation and quantified the differences in estimates of shear elasticity obtained from each of these measurements. We found that measures of group velocity consistently overestimate the shear elasticity of muscle. We used a Voigt model to characterize the phase velocity and found that the estimated time constant for the Voigt model provided a way to distinguish between passive and active force generation. Our results demonstrate that shear wave elastography can be used to distinguish between passive and active force generation when it is used to characterize the phase velocity of shear waves propagating in muscle.     

On the formation of unique dissipative structures

We consider a simple model for the formation of dissipative structures. In general there exists a multitude of stable final states. We show, however, that when the diffusion constant increases during the development of the system, a stationary state is reached which does not depend on the choice of initial conditions. We also show that a uniquely defined final state builds up when the system is initially strongly excited on one side.     

Trajectory of a short radio wave in the multilayer ionosphere

An exact solution of the ray trajectory equation in the spherically symmetric ionosphere is derived by approximating the height distribution of the electron density by a set of quasi-linear and quasi-parabolic functions.     

Travelling wave dynamics and self-organization in a spatio-temporally structured population

We analyse spatial population dynamics showing that periodic or period-like chaotic dynamics produce self-organization structures, such as travelling waves. We suggest that self-organized patterns are associated with spatial synchrony patterns that often depend on geographical distance between subpopulations. The population dynamics also show statistical spatial autocorrelation patterns. We contrast our theoretical simulations with empirical data on annual damages in young sapling stands caused by voles. We conclude, on the basis of the periodicity, synchrony, and spatial autocorrelation patterns, and our simulation results, that vole dynamics represent travelling waves in population dynamics. We suggest that because such synchrony patterns are frequently observed in natural populations, spatial self-organization may be more common in population dynamics than reported in the literature.     

Interstitial flow through the internal elastic lamina affects shear stress on arterial smooth muscle cells

Interstitial flow through the tunica media of an artery wall in the presence of the internal elastic lamina (IEL), which separates it from the subendothelial intima, has been studied numerically. A two-dimensional analysis applying the Brinkman model as the governing equation for the porous media flow field was performed. In the numerical simulation, the IEL was modeled as an impermeable barrier to water flux, except for the fenestral pores, which were uniformly distributed over the IEL. The tunica media was modeled as a heterogeneous medium composed of a periodic array of cylindrical smooth muscle cells (SMCs) embedded in a fiber matrix simulating the interstitial proteoglycan and collagen fibers. A series of calculations was conducted by varying the physical parameters describing the problem: the area fraction of the fenestral pore (0. 001-0.036), the diameter of the fenestral pore (0.4-4.0 microm), and the distance between the IEL and the nearest SMC (0.2-0.8 microm). The results indicate that the value of the average shear stress around the circumference of the SMC in the immediate vicinity of the fenestral pore could be as much as 100 times greater than that around an SMC in the fully developed interstitial flow region away from the IEL. These high shear stresses can affect SMC physiological function.     

Membrane stress and internal pressure in a red blood cell freely suspended in a shear flow.

Presented is an algorithm for the approximate calculation of the membrane stress distribution and the internal pressure of a steadily tank-treading red cell. The algorithm is based on an idealized ellipsoidal model of the tank-treading cell (Keller, S.R., and R. Skalak, 1982, J. Fluid Mech., 120:27-47) joined with experimental observations of projected length, width, and tank-treading frequency. The results are inexact because the membrane shape and velocity are assumed a priori, rather than being determined via appropriate material constitutive relations for the membrane; these results are, nevertheless, believed to be approximately correct, and show that internal pressure builds up slowly as cell elongation increases, rising more rapidly as the deformed cell approaches the limiting geometry of a prolate ellipsoid. The maximum shear stress resultant in the membrane was found to be below but approaching the yield point range at the highest shear rate applied.     

