Photon Equivalents as a Parameter for Scaling Photoredox Reactions in Flow: Translation of Photocatalytic C−N Cross‐Coupling from Lab Scale to Multikilogram Scale

With the development of new photocatalytic methods over recent decades, the translation of these chemical reactions to industrial‐production scales using continuous‐flow reactors has become a topic of increasing interest. In this context, we describe our studies toward elucidating an empirically derived parameter for scaling photocatalytic reactions in flow. By evaluating the performance of a photocatalytic C?N cross‐coupling reaction across multiple reactor sizes and geometries, it was demonstrated that expressing product yield as a function of the absorbed photon equivalents provides a predictive, empirical scaling parameter. Through the use of this scaling factor and characterization of the photonic flux within each reactor, the cross‐coupling was scaled successfully from the milligram scale in batch to a multi‐kilogram reaction in flow.     

Comprehensive Characterization of Shredded Lithium-Ion Battery Recycling Material

Herein we report on an analytical study of dry-shredded lithium-ion battery (LIB) materials with unknown composition. Samples from an industrial recycling process were analyzed concerning the elemental composition and (organic) compound speciation. Deep understanding of the base material for LIB recycling was obtained by identification and analysis of transition metal stoichiometry, current collector metals, base electrolyte and electrolyte additive residues, aging marker molecules and polymer binder fingerprints. For reversed engineering purposes, the main electrode and electrolyte chemistries were traced back to pristine materials. Furthermore, possible lifetime application and accompanied aging was evaluated based on target analysis on characteristic molecules described in literature. With this, the reported analytics provided precious information for value estimation of the undefined spent batteries and enabled tailored recycling process deliberations. The comprehensive feedstock characterization shown in this work paves the way for targeted process control in LIB recycling processes.     

Critical Sets of Elliptic Equations

Given a solution u to a linear, homogeneous, second‐order elliptic equation with Lipschitz coefficients, we introduce techniques for giving improved estimates of the critical set ??(u)u {x :|δu|(x) = 0}, as well as the first estimates on the effective critical set ??_r(u), which roughly consists of points x such that the gradient of u is small somewhere on B_r(x) compared to the nonconstancy of u. The results are new even for harmonic functions on ?ⁿ. Given such a u, the standard first‐order stratification {l^k} of u separates points x based on the degrees of symmetry of the leading‐order polynomial of u‐u(x). In this paper we give a quantitative stratification of u, which separates points based on the number of almost symmetries of approximate leading‐order polynomials of u at various scales. We prove effective estimates on the volume of the tubular neighborhood of each , which lead directly to (n‐2 + ?)‐Minkowski type estimates for the critical set of u. With some additional regularity assumptions on the coefficients of the equation, we refine the estimate to give new proofs of the uniform (n‐2)‐Hausdorff measure estimate on the critical set and singular sets of u.© 2014 Wiley Periodicals, Inc.     

Mode-locking of self-generated oscillations in a semiconductor model for low-temperature impurity breakdown

The nonlinear dynamic behaviour of a model for self-generated, spatially coupled current oscillations in two separated parts of a semiconductor is analysed. The model involves impurity impact ionization, nonlinear energy relaxation of hot carriers, and energy exchange between the two subsystems. Quasiperiodicity and mode-locking are obtained, and characterized by a suitably defined rotation number and a spectral bifurcation diagram. The mode-locking structure is found to obey the Farey tree ordering, and can be understood on the basis of the circle map theory, assuming a particular path in the two-dimensional phase diagram of the circle map.     

Bit-number cumulants as a correlation measure of self-generated oscillations in a semiconductor model for low-temperature impurity breakdown

A semiconductor model for self-generated, coupled oscillations in the regime of lowtemperature impurity breakdown is used to show that the bit-number cumulants of the invariant density of a dynamic system represent a measure for internal correlations between certain subsystems of this system. The bit-number cumulants appear to be an appropriate measure for linear as well as for nonlinear correlations.     

Specimen storage and the use of a relational database.

Advances in genetic research make laboratory specimens a valuable source of DNA. Regulations call for quick turnaround time in locating stored specimens. Personal computers and database software make it possible to store, locate, and inventory samples efficiently and assist in research work and cooperation between laboratory sites.     

Characterization of Tangent Cones of Noncollapsed Limits with Lower Ricci Bounds and Applications

Consider a limit space ${(M_\alpha,g_\alpha,p_\alpha)\stackrel{GH}{\rightarrow} (Y,d_Y,p)}$ , where the ${M_\alpha^n}$ have a lower Ricci curvature bound and are volume noncollapsed. The tangent cones of Y at a point ${p\in Y}$ are known to be metric cones C(X), however they need not be unique. Let ${\overline\Omega_{Y,p}\subseteq\mathcal{M}_{GH}}$ be the closed subset of compact metric spaces X which arise as cross sections for the tangents cones of Y at p. In this paper we study the properties of ${\overline\Omega_{Y,p}}$ . In particular, we give necessary and sufficient conditions for an open smooth family ${\Omega\equiv (X,g_s)}$ of closed manifolds to satisfy ${\overline\Omega =\overline\Omega_{Y,p}}$ for some limit Y and point ${p\in Y}$ as above, where ${\overline\Omega}$ is the closure of Ω in the set of metric spaces equipped with the Gromov–Hausdorff topology. We use this characterization to construct examples which exhibit fundamentally new behaviors. The first application is to construct limit spaces (Y ⁿ , d _Y , p) with n ≥ 3 such that at p there exists for every 0 ≤ k ≤ n?2 a tangent cone at p of the form , where X ^n-k-1 is a smooth manifold not isometric to the standard sphere. In particular, this is the first example which shows that a stratification of a limit space Y based on the Euclidean behavior of tangent cones is not possible or even well defined. It is also the first example of a three dimensional limit space with nonunique tangent cones. The second application is to construct a limit space (Y ⁵ , d _Y , p), such that at p the tangent cones are not only not unique, but not homeomorphic. Specifically, some tangent cones are homeomorphic to cones over while others are homeomorphic to cones over .