Bubble extinction in Hele-Shaw flow with surface tension and kinetic undercooling regularisation

We perform an analytic and numerical study of an inviscid contracting bubble in a two-dimensional Hele-Shaw cell, where the effects of both surface tension and kinetic undercooling on the moving bubble boundary are not neglected. In contrast to expanding bubbles, in which both boundary effects regularise the ill-posedness arising from the viscous (Saffman-Taylor) instability, we show that in contracting bubbles the two boundary effects are in competition, with surface tension stabilising the boundary, and kinetic undercooling destabilising it. This competition leads to interesting bifurcation behaviour in the asymptotic shape of the bubble in the limit it approaches extinction. In this limit, the boundary may tend to become either circular, or approach a line or "slit" of zero thickness, depending on the initial condition and the value of a nondimensional surface tension parameter. We show that over a critical range of surface tension values, both these asymptotic shapes are stable. In this regime there exists a third, unstable branch of limiting self-similar bubble shapes, with an asymptotic aspect ratio (dependent on the surface tension) between zero and one. We support our asymptotic analysis with a numerical scheme that utilises the applicability of complex variable theory to Hele-Shaw flow.

Numerical solutions for thin film flow down the outside and inside of a vertical cylinder

We consider a model for thin film flow down the outside and inside of a vertical cylinder. Our focus is to study the effect that the curvature of the cylinder has on the gravity-driven instability of the advancing contact line and to simulate the resulting fingering patterns that form due to this instability. The governing partial differential equation is fourth order with a nonlinear degenerate diffusion term that represents the stabilising effect of surface tension. We present numerical solutions obtained by implementing an efficient alternating direction implicit scheme. When compared to the problem of flow down a vertical plane, we find that increasing substrate curvature tends to increase the fingering instability for flow down the outside of the cylinder, whereas flow down the inside of the cylinder substrate curvature has the opposite effect. Further, we demonstrate the existence of nontrivial travelling wave solutions which describe fingering patterns that propagate down the inside of a cylinder at constant speed without changing form. These solutions are perfectly analogous to those found previously for thin film flow down an inclined plane.

Vibrational spectroscopic characterization of the sulphate mineral khademite Al(SO4)F⋅5(H2O)

Vibrational spectroscopy has been used to characterize the sulphate mineral khademite Al(SO4)F∙5(H2O). Raman band at 991 cm-1 with a shoulder at 975 cm-1 is assigned to the ν1 (SO4)2- symmetric stretching mode. The observation of two symmetric stretching modes suggests that the sulphate units are not equivalent. Two low intensity Raman bands at 1104 and 1132 cm-1 are assigned to the ν3 (SO4)2- antisymmetric stretching mode. The broad Raman band at 618 cm-1 is assigned to the v4 (SO4)2- bending modes. Raman bands at 455, 505 and 534 cm-1 are attributable to the doubly degenerate v2 (SO4)2- bending modes. Raman bands at 2991, 3146 and 3380 cm-1 are assigned to the OH stretching bands of water. Five infrared bands are noted at 2458, 2896, 3203, 3348 and 3489 cm-1 are also due to water stretching bands. The observation of multiple water stretching vibrations gives credence to the non-equivalence of water units in the khademite structure. Vibrational spectroscopy enables an assessment of the structure of khademite.

Infrared and Raman spectroscopic characterization of the arsenate mineral ceruleite Cu2Al7(AsO4)4(OH)13⋅11.5(H2O)

The molecular structure of the arsenate mineral ceruleite has been assessed using a combination of Raman and infrared spectroscopy. The most intense band observed at 903 cm-1 is assigned to the (AsO4)3- symmetric stretching vibrational mode. The infrared spectrum shows intense bands at 787, 827 and 886 cm-1, ascribed to the triply degenerate m3 antisymmetric stretching vibration. Raman bands observed at 373, 400, 417 and 430 cm-1 are attributed to the m2 vibrational mode. Three broad bands for ceruleite found at 3056, 3198 and 3384 cm-1 are assigned to water OH stretching bands. By using a Libowitzky empirical equation, hydrogen bond distances of 2.65 and 2.75 Å are calculated. Vibrational spectra enable the molecular structure of the ceruleite mineral to be determined and whilst similarities exist in the spectral patterns with the roselite mineral group, sufficient differences exist to be able to determine the identification of the minerals.

Molecular cytogenetic analysis of basal cell carcinoma DNA using comparative genomic hybridization

In an attempt to define genomic copy number changes associated with the development of basal cell carcinoma, we investigated 15 sporadic tumors by comparative genomic hybridization. With the incorporation of tissue microdissection and degenerate oligonucleotide primed-polymerase chain reaction we were able to isolate, and then universally amplify, DNA from the tumor type. This combined approach allows the investigation of chromosomal imbalances within a histologically distinct region of tissue. Using comparative genomic hybridization we have observed novel and recurrent chromosomal gains at 6p (47%), 6q (20%), 9p (20%), 7 (13%), and X (13%). In addition comparative genomic hybridization revealed regional loss on 9q in 33% of tested tumors encompassing 9q22.3 to which the putative tumor suppressor gene, Patched, has been mapped. The deletion of Patched has been indicated in the development of hereditary and sporadic basal cell carcinomas. The identification of these recurrent genetic aberrations suggests that basal cell carcinomas may not be as genetically stable as previously thought. Further investigation of these regions may lead to the identification of other genes responsible for basal cell carcinoma formation.

