Narrow Transition Region Research Articles

On the thermodynamic boundary conditions of a solidifying mushy layer with outflow

AbstractThe free-boundary problem between a liquid region and a mushy layer (a reactive porous medium) must respect both thermodynamic and fluid dynamical considerations. We develop a steady two-dimensional forced-flow configuration to investigate the thermodynamic condition of marginal equilibrium that applies to a solidifying mushy layer with outflow and requires that streamlines are tangent to isotherms at the interface. We show that a ‘two-domain’ approach in which the mushy layer and liquid region are distinct domains is consistent with marginal equilibrium by extending the Stokes equations in a narrow transition region within the mushy layer. We show that the tangential fluid velocity changes rapidly in the transition region to satisfy marginal equilibrium. In convecting mushy layers with liquid channels, a buoyancy gradient can drive this tangential flow. We use asymptotic analysis in the limit of small Darcy number to derive a regime diagram for the existence of steady solutions. Thus we show that marginal equilibrium is a robust boundary condition and can be used without precise knowledge of the fluid flow near the interface.

Thermodynamic properties and entropy scaling law for diffusivity in soft spheres.

The purely repulsive soft-sphere system, where the interaction potential is inversely proportional to the pair separation raised to the power n, is considered. The Laplace transform technique is used to derive its thermodynamic properties in terms of the potential energy and its density derivative obtained from molecular dynamics simulations. The derived expressions provide an analytic framework with which to explore soft-sphere thermodynamics across the whole softness-density fluid domain. The trends in the isochoric and isobaric heat capacity, thermal expansion coefficient, isothermal and adiabatic bulk moduli, Grüneisen parameter, isothermal pressure, and the Joule-Thomson coefficient as a function of fluid density and potential softness are described using these formulas supplemented by the simulation-derived equation of state. At low densities a minimum in the isobaric heat capacity with density is found, which is a new feature for a purely repulsive pair interaction. The hard-sphere and n = 3 limits are obtained, and the low density limit specified analytically for any n is discussed. The softness dependence of calculated quantities indicates freezing criteria based on features of the radial distribution function or derived functions of it are not expected to be universal. A new and accurate formula linking the self-diffusion coefficient to the excess entropy for the entire fluid softness-density domain is proposed, which incorporates the kinetic theory solution for the low density limit and an entropy-dependent function in an exponential form. The thermodynamic properties (or their derivatives), structural quantities, and diffusion coefficient indicate that three regions specified by a convex, concave, and intermediate density dependence can be expected as a function of n, with a narrow transition region within the range 5 < n < 8.

Vacancies in NiTi shape memory alloys

NiTi shape memory alloys were examined with a mono-energetic positron beam. The thermal vacancy formation enthalpy was found to be 0.77±0.08 eV. Upon heating NiTi the martensitic S value is retained to temperatures significantly above the phase transition temperature and then decreases towards the austenitic value only gradually. In contrast upon cooling, a narrow transition region at 81.5±1.5 °C is observed. The magnitude of the transition strongly depends on the annealing temperature.

Matrix model for deconfinement in aSU(Nc)gauge theory in2+1dimensions

We use an effective matrix model to study deconfinement in a pure SU(Nc) gauge theory, without quarks, in d=2+1 dimensions. Expanding about a constant background A0 field we construct an effective potential for the eigenvalues of the thermal Wilson line for general Nc and in the large-Nc limit. The numerical results are presented using one, two, and four free parameters, which are determined by fitting directly to the lattice data for the pressure. The matrix model shows a good agreement with numerical lattice simulations for the pressure and the interaction measure, starting from the perturbative limit up to the critical temperature. For the pressure, the details of A0- dependent nonperturbative terms are relevant only in a narrow transition region below ~1.2 Td. This is also the range where the Polyakov loop deviates notably from one. In accordance with the lattice results we find that, up to a trivial factor Nc^2-1, there is only a mild dependence on the number of colors.

