Role of viscoelasticity in the appearance of low-Reynolds turbulence: considerations for modelling.

Inertial effects caused by perturbations of dynamical equilibrium during the flow of soft matter constitute a hallmark of turbulence. Such perturbations are attributable to an imbalance between energy storage and energy dissipation. During the flow of Newtonian fluids, kinetic energy can be both stored and dissipated, while the flow of viscoelastic soft matter systems, such as polymer fluids, induces the accumulation of both kinetic and elastic energies. The accumulation of elastic energy causes local stiffening of stretched polymer chains, which can destabilise the flow. Migrating multicellular systems are hugely complex and are capable of self-regulating their viscoelasticity and mechanical stress generation, as well as controlling their energy storage and energy dissipation. Since the flow perturbation of viscoelastic systems is caused by the inhomogeneous accumulation of elastic energy, rather than of kinetic energy, turbulence can occur at low Reynolds numbers.This theoretical review is focused on clarifying the role of viscoelasticity in the appearance of low-Reynolds turbulence. Three types of system are considered and compared: (1) high-Reynolds turbulent flow of Newtonian fluids, (2) low and moderate-Reynolds flow of polymer solutions, and (3) migration of epithelial collectives, discussed in terms of two model systems. The models considered involve the fusion of two epithelial aggregates, and the free expansion of epithelial monolayers on a substrate matrix.

Aging affects the phase coherence between spontaneous oscillations in brain oxygenation and neural activity.

The risk of neurodegenerative disorders increases with age, due to reduced vascular nutrition and impaired neural function. However, the interactions between cardiovascular dynamics and neural activity, and how these interactions evolve in healthy aging, are not well understood. Here, the interactions are studied by assessment of the phase coherence between spontaneous oscillations in cerebral oxygenation measured by fNIRS, the electrical activity of the brain measured by EEG, and cardiovascular functions extracted from ECG and respiration effort, all simultaneously recorded. Signals measured at rest in 21 younger participants (31.1 ± 6.9 years) and 24 older participants (64.9 ± 6.9 years) were analysed by wavelet transform, wavelet phase coherence and ridge extraction for frequencies between 0.007 and 4 Hz. Coherence between the neural and oxygenation oscillations at ∼ 0.1 Hz is significantly reduced in the older adults in 46/176 fNIRS-EEG probe combinations. This reduction in coherence cannot be accounted for in terms of reduced power, thus indicating that neurovascular interactions change with age. The approach presented promises a noninvasive means of evaluating the efficiency of the neurovascular unit in aging and disease.

Introduction to the Physics of Ionic Conduction in Narrow Biological and Artificial Channels.

"There is plenty of room at the bottom" [...].

Field-Dependent Dehydration and Optimal Ionic Escape Paths for C2N Membranes.

Most analytic theories describing electrostatically driven ion transport through water-filled nanopores assume that the corresponding permeation barriers are bias-independent. While this assumption may hold for sufficiently wide pores under infinitely small bias, transport through subnanometer pores under finite bias is difficult to interpret analytically. Given recent advances in subnanometer pore fabrication and the rapid progress in detailed computer simulations, it is important to identify and understand the specific field-induced phenomena arising during ion transport. Here we consider an atomistic model of electrostatically driven ion permeation through subnanoporous C2N membranes. We analyze probability distributions of ionic escape trajectories and show that the optimal escape path switches between two different configurations depending on the bias magnitude. We identify two distinct mechanisms contributing to field-induced changes in transport-opposing barriers: a weak one arising from field-induced ion dehydration and a strong one due to the field-induced asymmetry of the hydration shells. The simulated current-voltage characteristics are compared with the solution of the 1D Nernst-Planck model. Finally, we show that the deviation of simulated currents from analytic estimates for large fields is consistent with the field-induced barriers and the observed changes in the optimal ion escape path.

Application of a Statistical and Linear Response Theory to Multi-Ion Na+ Conduction in NaChBac.

