Nonlinear dynamics of the interaction of a modulated electron beam with a plasma

The excitation of plasma waves during the injection of an unmodulated and a density-modulated electron beam into a semi-infinite cold plasma is investigated. It is shown that the Langmuir oscillation energy accumulated in the plasma increases substantially near the plasma boundary and that the dimension of the region where the Langmuir oscillation energy is localized decreases with time.     

Nonlinear dynamics of diocotron instability

The nonlinear dynamics of the diocotron instability of an electron beam in a waveguide is investigated by numerical simulations. A study is made of how the structures arising in the beam depend on the geometric parameters of the problem. It is shown that the energy source for such azimuthal structures is the initial (stored in the formation of the beam) electrostatic energy of the unneutralized beam charge.     

Helical waves in the vortex electron anisotropic hydrodynamic model

Solutions to the vortex electron anisotropic hydrodynamic equations are investigated that describe nonlinear helical waves in an anisotropic magnetized plasma. The possibility of constructing such solutions is provided by the symmetry properties of the equations. An optimum family of one-dimensional subgroups of a symmetry group consistent with the equations is constructed that makes it possible to derive other, essentially different solutions.     

Experimental study of electron vortex structures in an electrostatic plasma lens

Results are presented from experimental studies of electron vortex bunches in a cold ion-beam plasma consisting of strongly magnetized electrons and a beam of almost free positive ions. The existence of electron vortex bunches was detected from local minima of the electric potential on surfaces perpendicular to the magnetic field lines. It is found that the vortices have the form of magnetic-field-aligned filaments, in which electrons rotate with a velocity significantly exceeding both the velocity of the vortex as a whole and the electron velocity in the ambient plasma. It is shown that, in a sufficiently strong magnetic field, the accumulation of electrons in the vortices terminates when the condition for the longitudinal confinement of electrons by the electric field fails to hold.     

Nonlinear elasticity and dynamics of globular proteins

A molecule of native protein exhibits a high degree of mechanical nonlinearity, which gives rise to a peculiar dynamics behavior of globular proteins. Intramolecular motions strongly depend on pressure. The reaction of specific volume to the action of electric field (electrostriction) inside the molecule has a sign opposite to that observed in liquids. The probability that a small ion would penetrate inside the globule from the solvent depends nonmonotonously on hydrostatic pressure. The nonmonotonicity should manifest itself in all processes related to the transfer of ions inside the globule. The relationship between the mechanical properties of the protein and the kinetics of hydrogen exchange at normal and high pressure is discussed.     

Nonlinear dynamics of a nonisothermal collisionless plasma flow

It is shown that the two-fluid electrohydrodynamic equations for a transversely homogeneous flow of cold ions and Boltzmannian electrons in the ion-acoustic region are reduced to the Boussinesq equation. Using a two-soliton solution as an example, the nonlinear mechanism of collisionless relaxation of a supersonic plasma flow toward a steady state in the form of a double space charge layer is demonstrated.     

Electrostatic electron vortex structure in a plasma in an external magnetic field

A previously developed method for describing vortex structures is used to construct electrostatic vortices in a plasma in an external magnetic field. An equation for the radial electric field that gives rise to azimuthal electron drift in crossed electric (E _r ) and magnetic (B _z ) fields is derived without allowance for the magnetic field of the electron currents. Two types of the resulting electrostatic vortex structures with a positive and a negative electric potential at the axis are analyzed. The results obtained are compared with experimental data on vortex structures.     

Nonlinear dynamics and chaotization of oscillations of a virtual cathode in an annular electron beam in a uniform external magnetic field

Results are presented from a numerical study of the effect of an external magnetic field on the conditions and mechanisms for the formation of a virtual cathode in a relativistic electron beam. Characteristic features of the nonlinear dynamics of an electron beam with a virtual cathode are considered when the external magnetic field is varied. Various mechanisms are investigated by which the virtual cathode oscillations become chaotic and their spectrum becomes a multifrequency spectrum, thereby complicating the dynamics of the vircator system. A general mechanism for chaotization of the oscillations of a virtual cathode in a vircator system is revealed: the electron structures that form in an electron beam interact by means of a common space charge field to give rise to additional internal feedback. That the oscillations of a virtual cathode change from the chaotic to the periodic regime is due to the suppression of the mechanism for forming secondary electron structures.     

Nonlinear isothermal waves in a degenerate electron plasma

A nonlinear differential equation describing oscillations of the chemical potential in a one-dimensional steady-state wave propagating in a degenerate electron gas against an immobile neutralizing ion background is derived, investigated, and solved exactly. It is found that the wave phase velocity is bounded below by a critical velocity, whose exact value is obtained.     

Classical molecular dynamics simulation of the photoinduced electron transfer dynamics of plastocyanin.

Classical molecular dynamics simulations are used to investigate the nuclear motions associated with photoinduced electron transfer in plastocyanin. The blue copper protein is modeled using a molecular mechanics potential; potential parameters for the copper-protein interactions are determined using an x-ray crystallographic structure and absorption and resonance Raman spectra. Molecular dynamics simulations yield a variety of information about the ground (oxidized) and optically excited (charge-transfer) states: 1) The probability distribution of the potential difference between the states, which is used to determine the coordinate and energy displacements, places the states well within the Marcus inverted region. 2) The two-time autocorrelation function of the difference potential in the ground state and the average of the difference potential after instantaneous excitation to the excited state are very similar (confirming linear response in this system); their decay indicates that vibrational relaxation occurs in about 1 ps in both states. 3) The spectral densities of various internal coordinates begin to identify the vibrations that affect the optical transition; the spectral density of the difference potential correlation function should also prove useful in quantum simulations of the back electron transfer. 4) Correlation functions of the protein atomic motions with the difference potential show that the nuclear motions are correlated over a distance of more than 20 A, especially along proposed electron transport paths.     

