Synchronization transitions in Kuramoto networks with higher-mode interaction.

Synchronization is an omnipresent collective phenomenon in nature and technology, whose understanding is still elusive for real-world systems in particular. We study the synchronization transition in a phase oscillator system with two nonvanishing Fourier-modes in the interaction function, hence going beyond the Kuramoto paradigm. We show that the transition scenarios crucially depend on the interplay of the two coupling modes. We describe the multistability induced by the presence of a second coupling mode. By extending the collective coordinate approach, we describe the emergence of various states observed in the transition from incoherence to coherence. Remarkably, our analysis suggests that, in essence, the two-mode coupling gives rise to states characterized by two independent but interacting groups of oscillators. We believe that these findings will stimulate future research on dynamical systems, including complex interaction functions beyond the Kuramoto-type.

Eight new species of the genus Nesamblyops Jeannel (Anillini: Carabidae: Coleoptera) from New Zealand with notes about dispersal of the genus to the North Island.

Species of flightless litter ground beetles of the tribe Anillini, genus Nesamblyops, from the North Island and from the north-eastern part of the South Island are revised. Eight new species are described and one previously known species, Nesamblyops oreobius (Broun), is re-described. Nesamblyops oreobius, the only hitherto recorded species from the North Island, is most similar to the group of two new species from the South Island, N. confusus n. sp. (type locality: New Zealand, Marlborough Sounds, Mount Stokes) and N. lescheni n. sp. (type locality: New Zealand, Marlborough Sounds, D'Urville Island), based on the structure of the male genitalia. The second species of the genus known from the North Island, N. tararua n. sp. (type locality: New Zealand, Wellington, Tararua Range) represents another lineage, based on the structure of the male genitalia, and is closely related to a group of three new species from the South Island, N. brouni n. sp. (type locality: New Zealand, Canterbury, Southern Alps, Lewis Pass), N. distinctus n. sp. (type locality: New Zealand, Marlborough, Richmond Range, Fabians Valley), and N. townsendi n. sp. (type locality: New Zealand, Marlborough Sounds, Tennyson Inlet). Nesamblyops carltoni n. sp. (type locality: New Zealand, Nelson, Richmond Range, Dun Mountain) and N. parvulus n. sp. (type locality: New Zealand, Marlborough Sounds, Mount Stokes), both from the South Island occupy an isolated position among the examined species. All species are illustrated with digital images of habitus, body parts, and drawings of genitalia. Distribution maps for all species are also provided. Geographical evidence of Nesamblyops dispersal to the North Island is discussed, based on distributional data.

Heterogeneous Nucleation in Finite-Size Adaptive Dynamical Networks.

Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural sciences. In dynamical networks, phase transitions organize qualitative changes in the collective behavior of coupled dynamical units. Adaptive dynamical networks feature a connectivity structure that changes over time, coevolving with the nodes' dynamical state. In this Letter, we show the emergence of two distinct first-order nonequilibrium phase transitions in a finite-size adaptive network of heterogeneous phase oscillators. Depending on the nature of defects in the internal frequency distribution, we observe either an abrupt single-step transition to full synchronization or a more gradual multistep transition. This observation has a striking resemblance to heterogeneous nucleation. We develop a mean-field approach to study the interplay between adaptivity and nodal heterogeneity and describe the dynamics of multicluster states and their role in determining the character of the phase transition. Our work provides a theoretical framework for studying the interplay between adaptivity and nodal heterogeneity.

Linear Response and Fluctuation-Dissipation Relations for Brownian Motion under Resetting.

We consider fluctuation-dissipation relations (FDRs) for a Brownian motion under renewal resetting with arbitrary waiting time distribution between the resetting events. We show that if the distribution of waiting times of the resetting process possesses the second moment, the usual (generalized) FDR and the equivalent generalized Einstein's relation (GER) apply for the response function of the coordinate. If the second moment of waiting times diverges but the first one stays finite, the static susceptibility diverges, the usual FDR breaks down, but the GER still applies. In any of these situations, the fluctuation dissipation relations define the effective temperature of the system which is twice as high as the temperature of the medium in which the Brownian motion takes place.

Decoding the double trouble: A mathematical modelling of co-infection dynamics of SARS-CoV-2 and influenza-like illness.