Accretion on to Magnetic White Dwarfs

The Magnetic Cataclysmic Variables (MCVs) are close interacting binaries where mass is transferred from a late type secondary star to a magnetic white dwarf. Two modes of accretion can be identified depending on the strength of the magnetic field, the mass transfer rate and orbital parameters. (a) Disced Accretion: In the Intermediate polars (IPs), the mass transfer stream circularises and forms an accretion disc. Material couples on to field lines in a narrow inner transition region where the velocity in the orbital plane changes from Keplerian to co-rotation (b) Discless Accretion: In the polars, the accretion stream is disrupted by the magnetic field before it can circularise. Material couples on to field lines via an inner transition region where the velocity changes from essentially free fall to co-rotation. The polars have no counterparts in neutron star systems and their study provides unique insights into the complex nature of the magnetospheric boundary. The observed prop- erties of accretion shocks at the white dwarf surface such as the anomalous soft-X-ray excess and its time variability provide strong support for the hypothesis that under certain circumstances the field channelled funnel flow is blobby. This has been attributed to in- terchange instabilities such as the Magnetic Rayleigh-Taylor instability in the shocked gas at the stream-magnetosphere boundary where the stream fragments into discrete clumps of gas. As the clumps penetrate into the magnetosphere, they are shredded into smaller mass blobs via the Kelvin-Helmholtz instability that then couple on to field lines over an extended inner transition region in the orbital plane. The more massive blobs penetrate deep into the photosphere of the white dwarf releasing their energy as a reprocessed soft- X-ray black body component. Although similar instabilities are expected in the inner transition region in disced accretion albeit on a di erent scale there has been no direct observational evidence for blobby accretion in the generally lower field and disced IPs.

Matching disc and curtain flows in magnetically disrupted accretion discs

An accretion curtain forms when a strongly magnetic star disrupts the inner region of its surrounding disc. It was previously shown that the disc expands vertically due to rapidly growing thermal pressure caused by magnetic heating over a narrow radial transition region inside the corotation radius. This allows material to flow from the disc into a magnetically channelled curtain through which it is transferred to the star. The curtain flow is trans-sonic and sub-Alfvénic, with small distortions of the stellar magnetic field. In the present paper, the disc and curtain flows are matched across the upper boundary of the disc transition region, and this is shown to determine the width of this region as a function of the stellar rotation rate. The sonic point position can adjust to allow steady mass transfer from the disc to the curtain flow. An upper limit can be defined for the rotation period of the star below which a strong magnetic channelling regime applies, with the outer edge of the disruption region lying inside a spherical Alfvén radius. The picture of a thin, magnetically channelled curtain flow fed from a thermally disrupted disc is self-consistent in this regime. A lower limit arises for the stellar angular velocity below which the sonic point merges with the curtain base, resulting in excessive mass loss from the disc which would be inconsistent with a steady solution. This corresponds to a lower limit on the disruption radius as a fraction of the corotation radius. It is noted that the spin-up timescale of the accreting star is significantly less than the lifetime of the system so that typical observed systems should lie in the strong magnetic regime.

Effect of the Substrate Temperature on the Transition from Amorphous to Microcrystalline Silicon with High Hydrogen Dilution

Transition films of amorphous hydrogenated silicon (a-Si:H) to microcrystalline silicon (μc-Si:H) have attracted much attention due to the stability, high overall quality for solar cells configuration. Hydrogenated amorphous and microcrystalline silicon films were deposited on glass substrates by a conventional plasma enhanced chemical vapor deposition (PEVCD) varying the substrate temperature from 275 to 350 °C. A silane concentration of 4% and a total flow rate of 100 sccm were used at a gas pressure of 267 Pa. The film thicknesses of the prepared samples were between 700 and 900 nm estimated from the optical transmission spectra. The deposition rates were between 0.2 and 0.3 nm/s. The phase composition of the deposited silicon films were investigated by Raman spectroscopy. The transition from amorphous to microcrystalline silicon was found at the higher temperatures. The crystallization process of the amorphous silicon can be affected by the substrate temperature. A narrow structural transition region was observed from the changes of the crystalline volume fraction. The dark electrical conductivity of the silicon films increased as the substrate temperature increasing.

