Non-perturbative approach to high-index-contrast variations in electromagnetic systems

We present a method that formally calculates exact frequency shifts of an electromagnetic field for arbitrary changes in the refractive index. The possible refractive index changes include both anisotropic changes and boundary shifts. Degenerate eigenmode frequencies pose no problems in the presented method. The approach relies on operator algebra to derive an equation for the frequency shifts, which eventually turn out in a simple and physically sound form. Numerically the equations are well-behaved, easy implementable, and can be solved very fast. Like in perturbation theory a reference system is first considered, which then subsequently is used to solve another related, but different system. For our method precision is only limited by the reference system basis functions and the error induced in frequency is of second order for first-order basis set error. As an example we apply our method to the problem of variations in the air-hole diameter in a photonic crystal fiber.     

Entropy estimate for high-dimensional monotonic functions

We establish upper and lower bounds for the metric entropy and bracketing entropy of the class of d-dimensional bounded monotonic functions under L^p norms. It is interesting to see that both the metric entropy and bracketing entropy have different behaviors for p<d/(d-1) and p>d/(d-1). We apply the new bounds for bracketing entropy to establish a global rate of convergence of the MLE of a d-dimensional monotone density.     

Slow-light enhanced optical detection in liquid-infiltrated photonic crystals

Slow-light enhanced optical detection in liquid-infiltrated photonic crystals is theoretically studied. Using a scattering-matrix approach and the Wigner–Smith delay time concept, we show that optical absorbance benefits both from slow-light phenomena as well as a high filling factor of the energy residing in the liquid. Utilizing strongly dispersive photonic crystal structures, we numerically demonstrate how liquid-infiltrated photonic crystals facilitate enhanced light–matter interactions, by potentially up to an order of magnitude. The proposed concept provides strong opportunities for improving existing miniaturized absorbance cells for optical detection in lab-on-a-chip systems.     

Optimization of bolt thread stress concentrations

Designs of threaded fasteners are controlled by different standards, and the number of different thread definitions is large. The most commonly used thread is probably the metric ISO thread, and this design is therefore used in the present paper. Thread root design controls the stress concentration factor of threads and therefore indirectly the bolt fatigue life. The root shape is circular, and from shape optimization for minimum stress concentration it is well known that the circular shape is seldom optimal. An axisymmetric Finite Element formulation is used to analyze the bolted connection, and a study is performed to establish the need for contact modeling with regard to finding the correct stress concentration factor. Optimization is performed with a simple parameterization with two design variables. Stress reduction of up to 9% is found in the optimization process, and some similarities are found in the optimized designs leading to the proposal of a new standard. The reductions in the stress are achieved by rather simple changes made to the cutting tool.     

Synthesis of 3,4-Dihydro-2H-Pyrroles from Ketones,Aldehydes, and Nitro Alkanes via Hydrogenative Cyclization

Syntheses of N-heterocyclic compounds that permit a flexible introduction of various substitution patterns by using inexpensive and diversely available starting materials are highly desirable. Easy to handle and reusable catalysts based on earth-abundant metals are especially attractive for these syntheses. We report here on the synthesis of 3,4-dihydro-2H-pyrroles via the hydrogenation and cyclization of nitro ketones. The latter are easily accessible from three components: a ketone, an aldehyde and a nitroalkane. Our reaction has a broad scope and 23 of the 33 products synthesized are compounds which have not yet been reported. The key to the general hydrogenation/cyclization reaction is a highly active, selective and reusable nickel catalyst, which was identified from a library of 24 earth-abundant metal catalysts.     

Quantitative Derivation of the Gross‐Pitaevskii Equation

Starting from first‐principle many‐body quantum dynamics, we show that the dynamics of Bose‐Einstein condensates can be approximated by the time‐dependent nonlinear Gross‐Pitaevskii equation, giving a bound on the rate of the convergence. Initial data are constructed on the bosonic Fock space applying an appropriate Bogoliubov transformation on a coherent state with expected number of particles N. The Bogoliubov transformation plays a crucial role; it produces the correct microscopic correlations among the particles. Our analysis shows that, on the level of the one‐particle reduced density, the form of the initial data is preserved by the many‐body evolution, up to a small error that vanishes as N^?1/2 in the limit of large N.© 2015 Wiley Periodicals, Inc.     

The rheological properties of hydrogenated castor oil crystals

The present study focuses on the rheological performance of a surfactant-rich aqueous suspension containing hydrogenated castor oil (HCO) crystals. HCO can be typically crystallized in five distinct shapes: spherically shaped, irregularly shaped, star-shaped (also called rosettes), short needles, and thick or thin fibers. The effect of the differences in shape on the rheological performance is studied, and the rheological properties are compared to the behavior of other triacylglycerol’s (TAG) suspensions. A suspension of TAG crystals usually behaves as a colloidal gel wherein a colloidal gel is defined as a network of flocs, with each floc being an aggregate of smaller subunits. All of these surfactant-rich aqueous suspensions of HCO crystals behaved according to a colloidal gel in the transient regime, independent of the studied crystal shapes, except the long thin fibers at a concentration above 0.1 wt% HCO transitioning from a heterogeneous fractal rod network to a homogeneous rod network, shifting from a colloidal gel to a glass.     

Implementation of a separate fluid-neutral energy equation in SOLPS-ITER and its impact on the validity range of advanced fluid-neutral models

In plasma edge transport codes for nuclear fusion devices, fluid-neutral models offer an interesting alternative to the currently used kinetic Monte Carlo simulations, especially for cases of high ion-neutral collisionality. In this paper, we elaborate a separate neutral energy equation in the state-of-the-art SOLPS-ITER code suite, which previously assumed perfect ion-neutral temperature equilibration. Furthermore, we study the coupled plasma-neutral solutions for a range of divertor operating regimes, proving the validity of these fluid-neutral models for high-recycling and detached regimes.     

Compact causal data interpolation

Consider a Hilbert space equipped with a time-structure, i.e., a resolution E of the identity on defined on subsets of some linearly ordered set Λ. For which x and y in is it possible to find a causal (time respecting) compact operator T, so that Tx = y? When T is required to be a Hilbert-Schmidt operator and (Λ, E) is sufficiently regular, this question is answered in terms of the “time-densities” of x and y. The condition is that the integral ∝_gLμ_x({s t})⁻¹ dμ_y(t) should be finite, where μ_x and μ_y are the measures on Λ given by μ_x(Ω) = ¦|E(Ω)x¦|² and μ_y(Ω) = ¦|E(Ω)y¦|². Further a solution is given for the related problem of minimizing the sum of ¦|Tx − y¦|² and the squared Hilbert-Schmidt norm ¦|R¦|₂² of T.