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.     

The metrical structure of aging (dissipative) systems

A quantification of the aging of a system is achieved by establishing a metric algebra based upon the dissipation function associated with the system. The phenomenological coefficient, L_ij, of irreversible thermodynamics is shown to be a dynamical analogue of the metric tensor, g_ij, of geometry. Given this metric for aging systems, it then becomes possible to compare the aging of two similar systems exposed to different environmental forces and to use the concept of age-preserving transformations to determine under what conditions two different systems will age at the same rate.     

Pattern formation in systems with one spatially distributed species

We describe a three-species mechanism for spatial pattern formation in which only one species spatially moves. We show that a bifurcation to traveling or standing waves occurs. We contrast this mechanism for pattern formation with the better known cases where more than one species moves.     

Species loss and the structure and functioning of multitrophic aquatic systems

Experiments and theory in single trophic level systems dominate biodiversity and ecosystem functioning research and recent debates. All natural ecosystems contain communities with multiple trophic levels, however, and this can have important effects on ecosystem structure and functioning. Furthermore, many experiments compare assembled communities, rather than examining loss of species directly. We identify three questions around which to organise an investigation of how species loss affects the structure and functioning of multitrophic systems. 1) What is the distribution of species richness among trophic levels; 2) from which trophic levels are species most often lost; and 3) does loss of species from different trophic levels influence ecosystem functioning differently? Our analyses show that: 1) Relatively few high‐quality data are available concerning the distribution of species richness among trophic levels. A new data‐set provides evidence of a decrease in species richness as trophic height increases. 2) Multiple lines of evidence indicate that species are lost from higher trophic levels more frequently than lower trophic levels. 3) A theoretical model suggests that both the structure of food webs (occurrence of omnivory and the distribution of species richness among trophic levels) and the trophic level from which species are lost determines the impact of species loss on ecosystem functioning, which can even vary in the sign of the effect. These results indicate that, at least for aquatic systems, models of single trophic level ecosystems are insufficient for understanding the functional consequences of extinctions. Knowledge is required of food web structure, which species are likely to be lost, and also whether cascading extinctions will occur.     

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.     

Nonlinear population dynamics: complication in the age structure influences transition-to-chaos scenarios

The work continues a series of studies on the evolution of a natural population of explicitly seasonal organisms. Model analyses have revealed relationships between the duration of ontogenesis and the pattern of temporal dynamics in size of an isolated population (i.e., the structure and dimensionality of the chaotic attractors). For nonlinear models of age-structured population dynamics (under long-lasting ontogenesis), increase in the reproductive potential is shown to result in the chaotic attractors whose structure and dimensionality changes in response to variations in the model parameters. When the ontogenesis becomes longer and more complicated, it does not, "on the average", augment the level of chaos in the attractors observed. There are wide enough regions in the space of the birth and death parameter values that provide for windows in the chaotic dynamics where the total or partial regularization occurs.     

Periodic band pattern as a dissipative structure in ion transport systems with cylindrical shape

A theory is presented for appearance of periodic band patterns of ion concentration and electric potential associated with electric current surrounding a unicellular or multicellular system of a cylindrical shape. A flux continuity at the membrane (or the surface) is reduced to a nonlinear equation expressing passive and active fluxes across the membrane and intracellular diffusion flux. It is shown that, when an external parameter is varied from the sub-critical region, i.e. the homogeneous flux state, a symmetry breaking along a longitudinal axis usually appears prior to the one along a circumferential direction. The spectrum analysis shows that the correlation length is longer in the longitudinal direction. Growth of the band pattern from a patch-shaped pattern is demonstrated by the use of numerical calculations of proton concentration on the two-dimensional space of cylindrical surface. An experimental example of formative process of H⁺ banding is given for the internodal cell ofChara. It is shown that small patches on the surface decline or are sometimes gathered to the band surrounding the circle. The resulting pattern is suggested as a kind of dissipative structure appearing far from equilibrium.     

Visualizing the dynamics of chromosome structure formation coupled with DNA replication

A basic question of cell biology is how DNA folds to chromosome. Numbers of examples have suggested the involvement of DNA replication in chromosome structure formation. To visualize and identify the dynamics of chromosome structure formation and to elucidate the involvement of DNA replication in chromosome construction, Cy3-2′-deoxyuridine-5′-triphosphate direct-labeled active replicating DNA was observed in prematurely condensed chromosomes (PCCs) under a confocal scanning microscope utilized with drug-induced premature chromosome condensation (PCC) technique that facilitates the visualization of interphase chromatin as condensed chromosome form. S-phase PCCs revealed clearly the drastic dynamics of chromosome formation that transits during S-phase from a ‘cloudy nebula’ to numerous numbers of ‘beads on a string’ and finally to ‘striped arrays of banding structured chromosome’ along with the progress of DNA replication. The number, distribution, and shape of replication foci were also measured in individual subphases of S-phase more precisely than reported previously; maximally, ∼1,400 foci of 0.35 μm average radius size were scored at the beginning of the S-phase, and the number reduced to ∼100 at the end of the S-phase. Drug-induced PCC clearly provided the new insight that eukaryote DNA replication is tightly coupled with the chromosome condensation/compaction for the construction of the higher-ordered structure of the eukaryote chromosome.     

