Homogenization of elliptic problems in thin domains with oscillatory boundaries

Los dominios finos, es decir, dominios sustancialmente más pequeños en alguna o varias de sus direcciones que en el resto, aparecen en muchos campos de la ciencia. Por ejemplo, dinámica de fluídos (lubricación, conducción de fluídos en tubos delgados, dinámica de oceanos...), mecánica de sólidos (barras delgadas, placas o cáscaras) o incluso en fisiología (circulación de la sangre). Así, el amplio número de posibles aplicaciones a situaciones reales ha hecho que la investigación de modelos de ecuaciones en derivadas parciales en dominios finos se convierta en un tema muy estudiado en los últimos años. Desde un punto de vista matemático, el estudio de las soluciones de una EDP en un dominio fino es un caso particular de la cuestión general relativa a cómo la variación de los dominios afecta al comportamiento de las soluciones de la EDP. En este marco, obtener la ecuación límite del modelo considerado, comparar la solución de la ecuación límite y las soluciones del problema en el dominio fino, analizar los coeficientes de la ecuación límite y comprender cómo la geometría del dominio afecta a la ecuación límite son algunos de los objetivos que deberían ser alcanzados. De hecho, es importante señalar que este tipo de cuestiones no sólo proporcionan importantes resultados teóricos sino que son muy relevantes desde el punto de vista de las aplicaciones. Por ejemplo, ser capaz de reducir el problema original a un problema mucho más sencillo, problema límite, que refleje las principales características del problema de partida puede ser muy útil para ingenieros y físicos...

Transactions, space and otherness : borders and boundaries in Palestine-Israel

Peer reviewed

Economising, Strategising and the Vertical Boundaries of the Firm

Acknowledgments: We are grateful to Celine Azemar, Ron Davies, Rodolphe Desbordes, Hartmut Egger, Holger Görg, Michael Moore, Ali Naghavi, Peter Neary, Pascalis RaimondosMøller, Ian Wooton and two anonymous referees for useful comments and suggestions. The usual disclaimer applies.

Advancing atomic nanolithography: cold atomic Cs beam exposure of alkanethiol self-assembled monolayers

We report the results of a study into the quality of functionalized surfaces for nanolithographic imaging. Self-assembled monolayer (SAM) coverage, subsequent post-etch pattern definition and minimum feature size all depend on the quality of the Au substrate used in atomic nanolithographic experiments. We find sputtered Au substrates yield much smoother surfaces and a higher density of {111} oriented grains than evaporated Au surfaces. A detailed study of the self-assembly mechanism using molecular resolution AFM and STM has shown that the monolayer is composed of domains with sizes typically of 5-25 nm, and multiple molecular domains can exist within one Au grain. Exposure of the SAM to an optically-cooled atomic Cs beam traversing a two-dimensional array of submicron material masks ans also standing wave optical masks allowed determination of the minimum average Cs dose (2 Cs atoms per SAM molecule) and the realization of < 50 nm structures. The SAM monolayer contains many non-uniformities such as pin-holes, domain boundaries and monoatomic depressions which are present in the Au surface prior to SAM adsorption. These imperfections limit the use of alkanethiols as a resist in atomic nanolithography experiments. These studies have allowed us to realize an Atom Pencil suitable for deposition of precision quantities of material at the microand nanoscale to an active surface.

Atomic nanolithography patterning of submicron features: writing an organic self-assembled monolayer with cold bright Cs atom beams

Cs atom beams, transversely collimated and cooled, passing through material masks in the form of arrays of reactive-ion-etched hollow Si pyramidal tips and optical masks formed by intense standing light waves, write submicron features on self-assembled monolayers (SAMs). Features with widths as narrow as 43 ± 6 nm and spatial resolution limited only by the grain boundaries of the substrate have been realized in SAMs of alkanethiols. The material masks write two-dimensional arrays of submicron holes; the optical masks result in parallel lines spaced by half the optical wavelength. Both types of feature are written to the substrate by exposure of the masked SAM to the Cs flux and a subsequent wet chemical etch. For the arrays of pyramidal tips, acting as passive shadow masks, the resolution and size of the resultant feature depends on the distance of the mask array from the SAM, an effect caused by the residual divergence of the Cs atom beam. The standing wave optical mask acts as an array of microlenses focusing the atom flux onto the substrate. Atom 'pencils' writing on SAMs have the potential to create arbitrary submicron figures in massively parallel arrays. The smallest features and highest resolutions were realized with SAMs grown on smooth, sputtered gold substrates.

Resist-substrate interface tailoring for generating high density arrays of Ge and Bi2Se3 nanowires by electron beam lithography

The authors report a chemical process to remove the native oxide on Ge and Bi2Se3 crystals, thus facilitating high-resolution electron beam lithography (EBL) on their surfaces using a hydrogen silsesquioxane (HSQ) resist. HSQ offers the highest resolution of all the commercially available EBL resists. However, aqueous HSQ developers such as NaOH and tetramethylammonium hydroxide have thus far prevented the fabrication of high-resolution structures via the direct application of HSQ to Ge and Bi2Se3, due to the solubility of components of their respective native oxides in these strong aqueous bases. Here we provide a route to the generation of ordered, high-resolution, high-density Ge and Bi2Se3 nanostructures with potential applications in microelectronics, thermoelectric, and photonics devices.                         

