Pseudospectra in non-Hermitian quantum mechanics

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

Biomechanical Evaluation of the Stabilizing Function of Three Atlantoaxial Implants Under Shear Loading: A Canine Cadaveric Study

OBJECTIVE: To compare the biomechanical properties of a ventral transarticular lag screw fixation technique, a new dorsal atlantoaxial instability (AAI) clamp, and a new ventral AAI hook plate under sagittal shear loading after transection of the ligaments of the atlantoaxial joint. STUDY DESIGN: Cadaveric biomechanical study. ANIMALS: Canine cadavers (n = 10). MATERIALS AND METHODS: The occipitoatlantoaxial region of Beagles euthanatized for reasons unrelated to the study was prepared leaving only ligamentous structures and the joint capsules between the first 2 cervical vertebrae (C1 and C2). The atlanto-occipital joints were stabilized with 2 transarticular diverging positive threaded K-wires. The occipital bone and the caudal end of C2 were embedded in polymethylmethacrylate and loaded in shear to a force of 50 Newtons. The range of motion (ROM) and neutral zone (NZ) of the atlantoaxial joint were determined after 3 loading cycles with atlantoaxial ligaments intact, after ligament transection, and after fixation with each implant. The testing order of implants was randomly assigned. The implants tested last were subjected to failure testing. RESULTS: All stabilization procedures decreased the ROM and NZ of the atlantoaxial joint compared to transected ligament specimens. Only stabilization with transarticular lag screws and ventral plates produced a significant reduction of ROM compare to intact specimens. CONCLUSION: Fixation with transarticular lag screws and a ventral hook plate was biomechanically similar and provided more rigidity compared to dorsal clamp fixation. Further load cycling to failure tests and clinical studies are required before making clinical recommendations.

FOXC2 and fluid shear stress stabilize postnatal lymphatic vasculature

Biomechanical forces, such as fluid shear stress, govern multiple aspects of endothelial cell biology. In blood vessels, disturbed flow is associated with vascular diseases, such as atherosclerosis, and promotes endothelial cell proliferation and apoptosis. Here, we identified an important role for disturbed flow in lymphatic vessels, in which it cooperates with the transcription factor FOXC2 to ensure lifelong stability of the lymphatic vasculature. In cultured lymphatic endothelial cells, FOXC2 inactivation conferred abnormal shear stress sensing, promoting junction disassembly and entry into the cell cycle. Loss of FOXC2-dependent quiescence was mediated by the Hippo pathway transcriptional coactivator TAZ and, ultimately, led to cell death. In murine models, inducible deletion of Foxc2 within the lymphatic vasculature led to cell-cell junction defects, regression of valves, and focal vascular lumen collapse, which triggered generalized lymphatic vascular dysfunction and lethality. Together, our work describes a fundamental mechanism by which FOXC2 and oscillatory shear stress maintain lymphatic endothelial cell quiescence through intercellular junction and cytoskeleton stabilization and provides an essential link between biomechanical forces and endothelial cell identity that is necessary for postnatal vessel homeostasis. As FOXC2 is mutated in lymphedema-distichiasis syndrome, our data also underscore the role of impaired mechanotransduction in the pathology of this hereditary human disease.

Computational fluid dynamics modelling in cardiovascular medicine.

This paper reviews the methods, benefits and challenges associated with the adoption and translation of computational fluid dynamics (CFD) modelling within cardiovascular medicine. CFD, a specialist area of mathematics and a branch of fluid mechanics, is used routinely in a diverse range of safety-critical engineering systems, which increasingly is being applied to the cardiovascular system. By facilitating rapid, economical, low-risk prototyping, CFD modelling has already revolutionised research and development of devices such as stents, valve prostheses, and ventricular assist devices. Combined with cardiovascular imaging, CFD simulation enables detailed characterisation of complex physiological pressure and flow fields and the computation of metrics which cannot be directly measured, for example, wall shear stress. CFD models are now being translated into clinical tools for physicians to use across the spectrum of coronary, valvular, congenital, myocardial and peripheral vascular diseases. CFD modelling is apposite for minimally-invasive patient assessment. Patient-specific (incorporating data unique to the individual) and multi-scale (combining models of different length- and time-scales) modelling enables individualised risk prediction and virtual treatment planning. This represents a significant departure from traditional dependence upon registry-based, population-averaged data. Model integration is progressively moving towards 'digital patient' or 'virtual physiological human' representations. When combined with population-scale numerical models, these models have the potential to reduce the cost, time and risk associated with clinical trials. The adoption of CFD modelling signals a new era in cardiovascular medicine. While potentially highly beneficial, a number of academic and commercial groups are addressing the associated methodological, regulatory, education- and service-related challenges.

