Mixed state geometric phases, entangled systems, and local unitary transformations

The geometric phase for a pure quantal state undergoing an arbitrary evolution is a ``memory'' of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution not only depends on the geometry of the path of the system alone but also on a constrained bi-local unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires uni-local transformations and is therefore essentially a property of the system alone.Comment: minor changes, journal reference adde

On the clustering of low-aspect-ratio oblate spheroids settling in ambient fluid

We have performed particle-resolved direct numerical simulations of many heavy non-spherical particles settling under gravity in the dilute regime. The particles are oblate spheroids of aspect ratio 1.5 and density ratio 1.5. Two Galileo numbers are considered, namely 111 and 152, for which a single oblate spheroid follows a steady vertical and a steady oblique path, respectively. In both cases, a strongly inhomogeneous spatial distribution of the disperse phase in the form of columnar clusters is observed, with a significantly enhanced average settling velocity as a consequence. Thus, in contrast to previous results for spheres, the qualitative difference in the single-particle regime does not result in a qualitatively different behaviour of the many-particle cases. In addition, we have carried out an analysis of pairwise interactions of particles in the well-known drafting–kissing–tumbling set-up, for oblate spheroids of aspect ratio 1.5 and for spheres. We have varied systematically the relative initial position between the particle pair and we have considered free-to-rotate particles and rotationally locked ones. We have found that the region of attraction for both particle shapes, with and without rotation, is very similar. However, significant differences occur during the drafting and tumbling phases. In particular, free-to-rotate spheres present longer drafting phases and separate quickly after the collision. Spheroids remain close to each other for longer times after the collision, and free-to-rotate ones experience two or more collision events. Therefore, we have observed a shape-induced increase in the interaction time which might explain the increased tendency to cluster of the many-particle cases

Operational approach to the Uhlmann holonomy

We suggest a physical interpretation of the Uhlmann amplitude of a density operator. Given this interpretation we propose an operational approach to obtain the Uhlmann condition for parallelity. This allows us to realize parallel transport along a sequence of density operators by an iterative preparation procedure. At the final step the resulting Uhlmann holonomy can be determined via interferometric measurements.Comment: Added material, references, and journal reference

Ehlers–Danlos syndrome, hypermobility type: A characterization of the patients' lived experience

Hypermobility type Ehlers–Danlos syndrome (EDS‐HT) is an inherited connective tissue disorder clinically diagnosed by the presence of significant joint hypermobility and associated skin manifestations. This article presents a large‐scale study that reports the lived experience of EDS‐HT patients, the broad range of symptoms that individuals with EDS‐HT experience, and the impact these symptoms have on daily functioning. A 237‐item online survey, including validated questions regarding pain and depression, was developed. Four hundred sixty‐six (466) adults (90% female, 52% college or higher degree) with a self‐reported diagnosis of EDS‐HT made in a clinic or hospital were included. The most frequently reported symptoms were joint pain (99%), hypermobility (99%), and limb pain (91%). They also reported a high frequency of other conditions including chronic fatigue (82%), anxiety (73%), depression (69%), and fibromyalgia (42%). Forty‐six percent of respondents reported constant pain often described as aching and tiring/exhausting. Despite multiple interventions and therapies, many individuals (53%) indicated that their diagnosis negatively affected their ability to work or attend school. Our results show that individuals with EDS‐HT can experience a wide array of symptoms and co‐morbid conditions. The degree of constant pain and disability experienced by the majority of EDS‐HT respondents is striking and illustrates the impact this disorder has on quality of life as well as the clinical challenges inherent in managing this complex connective tissue disorder. © 2013 Wiley Periodicals, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/101781/1/ajmga36293.pd

A computational framework for pharmaco-mechanical interactions in arterial walls using parallel monolithic domain decomposition methods

A computational framework is presented to numerically simulate the effects of antihypertensive drugs, in particular calcium channel blockers, on the mechanical response of arterial walls. A stretch-dependent smooth muscle model by Uhlmann and Balzani is modified to describe the interaction of pharmacological drugs and the inhibition of smooth muscle activation. The coupled deformation-diffusion problem is then solved using the finite element software FEDDLib and overlapping Schwarz preconditioners from the Trilinos package FROSch. These preconditioners include highly scalable parallel GDSW (generalized Dryja-Smith-Widlund) and RDSW (reduced GDSW) preconditioners. Simulation results show the expected increase in the lumen diameter of an idealized artery due to the drug-induced reduction of smooth muscle contraction, as well as a decrease in the rate of arterial contraction in the presence of calcium channel blockers. Strong and weak parallel scalability of the resulting computational implementation are also analyzed