After the detection of coronavirus disease 2019 (Covid-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in Wuhan, Hubei Province, China in late December, the cases of Covid-19 have spiralled out around the globe. Due to the clinical similarity of Covid-19 with other flulike syndromes, patients are assayed for other pathogens of influenza like illness. There have been reported cases of co-infection amongst patients with Covid-19. Bacteria for example Streptococcus pneumoniae, Staphylococcus aureus, Klebsiella pneumoniae, Mycoplasma pneumoniae, Chlamydia pneumonia, Legionella pneumophila etc and viruses such as influenza, coronavirus, rhinovirus/enterovirus, parainfluenza, metapneumovirus, influenza B virus etc are identified as co-pathogens. In our current effort, we develop and analysed a compartmental based Ordinary Differential Equation (ODE) type mathematical model to understand the co-infection dynamics of Covid-19 and other influenza type illness. In this work we have incorporated the saturated treatment rate to take account of the impact of limited treatment resources to control the possible Covid-19 cases. As results, we formulate the basic reproduction number of the model system. Finally, we have performed numerical simulations of the co-infection model to examine the solutions in different zones of parameter space.

Fourteen new species of the genus Nesamblyops Jeannel (Coleoptera: Carabidae: Anillini) from the South Island of New Zealand with redescription of the genus and description of a new subtribe.

Fourteen new species of flightless litter ground beetles of the tribe Anillini, genus Nesamblyops, from the South Island of New Zealand, are described. The only hitherto described species from the South Island, Nesamblyops subcaecus (Broun), is similar to the new species from Southland, N. viator n. sp. (type locality: New Zealand, South Island, Fiordland, Resolution Island), based on the structure of male genitalia. The species assembly inhabiting the northwest corner of the South Island comprises two partly sympatric groups composed of three related allopatric species each. The first group includes N. canaanensis n. sp. (type locality: New Zealand, South Island, Nelson, Abel Tasman National Park, Canaan area), N. hobbit n. sp. (type locality: New Zealand, South Island, Nelson, Kahurangi National Park, Mt Domett), and N. ovipennis n. sp. (type locality: New Zealand, South Island, Nelson, Kahurangi National Park, Mt Arthur). The second group represents another lineage and contains N. rotundicollis n. sp. (type locality: New Zealand, South Island, Nelson, Kahurangi National Park, Onekaka area), N. solitarius n. sp. (type locality: New Zealand, South Island, West Coast, western foothills of Victoria Range, Capleston area), and N. subrufus n. sp. (type locality: New Zealand, South Island, West Coast, Upper Buller Gorge, Dublin Terrace). Three additional species known from the northwest corner of the South Island, based on the structure of male genitalia, are unrelated to each other and remaining species of the region. These are N. karamea n. sp. (type locality: New Zealand, South Island, West Coast, Kahurangi National Park, the Karamea River Gorge area), N. montanus n. sp. (type locality: New Zealand, South Island, Nelson, Kahurangi National Park, Lake Sylvester area), and N. kuscheli n. sp. (type locality: New Zealand, South Island, Nelson, Kahurangi National Park, Mt Arthur). The latter species is presumably closely related to the species from the central parts of the West Coast, N. moorei n. sp., (type locality: New Zealand, South Island, West Coast, Ngahere area, Mawhera Forest). Additionally, the central part of the West Coast is inhabited by a small group of two species, N. disjunctus n. sp. (type locality: New Zealand, South Island, West Coast, E slope of the Paparoa Range, Fletcher Creek area), and N. victoriae n. sp. (type locality: New Zealand, South Island, West Coast, Victoria Range, Capleston area). According to the structure of the male genitalia, this group represents a separate lineage within the genus. The most unusual structure of male genitalia belongs to a species without eyes, a trait previously unknown in Nesamblyops, N. magnificus n. sp. (type locality: New Zealand, South Island, Coastal Otago, Allison Conservation Area) that inhabits the southeast corner of the South Island. Digital images of habitus, body parts, drawings of genitalia, as well as distribution maps are provided for all described species. Morphological evidence of the isolated position of Nesamblyops within the tribe Anillini is discussed, with a focus on the morphological comparison of Nesamblyops with the members of Anillini, Tachyini, Bembidiini, Zolini, and Sinozolini, and on the data of published molecular analyses. A new subtribe for the representatives of the genus, Nesamblyopina, n. subtr., is proposed; the newly discovered morphological characters have been incorporated in the redescription of the genus.

Finite-time recurrence analysis of chaotic trajectories in Hamiltonian systems.

In this work, we show that a finite-time recurrence analysis of different chaotic trajectories in two-dimensional non-linear Hamiltonian systems provides useful prior knowledge of their dynamical behavior. By defining an ensemble of initial conditions, evolving them until a given maximum iteration time, and computing the recurrence rate of each orbit, it is possible to find particular trajectories that widely differ from the average behavior. We show that orbits with high recurrence rates are the ones that experience stickiness, being dynamically trapped in specific regions of the phase space. We analyze three different non-linear maps and present our numerical observations considering particular features in each of them. We propose the described approach as a method to visually illustrate and characterize regions in phase space with distinct dynamical behaviors.

