On Fuzzy Regression Adapting Partial Least Squares

Partial Least Squared (PLS) regression is a model linking a dependent variable y to a set of X (numerical or categorical) explanatory variables. It can be obtained as a series of simple and multiple regressions of simple and multiple regressions. PLS is an alternative to classical regression model when there are many variables or the variables are correlated. On the other hand, an alternative method to regression in order to model data has been studied is called Fuzzy Linear Regression (FLR). FLR is one of the modelling techniques based on fuzzy set theory. It is applied to many diversified areas such as engineering, biology, finance and so on. Development of FLR follows mainly two paths. One of which depends on improving the parameter estimation methods. This enables to compute more reliable and more accurate parameter estimation in fuzzy setting. Second of which is related to applying these methods to data, which usually do not follow strict assumptions. The application point of view of FLR has not been examined widely except outlier case. For example, it has not been widely examined how FLR behaves under the multivariate case. To overcome such a problem in classic setting, one of the methods that are practically useful is PLS. In this paper, FLR is examined based on application point of view when it has several explanatory variables by adapting PLS

Determination of inorganic arsenic in water by a quartz crystal microbalance

A quartz crystal microbalance sensor has been developed for the determination of inorganic arsenic species in water. The gold electrode surface was modified by a self-assembled layer of dithiothreitol, and the frequency change of the modified crystal was proportional to the arsenic concentration from 0 to around 50 µg L-1, a range which spans the current US EPA maximum contaminent level of 10 µg L-1 in drinking water. As dithiothreitol is capable of reducing arsenate to arsenite, the sensor detects both species. The method was applied to the determination of arsenic in spiked rain, tap, pond and bottled water; recoveries not significantly different from 100% were obtained for a number of spike additions of less than 10 µg L -1. Arsenic was only detected in the bottled water sample, at a concentration of 8 µg L-1. This method is simple, fast, and inexpensive compared with other conventional arsenic detection methods, and has the potential to be used in the field. © 2013 The Royal Society of Chemistry

Forced Oscillations of Supported Drops

Oscillations of supported liquid drops are the subject of wide scientific interest, with applications in areas as diverse as liquid-liquid extraction, synthesis of ceramic powders, growing of pure crystals in low gravity, and measurement of dynamic surface tension. In this research, axisymmetric forced oscillations of arbitrary amplitude of viscous liquid drops of fixed volume which are pendant from or sessile on a rod with a fixed or moving contact line and surrounded by an inviscid ambient gas are induced by moving the rod in the vertical direction sinusiodally in time. In this paper, a preliminary report is made on the computational analysis of the oscillations of supported drops that have 'clean' interfaces and whose contact lines remain fixed throughout their motions. The relative importance of forcing to damping can be increased by either increasing the amplitude of rod motion A or Reynolds number Re. It is shown that as the ratio of forcing to damping rises, for drops starting from an initial rest state a sharp increase in deformation can occur when they are forced to oscillate in the vicinity of their resonance frequencies, indicating the incipience of hysteresis. However, it is also shown that the existence of a second stable limit cycle and the occurrence of hysteresis can be observed if the drop is subjected to a so-called frequency sweep, where the forcing frequency is first increased and then decreased over a suitable range. Because the change in drop deformation response is abrupt in the vicinity of the forcing frequencies where hysteresis occurs, it should be possible to exploit the phenomenon to accurately measure the viscosity and surface tension of the drop liquid

Very high two-dimensional hole gas mobilities in strained silicon germanium

We report on the growth by solid source MBE and characterization of remote doped Si/SiGe/Si two-dimensional hole gas structures. It has been found that by reducing the Ge composition to <=13% and limiting the thickness of the alloy layer, growth temperatures can be increased up to 950 °C for these structures while maintaining good structural integrity and planar interfaces. Record mobilities of 19 820 cm2 V−1 s−1 at 7 K were obtained in normal structures. Our calculations suggest that alloy scattering is not important in these structures and that interface roughness and interface charge scattering limit the low temperature mobilities

The inexorable resistance of inertia determines the initial regime of drop coalescence

