Introduction to Focus Issue: nonlinear and stochastic physics in biology

Frank Moss was a leading figure in the study of nonlinear and stochastic processes in biological systems. His work, particularly in the area of stochastic resonance, has been highly influential to the interdisciplinary scientific community. This Focus Issue pays tribute to Moss with articles that describe the most recent advances in the field he helped to create. In this Introduction, we review Moss's seminal scientific contributions and introduce the articles that make up this Focus Issue.     

Role of material amorphicity in laser-induced phase transition

The crystallization patterns induced by nano- and picosecond laser pulses within an amorphous matrix, with various degrees of relaxation, present morphological instabilities. We show by TEM observations that the final crystalline structures of the relaxed amorphous state, after nanosecond laser excitation, and the “as-deposited” amorphous state after picosecond excitation, present similar morphology. Structurally, metastable crystalline states have been formed under laser irradiation. A probable process for these instabilities is related to competition between the light-induced electronic excitation and thermal processes during the nucleation stage.     

Introduction: Cardiovascular physics

The number of patients suffering from cardiovascular diseases increases unproportionally high with the increase of the human population and aging, leading to very high expenses in the public health system. Therefore, the challenge of cardiovascular physics is to develop high-sophisticated methods which are able to, on the one hand, supplement and replace expensive medical devices and, on the other hand, improve the medical diagnostics with decreasing the patient's risk. Cardiovascular physics-which interconnects medicine, physics, biology, engineering, and mathematics-is based on interdisciplinary collaboration of specialists from the above scientific fields and attempts to gain deeper insights into pathophysiology and treatment options. This paper summarizes advances in cardiovascular physics with emphasis on a workshop held in Bad Honnef, Germany, in May 2005. The meeting attracted an interdisciplinary audience and led to a number of papers covering the main research fields of cardiovascular physics, including data analysis, modeling, and medical application. The variety of problems addressed by this issue underlines the complexity of the cardiovascular system. It could be demonstrated in this Focus Issue, that data analyses and modeling methods from cardiovascular physics have the ability to lead to significant improvements in different medical fields. Consequently, this Focus Issue of Chaos is a status report that may invite all interested readers to join the community and find competent discussion and cooperation partners.     

Introduction to focus issue on "randomness, structure, and causality: measures of complexity from theory to applications"

We introduce the contributions to this Focus Issue and describe their origin in a recent Santa Fe Institute workshop.     

Proton core heating and beam formation via parametrically unstable Alfvén-cyclotron waves

Vlasov theory and one-dimensional hybrid simulations are used to study the effects that compressible fluctuations driven by parametric instabilities Alfvén-cyclotron waves have on proton velocity distributions. Field-aligned proton beams are generated during the saturation phase of the wave-particle interaction, with a drift speed which is slightly greater than the Alfvén speed and is maintained until the end of the simulation. The main part of the distribution becomes anisotropic due to phase mixing as is typically observed in the velocity distributions measured in the fast solar wind. We identify the key instabilities and also find that, even in the parameter regime where fluid theory appears to be appropriate, strong kinetic effects still prevail.     

Impact of turbulence on flame brush development of acoustically excited rod-stabilized flames

Coherent structures, such as those arising from hydrodynamic instabilities or excited by thermoacoustic oscillations, can significantly impact flame structure and, consequently, the nature of heat release. The focus of this work is to study how coherent oscillations of varying amplitudes can impact the growth of the flame brush in a bluff-body stabilized flame and how this impact is influenced by the free stream turbulence intensity of the flow approaching the bluff body. We do this by providing external acoustic excitation at the natural frequency of vortex shedding to simulate a highly-coupled thermoacoustic instability, and we vary the in-flow turbulence intensity using perforated plates upstream of the flame. We use high-speed stereoscopic particle image velocimetry to obtain the three-component velocity field and we use the Mie-scattering images to quantify the behavior of the flame edge. Our results show that in the low-turbulence conditions, presence of high-amplitude acoustic excitation can cause the flame brush to exhibit a step-function growth, indicating that the presence of strong vortical structures close to the flame can suppress flame brush growth. This impact is strongly dependent on the in-flow turbulence intensity and the flame brush development in conditions with higher levels of in-flow turbulence are minimally impacted by increasing amplitudes of acoustic excitation. These findings suggest that the sensitivity of the flow and flame to high-amplitude coherent oscillations is a strong function of the in-flow turbulence intensity.     