Nonlinear dynamics of drift structures in a magnetized dissipative plasma

A study is made of the nonlinear dynamics of solitary vortex structures in an inhomogeneous magnetized dissipative plasma. A nonlinear transport equation for long-wavelength drift wave structures is derived with allowance for the nonuniformity of the plasma density and temperature equilibria, as well as the magnetic and collisional viscosity of the medium and its friction. The dynamic equation describes two types of nonlinearity: scalar (due to the temperature inhomogeneity) and vector (due to the convectively polarized motion of the particles of the medium). The equation is fourth order in the spatial derivatives, in contrast to the second-order Hasegawa-Mima equations. An analytic steady solution to the nonlinear equation is obtained that describes a new type of solitary dipole vortex. The nonlinear dynamic equation is integrated numerically. A new algorithm and a new finite difference scheme for solving the equation are proposed, and it is proved that the solution so obtained is unique. The equation is used to investigate how the initially steady dipole vortex constructed here behaves unsteadily under the action of the factors just mentioned. Numerical simulations revealed that the role of the vector nonlinearity is twofold: it helps the dispersion or the scalar nonlinearity (depending on their magnitude) to ensure the mutual equilibrium and, thereby, promote self-organization of the vortical structures. It is shown that dispersion breaks the initial dipole vortex into a set of tightly packed, smaller scale, less intense monopole vortices-alternating cyclones and anticyclones. When the dispersion of the evolving initial dipole vortex is weak, the scalar nonlinearity symmetrically breaks a cyclone-anticyclone pair into a cyclone and an anticyclone, which are independent of one another and have essentially the same intensity, shape, and size. The stronger the dispersion, the more anisotropic the process whereby the structures break: the anticyclone is more intense and localized, while the cyclone is less intense and has a larger size. In the course of further evolution, the cyclone persists for a relatively longer time, while the anticyclone breaks into small-scale vortices and dissipation hastens this process. It is found that the relaxation of the vortex by viscous dissipation differs in character from that by the frictional force. The time scale on which the vortex is damped depends strongly on its typical size: larger scale vortices are longer lived structures. It is shown that, as the instability develops, the initial vortex is amplified and the lifetime of the dipole pair components-cyclone and anticyclone-becomes longer. As time elapses, small-scale noise is generated in the system, and the spatial structure of the perturbation potential becomes irregular. The pattern of interaction of solitary vortex structures among themselves and with the medium shows that they can take part in strong drift turbulence and anomalous transport of heat and matter in an inhomogeneous magnetized plasma.     

Small-scale instability and nonlinear structures in current-carrying atmospheric plasma in the D region of the ionosphere

It is shown that the electric field may cause instability of low-frequency potential oscillations with a period of about 1 min in the D region of the ionosphere. This is related to the fact that the attachment rate of electrons to molecules is a nonmonotonic function of the temperature: it increases at low temperatures and decreases at high temperatures. The temperature corresponding to the maximum attachment rate is about 1000 K. The development of instability can result in the formation of quasi-steady layers of the electron density with a characteristic spatial period of several tens of meters. Such inhomogeneities can affect the propagation of radio waves with wavelengths on the order of or shorter than 10 m.     

Prediction of the ensembles of RNA secondary structures. Kinetic analysis of self-organization

A new approach to the problem of prediction of secondary structures of RNA, which is based on the kinetic analysis of self-organising molecules is proposed. Structural reconstructions that take place during formation of secondary structures are described in terms of Markov process. A set of states and probability transition were defined. Monte-Carlo methods were used to describe this process. Probability distributions of various secondary structures depending on time are given. Examples of calculations for ensembles of secondary structures of some tRNAs are described. An effective method of steady-state ensemble research, which is based on a quick RESETTING of all possible variance of the secondary structures of RNAs is given. By ascribing to each of these structures the value of probabilities as a function of free energy it was possible to obtain the Boltzmann ensemble of secondary structures.     

Dynamics of the primary cilium in shear flow

In this work, the equilibrium shape and dynamics of a primary cilium under flow are investigated by using both theoretical modeling and experiment. The cilium is modeled as an elastic beam that may undergo large deflection due to the hydrodynamic load. Equilibrium results show that the anchoring effects of the basal body on the cilium axoneme behave as a nonlinear rotational spring. Details of the rotational spring are elucidated by coupling the elastic beam with an elastic shell. We further study the dynamics of cilium under shear flow with the cilium base angle determined from the nonlinear rotational spring, and obtain good agreement in cilium bending and relaxing dynamics when comparing between modeling and experimental results. These results potentially shed light on the physics underlying the mechanosensitive ion channel transport through the ciliary membrane.     

The role of adaptive structures in the umbilical arteries in regulating the blood flow in the internal iliac artery system

A complex of special structures having compensatory-adaptive character has been found in the umbilical artery wall of a mature dog. The role of the structures revealed is to participate in an active regulation of the blood stream. In the test animals with a model of the blood stream disorder in the iliac artery reservoir, the importance of the structures of its active regulation increases. The investigations performed have stated the fact, that the canine umbilical artery during the postnatal period of ontogenesis actively participates in regulation of the blood stream in the internal iliac artery reservoir. In some cases the umbilical artery plays the role of a blocking artery, in others--as a powerful arteriovenous formation and it is able to participate in distribution and regulation of the blood stream.     