Deformation Studies of Tungsten-Gold Contacts at the Nanometer Scale.

The deformation behavior of atomically clean, nanometer sized tungsten / gold contacts was studied at room temperature in ultra-high vacuum. An instrument that combines atomic force microscopy (AFM), scanning tunneling microscopy (STM), and field ion microscopy (FIM) into a single experimental apparatus was designed, constructed, and calibrated. A cross-hair force sensor having a spring constant of - 442 N/m was developed and its motion was monitored during indentation experiments with a differential interferometer. Tungsten tips of controlled size (12.8 nm < tip radius < 2 1.6 nm) were first shaped and characterized using FIM and then indented into a Au (1 10) single crystal to depths ranging from 1.5 nrn to 18 nm using the force sensor. Continuum mechanics models were found to be valid in predicting elastic deformation during initial contact and plastic zone depths despite our small size regime. Multiple discrete yielding events lasting < 1.5 ms were observed during the plastic deformation regime; at the yield points a maximum value for the principal shear stress was measured to be 5 + 1 GPa. During tip withdrawal, "pop-out" events relating to material relaxation within the contact were observed. Adhesion between the tip and sample led to experimental signatures that suggest neck formation prior to the break of contact. STM images of indentation holes revealed various shapes that can be attributed to the (1 1 1 ) (1 10) crystallographic slip system in gold. FIM images of the tip after indentation showed no evidence of tip damage

The Harmonic Oscillator, a Review of Classical and Elementary Quantum Mechanics

The classical harmonic oscillator and an elementary discussion of the quantum mechanical solutions for the harmonic oscillator are discussed.

Molecular Mechanics of Water Monomer

Simulation of the classical molecular dynamics of a water molecule can be useful in explaining normal modes of motion, Fourier Transforms, and fundamental frequencies of vibration, as illustrated herein.

(Table 2) Compressional and shear wave velocites from basalts and sediments of the Atlantic and Pacific Ocean

Compressional (Vp) and shear (Vs) wave velocities have been measured to 1.0 kbar for 14 cores of well-consolidated sedimentary rock from Atlantic and Pacific sites of the Deep Sea Drilling Project. The range of VP (2.05-5.38 km/sec at 0.5 kbar) shows significant overlap with the range of oceanic layer-2 seismic velocities determined by marine refraction surveys, suggesting that sedimentary rocks may, in some regions, constitute the upper portion of layer 2. Differing linear relationships between VP and Vs for basalts and sedimentary rocks, however, may provide a method of resolving layer-2 composition. This is illustra ted for a refraction survey site on the flank of the Mid-Atlantic Ridge where layer-2 velocities agree with basalt, and two sites on the Saya de Malha Bank in the Indian Ocean where layer-2 velocities appear to represent sedimentary rock.

Index properties, shear strenghts and consolidation characteristics of ODP Hole 164-995A sediments

Geotechnical properties of sediment from Ocean Drilling Program Leg 164 are presented as: (1) normalized shipboard strength ratios from the Cape Fear Diapir, the Blake Ridge Diapir, and the Blake Ridge; and (2) Atterberg limit, vane shear strength, pocket-penetrometer strength, and constant-rate-of-strain consolidation results from Hole 995A, located on the Blake Ridge. This study was conducted to understand the stress history in a region characterized by high sedimentation rates and the presence of gas hydrates. Collectively, the results indicate that sediment from the Blake Ridge exhibits significant underconsolidated behavior, except near the seafloor. At least 10 m of additional overburden was removed by erosion or mass wasting at Hole 993A on the Cape Fear Diapir, compared to nearby sites.