Spectral analysis and the Aharonov-Bohm\~ effect on certain almost-Riemannian manifold

We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalised Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.

Studying the contact point and interface moving in a sinusoidal tube with lattice Boltzmann method

The multicomponent nonideal gas lattice Boltzmann model by Shan and Chen (S-C) is used to study the immiscible displacement in a sinusoidal tube. The movement of interface and the contact point (contact line in three-dimension) is studied. Due to the roughness of the boundary, the contact point shows "stick-slip" mechanics. The "stick-slip" effect decreases as the speed of the interface increases. For fluids that are nonwetting, the interface is almost perpendicular to the boundaries at most time, although its shapes at different position of the tube are rather different. When the tube becomes narrow, the interface turns a complex curves rather than remains simple menisci. The velocity is found to vary considerably between the neighbor nodes close to the contact point, consistent with the experimental observation that the velocity is multi-values on the contact line. Finally, the effect of three boundary conditions is discussed. The average speed is found different for different boundary conditions. The simple bounce-back rule makes the contact point move fastest. Both the simple bounce-back and the no-slip bounce-back rules are more sensitive to the roughness of the boundary in comparison with the half-way bounce-back rule. The simulation results suggest that the S-C model may be a promising tool in simulating the displacement behaviour of two immiscible fluids in complex geometry.

The effect of flow field & geometry on the dynamic contact angle

A number of recent experiments suggest that, at a given wetting speed, the dynamic contact angle formed by an advancing liquid-gas interface with a solid substrate depends on the flow field and geometry near the moving contact line. In the present work, this effect is investigated in the framework of an earlier developed theory that was based on the fact that dynamic wetting is, by its very name, a process of formation of a new liquid-solid interface (newly “wetted” solid surface) and hence should be considered not as a singular problem but as a particular case from a general class of flows with forming or/and disappearing interfaces. The results demonstrate that, in the flow configuration of curtain coating, where a liquid sheet (“curtain”) impinges onto a moving solid substrate, the actual dynamic contact angle indeed depends not only on the wetting speed and material constants of the contacting media, as in the so-called slip models, but also on the inlet velocity of the curtain, its height, and the angle between the falling curtain and the solid surface. In other words, for the same wetting speed the dynamic contact angle can be varied by manipulating the flow field and geometry near the moving contact line. The obtained results have important experimental implications: given that the dynamic contact angle is determined by the values of the surface tensions at the contact line and hence depends on the distributions of the surface parameters along the interfaces, which can be influenced by the flow field, one can use the overall flow conditions and the contact angle as a macroscopic multiparametric signal-response pair that probes the dynamics of the liquid-solid interface. This approach would allow one to investigate experimentally such properties of the interface as, for example, its equation of state and the rheological properties involved in the interface’s response to an external torque, and would help to measure its parameters, such as the coefficient of sliding friction, the surface-tension relaxation time, and so on.

Time-varying coefficients in the almost ideal demand system: An empirical appraisal

This paper provides a generalisation of the structural time series version of the Almost Ideal Demand System (AIDS) that allows for time-varying coefficients (TVC/AIDS) in the presence of cross-equation constraints. An empirical appraisal of the TVC/AIDS is made using a dynamic AIDS with trending intercept as the baseline model with a data set from the Italian Household Budget Survey (1986-2001). The assessment is based on four criteria: adherence to theoretical constraints, statistical diagnostics on residuals, forecasting performance and economic meaningfulness. No clear evidence is found for superior performance of the TVC/AIDS, apart from improved short-term forecasts.

Testing symmetry and homogeneity in the almost ideal demand system with co-integrated data using fully modified estimation and the bootstrap

Conventional seemingly unrelated estimation of the almost ideal demand system is shown to lead to small sample bias and distortions in the size of a Wald test for symmetry and homogeneity when the data are co-integrated. A fully modified estimator is developed in an attempt to remedy these problems. It is shown that this estimator reduces the small sample bias but fails to eliminate the size distortion.. Bootstrapping is shown to be ineffective as a method of removing small sample bias in both the conventional and fully modified estimators. Bootstrapping is effective, however, as a method of removing. size distortion and performs equally well in this respect with both estimators.