Biological ion channels are fundamental to maintaining life. In this manuscript we apply our recently developed statistical and linear response theory to investigate Na+ conduction through the prokaryotic Na+ channel NaChBac. This work is extended theoretically by the derivation of ionic conductivity and current in an electrochemical gradient, thus enabling us to compare to a range of whole-cell data sets performed on this channel. Furthermore, we also compare the magnitudes of the currents and populations at each binding site to previously published single-channel recordings and molecular dynamics simulations respectively. In doing so, we find excellent agreement between theory and data, with predicted energy barriers at each of the four binding sites of ∼4,2.9,3.6, and 4kT.

Diffusion phenomena in a mixed phase space.

We show that, in strongly chaotic dynamical systems, the average particle velocity can be calculated analytically by consideration of Brownian dynamics in a phase space, the method of images, and the use of the classical diffusion equation. The method is demonstrated on the simplified Fermi-Ulam accelerator model, which has a mixed phase space with chaotic seas, invariant tori, and Kolmogorov-Arnold-Moser islands. The calculated average velocities agree well with numerical simulations and with an earlier empirical theory.

Race-specific differences in the phase coherence between blood flow and oxygenation: A simultaneous NIRS, white light spectroscopy and LDF study.

Race-specific differences in the level of glycated hemoglobin are well known. However, these differences were detected by invasive measurement of mean oxygenation, and their understanding remains far from complete. Given that oxygen is delivered to the cells by hemoglobin through the cardiovascular system, a possible approach is to investigate the phase coherence between blood flow and oxygen transportation. Here we introduce a noninvasive optical method based on simultaneous recordings using NIRS, white light spectroscopy and LDF, combined with wavelet-based phase coherence analysis. Signals were recorded simultaneously for individuals in two groups of healthy subjects, 16 from Sub-Saharan Africa (BA group) and 16 Europeans (CA group). It was found that the power of myogenic oscillations in oxygenated and de-oxygenated hemoglobin is higher in the BA group, but that the phase coherence between blood flow and oxygen saturation, or blood flow and hemoglobin concentrations is higher in the CA group.

Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences.

Dynamical systems are widespread, with examples in physics, chemistry, biology, population dynamics, communications, climatology and social science. They are rarely isolated but generally interact with each other. These interactions can be characterized by coupling functions-which contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how each interaction occurs. Coupling functions can be used, not only to understand, but also to control and predict the outcome of the interactions. This theme issue assembles ground-breaking work on coupling functions by leading scientists. After overviewing the field and describing recent advances in the theory, it discusses novel methods for the detection and reconstruction of coupling functions from measured data. It then presents applications in chemistry, neuroscience, cardio-respiratory physiology, climate, electrical engineering and social science. Taken together, the collection summarizes earlier work on coupling functions, reviews recent developments, presents the state of the art, and looks forward to guide the future evolution of the field. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

Synchronization transitions caused by time-varying coupling functions.

Interacting dynamical systems are widespread in nature. The influence that one such system exerts on another is described by a coupling function; and the coupling functions extracted from the time-series of interacting dynamical systems are often found to be time-varying. Although much effort has been devoted to the analysis of coupling functions, the influence of time-variability on the associated dynamics remains largely unexplored. Motivated especially by coupling functions in biology, including the cardiorespiratory and neural delta-alpha coupling functions, this paper offers a contribution to the understanding of effects due to time-varying interactions. Through both numerics and mathematically rigorous theoretical consideration, we show that for time-variable coupling functions with time-independent net coupling strength, transitions into and out of phase- synchronization can occur, even though the frozen coupling functions determine phase-synchronization solely by virtue of their net coupling strength. Thus the information about interactions provided by the shape of coupling functions plays a greater role in determining behaviour when these coupling functions are time-variable. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

On the suitability of laser-Doppler flowmetry for capturing microvascular blood flow dynamics from darkly pigmented skin.

