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We introduce a low-frequency torsional oscillator suitable for studies of quantum fluids and solids. It operates at frequencies of ∼100 Hz, achieves velocities of several cm s−1, and exhibits a quality factor of Q ≃ 3 × 10 4. In order to reach such velocities at this relatively low frequency, the oscillator amplitude must exceed 100 μm, which would be impracticable for a conventional capacitor-driven device where the drive is applied parallel to the main motion and there are correspondingly large changes in the separation of the capacitor plates. For the different geometry of the oscillator that we now describe, however, the separations of both the drive and detect capacitor plates remain constant regardless of the amplitude of oscillation. We discuss its design and report our initial tests of its performance.

In order to permeate a nanopore, an ion must overcome a dehydration energy barrier caused by the redistribution of surrounding water molecules. The redistribution is inhomogeneous, anisotropic and strongly position-dependent, resulting in complex patterns that are routinely observed in molecular dynamics simulations. Here, we study the physical origin of these patterns and of how they can be predicted and controlled. We introduce an analytic model able to predict the patterns in a graphene nanopore in terms of experimentally accessible radial distribution functions, giving results that agree well with molecular dynamics simulations. The patterns are attributable to a complex interplay of ionic hydration shells with water layers adjacent to the graphene membrane and with the hydration cloud of the nanopore rim atoms, and we discuss ways of controlling them. Our findings pave the way to designing required transport properties into nanoionic devices by optimising the structure of the hydration patterns.

The permeation of ions through narrow water-filled channels is essential to life and of rapidly-growing importance in technology. Reaching an understanding of the mechanisms underlying the permeation process requires an interdisciplinary approach, where ideas drawn from physics are of particular importance and have brought encouraging progress in recent years. This Introduction sets into context the several ground-breaking papers presented in the Entropy Special Issue on “The Physics of Ionic Conduction in Narrow Biological and Artificial Channels.

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.

We analyse the time-series evolution of the cumulative number of confirmed cases of COVID-19, the novel coronavirus disease, for some African countries. We propose a mathematical model, incorporating non-pharmaceutical interventions to unravel the disease transmission dynamics. Analysis of the stability of the model's steady states was carried out, and the reproduction number R 0 , a vital key for flattening the time-evolution of COVID-19 cases, was obtained by means of the next generation matrix technique. By dividing the time evolution of the pandemic for the cumulative number of confirmed infected cases into different regimes or intervals, hereafter referred to as phases, numerical simulations were performed to fit the proposed model to the cumulative number of confirmed infections for different phases of COVID-19 during its first wave. The estimated R 0 declined from 2.452-9.179 during the first phase of the infection to 1.374-2.417 in the last phase. Using the Atangana-Baleanu fractional derivative, a fractional COVID-19 model is proposed and numerical simulations performed to establish the dependence of the disease dynamics on the order of the fractional derivatives. An elasticity and sensitivity analysis of R 0 was carried out to determine the most significant parameters for combating the disease outbreak. These were found to be the effective disease transmission rate, the disease diagnosis or case detection rate, the proportion of susceptible individuals taking precautions, and the disease infection rate. Our results show that if the disease infection rate is less than 0.082/day, then R 0 is always less than 1; and if at least 55.29% of the susceptible population take precautions such as regular hand washing with soap, use of sanitizers, and the wearing of face masks, then the reproduction number R 0 remains below unity irrespective of the disease infection rate. Keeping R 0 values below unity leads to a decrease in COVID-19 prevalence.

