DNS and LES of spark ignition with an automotive coil

The cycle to cycle combustion variability which is observed in spark-ignition engines is often caused by fluctuations of the early flame development. LES can be exploited for a better understanding and mastering of their origins. For that purpose appropriate models taking into account energy deposition, mixture ignition and transition to propagation are necessary requirements. This paper presents first DNS and LES of spark ignition with a real automotive coil and simplified pin-pin electrodes. The electrical circuit characteristics are provided by ISSIM while the energy deposition is modelled by Lagrangian particles. The ignition model is first evaluated in terms of initial spark radius on a pin-pin ignition experiment in pure air performed at CORIA and EM2C laboratories, showing that it pilots the radius of the torus formed by the initial shock wave. DNS of a quiescent lean propane/air mixture are then performed with this ignition system and a two-step mechanism. The impact of the modelled transferred energy during glow phase as well as the initial arc radius on the minimum ignition energy (MIE) are examined and compared to experimental values. Replacing the two-step chemistry by an analytically reduced mechanism leads to similar MIE but shows a different ignition kernel shape. Finally, LES of turbulent ignition using a Lagrangian arc model show a realistic prediction of the arc shape and its important role on the energy transfer location and thus on the flame kernel shape.     

A variational approach to the construction and Malliavin differentiability of strong solutions of SDE’s

In this article we develop a new approach to construct solutions of stochastic equations with merely measurable drift coefficients. We aim at demonstrating the principles of our technique by analyzing strong solutions of stochastic differential equations driven by Brownian motion. An important and rather surprising consequence of our method which is based on Malliavin calculus is that the solutions derived by Veretennikov (Theory Probab Appl 24:354–366, 1979) for Brownian motion with bounded and measurable drift in $\mathbb{R }^{d}$ are Malliavin differentiable. Further, a strength of our approach, which does not rely on a pathwise uniqueness argument, is that it can be transferred and applied to the analysis of various other types of (stochastic) equations: We obtain a Bismut–Elworthy–Li formula (Elworthy and Li, J Funct Anal 125:252–286, 1994) for spatial derivatives of solutions to the Kolmogorov equation with bounded and measurable drift coefficients. To derive the formula, we use that our approach can be applied to obtain Sobolev differentiability in the initial condition in addition to Malliavin differentiability of the associated stochastic differential equations. Another application of our technique is the construction of unique solutions of the stochastic transport equation with irregular vector fields. Moreover, our approach is also applicable to the construction of solutions of stochastic evolution equations on Hilbert spaces.     

Second-order hyperbolic s.p.d.e.'s driven by homogeneous Gaussian noise on a hyperplane

We study a class of hyperbolic stochastic partial differential equations in Euclidean space, that includes the wave equation and the telegraph equation, driven by Gaussian noise concentrated on a hyperplane. The noise is assumed to be white in time but spatially homogeneous within the hyperplane. Two natural notions of solutions are function-valued solutions and random field solutions. For the linear form of the equations, we identify the necessary and sufficient condition on the spectral measure of the spatial covariance for existence of each type of solution, and it turns out that the conditions differ. In spatial dimensions 2 and 3, under the condition for existence of a random field solution to the linear form of the equation, we prove existence and uniqueness of a random field solution to non-linear forms of the equation.

     

Weakly dependent chains with infinite memory

We prove the existence of a weakly dependent strictly stationary solution of the equation _Xt=F(_Xt−1,_Xt−2,_Xt−3,…;_ξt)$X_t=F(X_{t-1},X_{t-2},X_{t-3},\dots ;{\xi }_t)$ called a chain with infinite memory. Here the innovations  _ξt${\xi }_t$ constitute an independent and identically distributed sequence of random variables. The function F$F$ takes values in some Banach space and satisfies a Lipschitz-type condition. We also study the interplay between the existence of moments, the rate of decay of the Lipschitz coefficients of the function F$F$ and the weak dependence properties. From these weak dependence properties, we derive strong laws of large number, a central limit theorem and a strong invariance principle.     

Uniqueness results for nonlocal Hamilton-Jacobi equations

We are interested in nonlocal eikonal equations describing the evolution of interfaces moving with a nonlocal, non-monotone velocity. For these equations, only the existence of global-in-time weak solutions is available in some particular cases. In this paper, we propose a new approach for proving uniqueness of the solution when the front is expanding. This approach simplifies and extends existing results for dislocation dynamics. It also provides the first uniqueness result for a Fitzhugh-Nagumo system. The key ingredients are some new perimeter estimates for the evolving fronts as well as some uniform interior cone property for these fronts.     