The demand for a healthy diet: estimating the almost ideal demand system with infrequency of purchase

A Bayesian method of estimating multivariate sample selection models is introduced and applied to the estimation of a demand system for food in the UK to account for censoring arising from infrequency of purchase. We show how it is possible to impose identifying restrictions on the sample selection equations and that, unlike a maximum likelihood framework, the imposition of adding up at both latent and observed levels is straightforward. Our results emphasise the role played by low incomes and socio-economic circumstances in leading to poor diets and also indicate that the presence of children in a household has a negative impact on dietary quality.

Performance statistics of a head-operated force-reflecting rehabilitation robot system

Researchers in the rehabilitation engineering community have been designing and developing a variety of passive/active devices to help persons with limited upper extremity function to perform essential daily manipulations. Devices range from low-end tools such as head/mouth sticks to sophisticated robots using vision and speech input. While almost all of the high-end equipment developed to date relies on visual feedback alone to guide the user providing no tactile or proprioceptive cues, the “low-tech” head/mouth sticks deliver better “feel” because of the inherent force feedback through physical contact with the user's body. However, the disadvantage of a conventional head/mouth stick is that it can only function in a limited workspace and the performance is limited by the user's strength. It therefore seems reasonable to attempt to develop a system that exploits the advantages of the two approaches: the power and flexibility of robotic systems with the sensory feedback of a headstick. The system presented in this paper reflects the design philosophy stated above. This system contains a pair of master-slave robots with the master being operated by the user's head and the slave acting as a telestick. Described in this paper are the design, control strategies, implementation and performance evaluation of the head-controlled force-reflecting telestick system.

Out of the ivory tower: the impact of wider social contact on the values, religious beliefs and identities of Chinese postgraduate students in the UK

This article explores the impact of wider social contact on the experience of Chinese postgraduate students of adaptation to life in the UK. Focus group and individual interviews were conducted with a group of 11 Chinese students on an MA programme at a university in southern England and individual interviews with three representatives of a local volunteer group (LVG) offering support to the Chinese students. Although it was perceived that the students’ support needs were not adequately met by the University, the additional support offered outside the University was unanimously valued and considered as enriching their cultural and linguistic experiences and meeting their expectations. However, frequent social contact with the LVG, whose members were mostly Christians, also had an impact on their values, religious beliefs and identities. In a discussion framed within the sociological perspective of proselytization or religious conversion and the broad framework of international education and globalization, the different responses to this contact are described in terms of believers, doubters, empathisers and commentators. Implications are considered for universities, people involved in providing social support for international students, and sponsors of international students.

Direct contact membrane distillation

This review looks at the work carried out over the past 15 years on membrane distillation and reports the conditions utilized for research. The process is still used mainly at the laboratory scale, but a few pilot plants have been built across the world, mostly for desalination and the production of potable water. Studies into membrane distillation have been concerned with the effect of mass transfer, heat transfer, and stirring rate, but the most important effect that has to be considered with this process is temperature polarization. A section on temperature polarization and the effect of boundary layers is included in this review.

Amplifying vibrational circular dichroism by manipulation of the electronic manifold

Vibrational circular dichroism is a powerful technique to study the stereochemistry of chiral molecules, but often suffers from small signal intensities. Electrochemical modulation of the energies of the electronically excited state manifold is now demonstrated to lead to an order of magnitude enhancement of the differential absorption. Quantum-chemical calculations show that increased mixing between ground and excited states is at the origin of this amplification.

Exact design manifold control of a class of nonlinear singularly perturbed systems

The integral manifold approach captures from a geometric point of view the intrinsic two-time-scale behavior of singularly perturbed systems. An important class of nonlinear singularly perturbed systems considered in this note are fast actuator-type systems. For a class of fast actuator-type systems, which includes many physical systems, an explicit corrected composite control, the sum of a slow control and a fast control, is derived. This corrected control will steer the system exactly to a required design manifold.