Optimizing X‐ray mirror thermal performance using matched profile cooling

To cover a large photon energy range, the length of an X‐ray mirror is often longer than the beam footprint length for much of the applicable energy range. To limit thermal deformation of such a water‐cooled X‐ray mirror, a technique using side cooling with a cooled length shorter than the beam footprint length is proposed. This cooling length can be optimized by using finite‐element analysis. For the Kirkpatrick–Baez (KB) mirrors at LCLS‐II, the thermal deformation can be reduced by a factor of up to 30, compared with full‐length cooling. Furthermore, a second, alternative technique, based on a similar principle is presented: using a long, single‐length cooling block on each side of the mirror and adding electric heaters between the cooling blocks and the mirror substrate. The electric heaters consist of a number of cells, located along the mirror length. The total effective length of the electric heater can then be adjusted by choosing which cells to energize, using electric power supplies. The residual height error can be minimized to 0.02 nm RMS by using optimal heater parameters (length and power density). Compared with a case without heaters, this residual height error is reduced by a factor of up to 45. The residual height error in the LCLS‐II KB mirrors, due to free‐electron laser beam heat load, can be reduced by a factor of ～11 below the requirement. The proposed techniques are also effective in reducing thermal slope errors and are, therefore, applicable to white beam mirrors in synchrotron radiation beamlines.     

Nonlinear response of SDOF systems under combined deterministic and random excitations

Dynamical systems subjected to random excitations exhibit non-linear behavior for sufficiently large motion. The multiple time scale method has been extensively utilized in the framework of non-linear deterministic analysis to obtain two averaged first-order differential equations describing the slow time scale modulation of amplitude and phase response. In this paper the multiple time scale method, opportunely modified to take properly into account the correlation structure of the stochastic input process, is adopted to derive a stochastic frequency-response relationship involving the response amplitude statistics and the input power spectral density. A low-intensity noise is assumed to separate the strong mean motion from its weak fluctuations. The moment differential equations of phase and amplitude are derived and a linearization technique applied to evaluate the second order statistics. The theory is validated through digital simulations on a nonlinear single degree of freedom model for the transversal oscillation of a cantilever beam with tip force and to a Duffing-Rayleigh oscillator, to analyze non-linear damping effects.     

Corrections for underresolved scalar measurements in turbulent flows using a DNS database

We estimate the effect of finite spatial resolution of a probe for scalar measurements, using a database from direct numerical simulations (DNS). These are for homogeneous isotropic turbulence in temporal decay, Schmidt number unity, and low Taylor-microscale Reynolds number (≃27–42). The probe could be a cold wire for measuring temperature in a turbulent flow. Correction factors for the scalar variance, scalar dissipation rate, and mixed velocity-scalar derivative skewness are estimated, for a sensor length up to 15 times the Batchelor length scale. It is shown that the lack of resolution yields the largest attenuation on the dissipation rate, followed by the scalar variance. On the contrary, the mixed skewness, which is affected the least, is overestimated. Further, it is shown that if one estimates the mixed skewness via the scalar variance dynamical equation and neglects the term involving the time derivative of the scalar energy spectrum, large errors in the correction factor of the mixed skewness are introduced. Finally, it is found that correction factors obtained assuming Kraichnan scalar model spectrum and following Wyngaard (in Phys Fluids 14:2052–2054, 1971) approach are close to those from the DNS.     

Homogenization limit for electrical conduction in biological tissues in the radio-frequency rangeLimite d'homogénéisation pour la conduction électrique dans les tissus biologiques dans le domaine des radiofréquences

We study an evolutive model for electrical conduction in biological tissues, where the conductive intra-cellular and extracellular spaces are separated by insulating cell membranes. The mathematical scheme is an elliptic problem, with dynamical boundary conditions on the cell membranes. The problem is set in a finely mixed periodic medium. We show that the homogenization limit u₀ of the electric potential, obtained as the period of the microscopic structure approaches zero, solves the equation $\text{?}\text{div}\text{(σ}{}_0\text{?}{}_{\mathrm{x}}\text{u}{}_0\text{+A}{}^0\text{?}{}_{\mathrm{x}}\text{u}{}_0\text{+∫}{}_0{}^{\mathrm{t}}\text{A}{}^1\text{(t?τ)?}{}_{\mathrm{x}}\text{u}{}_0\text{(x,τ)}\text{d}\text{τ?}\text{F}\text{(x,t))=0}$ where σ₀>0 and the matrices A⁰, A¹ depend on geometric and material properties, while the vector function $\text{F}$ keeps trace of the initial data of the original problem. Memory effects explicitly appear here, making this elliptic equation of non standard type. To cite this article: M. Amar et al., C. R. Mecanique 331 (2003).     

