Fluid dynamics of bacterial turbulence

Self-sustained turbulent structures have been observed in a wide range of living fluids, yet no quantitative theory exists to explain their properties. We report experiments on active turbulence in highly concentrated 3D suspensions of Bacillus subtilis and compare them with a minimal fourth-order vector-field theory for incompressible bacterial dynamics. Velocimetry of bacteria and surrounding fluid, determined by imaging cells and tracking colloidal tracers, yields consistent results for velocity statistics and correlations over two orders of magnitude in kinetic energy, revealing a decrease of fluid memory with increasing swimming activity and linear scaling between energy and enstrophy. The best-fit model parameters allow for quantitative agreement with experimental data.Comment: 5 pages, 4 figure

Efficient approximation of high-dimensional exponentials by tensornetworks

In this work a general approach to compute a compressed representation of the exponential $\exp(h)$ of a high-dimensional function $h$ is presented. Such exponential functions play an important role in several problems in Uncertainty Quantification, e.g. the approximation of log-normal random fields or the evaluation of Bayesian posterior measures. Usually, these high-dimensional objects are intractable numerically and can only be accessed pointwise in sampling methods. In contrast, the proposed method constructs a functional representation of the exponential by exploiting its nature as a solution of an ordinary differential equation. The application of a Petrov--Galerkin scheme to this equation provides a tensor train representation of the solution for which we derive an efficient and reliable a posteriori error estimator. Numerical experiments with a log-normal random field and a Bayesian likelihood illustrate the performance of the approach in comparison to other recent low-rank representations for the respective applications. Although the present work considers only a specific differential equation, the presented method can be applied in a more general setting. We show that the composition of a generic holonomic function and a high-dimensional function corresponds to a differential equation that can be used in our method. Moreover, the differential equation can be modified to adapt the norm in the a posteriori error estimates to the problem at hand

A Systematic and Critical Review of Discrete Choice Experiments in Asthma and Chronic Obstructive Pulmonary Disease

BACKGROUND: Regulators have called for greater emphasis on the role of the patient voice to inform medical product development and decision making, and expert guidelines and reports for asthma and chronic obstructive pulmonary disease (COPD) both explicitly recommend the consideration of patient preferences in the management of these diseases. Discrete choice experiments (DCEs) are commonly used to quantify stakeholders’ treatment preferences and estimate the trade-offs they are willing to make between outcomes such as treatment benefits and risks. OBJECTIVE: The aim of this systematic literature review is to provide an up-to-date and critical review of DCEs published in asthma and COPD; specifically, we aim to evaluate the subject of preference studies conducted in asthma and COPD, what attributes have been included, stakeholders’ preferences, and the consistency in reporting of instrument development, testing and reporting of results. METHODS: A systematic review of published DCEs on asthma and COPD treatments was conducted using Embase, Medline and the Cochrane Database of Systematic Reviews. Studies were included if they included a DCE conducted in a relevant population (e.g. patients with asthma or COPD or their caregivers, asthma or COPD-treating clinicians, or the general population), and reported quantitative outcomes on participants’ preferences. Study characteristics were summarised descriptively, and descriptive analyses of attribute categories, consistency in reporting on key criteria, and stakeholder preferences were undertaken. RESULTS: A total of 33 eligible studies were identified, including 28 unique DCEs. The majority (n = 20; 71%) of studies were conducted in a patient sample. Studies focused on inhaler treatments, and included attributes in five key categories: symptoms and treatment benefits (n = 23; 82%), treatment convenience (n = 19; 68%), treatment cost (n = 17; 61%), treatment risks (n = 13; 46%), and other (n = 10; 36%). Symptoms and treatment benefits were the attributes most frequently ranked as important to patients (n = 26, 72%), followed by treatment risks (n = 7, 39%). Several studies (n = 9, 32%) did not qualitatively pre-test their DCE, and a majority did not report the uncertainty in estimated outcomes (n = 18; 64%). CONCLUSIONS: DCEs in asthma and COPD have focused on treatment benefits and convenience, with less evidence generated on participants’ risk tolerance. Quality criteria and reporting standards are needed to promote study quality and ensure consistency in reporting between studies. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s40271-021-00536-w

Decision heuristic or preference? Attribute non-attendance in discrete choice problems