OBJECTIVE: To assess the performance of laser Doppler flowmetry (LDF) in measuring blood perfusion from darkly-pigmented skin, i.e. skin with high melanin concentration. LDF provides for the noninvasive monitoring of microvascular blood flow dynamics. It has been used extensively on light-skinned subjects, i.e. on skin with low melanin concentration, in both the healthy and pathological states. Because the optical properties of human skin might affect the reliability of optically-based diagnostic equipment, the effectiveness of LDF needs to be checked and evaluated on dark skin, too, if this method is to be useful in global healthcare. APPROACH: Thirteen dark-skinned subjects and ten light-skinned subjects were included in the study. Microvascular blood flow dynamics was measured on both the right and left ankles using LDF with a laser diode of wavelength 780 nm. The characteristics of time-varying blood flow oscillations were investigated by wavelet analysis, nonlinear mode decomposition and wavelet phase coherence. An electrocardiogram (ECG), skin temperature, and respiratory effort were measured simultaneously with the LDF for each subject. MAIN RESULTS: No significant differences were observed between the groups in the mean blood perfusion (p  > 0.1), or wavelet power (p  > 0.6). The instantaneous heart rate (IHR), extracted from the LDF at each of the recording sites, and from the ECG, did not differ significantly between the groups (p  > 0.8). Nor did the wavelet power of the IHR differ (p  > 0.8) between the groups. The only significant difference found between the groups lay in left/right ankle blood flow coherence near the cardiac frequency, attributable to known ethnic physiological differences. SIGNIFICANCE: These results indicate that high melanin concentrations in skin exert no significant influence on the ability of LDF to monitor microvascular blood flow dynamics when using a laser diode of wavelength 780 nm. Hence LDF can help in the diagnosis and exploration of the pathogenesis of diseases such as diabetes, hypertension, or malaria in darkly pigmented patients across sub-Saharan Africa.

Exploring the pore charge dependence of K+ and Cl- permeation across a graphene monolayer: a molecular dynamics study.

Selective permeation through graphene nanopores is attracting increasing interest as an efficient and cost-effective technique for water desalination and purification. In this work, using umbrella sampling and molecular dynamics simulations with constant electric field, we analyze the influence of pore charge on potassium and chloride ion permeation. As pore charge is increased, the barrier of the potential of mean force (PMF) gradually decreases until it turns into a well split in two subminima. While in the case of K+ this pattern can be explained as an increasing electrostatic compensation of the desolvation cost, in the case of Cl- the pattern can be attributed to the accumulation of a concentration polarization layer of potassium ions screening pore charge. The analysis of potassium PMFs in terms of forces revealed a conflicting influence on permeation of van der Waals and electrostatic forces that both undergo an inversion of their direction as pore charge is increased. Even if the most important transition involves the interplay between the electrostatic forces exerted by graphene and water, the simulations also revealed an important role of the changing distribution of potassium and chloride ions. The influence of pore charge on the orientation of water molecules was also found to affect the van der Waals forces they exert on potassium.

Coherence and Coupling Functions Reveal Microvascular Impairment in Treated Hypertension.

The complex interactions that give rise to heart rate variability (HRV) involve coupled physiological oscillators operating over a wide range of different frequencies and length-scales. Based on the premise that interactions are key to the functioning of complex systems, the time-dependent deterministic coupling parameters underlying cardiac, respiratory and vascular regulation have been investigated at both the central and microvascular levels. Hypertension was considered as an example of a globally altered state of the complex dynamics of the cardiovascular system. Its effects were established through analysis of simultaneous recordings of the electrocardiogram (ECG), respiratory effort, and microvascular blood flow [by laser Doppler flowmetry (LDF)]. The signals were analyzed by methods developed to capture time-dependent dynamics, including the wavelet transform, wavelet-based phase coherence, non-linear mode decomposition, and dynamical Bayesian inference, all of which can encompass the inherent frequency and coupling variability of living systems. Phases of oscillatory modes corresponding to the cardiac (around 1.0 Hz), respiratory (around 0.25 Hz), and vascular myogenic activities (around 0.1 Hz) were extracted and combined into two coupled networks describing the central and peripheral systems, respectively. The corresponding spectral powers and coupling functions were computed. The same measurements and analyses were performed for three groups of subjects: healthy young (Y group, 24.4 ± 3.4 y), healthy aged (A group, 71.1 ± 6.6 y), and aged treated hypertensive patients (ATH group, 70.3 ± 6.7 y). It was established that the degree of coherence between low-frequency oscillations near 0.1 Hz in blood flow and in HRV time series differs markedly between the groups, declining with age and nearly disappearing in treated hypertension. Comparing the two healthy groups it was found that the couplings to the cardiac rhythm from both respiration and vascular myogenic activity decrease significantly in aging. Comparing the data from A and ATH groups it was found that the coupling from the vascular myogenic activity is significantly weaker in treated hypertension subjects, implying that the mechanisms of microcirculation are not completely restored by current anti-hypertension medications.