Nanomechanical mapping of the osteochondral interface with contact resonance force microscopy and nanoindentation

The bone–cartilage, or osteochondral, interface resists remarkably high shear stresses and rarely fails, yet its mechanical characteristics are largely unknown. A complete understanding of this hierarchical system requires mechanical-property information at the length scales of both the interface and the connecting tissues. Here, we combined nanoindentation and atomic force microscopy (AFM) methods to investigate the multiscale mechanical properties across the osteochondral region. The nanoindentation modulus M ranged from that of the subchondral bone (M=22.8±1.8GPa) to that of hyaline articular cartilage embedded in PMMA (M=5.7±1.0GPa) across a narrow transition region <5μm wide. Contact resonance force microscopy (CR-FM), which measures the frequency and quality factor of the AFM cantilever’s vibrational resonance in contact mode, was used to determine the relative storage modulus and loss tangent of the osteochondral interface. With better spatial resolution than nanoindentation, CR-FM measurements indicated an even narrower interface width of 2.3±1.2μm. Furthermore, CR-FM revealed a 24% increase in the viscoelastic loss tangent from the articular calcified cartilage into the PMMA-embedded hyaline articular cartilage. Quantitative backscattered electron imaging provided complementary measurement of mineral content. Our results provide insight into the multiscale functionality of the osteochondral interface that will advance understanding of disease states such as osteoarthritis and aid in the development of biomimetic interfaces.

Water Transport through Nanotubes with Varying Interaction Strength between Tube Wall and Water

We present the results from extensive molecular dynamics simulations to study the effect of varying interaction strength, εNT-OW, between the nanotube atoms and water's oxygen atom. We find the existence of a narrow transition region (εNT-OW ≈ 0.05 - 0.075 kcal/mol) in which water occupancy within a nanotube and flux through it increases dramatically with increasing εNT-OW, with the exact location defined by nanotube diameter and length. This transition region narrows with increasing nanotube diameter to nearly a step-change in water transport from no flow to high water flux between εNT-OW= 0.05 kcal/mol to 0.055 kcal/mol for tube diameter 1.6 nm. Interestingly, this transition region (εNT-OW= 0.05 - 0.075 kcal/mol) also coincides with water contact angles close to 90° on an unrolled nanotube surface hinting at a fundamental link between nanotube wetting characteristics and water transport through it. Finally, we find that the observed water flux is proportional to the average water occupancy divided by the average residence time within the nanotube, with a proportionality constant found to be 0.36, independent of the nanotube diameter and length.

Predictable 802.11 packet delivery from wireless channel measurements

RSSI is known to be a fickle indicator of whether a wireless link will work, for many reasons. This greatly complicates operation because it requires testing and adaptation to find the best rate, transmit power or other parameter that is tuned to boost performance. We show that, for the first time, wireless packet delivery can be accurately predicted for commodity 802.11 NICs from only the channel measurements that they provide. Our model uses 802.11n Channel State Information measurements as input to an OFDM receiver model we develop by using the concept of effective SNR. It is simple, easy to deploy, broadly useful, and accurate. It makes packet delivery predictions for 802.11a/g SISO rates and 802.11n MIMO rates, plus choices of transmit power and antennas. We report testbed experiments that show narrow transition regions (&lt;2 dB for most links) similar to the near-ideal case of narrowband, frequency-flat channels. Unlike RSSI, this lets us predict the highest rate that will work for a link, trim transmit power, and more. We use trace-driven simulation to show that our rate prediction is as good as the best rate adaptation algorithms for 802.11a/g, even over dynamic channels, and extends this good performance to 802.11n.

Strong nonlinearity and hysteresis of Hall resistance versus magnetization in nickel thin films

The anomalous Hall effect (AHE) in ferromagnetic materials is perhaps one of the oldest unresolved mysteries in physics. First observed in 1881, its mechanism is still a controversial topic today. The question remains whether AHE is caused by intrinsic (Berry phase and band structure) or extrinsic (defect scattering) effects or a combination of both. Here we present experimental observation in nickel thin films that seems to add to the mystery, but may in fact provide crucial clues for ultimately resolving the controversy. The key observation is that the Hall resistivity of nickel films is a strongly nonlinear function of the magnetization and displays clear hysteresis with respect to M. Specifically, at low temperatures, the anomalous Hall coefficient switches between two saturated values under the magnetic field with a narrow transition region, but with a strong hysteresis, in contrast to the slow saturation of the magnetization. The nonlinearity and the hysteresis become more apparent with decreasing temperature or film thickness. Despite the simplicity of the lattice and magnetic structure of nickel films, these results are outside our current understanding of AHE, whether using intrinsic or extrinsic mechanisms of AHE. It presents a challenge for these models, and may be used as a test of validity for both types of theories.