Review of collective beam instabilities in electron-positron storage rings

The review of studies of collective beam instabilities in electron-positron storage rings is presented. The processes of excitation and suppression of the longitudinal microwave instability, transverse mode coupling instability, longitudinal and transverse multi-bunch instabilities, and instabilities induced by an interaction of a beam with ions or electron clouds are discussed. Important equations for estimation of the threshold beam currents and the rise time of instabilities, as well as the references to the major original works are given. The methods for diagnostics and suppression of instabilities are considered using specific examples.     

Bounds on Instability Growth Rates for Cold Plasmas Streaming along an Infinite Magnetic Guide Field

We derive two bounds on growth rates for streaming instabilities of cold plasmas with inhomogeneous density and velocity profiles transverse to a unidirectional infinite magnetic field: 1) a uniform bound which is independent of wavenumber, and 2) a wavenumber-dependent bound which is less than the uniform bound for long wavelengths. Here streaming instabilities include both multistream instabilities in which two or more streams with different velocities overlap in configuration space, and the slipping stream instability in which a stream has a transverse velocity gradient. The bounds obtained are functions of only global steady-state parameters and are useful in bounding growth rates in experimental devices.     

Snake—Modulation Dynamics of an Optical—Terahertz Soliton in a Graded-Index Waveguide

A nonlinear stage of the effect of snake and modulation instabilities on the dynamics of an optical—terahertz soliton in a quadratically nonlinear graded-index waveguide has been studied theoretically. It has been shown that both instabilities are of fundamental importance and cannot be separated from each other. If the carrier frequency of the optical component is in the region of an anomalous dispersion of the group velocity, these instabilities are developed in a blow-up regime, leading to the self-focusing of the soliton. In the case of the normal dispersion of the group velocity, the mutual effect of the waveguide and snake—modulation dynamics results in the formation of a stable spatiotemporal soliton.

     

Introduction to focus issue: dynamics in systems biology

The methods of nonlinear systems form an extensive toolbox for the study of biology, and systems biology provides a rich source of motivation for the development of new mathematical techniques and the furthering of understanding of dynamical systems. This Focus Issue collects together a large variety of work which highlights the complementary nature of these two fields, showing what each has to offer the other. While a wide range of subjects is covered, the papers often have common themes such as "rhythms and oscillations," "networks and graph theory," and "switches and decision making." There is a particular emphasis on the links between experimental data and modeling and mathematical analysis.     

On the excitation of ion cyclotron and electron cyclotron waves by beams of charged particles

The instabilities of the electrostatic waves of a hot plasma in a magnetic field, excited by beams of charged particles, have been studied in some special cases within the framework of the linear theory. We are interested in short-wavelength oscillations with a transverse wavelength compareable with the Larmore radius of ions or electrons, with frequencies in the vicinity of the harmonic cyclotron frequency of ions or electrons. Expressions have been derived for the increments of these instabilities in the case of a beam with an isotropic distribution function in the velocity space, as well as with an anisotropic distribution function. The influence of the beam temperature on the character of the instabilities and the conditions of formation of the instabilities are discussed, and the order of magnitude of the increments is estimated.The authors thanks J. Václavík and V. Kopecký for valuable discussions and comments.     

Dissipative instabilities in a mesospheric plasma with the aerosol charging processes taken into account

We consider dissipative instabilities of a flow of large aerosol particles as a possible mechanism for generation of electric-field and charged-particle density irregularities in the middle atmosphere. A dispersion equation describing the properties of the spectral component of a quasistatic electric field with allowance for the aerosol charging inertia and external stationary electric field is obtained. The equation is used to study characteristics of two possible instabilities, namely, the instability of a dust-acoustic mode and the instability of an additional low-frequency mode stimulated by the charging inertia. Dependences of the growth rates of both instabilities on the parameters of the medium and the external stationary electric field are obtained. Quantitative estimates for the parameters of the aerosol, ion, and electron components and external factors that are necessary for the excitation of instabilities in the region of the existence of summer polar mesospheric echo, as well as those for spatial scales of unstable perturbations, are given.     