Highlights • Vibrational resonance (VR) is reported in a Rayleigh-Plesset gas bubble model. • The complex dynamics is described by a classical particle in a time-dependent single or double-well potential. • Single and multiple VR can occur by the variation of the parameters of the acoustic waves and the properties of the liquid., The phenomenon of vibrational resonance (VR) has been investigated in a Rayleigh-Plesset oscillator for a gas bubble oscillating in an incompressible liquid while driven by a dual-frequency force consisting of high-frequency, amplitude-modulated, weak, acoustic waves. The complex equation of the Rayleigh-Plesset bubble oscillator model was expressed as the dynamics of a classical particle in a potential well of the Liénard type, thus allowing us to use both numerical and analytic approaches to investigate the occurrence of VR. We provide clear evidence that an acoustically-driven bubble oscillates in a time-dependent single or double-well potential whose properties are determined by the density of the liquid and its surface tension. We show both theoretically and numerically that, besides the VR effect facilitated by the variation of the parameters on which the high-frequency depends, amplitude modulation, the properties of the liquid in which the gas bubble oscillates contribute significantly to the occurrence of VR. In addition, we discuss the observation of multiple resonances and their origin for the double-well case, as well as their connection to the low frequency, weak, acoustic force field.

We show how a non-autonomous dynamics approach using time-resolved analyses of power spectra and phase coherence can help in the noninvasive diagnosis of malaria. The work is based on studying oscillations in blood flow and the variability of the heart and respiratory frequencies. The model used assumes that the heart and respiration are two oscillatory pumps with variable frequencies and that the vascular resistance also changes in an oscillatory manner. Red blood cells circulating through the system deliver oxygen to each cell. Malaria changes the red blood cells so that this delivery is compromised. The oscillatory properties of both pumps are also affected. We quantify the latter and compare three groups of subjects: febrile malaria patients (37); non-febrile malaria patients (10); and healthy controls (51). For each subject, time series of skin blood flow, respiratory effort, cardiac activity (ECG) and skin temperature were recorded simultaneously over an interval of 30 minutes. The oscillatory components within the range 0.005–2 Hz were analysed and their degree of coordination throughout the cardiovascular system was assessed by wavelet phase coherence analysis. It is shown that malaria, either febrile or non-febrile, substantially reduces the coordination.

We have measured signals induced in 5 Corbino electrodes by spontaneous oscillations of 2D surface electrons on liquid helium at $\sim$0.3\,K, with a perpendicular magnetic field and microwave radiation. Analysis using multi-scale, time-resolved, methods yields results consistent with magnetoplasmons modulated by slow surface gravity waves, with the latter requiring consideration of the 3rd dimension. Calculation of phase differences and phase coherences between signals from differently-positioned pairs of electrodes enables reconstruction of the electron dynamics on the helium surface., Comment: 6 pages,4 figures

We introduce a statistical and linear response theory of selective conduction in biological ion channels with multiple binding sites and possible point mutations. We derive an effective grand-canonical ensemble and generalised Einstein relations for the selectivity filter, assuming strongly coordinated ionic motion, and allowing for ionic Coulomb blockade. The theory agrees well with data from the KcsA K$^+$ channel and a mutant. We show that the Eisenman relations for thermodynamic selectivity follow from the condition for fast conduction and find that maximum conduction requires the binding sites to be nearly identical.

We consider an atomistic model of thermal welding at the polymer-polymer interface of a polyetherimide/polycarbonate blend, motivated by applications to 3D manufacturing in space. We follow diffusion of semiflexible chains at the interface and analyze strengthening of the samples as a function of the welding time tw by simulating the strain-stress and shear viscosity curves. The time scales for initial wetting, and for fast and slow diffusion, are revealed. It is shown that each component of the polymer blend has its own characteristic time of slow diffusion at the interface. Analysis of strainstress demonstrates saturation of the Young’s modulus at tw = 240 ns, while the tensile strength continues to increase. The shear viscosity is found to have a very weak dependence on the welding time for tw > 60 ns. It is shown that both strain-stress and shear viscosity curves agree with experimental data.

We investigate the response of a quantum particle in the Tietz-Hua quantum potential driven by biharmonic fields: a low-frequency force and a very high frequency force. The response is characterized by the occurrence of a maximum in the first-order transition probability amplitude ${|s|}^{2}$ under the influence of the applied fields. It is shown that in the absence of the high-frequency component of the applied fields, ${|s|}^{2}$ shows a distinct sequence of resonances, whereas an increase in the amplitude of the high-frequency field induces minima in ${|s|}^{2}$. However, the ${|s|}^{2}$ maximum occurs in the low-frequency regime where it may be considered otherwise weak in the presence of a single harmonic force.