Effect of shear flow on the phase behavior of an aqueous gelatin-dextran emulsion

A rheo-optical methodology, based on small angle light scattering and transmitted light intensity measurements, has been used to study in situ and on a time resolved basis the shear induced morphology in ternary two-phase water-gelatin-dextran mixtures. Emulsions close to the binodal line as well as far from it have been investigated. It is shown that above a critical shear rate, shear-induced mixing occurs at the length scales probed by the laser light. It is hypothesized that the shear-induced homogenization is due to the shear forces that exceed the intermolecular forces of the self-association process of the gelatin. The isothermal phase diagram at a fixed shear rate has been determined. In addition, the structure evolution after cessation of flow has been studied. When flow is stopped after homogenization, phase separation occurs almost instantaneously. When subsequently applying a low shear rate, the structure coarsens due to coalescence of the dispersed droplets. The kinetics of this coalescence process is strain controlled.     

Domains of calcium channels as dissipative structures in a simulated neuron

The lateral distribution of open calcium channels of the fluid-mosaic membrane were investigated in a phenomenological model of a cylinder-shaped nerve cell. The local density of the channels changed due to their lateral diffusion and voltage- and calcium-dependent conformation transitions between open and closed states. Domains with an increased steady density of the open calcium channels were created as a result of action of intracellular calcium on its own channels, increasing the probability of the open state of the latter. These spatially nonuniform distributions of the channels are considered dissipative structures emerged in the active nonlinear medium at the expense of energy of active transport.Neirofiziologiya/Neurophysiology, Vol. 26, No. 2, pp. 99–107, March–April, 1994.     

Kinetics of actin-myosin binding. ATP-ase activity and sol-gel dissipative structures

The simple kinetic model of actin-myosin binding-dissociation process including ATP-ase activity is considered. We demonstrated how one may easily include cooperativity in such a model by using effectivity factors introduced in our previous papers. A possibility of further simplifying the model through quasi-stationary approximation for some variables is considered. Sol-gel dissipative structures and possible biological implications of such structures are discussed.     

Validation of shear wave elastography in skeletal muscle

Skeletal muscle is a very dynamic tissue, thus accurate quantification of skeletal muscle stiffness throughout its functional range is crucial to improve the physical functioning and independence following pathology. Shear wave elastography (SWE) is an ultrasound-based technique that characterizes tissue mechanical properties based on the propagation of remotely induced shear waves. The objective of this study is to validate SWE throughout the functional range of motion of skeletal muscle for three ultrasound transducer orientations. We hypothesized that combining traditional materials testing (MTS) techniques with SWE measurements will show increased stiffness measures with increasing tensile load, and will correlate well with each other for trials in which the transducer is parallel to underlying muscle fibers. To evaluate this hypothesis, we monitored the deformation throughout tensile loading of four porcine brachialis whole-muscle tissue specimens, while simultaneously making SWE measurements of the same specimen. We used regression to examine the correlation between Young′s modulus from MTS and shear modulus from SWE for each of the transducer orientations. We applied a generalized linear model to account for repeated testing. Model parameters were estimated via generalized estimating equations. The regression coefficient was 0.1944, with a 95% confidence interval of (0.1463–0.2425) for parallel transducer trials. Shear waves did not propagate well for both the 45° and perpendicular transducer orientations. Both parallel SWE and MTS showed increased stiffness with increasing tensile load. This study provides the necessary first step for additional studies that can evaluate the distribution of stiffness throughout muscle.     

Red blood cell deformation in shear flow. Effects of internal and external phase viscosity and of in vivo aging.

Shear deformation of young and old human red blood cells was examined over a range of shear stresses and suspending phase viscosities (eta o) using a cone-plate Rheoscope. The internal viscosities (eta i) of these cell types differ, and further changes in internal viscosity were induced by alteration of suspension osmolality and hence cell volume. For low suspending viscosities (0.0555 or 0.111 P) old cells tended to tumble in shear flow, whereas young cells achieved stable orientation and deformed. Changes in osmolality, at these external viscosities, altered the percentage of cells deforming, and for each cell type threshold osmolalities (Osm-50) were determined where 50% of cells deformed. The threshold osmolalities were higher for younger cells than for older cells, but the internal viscosities of the two cell types were similar at their respective Osm-50. Threshold osmolalities were also higher for the higher external viscosity, but the ratio of internal to external viscosities (i.e., eta i/eta o) was nearly constant for both external viscosities. Deformation of stably oriented cells increased with increasing shear stress and approached a value limited by cell surface area and volume. For isotonic media, over a wide range of external viscosities and shear stresses, deformation was greater for younger cells than for older cells. However, deformation vs. shear stress data for the two cell types became nearly coincident if young cells were osmotically shrunk to have their internal viscosity close to that for old cells. Increases in external viscosity, at constant shear stress, caused greater deformation for all cells. This effect of external viscosity was not equal for young and old cells; the ratio of old/young cell deformation increased with increasing eta o. However, if deformation was plotted as a function of the ratio lambda = eta i/eta o, at constant shear stress, young and old cell data followed similar paths. Thus the ratio lambda is a major determinant of cell deformation as well as a critical factor affecting stable orientation in shear flow.