Modeling the role of clusters and diffusion in the evolution of COVID-19 infections during lock-down

Epidemics such as the spreading of the SARS-CoV-2 virus are highly non linear, and therefore difficult to predict. In the present pandemic as time evolves, it appears more and more clearly that a clustered dynamics is a key element of description. This means that the disease rapidly evolves within spatially localized networks, that diffuse and eventually create new clusters. We improve upon the simplest possible compartmental model, the SIR model, by adding an additional compartment associated with the clustered individuals. This sophistication is compatible with more advanced compartmental models and allows, at the lowest level of complexity, to leverage the well-mixedness assumption. The so-obtained SBIR model takes into account the effect of inhomogeneity on epidemic spreading, and compares satisfactorily with results on the pandemic propagation in a number of European countries, during and immediately after lock-down. Especially, the decay exponent of the number of new cases after the first peak of the epidemic is captured without the need to vary the coefficients of the model with time. We show that this decay exponent is directly determined by the diffusion of the ensemble of clustered individuals and can be related to a global reproduction number, that overrides the classical, local reproduction number.

Imaging near-surface sharp lateral variations with surface-wave methods — Part 1: Detection and location

Near-surface sharp lateral variations can be either a target of investigation or an issue for the reconstruction of reliable subsurface models in surface-wave (SW) prospecting. Effective and computationally fast methods are consequently required for detection and location of these shallow heterogeneities. Four SW-based techniques, chosen between available literature methods, are tested for detection and location purposes. All of the techniques are updated for multifold data and then systematically applied on new synthetic and field data. The selected methods are based on computation of the energy, energy decay exponent, attenuation coefficient, and autospectrum. The multifold upgrade is based on the stacking of the computed parameters for single-shot or single-offset records and improves readability and interpretation of the final results. Detection and location capabilities are extensively evaluated on a variety of 2D synthetic models, simulating different target geometries, embedment conditions, and impedance contrasts with respect to the background. The methods are then validated on two field cases: a shallow low-velocity body in a sedimentary sequence and a hard-rock site with two embedded subvertical open fractures. For a quantitative comparison, the horizontal gradients of the four parameters are analyzed to establish uniform criteria for location estimation. All of the methods indicate ability in detecting and locating lateral variations having lower acoustic impedance than the surrounding material, with errors generally comparable or lower than the geophone spacing. More difficulties are encountered in locating targets with higher acoustic impedance than the background, especially in the presence of weak lateral contrasts, high embedment depths, and small dimensions of the object.

Resolution and dose dependence of radiation damage in biomolecular systems

The local Fourier-space relation between diffracted intensity I, diffraction wavevector q and dose D, \tilde I(q,D), is key to probing and understanding radiation damage by X-rays and energetic particles in both diffraction and imaging experiments. The models used in protein crystallography for the last 50 years provide good fits to experimental I(q) versus nominal dose data, but have unclear physical significance. More recently, a fit to diffraction and imaging experiments suggested that the maximum tolerable dose varies as q −1 or linearly with resolution. Here, it is shown that crystallographic data have been strongly perturbed by the effects of spatially nonuniform crystal irradiation and diffraction during data collection. Reanalysis shows that these data are consistent with a purely exponential local dose dependence, \tilde I(q,D) = I 0(q)exp[−D/D e(q)], where D e(q) ∝ q α with α ≃ 1.7. A physics-based model for radiation damage, in which damage events occurring at random locations within a sample each cause energy deposition and blurring of the electron density within a small volume, predicts this exponential variation with dose for all q values and a decay exponent α ≃ 2 in two and three dimensions, roughly consistent with both diffraction and imaging experiments over more than two orders of magnitude in resolution. The B-factor model used to account for radiation damage in crystallographic scaling programs is consistent with α = 2, but may not accurately capture the dose dependencies of structure factors under typical nonuniform illumination conditions. The strong q dependence of radiation-induced diffraction decays implies that the previously proposed 20–30 MGy dose limit for protein crystallography should be replaced by a resolution-dependent dose limit that, for atomic resolution data sets, will be much smaller. The results suggest that the physics underlying basic experimental trends in radiation damage at T ≃ 100 K is straightforward and universal. Deviations of the local I(q, D) from strictly exponential behavior may provide mechanistic insights, especially into the radiation-damage processes responsible for the greatly increased radiation sensitivity observed at T ≃ 300 K.