Funded by National Clinical Assessment Service (NCAS) and Institute of Applied Health SciencePeer reviewedPostprin

Correction to: A Systematic and Critical Review of Discrete Choice Experiments in Asthma and Chronic Obstructive Pulmonary Disease (Jul, 10.1007/s40271-.021-.00536-w, 2021)

The article “A Systematic and Critical Review of Discrete Choice Experiments in Asthma and Chronic Obstructive Pulmonary Disease”, written by Hannah Collacott, Dian Zhang, Sebastian Heidenreich and Tommi Tervonen1 was originally published electronically on the publisher’s internet portal on 12 July 2021 without open access.</p

Meso-scale turbulence in living fluids

Turbulence is ubiquitous, from oceanic currents to small-scale biological and quantum systems. Self-sustained turbulent motion in microbial suspensions presents an intriguing example of collective dynamical behavior amongst the simplest forms of life, and is important for fluid mixing and molecular transport on the microscale. The mathematical characterization of turbulence phenomena in active non-equilibrium fluids proves even more difficult than for conventional liquids or gases. It is not known which features of turbulent phases in living matter are universal or system-specific, or which generalizations of the Navier-Stokes equations are able to describe them adequately. Here, we combine experiments, particle simulations, and continuum theory to identify the statistical properties of self-sustained meso-scale turbulence in active systems. To study how dimensionality and boundary conditions affect collective bacterial dynamics, we measured energy spectra and structure functions in dense Bacillus subtilis suspensions in quasi-2D and 3D geometries. Our experimental results for the bacterial flow statistics agree well with predictions from a minimal model for self-propelled rods, suggesting that at high concentrations the collective motion of the bacteria is dominated by short-range interactions. To provide a basis for future theoretical studies, we propose a minimal continuum model for incompressible bacterial flow. A detailed numerical analysis of the 2D case shows that this theory can reproduce many of the experimentally observed features of self-sustained active turbulence.Comment: accepted PNAS version, 6 pages, click doi for Supplementary Informatio

Hydrodynamic length-scale selection in microswimmer suspensions

A universal characteristic of mesoscale turbulence in active suspensions is the emergence of a typical vortex length scale, distinctly different from the scale invariance of turbulent high-Reynolds number flows. Collective length-scale selection has been observed in bacterial fluids, endothelial tissue, and active colloids, yet the physical origins of this phenomenon remain elusive. Here, we systematically derive an effective fourth-order field theory from a generic microscopic model that allows us to predict the typical vortex size in microswimmer suspensions. Building on a self-consistent closure condition, the derivation shows that the vortex length scale is determined by the competition between local alignment forces, rotational diffusion, and intermediate-range hydrodynamic interactions. Vortex structures found in simulations of the theory agree with recent measurements in Bacillus subtilis suspensions. Moreover, our approach yields an effective viscosity enhancement (reduction), as reported experimentally for puller (pusher) microorganisms

Thermodynamic and mesoscopic modeling of tumbling nematics, of shear-thickening fluids and of stick-slip-like flow behavior

Shear thickening, i.e. the increase of the viscosity with increasing shear rate as it occurs in dense colloidal dispersions and polymeric fluids is an intriguing phenomenon with a considerable potential for technical applications. The theoretical description of this phenomenon is patterned after the thermodynamic and mesoscopic modeling of the orientational dynamics and the flow behavior of liquid crystals in the isotropic and nematic phases, where the theoretical basis is well-established. Even there the solutions of the relevant equations recently yielded surprises: not only stable flow alignment and a periodic behavior (tumbling) are found as response to an imposed stationary shear flow but also irregular and chaotic dynamics occurs for certain parameter ranges. To treat shear-thickening fluids, a non-linear Maxwell model equation for the symmetric traceless part of the stress tensor has been proposed in analogy to the equations obeyed by the alignment tensor of nematics. The fluid-solid transition is formally analogous to the isotropic-nematic transition. In addition to shear-thickening and shear-thinning fluids, substances with yield stress can be modeled. Furthermore, periodic stick-slip-like motions and also chaotic behavior are found. In the latter cases, the instantaneous entropy production is not always positive. Yet it is comforting that its long-time average is in accord with the second law