Full linear multistep methods as root-finders

Root-finders based on full linear multistep methods (LMMs) use previous function values, derivatives and root estimates to iteratively find a root of a nonlinear function. As ODE solvers, full LMMs are typically not zero-stable. However, used as root-finders, the interpolation points are convergent so that such stability issues are circumvented. A general analysis is provided based on inverse polynomial interpolation, which is used to prove a fundamental barrier on the convergence rate of any LMM-based method. We show, using numerical examples, that full LMM-based methods perform excellently. Finally, we also provide a robust implementation based on Brent's method that is guaranteed to converge.Comment: 20 pages, 1 figur

Color homogeneity in LED spotlights

LED is a rising technology in the field of lighting. Halogen spotlights are nowadays replaced by LED spotlights because of their energy efficiency and long lifetime. However, color variation in the light output is a common problem. Poorly designed LED spotlights tend to have yellowish or bluish rings in the beam, which is undesirable. In this article we outline a method to design an optical component that annihilates this color variation

Fresnel reflections in inverse double freeform lens design

In this paper we present a method for designing a double freeformlens that includes the effect of Fresnel reflections on the output intensity.We elaborate this method for the case of a point source and a far-field target. A new expression for the transmittance through a double freeform lens is derived, and we adapt a least-squares algorithm to account for this transmittance. A test case based on street lighting is used to show that our adaptation improves the accuracy of the algorithm and that it is possible to minimize Fresnel losses with this new method to design efficient lenses.</p

A Monge-Ampère-solver for free-form reflector design

In this article we present a method for the design of fully free-form reflectors for illumination systems. We derive an elliptic partial differential equation of the Monge-Ampère type for the surface of a reflector that converts an arbitrary parallel beam of light into a desired intensity output pattern. The differential equation has an unusual boundary condition known as the transport boundary condition. We find a convex or concave solution to the equation using a state of the art numerical method. The method uses a nonstandard discretization based on the diagonalization of the Hessian. The discretized system is solved using standard Newton iteration. The method was tested for a circular beam with uniform intensity, a street light, and a uniform beam that is transformed into a famous Dutch painting. The reflectors were verified using commercial ray tracing software

Label-free technology and patient cells: from early drug development to precision medicine

Drug development requires physiologically more appropriate model systems and assays to increase understanding of drug action and pathological processes in individual humans. Specifically, patient-derived cells offer great opportunities as representative cellular model systems. Moreover, with novel label-free cellular assays, it is often possible to investigate complex biological processes in their native environment. Combining these two offers distinct opportunities for increasing physiological relevance. Here, we review impedance-based label-free technologies in the context of patient samples, focusing on commonly used cell types, including fibroblasts, blood components, and stem cells. Applications extend as far as tissue-on-a-chip models. Thus, applying label-free technologies to patient samples can produce highly biorelevant data and, with them, unique opportunities for drug development and precision medicine.Medicinal Chemistr

Oxygen content dependent etch rate of single polymer microparticles confined in the sheath region of a low pressure radiofrequency argon/oxygen plasma

To study the etching of polymer microparticles confined in low pressure radiofrequency plasmas, the size and refractive index of single 2 μm particles are experimentally obtained as a function of both time and oxygen content (0%-50%) added to the argon background gas. The etch rate was found to depend heavily on the oxygen (O2) content, especially for mixtures with low fractions of O2. As expected the etch rate was found to be close to zero in absence of O2 and increases to a value of 2 nm min-1 for 0.5% O2 and to roughly 3.5 nm min-1 for 5% O2. Above 5% O2 the etch rate saturates. It is shown that these results are consistent with a steady state etch model taking the effects of both atomic oxygen and positive ions into account