Experimental study on the effect of glass transition on moisture profiles and stress-crack formation during continuous and time-varying drying of maize kernels

The concept of glass transition can help understand the drying process and provide insight into the stress-cracking behaviour of maize (Zea mays) kernels. Thin-layer drying experiments using continuous and time-varying temperature and humidity profiles were conducted and the stress crack index was evaluated. Overlaying glass-transition regimes over the continuous drying profiles demonstrated a broader transition region at lower temperatures and a narrower transition region at higher temperatures. The time taken by maize kernels to pass through the glass-transition regime was directly related to the stress-crack formation. High temperature drying at 90 °C decreased the drying time but showed a higher cracking index. Low temperature drying at 30 °C had the longest drying time but this caused the least amount of cracking in the samples. Time-varying temperature profiles were also tested using a combination of temperatures in the glass-transition zone. Introduction of a high humidity step along with high temperature in the time-varying drying profile offered advantages in terms of drying time and reduced cracking in comparison to continuous single temperature drying at 70 °C. To extend the findings of this study, future studies should be conducted using additional drying conditions and computer simulations.

3D refractive index profile for the characterization of necking phenomenon along stretched polypropylene fibres

The phenomenon of neck formation in polymers has attracted considerable attention. During the cold-drawing process an initial undrawn material is transformed into anisotropic one across a narrow transition region called ‘neck’. The Video Opto-Mechanical (VOM) device attached with multiple-beam Fizeau fringes techniques are used to stretch polypropylene (PP) fibres. A iPP sample is stretched to have a neck at room temperature. The optical properties of the deformed material over the necking region are examined. Another PP sample is stretched (without necking deformation) at room temperature and the optical properties are also examined. The task of this study is to characterize and assess the necking phenomenon along cold-drawn polypropylene (iPP) fibre axis. The effect of necking on the optical properties of the fibre is confirmed by the determination of the 3D refractive index profile at different regions along the deformed PP fibre. Also the orientation function is calculated for the necked sample. The contour lines of microinterferograms are given for illustrations.

Procedures for offline grid nesting in regional ocean models

One-way offline nesting of a primitive-equation regional ocean numerical model (ROMS) is investigated, with special attention to the boundary forcing file creation process. The model has a modified open boundary condition which minimises false wave reflections, and is optimised to utilise high-frequency boundary updates. The model configuration features a previously computed solution which supplies boundary forcing data to an interior domain with an increased grid resolution. At the open boundaries of the interior grid (the child) the topography is matched to that of the outer grid (the parent), over a narrow transition region. A correction is applied to the normal baroclinic and barotropic velocities at the open boundaries of the child to ensure volume conservation. It is shown that these steps, together with a carefully constructed interpolation of the parent data, lead to a high-quality child solution, with minimal artifacts such as persistent rim currents and wave reflections at the boundaries. Sensitivity experiments provide information about the robustness of the model open boundary condition to perturbations in the surface wind stress forcing field, to the perturbation of the volume conservation enforcement in the boundary forcing, and to perturbation of the vertical density structure in the boundary forcing. This knowledge is important when extending the nesting technique to include external data from alien sources, such as ocean models with physics and/or numerics different from ROMS, or from observed climatologies of temperature, salinity and sea level.