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.

We show that, in strongly chaotic dynamical systems, the average particle velocity can be calculated analytically by consideration of Brownian dynamics in phase space, the method of images and 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 (KAM) islands. The calculated average velocities agree well with numerical simulations and with an earlier empirical theory. The procedure can readily be extended to other systems including time-dependent billiards., Submitted to Chaos

Just lifting a finger involves the coordinated opening and closing of billions of ion channels. These natural nanotubes play an essential role in the physiology of all living creatures, from bacteria to humans [1, 2]. By providing for the exchange of ions across cellular membranes, they control a vast range of biological processes, and their dysfunction leads to numerous diseases.

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’.

We address the increase of electron drift velocity that arises in semiconductor superlattices (SLs) subjected to constant electric and magnetic fields. It occurs if the magnetic field possesses nonzero components both along and perpendicular to the SL axis and the Bloch oscillations along the SL axis become resonant with cyclotron rotation in the transverse plane. It is a phenomenon of considerable interest, so that it is important to understand the underlying mechanism. In an earlier Letter (Phys. Rev. Lett. 114, 166802 (2015)) we showed that, contrary to a general belief that drift enhancement occurs through chaotic diffusion along a stochastic web (SW) within semiclassical collisionless dynamics, the phenomenon actually arises through a non-chaotic mechanism. In fact, any chaos that occurs tends to reduce the drift. We now provide fuller details, elucidating the mechanism in physical terms, and extending the investigation. In particular, we: (i) demonstrate that pronounced drift enhancement can still occur even in the complete absence of an SW; (ii) show that, where an SW does exist and its characteristic slow dynamics comes into play, it suppresses the drift enhancement even before strong chaos is manifested; (iii) generalize our theory for non-small temperature, showing that heating does not affect the enhancement mechanism and accounting for some earlier numerical observations; (iv) demonstrate that certain analytic results reported previously are incorrect; (v) provide an extended critical review of the subject and closely related issues; and (vi) discuss some challenging problems for the future., 28 pages (including a detailed Contents, for convenience), 12 figures (some of them use postscript files of a reduced size: figures by the full-size files can be seen in the journal version)

Stars pulsate and their nature of their pulsations can provide a great deal of information about them including, for example, their masses, radii and ages. Oscillations in stellar brightness were first observed long ago, at the end of the sixteenth century. Since then, it has been established the phenomenon is seemingly a ubiquitous feature of stars and its study has been named asteroseismology.

Mutation-induced transformations of conductivity and selectivity in NaChBac bacterial channels are studied experimentally and interpreted within the framework of ionic Coulomb blockade (ICB), while also taking account of resonant quantised dehydration (QD) and site protonation. Site-directed mutagenesis and whole-cell patch-clamp experiments are used to investigate how the fixed charge Qf at the selectivity filter (SF) affects both valence selectivity and same-charge selectivity. The new ICB/QD model predicts that increasing |Qf | should lead to a shift in selectivity sequences towards larger ion sizes, in agreement with the present experiments and with earlier work. Comparison of the model with experimental data leads to the introduction of an effective charge Qf∗ at the SF, which was found to differ between Aspartate and Glutamate charged rings, and also to depend on position within the SF. It is suggested that protonation of the residues within the restricted space of the SF is important in significantly reducing the effective charge of the EEEE ring. Values of Qf∗ derived from experiments on divalent blockade agree well with expectations based on the ICB/QD model and have led to the first demonstration of ICB oscillations in Ca2+ conduction as a function of the fixed charge. Preliminary studies of the dependence of Ca2+ conduction on pH are qualitatively consistent with the predictions of the model.

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. Th 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.