Ticks on the Run: A Mathematical Model of Crimean-Congo Haemorrhagic Fever (CCHF)-Key Factors for Transmission.

Crimean-Congo haemorrhagic fever (CCHF) is a zoonotic disease caused by the Crimean-Congo hemorrhagic fever virus (CCHFV). Ticks of the genus Hyalomma are the main vectors and represent a reservoir for the virus. CCHF is maintained in nature in an endemic vertebrate-tick-vertebrate cycle. The disease is prevalent in wide geographical areas including Asia, Africa, South-Eastern Europe and the Middle East. It is of great importance for the public health given its occasionally high case/fatality ratio of CCHFV in humans. Climate change and the detection of possible CCHFV vectors in Central Europe suggest that the establishment of the transmission in Central Europe may be possible in future. We have developed a compartment-based nonlinear Ordinary Differential Equation (ODE) system to model the disease transmission cycle including blood sucking ticks, livestock and human. Sensitivity analysis of the basic reproduction number R0 shows that decreasing the tick survival time is an efficient method to control the disease. The model supports us in understanding the influence of different model parameters on the spread of CCHFV. Tick-to-tick transmission through co-feeding and the CCHFV circulation through transstadial and transovarial transmission are important factors to sustain the disease cycle. The proposed model dynamics are calibrated through an empirical multi-country analysis and multidimensional plot reveals that the disease-parameter sets of different countries burdened with CCHF are different. This information may help decision makers to select efficient control strategies.

Time-averaging and nonergodicity of reset geometric Brownian motion with drift.

How do near-bankruptcy events in the past affect the dynamics of stock-market prices in the future? Specifically, what are the long-time properties of a time-local exponential growth of stock-market prices under the influence of stochastically occurring economic crashes? Here, we derive the ensemble- and time-averaged properties of the respective "economic" or geometric Brownian motion (GBM) with a nonzero drift exposed to a Poissonian constant-rate price-restarting process of "resetting." We examine-based both on thorough analytical calculations and on findings from systematic stochastic computer simulations-the general situation of reset GBM with a nonzero [positive] drift and for all special cases emerging for varying parameters of drift, volatility, and reset rate in the model. We derive and summarize all short- and long-time dependencies for the mean-squared displacement (MSD), the variance, and the mean time-averaged MSD (TAMSD) of the process of Poisson-reset GBM under the conditions of both rare and frequent resetting. We consider three main regions of model parameters and categorize the crossovers between different functional behaviors of the statistical quantifiers of this process. The analytical relations are fully supported by the results of computer simulations. In particular, we obtain that Poisson-reset GBM is a nonergodic stochastic process, with generally MSD(Δ)≠TAMSD(Δ) and Variance(Δ)≠TAMSD(Δ) at short lag times Δ and for long trajectory lengths T. We investigate the behavior of the ergodicity-breaking parameter in each of the three regions of parameters and examine its dependence on the rate of reset at Δ/T≪1. Applications of these theoretical results to the analysis of prices of reset-containing options are pertinent.

At Least 10-fold Higher Lubricity of Molecularly Thin D2O vs H2O Films at Single-Layer Graphene-Mica Interfaces.

Interfacial water is a widespread lubricant down to the nanometer scale. We investigate the lubricities of molecularly thin H2O and D2O films confined between mica and graphene, via the relaxation of initially applied strain in graphene employing Raman spectroscopy. Surprisingly, the D2O films are at least 1 order of magnitude more lubricant than H2O films, despite the similar bulk viscosities of the two liquids. We propose a mechanism based on the known selective permeation of protons vs deuterons through graphene. Permeated protons and left behind hydroxides may form ion pairs clamping across the graphene sheet and thereby hindering the graphene from sliding on the water layer. This explains the lower lubricity but also the hindering diffusivity of the water layer, which yields a high effective viscosity in accordance with findings in dewetting experiments. Our work elucidates an unexpected effect and provides clues to the behavior of graphene on hydrous surfaces.

Nonergodicity of reset geometric Brownian motion.

We derive. the ensemble- and time-averaged mean-squared displacements (MSD, TAMSD) for Poisson-reset geometric Brownian motion (GBM), in agreement with simulations. We find MSD and TAMSD saturation for frequent resetting, quantify the spread of TAMSDs via the ergodicity-breaking parameter and compute distributions of prices. General MSD-TAMSD nonequivalence proves reset GBM nonergodic.