Simulating the rheology of surfactant solution using dissipative particle dynamics

Reverse non-equilibrium (RNE) method is applied to investigate the rheological properties of surfactant solutions by using dissipative particle dynamics algorithm. Results show that the surfactant solutions exhibit a shear-thinning behaviour. With the strengthening of shear, the worm-like micelles are gradually oriented in the x direction and then broken up into small spherical micelles. The process is also shown by the decrease of viscosity, which starts quickly, levels off for moderate shear rates and speeds up again over a critical value. We find that this critical value is independent of surfactant concentration. Compared with the shear flow method, the RNE method is credible for moderate shear rate and has more computational efficiency.     

A dissipative particle dynamics model of carbon nanotubes

A mesoscale dissipative particle dynamics model of single wall carbon nanotubes (CNTs) is designed and demonstrated. The coarse-grained model is produced by grouping together carbon atoms and by bonding the new lumped particles through pair and triplet forces. The mechanical properties of the simulated tube are determined by the bonding forces, which are derived by virtual experiments. Through the introduction of van der Waals interactions, tube–tube interactions were studied. Owing to the reduced number of particles, this model allows the simulation of relatively large systems. The applicability of the presented scheme to model CNT based mechanical devices is discussed.     

The dissipative contribution of myosin II in the cytoskeleton dynamics of myoblasts

We have determined the microrheological response of the actin meshwork for individual cells. We applied oscillating forces with an optical tweezer to a micrometric bead specifically bound to the actin meshwork of C2 myoblasts, and measured the amplitude and phase shift of the induced cell deformation. For a non-perturbed single cell, we have shown that the elastic and loss moduli G and G behave as power laws f and f of the frequency f (0.01<f <50 Hz), and being in the range 0.15–0.35. This demonstrates that the dissipation mechanisms in a single cell involve a broad and continuous distribution of relaxation times. After adding blebbistatin, an inhibitor of myosin II activity, the exponent of G decreases to about 0.10, and G becomes roughly constant for 0.01<f<10 Hz. The actin meshwork appears less rigid and less dissipative than in the control experiment. This is consistent with an inhibition of ATPase and reduction of the gliding mobility of myosin II on actin filaments. In this frequency range, the actomyosin activity appears as an essential mechanism allowing the cell to adapt to an external mechanical stress.     

The biochemical aspects of pineal gland functioning in the rat in ontogeny

We have studied metabolic pathways of serotonin in epiphysis of Wistar male rats at the age of 1; 1,5; 2; 3; 6; 12; 24 and 36 months. Epiphysis retains its functional activity throughout the life, however, serotonin metabolism in epiphysis undergoes marked changes. The main regulatory principle is the switch of serotonin metabolic pathways in the pineal gland. Most distinct changes between hydroxy- and methoxyindols in epiphysis have been observed during the periods of age-associated hormonal rearrangements like sexual maturation or involution of the gonad function at the old age.     

Theory of electric dissipative structure in Characean internode

A band-type alternating pattern of acidic and alkaline regions formed along the Characean cell wall is discussed theoretically. The model system is constructed from linear diffusion equations for the concentration of H+ outside the internode and in the protoplasm. The plasmalemma is taken as a boundary transporting H+ under energy supply by light. The sizes of the protoplasm and extracellular water phase are taken into account explicitly in the present model system to reproduce qualitatively the characteristics observed in various types of experiments. Theoretical analysis shows that the band pattern belongs to dissipative structures emerging far from equilibrium, and is stabilized through the electric current loops produced by locally activated electrogenic H+ pumps and spatially separated passive H+ influx (or OH- efflux) across the membrane. Both the numerical calculation and the theoretical analysis using a generalized time-dependent Ginzburg-Landau equation reveal the following points: (i) the intemodal cell with a larger vacuole in a smaller size of the extracellular water phase tends to exhibit a clearer band pattern; (ii) the increase in viscosity of the external aqueous medium makes the bands appear more easily and, furthermore, distinctly; (iii) the change in size of the extracellular water phase significantly affects the kinetics of the pattern- formation process. These results are interpreted reasonably by taking account of the electric current circulating between the acidic and alkaline regions.     

Normal mode analysis with simplified models to investigate the global dynamics of biological systems

Dynamical properties of macromolecules are increasingly being recognized as significantly contributing to biological functions, including catalysis, regulation of activity, etc. In this review, theoretical approaches to the study of dynamics of biological systems and their application are discussed. In particular, simplified models for the normal mode analysis are described.