On a problem of Yuzvinsky on separating the n-cube

AbstractThe following problem of Yuzvinsky is solved here: how many vertices of the n-cube must be removed from it in order that no connected component of the rest contains an antipodal pair of vertices? Some further results and problems are described as well

Configuration spaces of thick particles on graphs

In this thesis, we study the topology of configuration spaces of particles of variable radius r>0 moving on a metric graph. Our main tool is a piecewise linear (PL) Morse-Bott theory for affine polytope complexes, which extends the Morse theory for such complexes introduced by M. Bestvina and N. Brady. As the size parameter r increases, the topological properties of the corresponding configuration spaces vary. We show that there are finitely many critical values where the homotopy type of these spaces changes, and describe these critical values in terms of metric properties of the graph. This provides an upper bound on the number of critical values in terms of the metric data. Moreover, we apply PL Morse-Bott theory to analyse the change in homotopy type of configuration spaces of thick particles when the radius transits a critical value. Provided that r is sufficiently small, we show that the thick particle configuration space is homotopy equivalent to the familiar configuration space of zero-size points on the graph. We also investigate discrete models for configuration spaces of two thick particles. Moreover, given a metric graph and the size parameter r, we provide an algorithm for computing the number of path-components of the configuration space of two thick particles

Arrangements of Submanifolds and the Tangent Bundle Complement

Drawing parallels with the theory of hyperplane arrangements, we develop the theory of arrangements of submanifolds. Given a smooth, finite dimensional, real manifold $X$ we consider a finite collection \A of locally flat codimension $1$ submanifolds that intersect like hyperplanes. To such an arrangement we associate two posets: the \emph{poset of faces} (or strata) \FA and the \emph{poset of intersections} L(\A). We also associate two topological spaces to \A. First, the complement of the union of submanifolds in $X$ which we call the \emph{set of chambers} and denote by \Ch. Second, the complement of union of tangent bundles of these submanifolds inside $TX$ which we call the \emph{tangent bundle complement} and denote by M(\A). Our aim is to investigate the relationship between combinatorics of the posets and topology of the complements. We generalize the Salvetti complex construction in this setting and also charcterize its connected covers using incidence relations in the face poset. We also demonstrate some calculations of the fundamental group and the cohomology ring. We apply these general results to study arrangements of spheres, projective spaces, tori and pseudohyperplanes. Finally we generalize Zaslavsky\u27s classical result in order to count the number of chambers

Carbon nanotube bearings in theory and practice

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 157-170).Carbon Nanotubes (CNTs) are attractive elements for bearings in Micro-Electro-Mechanical Systems (MEMS), because their structure comprises nested shells with no bonding and sub-nanometer spacing between them, enabling relative motion with low friction and wear. A few demonstrations of CNT bearings have been reported in the literature, and atomistic simulations have been used to probe the properties of these bearings. This thesis extends the state of knowledge about these bearing systems, by building on these prior works in both the experimental and simulation domains. The prototype CNT rotor device presented in this thesis, and accompanying fabrication process, improve on existing CNT bearing demonstrators by establishing a vertical bearing orientation (enabling superior rotor balance and speed, and flexibility of placement for drive mechanisms) and a more manufacturable process (employing CNTs grown in place by chemical vapor deposition, and evaluating trade-offs in growth parameters). The device consists of a silicon rotor, supported on a cantilevered CNT shaft, and actuated by impingement of air jets on blades around its perimeter. For the fabrication development, extensive and consistent studies on the compatibility of CNTs with a suite of standard MEMS process were conducted, yielding valuable information for future CNT-based device designers on the effects of these processes on CNTs. Additionally, manual manipulation and placement of loose CNTs into the required vertical alignment was demonstrated, providing an alternate fabrication route, as well as a useful research technique for development of CNT devices. Simulation of friction in a CNT bearing system has been a popular topic, yet many questions remain open. For example, the quantitative estimates of this friction reported to date range by as much as eight orders of magnitude, and simulation techniques employ a variety of disparate simulation paradigms and parameters. This thesis presents a new suite of consistently implemented but complementary and independent simulations, which span the approaches reported to date, yet agree quantitatively within the error margin. Furthermore, the quantitative relationships between friction and sliding speed, temperature, geometry, and simulation implementation parameters are determined, and a description of the causes of friction based on phonon analyses is offered.by Eugene Hightower Cook.Ph.D

Pre-Clinical Development of Best-in-Class Zn0.4Fe2.6O4 Magnetic Nanoparticles for Thermal Treatment of Brain Glioblastoma