Convergence to a Gaussian by Narrowing of Central Peak in Brownian yet Non-Gaussian Diffusion in Disordered Environments.

In usual diffusion, the concentration profile, starting from an initial distribution showing sharp features, first gets smooth and then converges to a Gaussian. By considering several examples, we show that the art of convergence to a Gaussian in diffusion in disordered media with infinite contrast may be strikingly different: sharp features of initial distribution do not smooth out at long times. This peculiarity of the strong disorder may be of importance for diagnostics of disorder in complex, e.g., biological, systems.

Inertia triggers nonergodicity of fractional Brownian motion.

How related are the ergodic properties of the over- and underdamped Langevin equations driven by fractional Gaussian noise? We here find that for massive particles performing fractional Brownian motion (FBM) inertial effects not only destroy the stylized fact of the equivalence of the ensemble-averaged mean-squared displacement (MSD) to the time-averaged MSD (TAMSD) of overdamped or massless FBM, but also dramatically alter the values of the ergodicity-breaking parameter (EB). Our theoretical results for the behavior of EB for underdamped or massive FBM for varying particle mass m, Hurst exponent H, and trace length T are in excellent agreement with the findings of stochastic computer simulations. The current results can be of interest for the experimental community employing various single-particle-tracking techniques and aiming at assessing the degree of nonergodicity for the recorded time series (studying, e.g., the behavior of EB versus lag time). To infer FBM as a realizable model of anomalous diffusion for a set single-particle-tracking data when massive particles are being tracked, the EBs from the data should be compared to EBs of massive (rather than massless) FBM.

Time averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes.

How different are the results of constant-rate resetting of anomalous-diffusion processes in terms of their ensemble-averaged versus time-averaged mean-squared displacements (MSDs versus TAMSDs) and how does stochastic resetting impact nonergodicity? We examine, both analytically and by simulations, the implications of resetting on the MSD- and TAMSD-based spreading dynamics of particles executing fractional Brownian motion (FBM) with a long-time memory, heterogeneous diffusion processes (HDPs) with a power-law space-dependent diffusivity D(x)=D_{0}|x|^{γ} and their "combined" process of HDP-FBM. We find, inter alia, that the resetting dynamics of originally ergodic FBM for superdiffusive Hurst exponents develops disparities in scaling and magnitudes of the MSDs and mean TAMSDs indicating weak ergodicity breaking. For subdiffusive HDPs we also quantify the nonequivalence of the MSD and TAMSD and observe a new trimodal form of the probability density function. For reset FBM, HDPs and HDP-FBM we compute analytically and verify by simulations the short-time MSD and TAMSD asymptotes and long-time plateaus reminiscent of those for processes under confinement. We show that certain characteristics of these reset processes are functionally similar despite a different stochastic nature of their nonreset variants. Importantly, we discover nonmonotonicity of the ergodicity-breaking parameter EB as a function of the resetting rate r. For all reset processes studied we unveil a pronounced resetting-induced nonergodicity with a maximum of EB at intermediate r and EB∼(1/r)-decay at large r. Alongside the emerging MSD-versus-TAMSD disparity, this r-dependence of EB can be an experimentally testable prediction. We conclude by discussing some implications to experimental systems featuring resetting dynamics.

Scaled geometric Brownian motion features sub- or superexponential ensemble-averaged, but linear time-averaged mean-squared displacements.

Various mathematical Black-Scholes-Merton-like models of option pricing employ the paradigmatic stochastic process of geometric Brownian motion (GBM). The innate property of such models and of real stock-market prices is the roughly exponential growth of prices with time [on average, in crisis-free times]. We here explore the ensemble- and time averages of a multiplicative-noise stochastic process with power-law-like time-dependent volatility, σ(t)∼t^{α}, named scaled GBM (SGBM). For SGBM, the mean-squared displacement (MSD) computed for an ensemble of statistically equivalent trajectories can grow faster than exponentially in time, while the time-averaged MSD (TAMSD)-based on a sliding-window averaging along a single trajectory-is always linear at short lag times Δ. The proportionality factor between these the two averages of the time series is Δ/T at short lag times, where T is the trajectory length, similarly to GBM. This discrepancy of the scaling relations and pronounced nonequivalence of the MSD and TAMSD at Δ/T≪1 is a manifestation of weak ergodicity breaking for standard GBM and for SGBM with σ(t)-modulation, the main focus of our analysis. The analytical predictions for the MSD and mean TAMSD for SGBM are in quantitative agreement with the results of stochastic computer simulations.

