Microscopic calculations of Hugoniot curves of neat TATB and of its detonation products

We compute the Hugoniot curves of both neat TATB and its detonation products mixture using atomistic simulation tools. To compute the Hugoniot states, we adapted our "Sampling Constraints in Average" (SCA) method (Maillet et al., Applied Math. Research eXpress 2008, 2009) to Monte-Carlo simulations. For neat TATB, we show that the potential proposed by Rai (Rai et al., J. Chem. Phys. 129, 2008) is not accurate enough to predict the Hugoniot curve and requires some optimization of its parameters. Concerning detonation products, thermodynamic properties at chemical equilibrium are computed using a specific RxMC method (Bourasseau et al., Phys. Chem. Chem. Phys. 13, 2011) taking into account the presence of carbon clusters in the fluid mixture. We show that this explicit description of the solid phase immersed in the fluid phase modifies the chemical equilibrium

Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration

Invasion fronts in ecology are well studied but very few mathematical results concern the case with variable motility (possibly due to mutations). Based on an apparently simple reaction-diffusion equation, we explain the observed phenomena of front acceleration (when the motility is unbounded) as well as other quantitative results, such as the selection of the most motile individuals (when the motility is bounded). The key argument for the construction and analysis of traveling fronts is the derivation of the dispersion relation linking the speed of the wave and the spatial decay. When the motility is unbounded we show that the position of the front scales as $t^{3/2}$. When the mutation rate is low we show that the canonical equation for the dynamics of the fittest trait should be stated as a PDE in our context. It turns out to be a type of Burgers equation with source term.Comment: 7 page

Molecular Simulations of Hugoniots of detonation products mixtures at chemical equilibrium: Microscopic calculation of the Chapman-Jouguet State

International audienceIn this work, we used simultaneously the Reaction Ensemble Monte Carlo (ReMC) method and the Adaptive Erpenbeck Equation Of State (AE-EOS) method to directly calculate the thermodynamical and chemical equilibrium of mixtures of detonation products on the Hugoniot curve. The ReMC method (W. R. Smith and B. Triska, J. Chem. Phys. 100, pp 3019-3027 (1994)) allows to reach the chemical equilibrium of a reacting mixture, and the AE-EOS method (J. J. Erpenbeck, Phys. Rev. A, 46, p 6406 (1992)) constrains the system to satisfy the Hugoniot relation. Once the Hugoniot curve of the detonation products mixture is established, the CJ state of the explosive can be determined. Performing a NPT simulation at P(CJ) , T(CJ) , we then calculate the direct thermodynamic properties and the following derivative properties of the system using a fluctuation method: calorific capacities, sound velocity and Gruneisen coefficient. As the composition fluctuates, and the number of particles is not necessarily constant in this ensemble, a fluctuation formula has been developed to take into account the fluctuations of mole number and composition. This type of calculation has been applied to several usual energetic materials: nitromethane, tetranitromethane, hexanitroethane, PETN and RDX

From the hospital scale to nationwide: observability and identification of models for the COVID-19 epidemic waves

Two mathematical models of the COVID-19 dynamics are considered as the health system in some country consists in a network of regional hospital centers. The first macroscopic model for the virus dynamics at the level of the general population of the country is derived from a standard SIR model. The second local model refers to a single node of the health system network, i.e. it models the flows of patients with a smaller granularity at the level of a regional hospital care center for COVID-19 infected patients. Daily (low cost) data are easily collected at this level, and are worked out for a fast evaluation of the local health status thanks to control systems methods. Precisely, the identifiability of the parameters of the hospital model is proven and thanks to the availability of clinical data, essential characteristics of the local health status are identified. Those parameters are meaningful not only to alert on some increase of the infection, but also to assess the efficiency of the therapy and health polic

Characterization of Cs vapor cell coated with octadecyltrichlorosilane using coherent population trapping spectroscopy