Neural Cross-Frequency Coupling Functions.

Although neural interactions are usually characterized only by their coupling strength and directionality, there is often a need to go beyond this by establishing the functional mechanisms of the interaction. We introduce the use of dynamical Bayesian inference for estimation of the coupling functions of neural oscillations in the presence of noise. By grouping the partial functional contributions, the coupling is decomposed into its functional components and its most important characteristics-strength and form-are quantified. The method is applied to characterize the δ-to-α phase-to-phase neural coupling functions from electroencephalographic (EEG) data of the human resting state, and the differences that arise when the eyes are either open (EO) or closed (EC) are evaluated. The δ-to-α phase-to-phase coupling functions were reconstructed, quantified, compared, and followed as they evolved in time. Using phase-shuffled surrogates to test for significance, we show how the strength of the direct coupling, and the similarity and variability of the coupling functions, characterize the EO and EC states for different regions of the brain. We confirm an earlier observation that the direct coupling is stronger during EC, and we show for the first time that the coupling function is significantly less variable. Given the current understanding of the effects of e.g., aging and dementia on δ-waves, as well as the effect of cognitive and emotional tasks on α-waves, one may expect that new insights into the neural mechanisms underlying certain diseases will be obtained from studies of coupling functions. In principle, any pair of coupled oscillations could be studied in the same way as those shown here.

Alterations in the coupling functions between cortical and cardio-respiratory oscillations due to anaesthesia with propofol and sevoflurane.

The precise mechanisms underlying general anaesthesia pose important and still open questions. To address them, we have studied anaesthesia induced by the widely used (intravenous) propofol and (inhalational) sevoflurane anaesthetics, computing cross-frequency coupling functions between neuronal, cardiac and respiratory oscillations in order to determine their mutual interactions. The phase domain coupling function reveals the form of the function defining the mechanism of an interaction, as well as its coupling strength. Using a method based on dynamical Bayesian inference, we have thus identified and analysed the coupling functions for six relationships. By quantitative assessment of the forms and strengths of the couplings, we have revealed how these relationships are altered by anaesthesia, also showing that some of them are differently affected by propofol and sevoflurane. These findings, together with the novel coupling function analysis, offer a new direction in the assessment of general anaesthesia and neurophysiological interactions, in general.

Nonlinear mode decomposition: a noise-robust, adaptive decomposition method.

The signals emanating from complex systems are usually composed of a mixture of different oscillations which, for a reliable analysis, should be separated from each other and from the inevitable background of noise. Here we introduce an adaptive decomposition tool-nonlinear mode decomposition (NMD)-which decomposes a given signal into a set of physically meaningful oscillations for any wave form, simultaneously removing the noise. NMD is based on the powerful combination of time-frequency analysis techniques-which, together with the adaptive choice of their parameters, make it extremely noise robust-and surrogate data tests used to identify interdependent oscillations and to distinguish deterministic from random activity. We illustrate the application of NMD to both simulated and real signals and demonstrate its qualitative and quantitative superiority over other approaches, such as (ensemble) empirical mode decomposition, Karhunen-Loève expansion, and independent component analysis. We point out that NMD is likely to be applicable and useful in many different areas of research, such as geophysics, finance, and the life sciences. The necessary matlab codes for running NMD are freely available for download.

On-road heavy-duty vehicle emissions monitoring system.