General theory of microscopic dynamical response in surface probe microscopy: from imaging to dissipation

We present a general theory of atomistic dynamical response in surface probe microscopy when two solid surfaces move with respect to each other in close proximity, when atomic instabilities are likely to occur. These instabilities result in a bistable potential energy surface, leading to temperature dependent atomic scale topography and damping (dissipation) images. The theory is illustrated on noncontact atomic force microscopy and enables us to calculate, on the same footing, both the frequency shift and the excitation signal amplitude for tip oscillations. We show, using atomistic simulations, how dissipation occurs through reversible jumps of a surface atom between the minima when a tip is close to the surface, resulting in dissipated energies of 1.6 eV. We also demonstrate that atomic instabilities lead to jumps in the frequency shift that are smoothed out with increasing temperature.     

Tackiness and cohesive failure of granular pastes: Mechanistic aspects

Granular pastes are dense dispersions of non-colloidal grains in a simple or a complex fluid. Typical examples are the coating, gluing or sealing mortars used in building applications. We study the rupture of a thick layer of mortar paste in a simple pulling test where the paste is confined between two flat surfaces. It is shown that, depending on the rheological properties of the paste and the plate separation velocity, two main failure modes are obtained. The first mode is the inwards shear flow of the paste with viscous fingering instabilities, similarly to what has been observed with Newtonian fluids and with non-Newtonian colloidal suspensions or polymer solutions. The second failure mode is stemming from the expansion of bubbles, similarly to what has been observed in soft adhesive polymer layers and, more recently, in highly viscous fluids. It is shown that the crossover between the two failure modes is determined by the conditions required to generate a pressure drop able to trigger the growth of pre-existing micro-bubbles smaller than the inter-granular distance.     

Acoustic instabilities control using Helmholtz resonators

The main focus of the present work is to evaluate the performance of the Helmholtz resonators to control acoustic instabilities inside combustion chambers. In the present stage of this work, some tests were conducted with non-reactive flow inside the combustion chamber. This paper presents a methodology to design the resonators and the calculations to theoretically determine the acoustic performance of damp instabilities, an experimental setup especially developed to study instabilities in reactive and non-reactive flows, and the experimental results for non-reactive situation with and without flow. The results show that the resonator has an exceptional capacity to damp the oscillations in the frequency of the design; but, it has a narrow range of actuation close to the design frequency. In addition, the experiments show that the resonator presence can modify the spectrum of frequencies, and in some cases it amplifies the oscillations, having the flow velocity inside the chamber some considerable influence in the performance attenuation.     

Subharmonic resonances in plasmas: exponential and superexponential growth of driven relativistic plasma waves

Subharmonic resonant beat-wave excitation of nonlinear relativistic plasma waves is studied analytically and in particle-in-cell simulations. We find that if the frequency separation of the lasers, Deltaomega, is 2omega(p) or 3omega(p) ( omega(p) is the plasma frequency), then plasma waves are still excited at omega(p) but they grow exponentially or superexponentially rather than secularly. Both of these subharmonic resonant instabilities saturate due to relativistic detuning. The analytical growth rates and saturation levels agree with the simulation results.     

Mixed-mode oscillations in complex-plasma instabilities

Instabilities in dusty plasmas are frequent phenomena. We show that some instabilities can be described by mixed-mode oscillations often encountered in chemical systems or neuronal dynamics and studied through dynamical system theories. The time evolution of these instabilities is studied through the change in the associated waveform. Frequency and interspike interval are analyzed and compared to results obtained in other scientific fields concerned by mixed-mode oscillations.     

Introduction to Focus Issue: synchronization and cascading processes in complex networks

The study of collective dynamics in complex networks has emerged as a next frontier in the science of networks. This Focus Issue presents the latest developments on this exciting front, focusing in particular on synchronous and cascading dynamics, which are ubiquitous forms of network dynamics found in a wide range of physical, biological, social, and technological systems.