Bi-Lipschitz G-triviality and Newton polyhedra, G = R, C, K, R-V, C-V, K-V

In this work we provide estimates for the bi-Lipschitz G-triviality, G = C or K, for a family of map germs satisfying a Lojasiewicz condition. We work with two cases: the class of weighted homogeneous map germs and the class of non-degenerate map germs with respect to some Newton polyhedron. We also consider the bi-Lipschitz triviality for families of map germs defined on an analytic variety V. We give estimates for the bi-Lipschitz G(V)-triviality where G = R,C or K in the weighted homogeneous case. Here we assume that the map germ and the analytic variety are both weighted homogeneous with respect to the same weights. The method applied in this paper is based in the construction of controlled vector fields in the presence of a suitable Lojasiewicz condition. In the last section of this work we compare our results with other results related to this work showing tables with all estimates that we know, including ours.

C(0) and bi-Lipschitz K-equivalence of mappings

In this paper we investigate the classification of mappings up to K-equivalence. We give several results of this type. We study semialgebraic deformations up to semialgebraic C(0) K-equivalence and bi-Lipschitz K-equivalence. We give an algebraic criterion for bi-Lipschitz K-triviality in terms of semi-integral closure (Theorem 3.5). We also give a new proof of a result of Nishimura: we show that two germs of smooth mappings f, g : R(n) -> R(n), finitely determined with respect to K-equivalence are C(0)-K-equivalent if and only if they have the same degree in absolute value.

Bi-Lipschitz A-triviality of map germs and Newton filtrations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

K-bi-Lipschitz equivalence of real function-germs

In this paper we prove that the set of equivalence classes of germs of real polynomials of degree less than or equal to k, with respect to K-bi-Lipschitz equivalence, is finite.

Bi-Lipschitz A-equivalence of K-equivalent map-germs

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Lipschitz Correspondence between Metric Measure Spaces and Random Distance Matrices

Given a metric space with a Borel probability measure, for each integer N, we obtain a probability distribution on N x N distance matrices by considering the distances between pairs of points in a sample consisting of N points chosen independently from the metric space with respect to the given measure. We show that this gives an asymptotically bi-Lipschitz relation between metric measure spaces and the corresponding distance matrices. This is an effective version of a result of Vershik that metric measure spaces are determined by associated distributions on infinite random matrices.

On the Geometry of Rectifiable Sets with Carleson and Poincare-type inequlaities

Thesis (Ph.D.)--University of Washington, 2016-06

Washout hole for bi-ventricular assist device (BVAD) centrifugal blood pump

The shortage of donor hearts for patients with end stage heart failure has accelerated the development of ventricular assist devices (VAD) that act as a replacement heart. Mechanical devices involving pulsatile, axial and centrifugal devices have been proposed. Recent clinical developments indicate that centrifugal devices are not only beneficial for bridge to transplantation applications, but may also aid myocardial recovery. The results of a recent study have shown that patients who received a VAD have extended lives and improved quality of life compared to recipients of drug therapy. Unfortunately 25% of these patients develop right heart failure syndrome, sepsis and multi-organ failure. It was reported that 17% of patients initially receiving an LVAD later required a right ventricular assist device (RVAD). Hence, current research focus is in the development of a bi-ventricular assist device (BVAD). Current BVAD technology is either too bulky or necessitates having to implant two pumps working independently. The latter requires two different controllers for each pump leading to the potential complication of uneven flow dynamics and the requirements for a large amount of body space. This paper illustrates the combination of the LVAD and RVAD as one complete device to augment the function of both the left and right cardiac chambers with double impellers. The proposed device has two impellers rotating in counter directions, hence eliminating the necessity of the body muscles and tubing/heart connection to restrain the pump. The device will also have two separate chambers with independent rotating impeller for the left and right chambers. A problem with centrifugal impellers is the fluid stagnation underneath the impeller. This leads to thrombosis and blood clots.This paper presents the design, construction and location of washout hole to prevent thrombus for a Bi-VAD centrifugal pump. Results using CFD will be used to illustrate the superiority of our design concept in terms of preventing thrombus formation and hemolysis.

