A rigorous proof of the Landau-Peierls formula and much more

We present a rigorous mathematical treatment of the zero-field orbital magnetic susceptibility of a non-interacting Bloch electron gas, at fixed temperature and density, for both metals and semiconductors/insulators. In particular, we obtain the Landau-Peierls formula in the low temperature and density limit as conjectured by T. Kjeldaas and W. Kohn in 1957.Comment: 30 pages - Accepted for publication in A.H.

A Gaussian Mixture MRF for Model-Based Iterative Reconstruction with Applications to Low-Dose X-ray CT

Markov random fields (MRFs) have been widely used as prior models in various inverse problems such as tomographic reconstruction. While MRFs provide a simple and often effective way to model the spatial dependencies in images, they suffer from the fact that parameter estimation is difficult. In practice, this means that MRFs typically have very simple structure that cannot completely capture the subtle characteristics of complex images. In this paper, we present a novel Gaussian mixture Markov random field model (GM-MRF) that can be used as a very expressive prior model for inverse problems such as denoising and reconstruction. The GM-MRF forms a global image model by merging together individual Gaussian-mixture models (GMMs) for image patches. In addition, we present a novel analytical framework for computing MAP estimates using the GM-MRF prior model through the construction of surrogate functions that result in a sequence of quadratic optimizations. We also introduce a simple but effective method to adjust the GM-MRF so as to control the sharpness in low- and high-contrast regions of the reconstruction separately. We demonstrate the value of the model with experiments including image denoising and low-dose CT reconstruction.Comment: accepted by IEEE Transactions on Computed Imagin

Collective waves in dense and confined microfluidic droplet arrays

Excitation mechanisms for collective waves in confined dense one-dimensional microfluidic droplet arrays are investigated by experiments and computer simulations. We demonstrate that distinct modes can be excited by creating specific `defect' patterns in flowing droplet trains. Excited longitudinal modes exhibit a short-lived cascade of pairs of laterally displacing droplets. Transversely excited modes obey the dispersion relation of microfluidic phonons and induce a coupling between longitudinal and transverse modes, whose origin is the hydrodynamic interaction of the droplets with the confining walls. Moreover, we investigate the long-time behaviour of the oscillations and discuss possible mechanisms for the onset of instabilities. Our findings demonstrate that the collective dynamics of microfluidic droplet ensembles can be studied particularly well in dense and confined systems. Experimentally, the ability to control microfluidic droplets may allow to modulate the refractive index of optofluidic crystals which is a promising approach for the production of dynamically programmable metamaterials.Comment: 13 pages, 17 figure

On a fourth order nonlinear Helmholtz equation

In this paper, we study the mixed dispersion fourth order nonlinear Helmholtz equation $\Delta^2 u -\beta \Delta u + \alpha u= \Gamma|u|^{p-2} u$ in $\mathbb R^N$ for positive, bounded and $\mathbb Z^N$-periodic functions $\Gamma$. Using the dual method of Evequoz and Weth, we find solutions to this equation and establish some of their qualitative properties

MYSTIC: Michigan Young STar Imager at CHARA

We present the design for MYSTIC, the Michigan Young STar Imager at CHARA. MYSTIC will be a K-band, cryogenic, 6-beam combiner for the Georgia State University CHARA telescope array. The design follows the image-plane combination scheme of the MIRC instrument where single-mode fibers bring starlight into a non-redundant fringe pattern to feed a spectrograph. Beams will be injected in polarization-maintaining fibers outside the cryogenic dewar and then be transported through a vacuum feedthrough into the ~220K cold volume where combination is achieved and the light is dispersed. We will use a C-RED One camera (First Light Imaging) based on the eAPD SAPHIRA detector to allow for near-photon-counting performance. We also intend to support a 4-telescope mode using a leftover integrated optics component designed for the VLTI-GRAVITY experiment, allowing better sensitivity for the faintest targets. Our primary science driver motivation is to image disks around young stars in order to better understand planet formation and how forming planets might influence disk structures.Comment: Presented at the 2018 SPIE Astronomical Telescopes + Instrumentation, Austin, Texas, US

Models and Strategies for Variants of the Job Shop Scheduling Problem

Recently, a variety of constraint programming and Boolean satisfiability approaches to scheduling problems have been introduced. They have in common the use of relatively simple propagation mechanisms and an adaptive way to focus on the most constrained part of the problem. In some cases, these methods compare favorably to more classical constraint programming methods relying on propagation algorithms for global unary or cumulative resource constraints and dedicated search heuristics. In particular, we described an approach that combines restarting, with a generic adaptive heuristic and solution guided branching on a simple model based on a decomposition of disjunctive constraints. In this paper, we introduce an adaptation of this technique for an important subclass of job shop scheduling problems (JSPs), where the objective function involves minimization of earliness/tardiness costs. We further show that our technique can be improved by adding domain specific information for one variant of the JSP (involving time lag constraints). In particular we introduce a dedicated greedy heuristic, and an improved model for the case where the maximal time lag is 0 (also referred to as no-wait JSPs).Comment: Principles and Practice of Constraint Programming - CP 2011, Perugia : Italy (2011

Diamagnetism of quantum gases with singular potentials

We consider a gas of quasi-free quantum particles confined to a finite box, subjected to singular magnetic and electric fields. We prove in great generality that the finite volume grand-canonical pressure is jointly analytic in the chemical potential ant the intensity of the external magnetic field. We also discuss the thermodynamic limit

Gemini Planet Imager Observational Calibrations III: Empirical Measurement Methods and Applications of High-Resolution Microlens PSFs

The newly commissioned Gemini Planet Imager (GPI) combines extreme adaptive optics, an advanced coronagraph, precision wavefront control and a lenslet-based integral field spectrograph (IFS) to measure the spectra of young extrasolar giant planets between 0.9-2.5 um. Each GPI detector image, when in spectral model, consists of ~37,000 microspectra which are under or critically sampled in the spatial direction. This paper demonstrates how to obtain high-resolution microlens PSFs and discusses their use in enhancing the wavelength calibration, flexure compensation and spectral extraction. This method is generally applicable to any lenslet-based integral field spectrograph including proposed future instrument concepts for space missions.Comment: 10 pages, 6 figures. Proceedings of the SPIE, 9147-282 v2: reference adde

The inflation response of the posterior bovine sclera

An in vitro inflation test method was developed to characterize the mechanical behavior of the bovine posterior sclera. The method used digital image correlation to provide a spatially resolved, full-field deformation map of the surface of the posterior sclera in response to controlled pressurization. A series of experiments were performed in the range of 2-6 kPa (15-45 mmHg) to characterize the load-unload displacement response at various pressure rates and the time-dependent displacement response at different applied pressures. The magnitude of the displacement was largest in the peripapillary region, mainly between the apex and the optic nerve head. Further, the results showed that bovine scleral tissue exhibited nonlinear and viscoelastic behavior characterized by a rate-dependent displacement response, hysteresis during unloading and creep. The creep rate was insensitive to the applied pressure, suggesting that the tissue can be modeled as a quasilinear viscoelastic material in the physiological pressure range of 2-6 kPa