Nonlinear dynamics and information processing in pacemaker neurons

The paper treats some nonlinear dynamic phenomena in oscillatory activity of a single nerve cell. Based on experiments with CNS bursting pacemaker neurons ofHelix pomatia snail, a mathematical model was studied. The model demonstrates the majority of experimentally observable phenomena and allows one to investigate the role of its separate components. The phenomena demonstrated by model neuron (chaotic behavior, bistability, and sensitivity to parameter variations, initial conditions, and stimuli) may be relevant to information processing in nerve cells. The complexity of [Ca²⁺] _in −V phase diagrams of initial conditions depends on parameters. Transient synaptic impulse produces stable parameter-independent changes in activity of model neuron. These results indicate that a single bursting neuron can work in the neuronal ensemble as a dynamic switch. The sensitivity of this switch is regulated by a neurotransmitter.     

Nonlinear dynamics of paleocortex manifested in the olfactory EEG

The olfactory bulb is the first central component in a highly sensitive yet markedly stable sensory system. It receives a surge of receptor activity with each inspiration and transmits output as a brief burst of oscillatory activity that is most clearly seen in the EEG. These properties together with the known anatomy and physiology of the bulb are used as design criteria to synthesize, evaluate and solve a set of nonlinear differential equations that represent lumped bulbar dynamics. According to the model bulbar processing is in two stages. In the outer layers the interneurons perform the operations of input range compression, integration, clipping, holding, and bias control. In the inner layers the input surge is converted to a burst, which is transmitted by the mitral cells as a pulse density wave. The phase, frequency duration and amplitude of the wave convey information centrally about both the input and the state of the system. The model suffices to replicate the forms of the EEG burst; the pulse probability distributions conditional on the EEG; the waveforms of averaged evoked potentials (AEPs) and post stimulus time (PST) histograms from the bulb and cortex; and the changes in waveform induced by behavioral control of attentiveness and habituation. It is inferred that with selective attention there is a permanent change in the strength of mutually excitatory connections among excitatory neurons, and that with habituation there is a reversible change in the effectiveness of excitatory synapses. The limitations and deficiencies of the model and the need for centrifugal controls of bulbocortical function are discussed.     

Vortex electron dynamics in a high-current plasma lens

An analytic study is made of the following problems: the instability of a plasma against the excitation of vortex turbulence, the turbulence saturation amplitude, the types and spatial structures of the nascent vortices, and their nonlinear growth rates in an electrostatic plasma lens for focusing high-current ion beams.     

Formation of highly ordered cross-linked lattices between asparagine-linked oligosaccharides and lectins observed by electron microscopy

The interaction of asparagine-linked carbohydrates (N-linked) with carbohydrate binding proteins called lectins has been demonstrated to be involved in a variety of cellular recognition processes. Certain N-linked carbohydrates have been shown to be multivalent and capable of binding, cross-linking, and precipitating lectins (Bhattacharyya, L., Ceccarini, C., Lorenzoni, P., and Brewer, C. F. (1987) J. Biol. Chem. 262, 1288-1293; Bhattacharyya, L., Haraldsson, M., and Brewer, C. F. (1987) J. Biol. Chem. 262, 1294-1299; Bhattacharyya, L., Haraldsson, M., and Brewer, C. F. (1988) Biochemistry 27, 1034-1041). Recent data have further suggested that certain oligomannose and bisected hybrid-type N-linked glycopeptides form homogeneous cross-linked lattices with concanavalin A (Bhattacharyya, L., Khan, M. I., and Brewer, C. F. (1988) Biochemistry 27, 8762-8767). In the present study, evidence has been obtained from electron microscopy for the formation of highly ordered and distinct lattices for two bivalent complex type oligosaccharides cross-linked with soybean lectin (Glycine max) and isolectin A from Lotus tetragonolobus, respectively. The results indicate a new source of specificity for interactions of N-linked carbohydrates with lectins, namely their ability to form highly ordered homogeneous aggregates.     

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.     

Regulation of mouse oocyte microtubule and organelle dynamics by PADI6 and the cytoplasmic lattices

Organelle positioning and movement in oocytes is largely mediated by microtubules (MTs) and their associated motor proteins. While yet to be studied in germ cells, cargo trafficking in somatic cells is also facilitated by specific recognition of acetylated MTs by motor proteins. We have previously shown that oocyte-restricted PADI6 is essential for formation of a novel oocyte-restricted fibrous structure, the cytoplasmic lattices (CPLs). Here, we show that α-tubulin appears to be associated with the PADI6/CPL complex. Next, we demonstrate that organelle positioning and redistribution is defective in PADI6-null oocytes and that alteration of MT polymerization or MT motor activity does not induce organelle redistribution in these oocytes. Finally, we report that levels of acetylated microtubules are dramatically suppressed in the cytoplasm of PADI6-null oocytes, suggesting that the observed organelle redistribution failure is due to defects in stable cytoplasmic MTs. These results demonstrate that the PADI6/CPL superstructure plays a key role in regulating MT-mediated organelle positioning and movement.     

Nonlinear age-dependent population dynamics in continuously propagated bacterial cultures

Using results and techniques from the theory of Volterra integral equations, we investigate the existence, uniqueness, positivity, and boundedness of solutions, the existence of equilibrium solutions, and the stability of equilibria of a nonlinear age-dependent model for bacterial growth in a continuous fermentation process. The demographic parameters of the model, such as the growth, death, and fission rates of the cells, depend (in a nonlinear way) on the substrate concentration in the reactor tank.