Passive control of a bi-ventricular assist device : an experimental and numerical investigation

For the last two decades heart disease has been the highest single cause of death for the human population. With an alarming number of patients requiring heart transplant, and donations not able to satisfy the demand, treatment looks to mechanical alternatives. Rotary Ventricular Assist Devices, VADs, are miniature pumps which can be implanted alongside the heart to assist its pumping function. These constant flow devices are smaller, more efficient and promise a longer operational life than more traditional pulsatile VADs. The development of rotary VADs has focused on single pumps assisting the left ventricle only to supply blood for the body. In many patients however, failure of both ventricles demands that an additional pulsatile device be used to support the failing right ventricle. This condition renders them hospital bound while they wait for an unlikely heart donation. Reported attempts to use two rotary pumps to support both ventricles concurrently have warned of inherent haemodynamic instability. Poor balancing of the pumps’ flow rates quickly leads to vascular congestion increasing the risk of oedema and ventricular ‘suckdown’ occluding the inlet to the pump. This thesis introduces a novel Bi-Ventricular Assist Device (BiVAD) configuration where the pump outputs are passively balanced by vascular pressure. The BiVAD consists of two rotary pumps straddling the mechanical passive controller. Fluctuations in vascular pressure induce small deflections within both pumps adjusting their outputs allowing them to maintain arterial pressure. To optimise the passive controller’s interaction with the circulation, the controller’s dynamic response is optimised with a spring, mass, damper arrangement. This two part study presents a comprehensive assessment of the prototype’s ‘viability’ as a support device. Its ‘viability’ was considered based on its sensitivity to pathogenic haemodynamics and the ability of the passive response to maintain healthy circulation. The first part of the study is an experimental investigation where a prototype device was designed and built, and then tested in a pulsatile mock circulation loop. The BiVAD was subjected to a range of haemodynamic imbalances as well as a dynamic analysis to assess the functionality of the mechanical damper. The second part introduces the development of a numerical program to simulate human circulation supported by the passively controlled BiVAD. Both investigations showed that the prototype was able to mimic the native baroreceptor response. Simulating hypertension, poor flow balancing and subsequent ventricular failure during BiVAD support allowed the passive controller’s response to be assessed. Triggered by the resulting pressure imbalance, the controller responded by passively adjusting the VAD outputs in order to maintain healthy arterial pressures. This baroreceptor-like response demonstrated the inherent stability of the auto regulating BiVAD prototype. Simulating pulmonary hypertension in the more observable numerical model, however, revealed a serious issue with the passive response. The subsequent decrease in venous return into the left heart went unnoticed by the passive controller. Meanwhile the coupled nature of the passive response not only decreased RVAD output to reduce pulmonary arterial pressure, but it also increased LVAD output. Consequently, the LVAD increased fluid evacuation from the left ventricle, LV, and so actually accelerated the onset of LV collapse. It was concluded that despite the inherently stable baroreceptor-like response of the passive controller, its lack of sensitivity to venous return made it unviable in its present configuration. The study revealed a number of other important findings. Perhaps the most significant was that the reduced pulse experienced during constant flow support unbalanced the ratio of effective resistances of both vascular circuits. Even during steady rotary support therefore, the resulting ventricle volume imbalance increased the likelihood of suckdown. Additionally, mechanical damping of the passive controller’s response successfully filtered out pressure fluctuations from residual ventricular function. Finally, the importance of recognising inertial contributions to blood flow in the atria and ventricles in a numerical simulation were highlighted. This thesis documents the first attempt to create a fully auto regulated rotary cardiac assist device. Initial results encourage development of an inlet configuration sensitive to low flow such as collapsible inlet cannulae. Combining this with the existing baroreceptor-like response of the passive controller will render a highly stable passively controlled BiVAD configuration. The prototype controller’s passive interaction with the vasculature is a significant step towards a highly stable new generation of artificial heart.

Raman and infrared study of phyllosilicates containing heavy metals (Sb, Bi) : bismutoferrite and chapmanite.

The kaolinite-like phyllosilicate minerals bismutoferrite BiFe3+2Si2O8(OH) and chapmanite SbFe3+2Si2O8(OH) have been studied by Raman spectroscopy and complemented with infrared spectra. Tentatively interpreted spectra were related to their molecular structure. The antisymmetric and symmetric stretching vibrations of the Si-O-Si bridges,  SiOSi and  OSiO bending vibrations,  (Si-Oterminal)- stretching vibrations,  OH stretching vibrations of hydroxyl ions, and  OH bending vibrations were attributed to observed bands. Infrared bands 3289-3470 cm-1 and Raman bands 1590-1667 cm-1 were assigned to adsorbed water. O-H...O hydrogen bond lengths were calculated from the Raman and infrared spectra.

Testing for the non-separability of bi-ambiguous compounds

Separability is a concept that is very difficult to define, and yet much of our scientific method is implicitly based upon the assumption that systems can sensibly be reduced to a set of interacting components. This paper examines the notion of separability in the creation of bi-ambiguous compounds that is based upon the CHSH and CH inequalities. It reports results of an experiment showing that violations of the CHSH and CH inequality can occur in human conceptual combination.