Large deviations in continuous-time random walks.

We discuss large deviation properties of continuous-time random walks (CTRWs) and present a general expression for the large deviation rate in CTRWs in terms of the corresponding rates for the distributions of steps' lengths and waiting times. In the case of Gaussian distribution of steps' lengths the general expression reduces to a sequence of two Legendre transformations applied to the cumulant generating function of waiting times. The discussion of several examples (Bernoulli and Gaussian random walks with exponentially distributed waiting times, Gaussian random walks with one-sided Lévy and Pareto-distributed waiting times) reveals interesting general properties of such large deviations.

Two new species of the genus Anillinus Casey (Coleoptera, Carabidae, Anillini) from the southern United States.

Two new species of blind ground beetles are described from the southern United States. One species, Anillinus relictus sp. nov. (type locality: E of Oneonta, Blount County, Alabama), based on the structure of male genitalia, is similar to Texan Anillinus, in particular to the endogean A. sinuatus Jeannel. The second species, A. felicianus sp. nov. (type locality: 4 mi SW Jackson, West Feliciana Parish, Louisiana), is superficially similar to the endogean A. sinuaticollis Jeannel from Roane County, Tennessee, and represents the first record of the genus for the state of Louisiana. All species are illustrated with digital images of habitus, body parts, and male and female genitalia. Biogeographical and evolutionary implications of the new findings are discussed.

Non-Gaussian, transiently anomalous, and ergodic self-diffusion of flexible dumbbells in crowded two-dimensional environments: Coupled translational and rotational motions.

We employ Langevin-dynamics simulations to unveil non-Brownian and non-Gaussian center-of-mass self-diffusion of massive flexible dumbbell-shaped particles in crowded two-dimensional solutions. We study the intradumbbell dynamics of the relative motion of the two constituent elastically coupled disks. Our main focus is on effects of the crowding fraction ϕ and of the particle structure on the diffusion characteristics. We evaluate the time-averaged mean-squared displacement (TAMSD), the displacement probability-density function (PDF), and the displacement autocorrelation function (ACF) of the dimers. For the TAMSD at highly crowded conditions of dumbbells, e.g., we observe a transition from the short-time ballistic behavior, via an intermediate subdiffusive regime, to long-time Brownian-like spreading dynamics. The crowded system of dimers exhibits two distinct diffusion regimes distinguished by the scaling exponent of the TAMSD, the dependence of the diffusivity on ϕ, and the features of the displacement-ACF. We attribute these regimes to a crowding-induced transition from viscous to viscoelastic diffusion upon growing ϕ. We also analyze the relative motion in the dimers, finding that larger ϕ suppress their vibrations and yield strongly non-Gaussian PDFs of rotational displacements. For the diffusion coefficients D(ϕ) of translational and rotational motion of the dumbbells an exponential decay with ϕ for weak and a power-law variation D(ϕ)∝(ϕ-ϕ^{★})^{2.4} for strong crowding is found. A comparison of simulation results with theoretical predictions for D(ϕ) is discussed and some relevant experimental systems are overviewed.

Periodic coupling inhibits second-order consensus on networks.

Consensus algorithms on networks have received increasing attention in recent years for various applications, ranging from distributed decision making to multivehicle coordination. In particular, second-order consensus models take into account the Newtonian dynamics of interacting physical agents. For this model class, we uncover a mechanism inhibiting the formation of collective consensus states via rather small time-periodic coupling modulations. We treat the model in its spectral decomposition and find analytically that, for certain intermediate coupling frequencies, parametric resonance is induced on a network level-at odds with the expected emergence of consensus for very short and long coupling time scales. Our formalism precisely predicts those resonance frequencies and links them to the Laplacian spectrum of the static backbone network. The excitation of the system is furthermore quantified within the theory of parametric resonance, which we extend to the domain of networks with time-periodic couplings.

Brownian motion under noninstantaneous resetting in higher dimensions.

We consider Brownian motion under resetting in higher dimensions for the case when the return of the particle to the origin occurs at a constant speed. We investigate the behavior of the probability density function (PDF) and of the mean-squared displacement (MSD) in this process. We study two different resetting protocols: exponentially distributed time intervals between the resetting events (Poissonian resetting) and resetting at fixed time intervals (deterministic resetting). We moreover discuss a general problem of the invariance of the PDF with respect to the return speed, as observed in the one-dimensional system for Poissonian resetting, and show that this one-dimensional situation is the only one in which such an invariance can be found. However, the invariance of the MSD can still be observed in higher dimensions.