Time Fractional Diffusion: A Discrete Random Walk Approach

The time fractional diffusion equation is obtained from the standarddiffusion equation by replacing the first-order time derivative with afractional derivative of order (0, 1). From a physicalview-point this generalized diffusion equation is obtained from afractional Fick law which describes transport processes with longmemory. The fundamental solution for the Cauchy problem is interpretedas a probability density of a self-similar non-Markovian stochasticprocess related to a phenomenon of slow anomalous diffusion. By adoptinga suitable finite-difference scheme of solution, we generate discretemodels of random walk suitable for simulating random variables whosespatial probability density evolves in time according to this fractionaldiffusion equation.     

Minimum weight limit design under uncertainty

Summary The problem of probabilistic minimum weight limit design is formulated as a stochastic programming problem. The theoretical treatment considers monodimensional structures, geometrical parameters and integer design variables. An algorithm is proposed and illustrated for the case of pin-jointed structures with two random continuous variables. The paper follows previous researches of the Authors in the field of probabilistic approach to structural safety [29 ÷ 33].

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Sommario Il problema della progettazione a rottura per minimo peso su basi probabilistiche viene formulato quale problema di programmazione stocastica. La trattazione teorica si estende alle strutture monodimensionali, comprende variabili di tipo geometrico nonchè variabili intere: l'algoritmo proposto ed illustrato per la risoluzione numerica riguarda le strutture reticolari interessate da due variabili casuali continue. Il lavoro fa seguito a precedenti ricerche degli scriventi in tema di concezione probabilistica della sicurezza [29 ÷ 33].

     

Synthesis and Characterization of an Unusual 68-Electrons Os4Se3 Carbonyl Phosphane Cluster

The 68-electrons, phosphane-substituted, osmium selenido-carbonyl cluster [Os₄Se₃(CO)₁₀(dppm)] (cluster 3; dppm = bis(diphenylphosphino)methane) has been obtained by reaction under mild experimental conditions between [Os₃(CO)₁₂] and the diphosphane diselenide dppmSe₂. Its crystal and molecular structure has been elucidated by X-ray diffraction methods. Cluster 3 contains only two Os–Os bonds as suggested by its electron count. It can be described as derived from the open-triangular nido cluster [Os₃(μ₃-Se)₂(CO)₉] through substitution of one CO ligand by the four-electrons donor osmiaselone fragment [CH₂(Ph₂P)₂](CO)₂Os=Se. The replacement of a two-electrons donor carbonyl with a four-electron donor fragment produces the cleavage of one Os–Os bond in the nido cluster. Under the adopted experimental conditions, other products of the reaction between [Os₃(CO)₁₂] and dppmSe₂ are the clusters [Os₃(μ₃-Se)₂(CO)₉] (1), [Os₃(μ₃-Se)₂(CO)₇(μ-dppm)] (2), and [Os₃(μ₃-Se)(CO)₈(μ-dppm)] (4), already described in the literature.     

A Detailed Study of the (Electro)chemical Behavior of Bis(trifluoromethanesulfonyl)imide Based Ionic Liquids at Different Purification Steps

A systematic investigation of the major impurities content as well as of their effect on the electrochemical behavior of synthesized N‐butyl‐N‐methylpyrrolidinium (Py_1.4), N‐(2‐methoxyethyl)‐N‐methylpyrrolidinium (Py_1.102) and 1‐butyl‐3‐methylimidazolium (bmim) bis(trifluoromethanesulfonyl)imide has been carried out and the efficacy of an optimized multistep purification protocol for obtaining ILs suitable for electrochemical applications has been verified.     

The Structure of Sub‐nm Platinum Clusters at Elevated Temperatures

Little is known about metallic clusters consisting merely of a dozen of atoms or even less, despite of their importance in catalysis and crystal nucleation. Scanning transmission electron microscopy (STEM) provides direct atomic structure information but has inherently suffered from limited time resolution. We employ fast dynamic STEM combined with a spatio‐temporal image denoising algorithm to explore the structure and stability of Pt clusters on carbon, which represents a highly relevant catalysis system. At room temperature, dynamic amorphous 2D structures are found, while above ≈300 °C, the clusters transform into a crystalline state. Our experimental and theoretical data reveal an unexpected strong trend of the crystalline clusters to exhibit the face‐centered cubic, bulk structure of Pt with cuboidal geometries being most prominent.