NaturalWalk: An Anatomy-based Synthesizer for Human Walking Motions

We present a novel data-driven approach for synthesizing human gait motions with individual style characteristics and natural appearance. Our approach is based on the concept of a motion signature that captures the essential characteristic of an individual walking motion. For each joint angle our motion model consists of a shape template and feature functions that describe the variation of that shape with the stride length. For the synthesis of a walking motion, the feature functions are evaluated for a desired stride length. Then the templates are adapted to match the computed features and used as progressions for the joint angles of the skeleton. We demonstrate our data driven approach using motion data captured from 12 individuals. We report on an experiment showing that the synthesized motions have a natural appearance and maintain the individual style.:1. Introduction 2. Related Work 3. Preliminaries 3.1 Mathematics of motion 3.2 Walking motions 4. Data acquisition and analysis 5. Shape templates and feature functions 5.1 Definition of template functions 5.2 Continuous representation of template functions 5.3 Building the feature functions 6. Motion Generation 6.1 Adaption of template functions 6.2 Computing the poses 7 Experimental Results 7.1 Numerical Evaluation 7.2 User Study Acknowledgment Reference

An inverse problem from condensed matter physics

We consider the problem of reconstructing the features of a weak anisotropic background potential by the trajectories of vortex dipoles in a nonlinear Gross-Pitaevskii equation. At leading order, the dynamics of vortex dipoles are given by a Hamiltonian system. If the background potential is sufficiently smooth and flat, the background can be reconstructed using ideas from the boundary and the lens rigidity problems. We prove that reconstructions are unique, derive an approximate reconstruction formula, and present numerical examples.Peer reviewe

Generalization of geometric phase to completely positive maps

We generalize the notion of relative phase to completely positive maps with known unitary representation, based on interferometry. Parallel transport conditions that define the geometric phase for such maps are introduced. The interference effect is embodied in a set of interference patterns defined by flipping the environment state in one of the two paths. We show for the qubit that this structure gives rise to interesting additional information about the geometry of the evolution defined by the CP map.Comment: Minor revision. 2 authors added. 4 pages, 2 figures, RevTex

A comparative analysis of ceramic and cemented carbide end mills

Milling of ferrous metals is usually performed by applying cemented carbide tools due to their high hardness, temperature and wear resistance. Recently, ceramic tool materials have been on the rise and enhanced the efficiency in machining. As ceramics are brittle-hard materials, tool manufacturing requires a sound knowledge in order to meet the tool requirements such as sharp cutting edges and wear resistance. In this study, milling tools made of the high performance ceramic SiAlON were compared to tools made from cemented carbide. For both tool materials, the influence of a prepared cutting edge was investigated. Both the tool manufacturing process and the cutting edge preparation processes are presented, followed by the application of those tools within milling experiments. In order to evaluate the efficiency of both tool types, the cutting forces and the cumulative process energy demand were analyzed. Additionally, surface roughness of the machined workpieces and tool wear were examined. It was found that the ceramic tools, although process forces were higher than for cemented carbide tools, exhibited by far lower energy consumption, less tool wear and finally generated lower surface roughness. © 2020, The Author(s)

Combined QCM-D/GE as a tool to characterize stimuli-responsive swelling of and protein adsorption on polymer brushes grafted onto 3D-nanostructures

A combined setup of quartz crystal microbalance and generalized ellipsometry can be used to comprehensively investigate complex functional coatings comprising stimuli-responsive polymer brushes and 3D nanostructures in a dynamic, noninvasive in situ measurement. While the quartz crystal microbalance detects the overall change in areal mass, for instance, during a swelling or adsorption process, the generalized ellipsometry data can be evaluated in terms of a layered model to distinguish between processes occurring within the intercolumnar space or on top of the anisotropic nanocolumns. Silicon films with anisotropic nanocolumnar morphology were prepared by the glancing angle deposition technique and further functionalized by grafting of poly-(acrylic acid) or poly-(N-isopropylacrylamide) chains. Investigations of the thermoresponsive swelling of the poly-(N-isopropylacrylamide) brush on the Si nanocolumns proved the successful preparation of a stimuli-responsive coating. Furthermore, the potential of these novel coatings in the field of biotechnology was explored by investigation of the adsorption of the model protein bovine serum albumin. Adsorption, retention, and desorption triggered by a change in the pH value is observed using poly-(acrylic acid) functionalized nanostructures, although generalized ellipsometry data revealed that this process occurs only on top of the nanostructures. Poly-(N-isopropylacrylamide) is found to render the nanostructures non-fouling properties. Includes supplemental materials