Transient Pressure Behaviour Under Non- Darcy Flow, Formation Damage and Their Combined Effect for Dual Porosity Reservoirs

Abstract A semi-analytical model is presented to study transient pressure behaviour of vertical wells in a dual porosity reservoir under the influence of non-Darcy flow inside the reservoir (Forchheimer number), formation damage around the wellbore (mechanical skin factor), and their combined effect (near-wellbore non-Darcy skin factor). Unique transient pressure behaviour is presented in both semi-log pressure and log-log pressure derivative plots. Semi-log pressure plots suggest that for a vertical well producing with a constant sandface flow rate, its pressure responses exhibit two linear portions for Darcy flow, even with non-Darcy skin factor (i.e. the near-wellbore non-Darcy skin factor is larger than zero). However, the first linear portion will dismiss if non-Darcy flow presents inside the reservoir (i.e. the Forchheimer number is larger than zero). Further pressure derivative analyses in a log-log plot suggest that:both Forchheimer number and nearwellbore non-Darcy skin factor lead to a narrower and steeper transition region between pure wellbore storage and radial flow region for build up tests and a wider and gentler one for drawdown tests; andthe derivative curves under the effect of the Forchheimer number always exhibit a slight convex shape in the radial flow region, rather than a horizontal line with a constant value of 0.5 for Darcy flow. The type curves presented may be applied to estimate mechanical skin factor, Forchheimer number and near-wellbore non- Darcy skin factor from a single rate test. Synthetic cases show that ignoring the globally distributed non-Darcy flow causes errors of up to 300% in interpreting dual porosity characteristic parameters. Both synthetic and field case studies suggest that the non-Darcy flow has a significant effect on the interpretation of the inter-porosity flow coefficient, ?, and less effect on the interpretation of the storativity ratio, ?. Introduction The Forchheimer equation suggests that high velocity gas flow in porous media obeys the following quadratic equation: Equation (available in full paper) It has been recognized that Forchheimer non-Darcy flow is introduced by gas inertial effects; thus, ß?is called the inertial factor. Forchheimer non-Darcy flow is a universal phenomenon in gas reservoir development. It could affect reservoir parameter estimations, well productivity evaluation and production performance analysis. Observations in the field(1) and the laboratory(2, 3) have suggested that, in the fracture system of a naturally fractured reservoir, the pressure loss is dominated by the square term in the Forchheimer equation. Studies on modelling non-Darcy flow in naturally fractured reservoirs are limited. The first attempt was reported by Villalobos-L. et al.(4). Based on numerical results of a radial liquid flow model with the Forchheimer non-Darcy flow, these authors derived an expression of a rate-dependent pseudo-skin term similar to that in homogeneous single porosity reservoirs. Wu(5) modelled non-Darcy flow in a naturally fractured system using the Multiple Interacting Continua (MINC) method by applying the results of Darcy flow to approximate the characteristic length of non-Darcy flow distance between fractures and the matrix crossing the interface for the dual porosity formation. He observed that semi-log plots of pressure drop versus time are extremely sensitive to the values of non-Darcy coefficient.

SPECTRUM OF GLOBAL MAGNETOROTATIONAL INSTABILITY IN A NARROW TRANSITION LAYER

The Global Magnetorotational Instability (MRI) is investigated for a configuration in which the rotation frequency changes only in a narrow transition region. If the vertical wavelength of the unstable mode is of the same order or smaller than the width of this region, the growth rates can differ significantly from those given by a local analysis. In addition, the non-axisymmetric spectrum admits overstable modes with a non-trivial dependence on azimuthal wavelength, a feature missed by the local theory. In the limit of vanishing transition region width, the Rayleigh-centrifugal instability is recovered in the axisymmetric case, and the Kelvin-Helmholtz instability in the non-axisymmetric case.

Single-ensemble-based eigen-processing methods for color flow imaging - Part I. The Hankel-SVD filter