Metal hexaborides with Sc, Ti or Mn

Comparison of well-determined single crystal data for stoichiometric, or near-stoichiometric, metal hexaborides con-firm previously identified lattice parameter trends using powder diffraction. Trends for both divalent and trivalent forms suggest that potential new forms for synthesis include Sc and Mn hexaborides. Density Functional Theory (DFT) calculations for KB6, CaB6, YB6, LaB6, boron octahedral clusters and Sc and Mn forms, show that the shapes of bonding orbitals are defined by the boron framework. Inclusion of metal into the boron framework induces a reduction in energy ranging from 1 eV to 6 eV increasing with ionic charge. For metals with d1 character, such a shift in energy brings a doubly degenerate band section along the G-M reciprocal space direction within the conduction bands tangential to the Fermi surface. ScB6 band structure and density of states calculations show directional and gap characteristics similar to those of YB6 and LaB6. These calculations for ScB6 suggest it may be possible to realize superconductivity in this compound if synthesized.

Bifurcations to travelling planar spots in a three-component FitzHugh-Nagumo system

In this article, we analyse bifurcations from stationary stable spots to travelling spots in a planar three-component FitzHugh-Nagumo system that was proposed previously as a phenomenological model of gas-discharge systems. By combining formal analyses, center-manifold reductions, and detailed numerical continuation studies, we show that, in the parameter regime under consideration, the stationary spot destabilizes either through its zeroth Fourier mode in a Hopf bifurcation or through its first Fourier mode in a pitchfork or drift bifurcation, whilst the remaining Fourier modes appear to create only secondary bifurcations. Pitchfork bifurcations result in travelling spots, and we derive criteria for the criticality of these bifurcations. Our main finding is that supercritical drift bifurcations, leading to stable travelling spots, arise in this model, which does not seem possible for its two-component version.

Raman spectroscopy of the arsenate minerals maxwellite and in comparison with tilasite

Maxwellite NaFe3+(AsO4)F is an arsenate mineral containing fluoride and forms a continuous series with tilasite CaMg(AsO4)F. Both maxwellite and tilasite form a continuous series with durangite NaAl3+(AsO4)-F. We have used the combination of scanning electron microscopy with EDS and vibrational spectroscopy to chemically analyse the mineral maxwellite and make an assessment of the molecular structure. Chemical analysis shows that maxwellite is composed of Fe, Na and Ca with minor amounts of Mn and Al. Raman bands for tilasite at 851 and 831 cm�1 are assigned to the Raman active m1 symmetric stretching vibration (A1) and the Raman active triply degenerate m3 antisymmetric stretching vibration (F2). The Raman band of maxwellite at 871 cm�1 is assigned to the m1 symmetric stretching vibration and the Raman band at 812 cm�1 is assigned to the m3 antisymmetric stretching vibration. The intense Raman band of tilasite at 467 cm�1 is assigned to the Raman active triply degenerate m4 bending vibration (F2). Raman band at 331 cm�1 for tilasite is assigned to the Raman active doubly degenerate m2 symmetric bending vibration (E). Both Raman and infrared spectroscopy do not identify any bands in the hydroxyl stretching region as is expected.

Molecular structural studies of the amorphous mineral pitticite Fe, AsO4, SO4, H2O

Some minerals are colloidal and show no X-ray diffraction patterns. Vibrational spectroscopy offers one of the few methods for the assessment of the structure of these types of mineral. Among this group of minerals is pitticite simply described as Fe, AsO4, SO4, H2O. The objective of this research is to determine the molecular structure of the mineral pitticite using vibrational spectroscopy. Raman microscopy offers a useful method for the analysis of such colloidal minerals. Raman and infrared bands are attributed to the , and water stretching vibrations. The Raman spectrum is dominated by a very intense sharp band at 983 cm−1 assigned to the symmetric stretching mode. A strong Raman band at 1041 cm−1 is observed and is assigned to the antisymmetric stretching mode. Low intensity Raman bands at 757 and 808 cm−1 may be assigned to the antisymmetric and symmetric stretching modes. Raman bands observed at 432 and 465 cm−1 are attributable to the doubly degenerate ν2(SO4)2- bending mode.