We report the realization and characterization using coherent population trapping (CPT) spectroscopy of an octadecyltrichlorosilane (OTS)-coated centimeter-scale Cs vapor cell. The dual-structure of the resonance lineshape, with presence of a narrow structure line at the top of a Doppler-broadened structure, is clearly observed. The linewidth of the narrow resonance is compared to the linewidth of an evacuated Cs cell and of a buffer gas Cs cell of similar size. The Cs-OTS adsorption energy is measured to be (0.42 $\pm$ 0.03) eV, leading to a clock frequency shift rate of $2.7\times10^{-9}/$K in fractional unit. A hyperfine population lifetime, $T_1$, and a microwave coherence lifetime, $T_2$, of 1.6 and 0.5 ms are reported, corresponding to about 37 and 12 useful bounces, respectively. Atomic-motion induced Ramsey narrowing of dark resonances is observed in Cs-OTS cells by reducing the optical beam diameter. Ramsey CPT fringes are detected using a pulsed CPT interrogation scheme. Potential applications of the Cs-OTS cell to the development of a vapor cell atomic clock are discussed.Comment: 33 pages, 13 figure

Molecular Simulations of Shock to Detonation Transition in Nitromethane

An extension of the model described in a previous work of Maillet, Soulard and Stoltz based on a Dissipative Particule Dynamics is presented and applied to liquid nitromethane. Large scale non-equilibrium simulations of reacting nitromethane under sustained shock conditions allow a better understanding of the shock-to-detonation transition in homogeneous explosives. Moreover, the propagation of the reactive wave appears discontinuous since ignition points in the shocked material can be activated by the compressive waves emitted from the onset of chemical reactions

Potential optimization for the calculation of shocked liquid nitromethane properties

International audienceWe present the results of the optimization of a classical molecular force field used to calculate the properties of shocked nitromethane by Monte Carlo simulations. The optimization technique allows a good transferability of the potential parameters on a broad range of thermodynamic conditions (temperature and pressure) since a large variety of reference data can be used in the optimization procedure, including densities, vaporization enthalpies or pressures along the Hugoniot curve. Results of calculated properties of shocked nitromethane are in good agreement with experimental shock hugoniot data, including temperature measurements of second shock hugoniot

Multi-Spectral Reflection Matrix for Ultra-Fast 3D Label-Free Microscopy

Label-free microscopy exploits light scattering to obtain a three-dimensional image of biological tissues. However, light propagation is affected by aberrations and multiple scattering, which drastically degrade the image quality and limit the penetration depth. Multi-conjugate adaptive optics and time-gated matrix approaches have been developed to compensate for aberrations but the associated frame rate is extremely limited for 3D imaging. Here we develop a multi-spectral matrix approach to solve these fundamental problems. Based on an interferometric measurement of a polychromatic reflection matrix, the focusing process can be optimized in post-processing at any voxel by addressing independently each frequency component of the wave-field. A proof-of-concept experiment demonstrates the three-dimensional image of an opaque human cornea over a 0.1 mm^3-field-of-view at a 290 nm-resolution and a 1 Hz-frame rate. This work paves the way towards a fully-digital microscope allowing real-time, in-vivo, quantitative and deep inspection of tissues.Comment: 27 pages, 4 figure

Laser light routing in an elongated micromachined vapor cell with diffraction gratings for atomic clock applications

International audienceThis paper reports on an original architecture of microfabricated alkali vapor cell designed for miniature atomic clocks. The cell combines diffraction gratings with anisotropically etched single-crystalline silicon sidewalls to route a normally-incident beam in a cavity oriented along the substrate plane. Gratings have been specifically designed to diffract circularly polarized light in the first order, the latter having an angle of diffraction matching the (111) sidewalls orientation. Then, the length of the cavity where light interacts with alkali atoms can be extended. We demonstrate that a longer cell allows to reduce the beam diameter, while preserving the clock performances. As the cavity depth and the beam diameter are reduced, collimation can be performed in a tighter space. This solution relaxes the constraints on the device packaging and is suitable for wafer-level assembly. Several cells have been fabricated and characterized in a clock setup using coherent population trapping spectroscopy. The measured signals exhibit null power linewidths down to 2.23 kHz and high transmission contrasts up to 17%. A high contrast-to-linewidth ratio is found at a linewidth of 4.17 kHz and a contrast of 5.2% in a 7-mm-long cell despite a beam diameter reduced to 600 μm