Stability and convergence of implicit numerical methods for a class of fractional advection-dispersion models

In this paper, a class of fractional advection-dispersion models (FADM) is investigated. These models include five fractional advection-dispersion models: the immobile, mobile/immobile time FADM with a temporal fractional derivative 0 < γ < 1, the space FADM with skewness, both the time and space FADM and the time fractional advection-diffusion-wave model with damping with index 1 < γ < 2. They describe nonlocal dependence on either time or space, or both, to explain the development of anomalous dispersion. These equations can be used to simulate regional-scale anomalous dispersion with heavy tails, for example, the solute transport in watershed catchments and rivers. We propose computationally effective implicit numerical methods for these FADM. The stability and convergence of the implicit numerical methods are analyzed and compared systematically. Finally, some results are given to demonstrate the effectiveness of our theoretical analysis.

Total energy shaping of a class of underactuated Port-Hamiltonian Systems using a new set of closed-loop potential shape variables

This paper proposes a method for designing set-point regulation controllers for a class of underactuated mechanical systems in Port-Hamiltonian System (PHS) form. A new set of potential shape variables in closed loop is proposed, which can replace the set of open loop shape variables-the configuration variables that appear in the kinetic energy. With this choice, the closed-loop potential energy contains free functions of the new variables. By expressing the regulation objective in terms of these new potential shape variables, the desired equilibrium can be assigned and there is freedom to reshape the potential energy to achieve performance whilst maintaining the PHS form in closed loop. This complements contemporary results in the literature, which preserve the open-loop shape variables. As a case study, we consider a robotic manipulator mounted on a flexible base and compensate for the motion of the base while positioning the end effector with respect to the ground reference. We compare the proposed control strategy with special cases that correspond to other energy shaping strategies previously proposed in the literature.

Tracking control of a class of Hamiltonian mechanical systems with disturbances

This paper presents a trajectory-tracking control strategy for a class of mechanical systems in Hamiltonian form. The class is characterised by a simplectic interconnection arising from the use of generalised coordinates and full actuation. The tracking error dynamic is modelled as a port-Hamiltonian Systems (PHS). The control action is designed to take the error dynamics into a desired closed-loop PHS characterised by a constant mass matrix and a potential energy with a minimum at the origin. A transformation of the momentum and a feedback control is exploited to obtain a constant generalised mass matrix in closed loop. The stability of the close-loop system is shown using the close-loop Hamiltonian as a Lyapunov function. The paper also considers the addition of integral action to design a robust controller that ensures tracking in spite of disturbances. As a case study, the proposed control design methodology is applied to a fully actuated robotic manipulator.

3D QSAR studies of N-4-arylacryloylpiperazin-1-yl-phenyl-oxazolidinones: A novel class of antibacterial agents

Three-dimensional QSAR studies for N-4-arylacryloylpiperazin-1-yl-phenyl-oxazolidinones were conducted using TSAR 3.3. The in vitro activities (MICs) of the compounds against Staphylococcus aureus ATCC 25923 exhibited a strong correlation with the prediction made by the model developed in the present study.

A potent nonporphyrin class of photodynamic therapeutic agent: Cellular localisation, cytotoxic potential and influence of hypoxia

We have developed a totally new class of nonporphyrin photodynamic therapeutic agents with a specific focus on two lead candidates azadipyrromethene (ADPM)01 and ADPM06. Confocal laser scanning microscopy imaging showed that these compounds are exclusively localised to the cytosolic compartment, with specific accumulation in the endoplasmic reticulum and to a lesser extent in the mitochondria. Light-induced toxicity assays, carried out over a broad range of human tumour cell lines, displayed EC50 values in the micro-molar range for ADPM01 and nano-molar range for ADPM06, with no discernable activity bias for a specific cell type. Strikingly, the more active agent, ADPM06, even retained significant activity under hypoxic conditions. Both photosensitisers showed low to nondeterminable dark toxicity. Flow cytometric analysis revealed that ADPM01 and ADPM06 were highly effective at inducing apoptosis as a mode of cell death. The photophysical and biological characteristics of these PDT agents suggest that they have potential for the development of new anticancer therapeutics. © 2005 Cancer Research UK.