Drop coalescence is central to diverse processes involving dispersions of drops in industrial, engineering and scientific realms. During coalescence, two drops first touch and then merge as the liquid neck connecting them grows from initially microscopic scales to a size comparable to the drop diameters. The curvature of the interface is infinite at the point where the drops first make contact, and the flows that ensue as the two drops coalesce are intimately coupled to this singularity in the dynamics. Conventionally, this process has been thought to have just two dynamical regimes: a viscous and an inertial regime with a crossover region between them. We use experiments and simulations to reveal that a third regime, one that describes the initial dynamics of coalescence for all drop viscosities, has been missed. An argument based on force balance allows the construction of a new coalescence phase diagram

Thin-sheet flow between coalescing bubbles

When two spherical bubbles touch, a hole is formed in the fluid sheet between them, and capillary pressure acting on its tightly curved edge drives an outward radial flow which widens the hole joining the bubbles. Recent images of the early stages of this process (Paulsen et al., Nat. Commun., vol. 5, 2014) show that the radius of the hole $r_{\!E}$ at time $t$ grows proportional to $t^{1/2}$, and that the rate is dependent on the fluid viscosity. Here, we explain this behaviour in terms of similarity solutions to a third-order system of radial extensional-flow equations for the thickness and velocity of the sheet of fluid between the bubbles, and determine the growth rate as a function of the Ohnesorge number $\mathit{Oh}$. The initially quadratic sheet profile allows the ratio of viscous and inertial effects to be independent of time. We show that the sheet is slender for $r_{\!E}\ll a$ if $\mathit{Oh}\gg 1$, where $a$ is the bubble radius, but only slender for $r_{\!E}\ll \mathit{Oh}^{2}a$ if $\mathit{Oh}\ll 1$ due to a compressional boundary layer of length $L\propto \mathit{Oh}\,r_{\!E}$, after which there is a change in the structure but not the speed of the retracting sheet. For $\mathit{Oh}\ll 1$, the detailed analysis justifies a simple momentum-balance argument, which gives the analytic prediction $r_{\!E}\sim (32a{\it\gamma}/3{\it\rho})^{1/4}t^{1/2}$, where ${\it\gamma}$ is the surface tension and ${\it\rho}$ is the density.J.P.M. acknowledges an Engineering and Physical Sciences Research Council studentship. C.R.A. and O.A.B. acknowledge the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research. All data accompanying this publication are directly available within the publication.This is the accepted manuscript of a paper published in the Journal of Fluid Mechanics (Munro JP, Anthony CR, Basaran OA, Lister JR, Journal of Fluid Mechanics, 2015, 773, doi:10.1017/jfm.2015.253). The final version is available at http://dx.doi.org/10.1017/jfm.2015.25

Inertial impedance of coalescence during collision of liquid drops

The fluid dynamics of the collision and coalescence of liquid drops has intrigued scientists and engineers for more than a century owing to its ubiquitousness in nature, e.g. raindrop coalescence, and industrial applications, e.g. breaking of emulsions in the oil and gas industry. The complexity of the underlying dynamics, which includes occurrence of hydrodynamic singularities, has required study of the problem at different scales – macroscopic, mesoscopic and molecular – using stochastic and deterministic methods. In this work, a multi-scale, deterministic method is adopted to simulate the approach, collision, and eventual coalescence of two drops where the drops as well as the ambient fluid are incompressible, Newtonian fluids. The free boundary problem governing the dynamics consists of the Navier–Stokes system and associated initial and boundary conditions that have been augmented to account for the effects of disjoining pressure as the separation between the drops becomes of the order of a few hundred nanometres. This free boundary problem is solved by a Galerkin finite element-based algorithm. The interplay of inertial, viscous, capillary and van der Waals forces on the coalescence dynamics is investigated. It is shown that, in certain situations, because of inertia two drops that are driven together can first bounce before ultimately coalescing. This bounce delays coalescence and can result in the computed value of the film drainage time departing significantly from that predicted from existing scaling theories

Effective mass and band nonparabolicity in remote doped Si/Si0.8Ge0.2 quantum wells

The effective masses in remote doped Si/Si0.8Ge0.2/Si quantum wells having sheet densities, Ns in the range 2 × 1011–1.1 × 1012 cm – 2 have been determined from the temperature dependencies of the Shubnikov–de Haas oscillations. The values obtained increase with magnetic field and Ns. This behavior is taken as evidence for the nonparabolicity of the valence band and accounts for the discrepancies in previously reported masses. Self-consistent band structure calculations for a triangular confinement of the carriers have also been carried out and provide confirmation of the increase in mass with Ns. Theory and experiment give extrapolated Gamma point effective masses of 0.21 and 0.20 of the free-electron mass, respectively