A variational approach to probing extreme events in turbulent dynamical systems

Extreme events are ubiquitous in a wide range of dynamical systems, including turbulent fluid flows, nonlinear waves, large scale networks and biological systems. Here, we propose a variational framework for probing conditions that trigger intermittent extreme events in high-dimensional nonlinear dynamical systems. We seek the triggers as the probabilistically feasible solutions of an appropriately constrained optimization problem, where the function to be maximized is a system observable exhibiting intermittent extreme bursts. The constraints are imposed to ensure the physical admissibility of the optimal solutions, i.e., significant probability for their occurrence under the natural flow of the dynamical system. We apply the method to a body-forced incompressible Navier--Stokes equation, known as the Kolmogorov flow. We find that the intermittent bursts of the energy dissipation are independent of the external forcing and are instead caused by the spontaneous transfer of energy from large scales to the mean flow via nonlinear triad interactions. The global maximizer of the corresponding variational problem identifies the responsible triad, hence providing a precursor for the occurrence of extreme dissipation events. Specifically, monitoring the energy transfers within this triad, allows us to develop a data-driven short-term predictor for the intermittent bursts of energy dissipation. We assess the performance of this predictor through direct numerical simulations.Comment: Minor revisions, generalized the constraints in Eq. (2

Closed-loop adaptive control of extreme events in a turbulent flow

Extreme events that arise spontaneously in chaotic dynamical systems often have an adverse impact on the system or the surrounding environment. As such, their mitigation is highly desirable. Here, we introduce a novel control strategy for mitigating extreme events in a turbulent shear flow. The controller combines a probabilistic prediction of the extreme events with a deterministic actuator. The predictions are used to actuate the controller only when an extreme event is imminent. When actuated, the controller only acts on the degrees of freedom that are involved in the formation of the extreme events, exerting minimal interference with the flow dynamics. As a result, the attractors of the controlled and uncontrolled systems share the same chaotic core (containing the non-extreme events) and only differ in the tail of their distributions. We propose that such adaptive low-dimensional controllers should be used to mitigate extreme events in general chaotic dynamical systems, beyond the shear flow considered here.Comment: In press in Phys. Rev. E. Includes minor revision

Reduced-order Description of Transient Instabilities and Computation of Finite-Time Lyapunov Exponents

High-dimensional chaotic dynamical systems can exhibit strongly transient features. These are often associated with instabilities that have finite-time duration. Because of the finite-time character of these transient events, their detection through infinite-time methods, e.g. long term averages, Lyapunov exponents or information about the statistical steady-state, is not possible. Here we utilize a recently developed framework, the Optimally Time-Dependent (OTD) modes, to extract a time-dependent subspace that spans the modes associated with transient features associated with finite-time instabilities. As the main result, we prove that the OTD modes, under appropriate conditions, converge exponentially fast to the eigendirections of the Cauchy--Green tensor associated with the most intense finite-time instabilities. Based on this observation, we develop a reduced-order method for the computation of finite-time Lyapunov exponents (FTLE) and vectors. In high-dimensional systems, the computational cost of the reduced-order method is orders of magnitude lower than the full FTLE computation. We demonstrate the validity of the theoretical findings on two numerical examples

Relative periodic orbits form the backbone of turbulent pipe flow

The chaotic dynamics of low-dimensional systems, such as Lorenz or Rössler flows, is guided by the infinity of periodic orbits embedded in their strange attractors. Whether this is also the case for the infinite-dimensional dynamics of Navier–Stokes equations has long been speculated, and is a topic of ongoing study. Periodic and relative periodic solutions have been shown to be involved in transitions to turbulence. Their relevance to turbulent dynamics – specifically, whether periodic orbits play the same role in high-dimensional nonlinear systems like the Navier–Stokes equations as they do in lower-dimensional systems – is the focus of the present investigation. We perform here a detailed study of pipe flow relative periodic orbits with energies and mean dissipations close to turbulent values. We outline several approaches to reduction of the translational symmetry of the system. We study pipe flow in a minimal computational cell at , and report a library of invariant solutions found with the aid of the method of slices. Detailed study of the unstable manifolds of a sample of these solutions is consistent with the picture that relative periodic orbits are embedded in the chaotic saddle and that they guide the turbulent dynamics