Because of their adaptability to the slow-time signal contents, eigen-based filters have shown potential in improving the flow detection performance of color flow images. This paper proposes a new eigen-based filter called the Hankel-SVD filter that is intended to process each slowtime ensemble individually. The new filter is derived using the notion of principal Hankel component analysis, and it achieves clutter suppression by retaining only the principal components whose order is greater than the clutter eigen-space dimension estimated from a frequency based analysis algorithm. To assess its efficacy, the Hankel-SVD filter was first applied to synthetic slow-time data (ensemble size: 10) simulated from two different sets of flow parameters that model: 1) arterial imaging (blood velocity: 0 to 38.5 cm/s, tissue motion: up to 2 mm/s, transmit frequency: 5 MHz, pulse repetition period: 0.4 ms) and 2) deep vessel imaging (blood velocity: 0 to 19.2 cm/s, tissue motion: up to 2 cm/s, transmit frequency: 2 MHz, pulse repetition period: 2.0 ms). In the simulation analysis, the post-filter clutter-to- blood signal ratio (CBR) was computed as a function of blood velocity. Results show that for the same effective stopband size (50 Hz), the Hankel-SVD filter has a narrower transition region in the post-filter CBR curve than that of another type of adaptive filter called the clutter-downmixing filter. The practical efficacy of the proposed filter was tested by application to in vivo color flow data obtained from the human carotid arteries (transmit frequency: 4 MHz, pulse repetition period: 0.333 ms, ensemble size: 10). The resulting power images show that the Hankel-SVD filter can better distinguish between blood and moving-tissue regions (about 9 dB separation in power) than the clutter-downmixing filter and a fixed-rank multi ensemble-based eigen-filter (which showed a 2 to 3 dB separation).

Education

Extolling laziness as a virtue is likely to produce a frown from most of the SIREV readership, but, in fact, most applied mathematicians strive to produce solutions that economize the effort needed to understand them. This aesthetic of finding just the right set of keys to unlock a problem concisely, yielding clarity and insight, is part of our heritage. Our paper this issue, “The Blasius Function: Computations Before Computers, the Value of Tricks, Undergraduate Projects, and Open Research Problems,” provides an elegant illustration of this philosophy. Blasius's eponymous function describes the flow in the narrow transition region (a boundary layer) of a fluid encountering a solid surface, such as air over an airplane wing. Amazingly, the solution to this problem was well understood in the early 1900s, well before the age of serious computation. The historical development of our understanding of this problem is a fascinating story which illustrates that clever use of analysis, symmetry, and asymptotics can yield insights with an economy rarely associated with numerical computation. This paper uses a knowledge of differential equations as a springboard to introduce the reader to similarity solutions, asymptotic methods, and complex analysis. It is a great starting point for students looking to dig deeper into this area, and the author both suggests a set of projects suitable for undergraduates and summarizes some open research problems associated with the Blasius function. Moreover, encouraging your students to read this paper may help them find the right balance of industriousness and laziness needed to succeed in applied mathematics.

SHAPED BEAM PATTERN SYNTHESIS WITH NON-UNIFORM SAMPLE PHASES

For a long time power pattern synthesis has been considered to produce shaped beam patterns due to the number of degrees of freedom when compared with field pattern synthesis. However, severaladvantages exist if synthesis techniques are based on field patterns, since the relationship between the array factor and the source distribution is a Fourier transform. In this case, quicker and efficient algorithms are obtained with the Fast Fourier Transform (FFT) to perform the calculations. Therefore, this work presents a new technique that synthesizes shaped beam patterns through the control of non-uniformly samples of the array factor, both in amplitude and phase. The sample phases increase the number of degrees of freedom. To produce complex patterns, the sample phases of the shaped beam region are used to create more oscillations in the ripple structure than the ones produced with the realpatterns. Not onl y this procedure yields a narrower transition region between the beam zone and the sidelobe zone but also smaller dynamic range ratios are obtained. Furthermore, it is described how to impose nulls in prescribed directions of the complex patterns. Some examples are presented to demonstrate the application of the synthesis technique.

Micromagnetic study of magnetization reversal in patterned DyFeCo thin films

AbstractMagnetization reversal in patterned perpendicular anisotropic DyFeCo films was investigated using micromagnetic simulations. The model consists of a square film of dimension 1 μm × 1 μm × 50 nm and a circular hole of diameter 500 nm on the top surface, with depth varying from 0‐30 nm. The results show that for shallower holes the coercivity decreases rapidly with the hole depth, but for the deeper holes, the coercivity in the hole region is much larger than in the land region. Further analysis indicates the variation in coercivity is due to the narrow transition region formed near the hole boundary where the magnetization has a tilted distribution determined mainly by the competition between anisotropy and exchange interactions. The simulation results are qualitatively consistent with our previous experimental outcome. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)