Nanomaterials are intensely researched and developed for a wide range of applications. The focus of this work is on developing novel nanomaterials with augmented physicochemical properties for biomedical applications. Specifically, developing magnetic nanoparticles for thermal treatment of neoplasms as this method offers a potentially drug-free approach to cancer treatment currently approved for clinical use for a limited number of malignancies and undergoing further trials for assessing its effect on others. To date, several procedures have been established to produce nanoparticles with variable shapes, sizes and compositions and their effect on various technologies are intensely investigated. Among both anisotropic and isotropic magnetic nanoparticles synthesised as part of this work, superparamagnetic zinc doped ferrite nanoparticles were the most suitable for further development owing to their high magnetisation, superparamagnetic nature, low anisotropy and biocompatibility as characterised by their chemical and physical attributes and compared with iron oxide nanoparticles of same size and morphology. These nanoparticles have been developed using liquid chemistry routes under high temperature and pressure. Their extensive characterisation renders them as the best-in-class nanoparticles in terms of their magnetic properties and size exceeding the magnetic properties of the next most magnetic zinc ferrite synthesised to date whilst having ten times smaller magnetic volume. Their ability to convert magnetic energy to heat (magnetothermal) and light to heat (photothermal) has been assessed with photothermia being far more efficient than magnetothermia both in suspension and in cellular confinement. Magnetothermal conversion was similar to other superparamagnetic materials and of limited clinical use while photothermal conversion showed enhanced performance achieving complete cell death in 10 minutes using clinically relevant settings. The nanoparticles showed extensive cellular uptake in vitro on brain glioblastoma cells as indicated by imaging and magnetometry. The biocompatibility of the nanoparticles has been assessed with several techniques to assess mitochondrial function, cell membrane integrity and clonogenicity indicating a well-tolerated material of similar toxicity to iron oxide which itself is cleared for medical use by the Food and Drug Administration and the European medicines Agency. A practical treatment time has been determined to induce preferentially irreversible apoptosis than necrosis in in vitro experiments as a result of apoptosis-related proteins expression or inhibition and reactive oxygen species formation before, during and after thermal treatment. Biodistribution studies made use of nuclear medicine tomographic imaging techniques to monitor the biodistribution profile of the nanomaterial in real-time including positron emission tomography and single photon emission computed tomography integrated with computed tomography on physiological and immunocompromised mice via intravenous and intranasal administration. The nanomaterial mainly accumulates in organs involved in the clearance pathway; the liver and the kidneys with a small amount of material reaching the brain

Ultrafast Spin Dynamics of Next-Generation Nanomagnetic Technologies

Over the past 50 years, our society has experienced a technological revolution that has fundamentally changed the way our world operates. At the heart of this revolution are the computational building blocks that work together to perform mathematical operations and save the results. For many years, the size of the computing elements (e.g. transistors) has been consistently shrunk so that more devices could fit on a chip in order to increase computational power. To provide adequate data storage for the ever-increasing number of computations, the hard-disk drive (HDD) was developed in the 1980s and would forever revolutionize the landscape of memory storage. Today, HDDs still account for a vast majority of the data stored worldwide. These devices store information using the magnetization of nanoscopic domains in a granular magnetic film, however, in recent years it has become increasingly challenging to reduce the size of the domains further without fundamentally changing the HDD. Indeed, the latest iteration of this technology has incorporated lasers into the devices to leverage multiple degrees of freedom in order to achieve higher bit densities. This example highlights a common trend for all next-generation computational technologies – the strong coupling between distinct physical systems must be utilized to sustain the improvements our society has become accustomed to. In order to realize this lofty goal, the physics of nanoscale systems must be well understood to predict their behavior. As our collective understanding of this field continues to flourish, novel effects are found that open doors to previously unimaginable technologies that may usher in a revolution of their own. Indeed, there are both technological and fundamental interests to study nanostructured devices.In this thesis, the time-resolved magneto-optic Kerr effect (TR-MOKE) will be utilized to probe the ultrafast spin dynamics of magnetic films, multilayer heterostructures, and nanostructures. Our experimental observations of these systems are evaluated by combining various field of science and technology, including (but not limited to) condensed matter theory, signal processing, and optics. In doing so, we seek to fully explain the data and to enrich the understanding of these underexplored systems to inform the rational design of next-generation technologies. Specifically, a great deal of attention will be paid to emergent nanotechnologies that leverage the coupling between the magnetic system and either the electronic or mechanical properties of the device to tailor the performance. In this work, a novel method to restore the intrinsic magnetization dynamics and simultaneously improve the magneto-optical response of dense nanomagnet arrays will be presented. Then, our work on the spin dynamics of isolated nanomagnets resonantly excited by microwave-frequency acoustic waves will be reviewed, wherein we show for the first time that the coupling efficiency is ultimately limited by the damping of the magnetic system. In addition, the role of the nanomagnet geometry and the acoustic wavelength will be fully explored to determine critical parameters that govern the dynamic magneto-elastic resonance. Lastly, the development of an optical system to study the interplay between ultrafast all-optical switching and surface acoustic waves will be reviewed