The introduction of particulate and oxides of nitrogen (NOx) after-treatment controls on heavy-duty vehicles has spurred the need for fleet emissions data to monitor their reliability and effectiveness. The University of Denver has developed a new method for rapidly measuring heavy-duty vehicles for gaseous and particulate fuel specific emissions. The method was recently used to collect 3088 measurements at a Port of Los Angeles location and a weigh station on I-5 in northern California. The weigh station NOx emissions for 2014 models are 73% lower than 2010 models (3.8 vs 13.9 gNOx/kg of fuel) and look to continue to decrease with newer models. The Port site has a heavy-duty fleet that has been entirely equipped with diesel particulate filters since 2010. Total particulate mass and black carbon measurements showed that only 3% of the Port vehicles measured exceed expected emission limits with mean gPM/kg of fuel emissions of 0.031 ± 0.007 and mean gBC/kg of fuel emissions of 0.020 ± 0.003. Mean particulate emissions were higher for the older weigh station fleet but 2011 and newer trucks gPM/kg of fuel emissions were nevertheless more than a factor of 30 lower than the means for pre-DPF (2007 and older) model years.

Ageing of the couplings between cardiac, respiratory and myogenic activity in humans.

The balance and functionality of the cardiovascular system are maintained by a network of couplings between the different oscillations involved. We study the effect of ageing on these interactions through the application of wavelet analysis, and by the use of dynamical Bayesian inference to compute coupling functions. The method, applied to phases extracted from microvascular flow recorded by laser Doppler flowmetry (LDF), reveals the coupling functions between oscillations propagated to the smallest vessels. Consistent with earlier work based on analysis of cardiac and respiratory phases obtained from direct measurements, our analysis demonstrates an impairment of the propagated cardio-respiratory coupling with ageing. The coupling weakens despite the increased cardiac component in the LDF with ageing. Our results bring new insight to the effect of ageing on cardiovascular regulation that might help improve the diagnostic potential of LDF monitors.

Dynamical inference: where phase synchronization and generalized synchronization meet.

Synchronization is a widespread phenomenon that occurs among interacting oscillatory systems. It facilitates their temporal coordination and can lead to the emergence of spontaneous order. The detection of synchronization from the time series of such systems is of great importance for the understanding and prediction of their dynamics, and several methods for doing so have been introduced. However, the common case where the interacting systems have time-variable characteristic frequencies and coupling parameters, and may also be subject to continuous external perturbation and noise, still presents a major challenge. Here we apply recent developments in dynamical Bayesian inference to tackle these problems. In particular, we discuss how to detect phase slips and the existence of deterministic coupling from measured data, and we unify the concepts of phase synchronization and general synchronization. Starting from phase or state observables, we present methods for the detection of both phase and generalized synchronization. The consistency and equivalence of phase and generalized synchronization are further demonstrated, by the analysis of time series from analog electronic simulations of coupled nonautonomous van der Pol oscillators. We demonstrate that the detection methods work equally well on numerically simulated chaotic systems. In all the cases considered, we show that dynamical Bayesian inference can clearly identify noise-induced phase slips and distinguish coherence from intrinsic coupling-induced synchronization.

Wave turbulence in quantum fluids.

Wave turbulence (WT) occurs in systems of strongly interacting nonlinear waves and can lead to energy flows across length and frequency scales much like those that are well known in vortex turbulence. Typically, the energy passes although a nondissipative inertial range until it reaches a small enough scale that viscosity becomes important and terminates the cascade by dissipating the energy as heat. Wave turbulence in quantum fluids is of particular interest, partly because revealing experiments can be performed on a laboratory scale, and partly because WT among the Kelvin waves on quantized vortices is believed to play a crucial role in the final stages of the decay of (vortex) quantum turbulence. In this short review, we provide a perspective on recent work on WT in quantum fluids, setting it in context and discussing the outlook for the next few years. We outline the theory, review briefly the experiments carried out to date using liquid H2 and liquid (4)He, and discuss some nonequilibrium excitonic superfluids in which WT has been predicted but not yet observed experimentally. By way of conclusion, we consider the medium- and longer-term outlook for the field.