Catalyst and substrate effects in enantioselective C–H insertion reactions of α-diazosulfones

This thesis describes a systematic investigation of the mechanistic and synthetic aspects of intramolecular reactions of a series of α-diazo-β-oxo sulfone derivatives using copper and, to a lesser extent, rhodium catalysts. The key reaction pathways explored were C–H insertion and cyclopropanation, with hydride transfer competing in certain instances. Significantly, up to 98% ee has been achieved in the C–H insertion processes using copper-NaBARF-bisoxazoline catalysts, with the presence of the additive NaBARF critical to the efficiency of the transformations. This novel synthetic methodology provides access to a diverse range of enantioenriched heterocyclic compounds including thiopyrans, sulfolanes, β- and γ-lactams, in addition to carbocycles such as fused cyclopropanes. The synthesis of the α-diazosulfones required for subsequent investigations is initially described. Of the twenty seven diazo sulfones described, nineteen are novel and are fully characterised in this work. The discussion is subsequently focused on a study of the copper and rhodium catalysed reactions of the α-diazosulfones with Chapter Four concentrated on highly enantioselective C–H insertion to form thiopyrans and sufolanes, Chapter Five focused on C–H insertion to form fused sulfolanes, Chapter Six focused on C–H insertion in sulfonyl α-diazoamides where both lactam formation and / or thiopyran / sulfolane formation can result from competing C–H insertion pathways, while Chapter Seven focuses on cyclopropanation to yield fused cyclopropane derviatives. One of the key outcomes of this work is an insight into the steric and / or electronic factors on both the substrate and the catalyst which control regio-, diastereo- and enantioselectivity patterns in these synthetically powerful transformations. Full experimental details for the synthesis and spectral characterisation of the compounds are included at the end of each Chapter, with details of chiral stationary phase HPLC analysis and assignment of absolute stereochemistry included in the appendix.

Annotated record of the detailed examination of Mn deposits from DSDP Site 161, Leg 16 (Cores 16-161-1 and 16-161A-14)

DSDP 161 is located on the lower west flank of the East Pacific Rise about midway between the Clipperton and Clarion fracture zones which define the boundaries of a large structural block in the eastern Pacific. The site is about 4,000 km west of the present crest of the Rise. It is located near the northern edge of a zone of thick Cenozoic sediments which marks the general location of the equatorial zone of high biological productivity.

Stepped-bend Substrate Integrated Waveguide to Rectangular Waveguide Transition

A new wideband transition between substrate integrated waveguide (SIW) and rectangular waveguide (RWG) that resembles a right angle waveguide E-bend at Ku/K band is presented. The transition has removable but stable mounting, requires only PCB fabrication and has adaptable quality and bandwidth characteristics depending on the number of substrate layers used.

Nagaland: Borders, Boundaries, Belonging: Contested spaces and disputed narratives

In 2011 I travelled to three of the ‘Seven Sister’ states of old Assam, Nagaland, Meghalaya & Assam. My journey to this remote and politically sensitive region, bordering Chinese occupied Tibet, Bangladesh and Myanmar was prompted by my father’s experiences in the region during WW2 in the Burma Campaign and brought into sharp relief on-going themes in my work, the impact the past has on the present, the relationship of time and place, identity and memory and the transcultural experiences caused by war, colonisation and migration. The drawings I made on location, the objects I collected and the notes and photographs I took formed the basis of the bookwork: NAGALAND borders boundaries belonging. When making the finished work the material quality of the object and the processes by which it was made become very important. The historical resonance of the medium and the time consuming nature of the process reflect the embedding of form and idea, and paid homage to the material culture of the Naga hill tribes. The bookwork was hand-bound, handset and printed by letterpress. Some spreads were printed in 6 colours and the book took over a year to produce. I see my practice as echoing that of generations of Lady travellers; embracing the need to journey, be in a liminal space, to have a plan but not be afraid to divert from it. To be alone, take a sketchbook and make images is, for me, the definition of the itinerant illustrator; one who travels widely in geographic space, visual forms and ideas, in order to get lost and find the unlooked for.

Dynamically mechanical and nano-impact (fatigue) analysis of touch screen thin films deposited on polyethylene terephthalate substrate

Nano-scale touch screen thin film have not been thoroughly investigated in terms of dynamic impact analysis under various strain rates. This research is focused on two different thin films, Zinc Oxide (ZnO) film and Indium Tin Oxide (ITO) film, deposited on Polyethylene Terephthalate (PET) substrate for the standard touch screen panels. Dynamic Mechanical Analysis (DMA) was performed on the ZnO film coated PET substrates. Nano-impact (fatigue) testing was performed on ITO film coated PET substrates. Other analysis includes hardness and the elastic modulus measurements, atomic force microscopy (AFM), Fourier Transform Infrared Spectroscopy (FTIR) and the Scanning Electron Microscopy (SEM) of the film surface.
Ten delta of DMA is described as the ratio of loss modulus (viscous properties) and storage modulus (elastic properties) of the material and its peak against time identifies the glass transition temperature (Tg). Thus, in essence the Tg recognizes changes from glassy to rubber state of the material and for our sample ZnO film, Tg was found as 388.3 K. The DMA results also showed that the Ten delta curve for Tg increases monotonically in the viscoelastic state (before Tg) and decreases sharply in the rubber state (after Tg) until recrystallization of ZnO takes place. This led to an interpretation that enhanced ductility can be achieved by negating the strength of the material.
For the nano-impact testing using the ITO coated PET, the damage started with the crack initiation and propagation. The interpretation of the nano-impact results depended on the characteristics of the loading history. Under the nano-impact loading, the surface structure of ITO film suffered from several forms of failure damages that range from deformation to catastrophic failures. It is concluded that in such type of application, the films should have low residual stress to prevent deformation, good adhesive strength, durable and good resistance to wear.