Laboratory experiments on the temporal decay of homogeneous anisotropic turbulence

We experimentally investigate the temporal decay of homogeneous anisotropic turbulence, monitoring the evolution of velocity fluctuations, dissipation and turbulent length scales over time. We employ an apparatus in which two facing random jet arrays of water pumps generate turbulence with negligible mean flow and shear over a volume that is much larger than the initial characteristic turbulent large scale of the flow. The Reynolds number based on the Taylor microscale for forced turbulence is $Re_{\unicode[STIX]{x1D706}}\approx 580$ and the axial-to-radial ratio of the root mean square velocity fluctuations is $1.22$. Two velocity components are measured by particle image velocimetry at the symmetry plane of the water tank. Measurements are taken for both ‘stationary’ forced turbulence and natural decaying turbulence. For decaying turbulence, power-law fits to the decay of turbulent kinetic energy reveal two regions over time; in the near-field region ($t/t_{L}<10$, $t_{L}$ is the integral time scale of the forced turbulence) a decay exponent $m\approx -2.3$ is found whereas for the far-field region ($t/t_{L}>10$) the value of the decay exponent was found to be affected by turbulence saturation. The near-field exhibits features of non-equilibrium turbulence with constant $L/\unicode[STIX]{x1D706}$ and varying $C_{\unicode[STIX]{x1D716}}$ (dissipation constant). We found a decay exponent $m\approx -1.4$ for the unsaturated regime and $m\approx -1.8$ for the saturated regime, in good agreement with previous numerical and experimental studies. We also observe a fast evolution towards isotropy at small scales, whereas anisotropy at large scales remains in the flow over more than $100t_{L}$. Direct estimates of dissipation are obtained and the decay exponent agrees well with the prediction $m_{\unicode[STIX]{x1D716}}=m-1$ throughout the decay process.

On non-self-similar regimes in homogeneous isotropic turbulence decay

Both theoretical analysis and eddy-damped quasi-normal Markovian (EDQNM) simulations are carried out to investigate the different decay regimes of an initially non-self-similar isotropic turbulence. Breakdown of self-similarity is due to the consideration of a composite three-range energy spectrum, with two different slopes at scales larger than the integral length scale. It is shown that, depending on the initial conditions, the solution can bifurcate towards a true self-similar decay regime, or sustain a non-self-similar state over an arbitrarily long time. It is observed that these non-self-similar regimes cannot be detected, restricting the observation to time exponents of global quantities such as kinetic energy or dissipation. The actual reason is that the decay is controlled by large scales close to the energy spectrum peak. This theoretical prediction is assessed by a detailed analysis of triadic energy transfers, which show that the largest scales have a negligible impact on the total transfers. Therefore, it is concluded that details of the energy spectrum near the peak, which may be related to the turbulence production mechanisms, are important. Since these mechanisms are certainly not universal, this may at least partially explain the significant discrepancies that exist between experimental data and theoretical predictions. Another conclusion is that classical self-similarity theories, which connect the asymptotic behaviour of either the energy spectrum $E(k\ensuremath{\rightarrow} 0)$ or the velocity correlation function $f(r\ensuremath{\rightarrow} + \infty )$ and the turbulence decay exponent, are not particularly relevant when the large-scale spectrum shape exhibits more than one range.

Is grid turbulence Saffman turbulence?

There has been a longstanding debate as to whether the large scales in grid turbulence should be classified as of the Batchelor or Saffman type. In the former, the integral scales, u and ℓ, satisfy u2ℓ5 ≈ constant, while in Saffman turbulence we have u2ℓ3 = constant. For strictly homogeneous turbulence the energy decay rates in these two types of turbulence differ, with u2 ~ t−10/7 in Batchelor turbulence and u2 ~ t−6/5 in Saffman turbulence. We present high-resolution measurements of grid turbulence taken in a large wind tunnel. The particularly large test section allows us to measure energy decay exponents with high accuracy. We find that the turbulence behind the grid is almost certainly of the Saffman type, with u2ℓ3 = constant. The measured energy decay exponent, however, is found to lie slightly below the theoretical prediction of u2 ~ t−1.2. Rather we find u2 ~ t−n, with n = 1.13±0.02. This discrepancy is shown to arise from a weak temporal decay of the dimensionless energy dissipation coefficient, εℓ/u3, which is normally taken to be constant in strictly homogeneous turbulence, but which varies very slowly in grid turbulence.