A dynamic reduced order model using integral manifold theory has been derived, which can be used to simulate the DOIG wind turbine using a double-winding representation of the generator rotor. The model is suitable for use in transient stability programs that can be used to investigate large power systems. The behavior of a wind farm and the network under various system disturbances was stu...

The aim of this work is to describe the qualitative behavior of the solution set of a given system of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. In order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. This is done by the extension of...

This paper reports an ethnography of ambulance dispatch work in a large UK metropolitan region. The interplay between control centre ecology, usage of a computerised dispatch system, and cooperative work of control personnel is analysed. The methods by which a 'working division of labour' is sustained to effectively manage dispatch in the face of high workload and manifold contingency are expli...

We consider a ring of identical elements with time delayed, nearest neighbour coupling. The individual elements are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. The linear stability of the trivial solution is completely analyzed and illustrated in the parameter space of the coupling strength and the coupling delay. Conditions for g...

DNA polymerases are the key enzymes for DNA synthesis involved in DNA replication, recombination, and repair. These enzymes undergo manifold contacts with the primer-template-substrates reaching up to several nucleotide pairs beyond the catalytic centre. To evaluate these enzyme contacts with the DNA substrates we applied novel synthetic steric probes in functional studies. We found that throug...

In classical epidemic models, it is common to observe that a disease-free equilibrium looses its stability for R0 = 1 and a transcritical bifurcation takes place. We analyze this aspect from the point of view of the mathematical structure of models, in order to assess which parts of the structure might be responsible of the direction of the transcritical bifurcation. We formulate a general crit...

This paper deals with a plant-pollinator model with diffusion and time delay effects. By considering the distribution of eigenvalues of the corresponding linearized equation, we first study stability of the positive constant steady-state and existence of spatially homogeneous and spatially inhomogeneous periodic solutions are investigated. We then derive an explicit formula for determining the ...

Consider the three-dimensional flow of a viscous Newtonian fluid upon an abitrarily curved substrate when the fluid film is thin as occurs in many draining, coating and biological flows. We derive a model of the dynamics of the film, the model being expressed in terms of the film thickness and the curvature tensor of the substrate. The model accurately includes the effects of the curvature of t...

We analyse dispersion of contaminants in turbulent boundary layer using centre manifold technique. The method describes long-term asymptotics of the contaminant concentration as it becomes spread across the entire layer and is weakly distorted by the velocity shear. The dispersion is investigated in two cases: (a) logarithmic and (b) power velocity profile across the layer according to a tradit...

We present the exact and explicit solution of the principal chiral field in two dimensions for an infinitely large rank group manifold. The energy of the ground state is explicitly found for the external Noether’s fields of an arbitrary magnitude. At small field we found an inverse logarithmic singularity in the ground state energy at the mass gap which indicates that at N = ∞ the spectrum of t...