Recreational drug use and use of drugs associated with chemsex among HIV-negative and HIV-positive heterosexual men and women attending sexual health and HIV clinics in England

Background: There is little information on the prevalence of recreational drug use among UK heterosexual men and women, in particular on use of drugs associated with ‘chemsex’ within gay communities. The aim of this study was to examine among HIV-negative and HIV-positive heterosexual men and women in England: (i) the prevalence of recreational drug use (including use of drugs associated with chemsex), (ii) socio-economic/lifestyle correlates of drug use, and (iii) the association of drug use with sexual behavior measures and mental health symptoms. Methods: Data are from the AURAH study of HIV-negative individuals attending sexual health clinics across England (2013–2014) and the ASTRA study of HIV-positive individuals attending HIV outpatient clinics in England (2011–2012). Prevalence of recreational drug use (past three months) and associations are presented separately among the four sample groups: HIV-negative (N = 470) and HIV-positive (N = 373) heterosexual men and HIVnegative (N = 676) and HIV-positive (N = 637) women. Results: The age standardized prevalence of any drug use was 22.9%, 17.1%, 15.3%, and 7.1% in the four sample groups respectively. In all groups, cannabis was the drug most commonly used (range from 4.7% to 17.9%) followed by cocaine (1.6% to 8.5%). The prevalence of use of drugs associated with chemsex was very low among HIV-negative participants (1.0% heterosexual men, 0.2% women) and zero among HIV-positive men and women. In age-adjusted analysis, factors linked to drug use overall and/or to cannabis and cocaine use specifically in the four sample groups included Black/mixed Caribbean and white (vs. Black/mixed African) ethnicity, lower level of education , cigarette smoking, and higher risk alcohol consumption. Associations of recreational drug use with measures of condomless sex, depression, and anxiety were observed in the four groups, but were particularly strong/apparent among women. Conclusion: Providers need to be aware of cannabis and cocaine use and its potential link with sexual risk behavior and symptoms of depression and anxiety among heterosexual men and women attending sexual health and HIV clinics

A Cross-Sectional Study on Attitudes to and Understanding of Risk of Acquisition of HIV: Design, Methods and Participant Characteristics

Background: The annual number of new human immunodeficiency virus (HIV) infections in the United Kingdom among men who have sex with men (MSM) has risen, and remains high among heterosexuals. Increasing HIV transmission among MSM is consistent with evidence of ongoing sexual risk behavior in this group, and targeted prevention strategies are needed for those at risk of acquiring HIV. Objective: The Attitudes to and Understanding of Risk of Acquisition of HIV (AURAH) study was designed to collect information on HIV negative adults at risk of HIV infection in the United Kingdom, based on the following parameters: physical and mental health, lifestyle, patterns of sexual behaviour, and attitudes to sexual risk. Methods: Cross-sectional questionnaire study of HIV negative or undiagnosed sexual health clinic attendees in the United Kingdom from 2013-2014. Results: Of 2630 participants in the AURAH study, 2064 (78%) were in the key subgroups of interest; 580 were black Africans (325 females and 255 males) and 1484 were MSM, with 27 participants belonging to both categories. Conclusions: The results from AURAH will be a significant resource to understand the attitudes and sexual behaviour of those at risk of acquiring HIV within the United Kingdom. AURAH will inform future prevention efforts and targeted health promotion initiatives in the HIV negative population

Partnership and Capacity Building of Local Governance

Partnership is about sharing of power, responsibility and achievements. According to the World Bank Public Private Partnership (PPP) promoting group, ―partnership refer to informal and shortterm engagements of non-governmental organizations, the private sector and/or government agencies that join forces for a shared objective; to more formal, but still short-term private sector engagements for the provision of specific services, for example, annual outsourcing arrangements for janitorial services for a school or operations of the school cafeteria; to more complex contractual arrangements, such as build, operate, transfer regimes, where the private sector takes on considerable risk and remains engaged long term; or to full privatizations‖ (World Bank Group 2014, 29).© Springer Nature Switzerland AG 2020. This is a post-peer-review, pre-copyedit version of an article published in Partnerships for the Goals. Encyclopedia of the UN Sustainable Development Goals. The final authenticated version is available online at: http://dx.doi.org/10.1007/978-3-319-71067-9_21-1.fi=vertaisarvioitu|en=peerReviewed