Incorporation of nanogels within calcite single crystals for the storage,protection and controlled release of active compounds

Nanocarriers have tremendous potential for the encapsulation, storage and delivery of active compounds. However, current formulations often employ open structures that achieve efficient loading of active agents, but that suffer undesired leakage and instability of the payloads over time. Here, a straightforward strategy that overcomes these issues is presented, in which protein nanogels are encapsulated within single crystals of calcite (CaCO₃). Demonstrating our approach with bovine serum albumin (BSA) nanogels loaded with (bio)active compounds, including doxorubicin (a chemotherapeutic drug) and lysozyme (an antibacterial enzyme), we show that these nanogels can be occluded within calcite host crystals at levels of up to 45 vol%. Encapsulated within the dense mineral, the active compounds are stable against harsh conditions such as high temperature and pH, and controlled release can be triggered by a simple reduction of the pH. Comparisons with analogous systems – amorphous calcium carbonate, mesoporous vaterite (CaCO₃) polycrystals, and calcite crystals containing polymer vesicles – demonstrate the superior encapsulation performance of the nanogel/calcite system. This opens the door to encapsulating a broad range of existing nanocarrier systems within single crystal hosts for the efficient storage, transport and controlled release of various active guest species.

Nanocarriers have tremendous potential for the encapsulation, storage and delivery of active compounds.     

An Efficient RuII–RhIII–RuII Polypyridyl Photocatalyst for Visible‐Light‐Driven Hydrogen Production in Aqueous Solution

The development of multicomponent molecular systems for the photocatalytic reduction of water to hydrogen has experienced considerable growth since the end of the 1970s. Recently, with the aim of improving the efficiency of the catalysis, single‐component photocatalysts have been developed in which the photosensitizer is chemically coupled to the hydrogen‐evolving catalyst in the same molecule through a bridging ligand. Until now, none of these photocatalysts has operated efficiently in pure aqueous solution: a highly desirable medium for energy‐conversion applications. Herein, we introduce a new ruthenium–rhodium polypyridyl complex as the first efficient homogeneous photocatalyst for H₂ production in water with turnover numbers of several hundred. This study also demonstrates unambiguously that the catalytic performance of such systems linked through a nonconjugated bridge is significantly improved as compared to that of a mixture of the separate components.     

NIR‐to‐NIR Two‐Photon Scanning Laser Microscopy Imaging of Single Nanoparticles Doped by YbIII Complexes

The photophysical and nonlinear optical properties of water‐soluble chromophore‐functionalised tris‐dipicolinate complexes [LnL₃]^3? (Ln=Yb and Nd) are thoroughly studied, revealing that only the Yb^III luminescence can be sensitized by a two‐photon excitation process. The stability of the complex in water is strongly enhanced by embedding in dispersible organosilicate nanoparticles (NPs). Finally, the spectroscopic properties of [NBu₄]₃[YbL₃] are studied in solution and in the solid state. The high brightness of the NPs allows imaging them as single objects using a modified two‐photon microscopy setup in a NIR‐to‐NIR configuration.     

Building Giant Carbocycles by Reversible C−C Bond Formation

We describe a simple way to build giant macrocyclic hydrocarbons by the reversible formation of carbon–carbon bonds. Specifically, extended spirobifluorene‐substituted derivatives of Wittig's hydrocarbon were synthesized and found to undergo oligomerization, giving the largest hydrocarbon that has been crystallized and characterized by X‐ray diffraction to date.     

Quantitation of protein binding to the capillary wall in acidic, isoelectric buffers and means for minimizing the phenomenon

Notwithstanding the use of acidic, amphoteric, isoelectric buffers with isoelectric points (pI) in the pH 2-3 range, adsorption of proteins to the naked silica wall can be non-negligible. Two such buffers have been tested: iminodiacetic acid (IDA; pI 2.23, apparent pH 3.2 in 7 M urea) and aspartic acid (pI 2.77, apparent pH 3.7 in 7 M urea). Three potential quenchers of such interactions have been tested: hydroxyethylcellulose (HEC; number average molecular mass, Mr 27,000), TEPA (tetraethylenepentamine) and a novel, quatemarized piperazine [N(methyl-N-omega-iodobutyl)-N'-methylpiperazine] (Q-Pip), either alone or in binary and ternary mixtures. Human alpha- and beta-globin chains have been used as test proteins in capillary electrophoresis separations. It has been found that mixtures of these compounds are the worst possible remedy. E.g., a ternary mixture comprising 0.5% HEC, 0.5 mM TEPA and 1 mM Q-Pip still leaves behind 4.5% adsorbed protein onto the silica surface in runs in IDA buffer and 7 M urea (pH 3.2). Conversely, 0.5 mM TEPA or 1 mM Q-Pip, when used alone, minimize adsorption down to only 1.8% and 0.5%, respectively. When the same globin chain separations are performed in Asp and 7 M urea (pH 3.7), the situation is much worse: 44% protein is adsorbed in a ternary mixture of 0.5% HEC, 1 mM Q-Pip and 0.5 mM TEPA. However, when used alone, 0.5 mM TEPA and 1 mM Q-Pip reduce globin adsorption to levels of 8% and 5%, respectively. TEPA and Q-Pip are found to be in all cases the best quenchers of protein interaction to naked fused-silica; in addition they exhibit the unique property of smoothing the base-line and giving reproducible runs. The best method for desorbing bound protein was found to be an electrophoretic step consisting in driving sodium dodecylsulphate micelles from the cathodic reservoir.