Electron capture of tetracyanoethylene oxide in the gas phase. Rearrangement of the parent radical anion to form [(NC)(3)C](-). A joint experimental and ab initio study

Capture of an electron by tetracyanoethylene oxide can initiate a number of decomposition pathways. One of these decompositions yields [(NC)3C]− as the ionic product. Ab initio calculations (at the B3LYP/6-31+G∗ level of theory) indicate that the formation of [(NC)3C]− is initiated by capture of an electron into the LUMO of tetracyanoethylene oxide to yield the anion radical [(NC)2C–O–C(CN)2]−· that undergoes internal nucleophilic substitution to form intermediate [(NC)3C–OCCN]−·. This intermediate dissociates to form [(NC)3C]− (m/z 90) as the ionic product. The radical (NC)3C· has an electron affinity of 4.0 eV (385 kJ mol−1). Ab initio calculations show that [(NC)3C]− is trigonal planar with the negative charge mainly on the nitrogens. A pictorial representation of this structure is the resonance structure formed from three degenerate contributing structures (NC)2–CCN−. The other product of the reaction is nominally (NCCO)·, but there is no definitive experimental evidence to indicate whether this radical survives intact, or decomposes to NC· and CO. The overall process [(NC)2C–O–C(CN)2]−· → [(NC)3C]− + (NCCO)· is calculated to be endothermic by 21 kJ mol−1 with an overall barrier of 268 kJ mol−1.

Stabilization of parametric roll resonance with active u-tanks via Lyapunov control design

Parametric ship roll resonance is a phenomenon where a ship can rapidly develop high roll motion while sailing in longitudinal waves. This effect can be described mathematically by periodic changes of the parameters of the equations of motion, which lead to a bifurcation. In this paper, the control design of an active u-tank stabilizer is carried out using Lyapunov theory. A nonlinear backstepping controller is developed to provide global exponential stability of roll. An extension of commonly used u-tank models is presented to account for large roll angles, and the control design is tested via simulation on a high-fidelity model of a vessel under parametric roll resonance.

Butterfly catastrophe for fronts in a three-component reaction–diffusion system

We study the dynamics of front solutions in a three-component reaction–diffusion system via a combination of geometric singular perturbation theory, Evans function analysis, and center manifold reduction. The reduced system exhibits a surprisingly complicated bifurcation structure including a butterfly catastrophe. Our results shed light on numerically observed accelerations and oscillations and pave the way for the analysis of front interactions in a parameter regime where the essential spectrum of a single front approaches the imaginary axis asymptotically.

Stability analysis of STATCOM in distribution networks

This chapter presents the stability analysis based on bifurcation theory of the distribution static compensator (DSTATCOM) operating both in current control mode as in voltage control mode. The bifurcation analysis allows delimiting the operating zones of nonlinear power systems and hence the computation of these boundaries is of interest for practical design and planning purposes. Suitable mathematical representations of the DSTATCOM are proposed to carry out the bifurcation analyses efficiently. The stability regions in the Thevenin equivalent plane are computed for different power factors at the Point of Common Coupling (PCC). In addition, the stability regions in the control gain space are computed, and the DC capacitor and AC capacitor impact on the stability are analyzed in detail. It is shown through bifurcation analysis that the loss of stability in the DSTATCOM is in general due to the emergence of oscillatory dynamics. The observations are verified through detailed simulation studies.

Analysis of impedance matched circuit for wireless power transfer

Typical wireless power transfer systems utilize series compensation circuit which is based on magnetic coupling and resonance principles that was first developed by Tesla. However, changes in coupling caused by gap distance, alignment and orientation variations can lead to reduce power transfer efficiencies and the transferred power levels. This paper proposes impedance matched circuit to reduce frequency bifurcation effect and improve on the transferred power level, efficiency and total harmonic distortion (THD) performance of the series compensation circuit. A comprehensive mathematical analysis is performed for both series and impedance matched circuits to show the frequency bifurcation effects in terms of input impedance, variations in transferred power levels and efficiencies. Matlab/Simulink results validate the theoretical analysis and shows the circuits’ THD performance when circuits are fed with power electronic converters.

Vibrational spectroscopic characterization of the arsenate mineral barahonaite: Implications for the molecular structure

The mineral barahonaite is in all probability a member of the smolianinovite group. The mineral is an arsenate mineral formed as a secondary mineral in the oxidized zone of sulphide deposits. We have studied the barahonaite mineral using a combination of Raman and infrared spectroscopy. The mineral is characterized by a series of Raman bands at 863 cm−1 with low wavenumber shoulders at 802 and 828 cm−1. These bands are assigned to the arsenate and hydrogen arsenate stretching vibrations. The infrared spectrum shows a broad spectral profile. Two Raman bands at 506 and 529 cm−1 are assigned to the triply degenerate arsenate bending vibration (F 2, ν4), and the Raman bands at 325, 360, and 399 cm−1 are attributed to the arsenate ν2 bending vibration. Raman and infrared bands in the 2500–3800 cm−1 spectral range are assigned to water and hydroxyl stretching vibrations. The application of Raman spectroscopy to study the structure of barahonaite is better than infrared spectroscopy, probably because of the much higher spatial resolution.