Stability of solutions of linear difference equations with periodic coefficients

This paper represents the last technical contribution of Professor Patrick Parks before his untimely death in February 1995. The remaining authors of the paper, which was subsequently completed, wish to dedicate the article to Patrick. A frequency criterion for the stability of solutions of linear difference equations with periodic coefficients is established. The stability criterion is based on a consideration of the behaviour of a frequency hodograph with respect to the origin of coordinates in the complex plane. The formulation of this criterion does not depend on the order of the difference equation.

Experimental measurement and numerical simulation of horizontal-coupled slinky ground source heat exchangers

Results from both experimental measurements and 3D numerical simulations of Ground Source Heat Pump systems (GSHP) at a UK climate are presented. Experimental measurements of a horizontal-coupled slinky GSHP were undertaken in Talbot Cottage at Drayton St Leonard site, Oxfordshire, UK. The measured thermophysical properties of in situ soil were used in the CFD model. The thermal performance of slinky heat exchangers for the horizontal-coupled GSHP system for different coil diameters and slinky interval distances was investigated using a validated 3D model. Results from a two month period of monitoring the performance of the GSHP system showed that the COP decreased with the running time. The average COP of the horizontal-coupled GSHP was 2.5. The numerical prediction showed that there was no significant difference in the specific heat extraction of the slinky heat exchanger at different coil diameters. However, the larger the diameter of coil, the higher the heat extraction per meter length of soil. The specific heat extraction also increased, but the heat extraction per meter length of soil decreased with the increase of coil central interval distance.

Genetic analysis of heat tolerance at anthesis in rice

Genetic analysis of heat tolerance will help breeders produce rice (Oryza sativa L.) varieties adapted to future climates. An F6 population of 181 recombinant inbred lines of Bala (tolerant) × Azucena (susceptible) was screened for heat tolerance at anthesis by measuring spikelet fertility at 30°C (control) and 38°C (high temperature) in experiments conducted in the Philippines and the United Kingdom. The parents varied significantly for absolute spikelet fertility under control (79–87%) and at high temperature (2.9–47.1%), and for relative spikelet fertility (high temperature/control) at high temperature (3.7–54.9%). There was no correlation between spikelet fertility in control and high-temperature conditions and no common quantitative trait loci (QTLs) were identified. Two QTLs for spikelet fertility under control conditions were identified on chromosomes 2 and 4. Eight QTLs for spikelet fertility under high-temperature conditions were identified on chromosomes 1, 2, 3, 8, 10, and 11. The most significant heat-responsive QTL, contributed by Bala and explaining up to 18% of the phenotypic variation, was identified on chromosome 1 (38.35 mega base pairs on the rice physical genome map). This QTL was also found to influence plant height, explaining 36.6% of the phenotypic variation. A comparison with other studies of abiotic (drought, cold, salinity) stresses showed QTLs at similar positions on chromosomes 1, 3, 8, and 10, suggesting common underlying stress-responsive regions of the genome.

Cumulant-based deconvolution and identification: several new families of linear equations

This paper presents several new families of cumulant-based linear equations with respect to the inverse filter coefficients for deconvolution (equalisation) and identification of nonminimum phase systems. Based on noncausal autoregressive (AR) modeling of the output signals and three theorems, these equations are derived for the cases of 2nd-, 3rd and 4th-order cumulants, respectively, and can be expressed as identical or similar forms. The algorithms constructed from these equations are simpler in form, but can offer more accurate results than the existing methods. Since the inverse filter coefficients are simply the solution of a set of linear equations, their uniqueness can normally be guaranteed. Simulations are presented for the cases of skewed series, unskewed continuous series and unskewed discrete series. The results of these simulations confirm the feasibility and efficiency of the algorithms.

A simplified mathematical model for urban microclimate simulation

Techniques for modelling urban microclimates and urban block surfaces temperatures are desired by urban planners and architects for strategic urban designs at the early design stages. This paper introduces a simplified mathematical model for urban simulations (UMsim) including urban surfaces temperatures and microclimates. The nodal network model has been developed by integrating coupled thermal and airflow model. Direct solar radiation, diffuse radiation, reflected radiation, long-wave radiation, heat convection in air and heat transfer in the exterior walls and ground within the complex have been taken into account. The relevant equations have been solved using the finite difference method under the Matlab platform. Comparisons have been conducted between the data produced from the simulation and that from an urban experimental study carried out in a real architectural complex on the campus of Chongqing University, China in July 2005 and January 2006. The results show a satisfactory agreement between the two sets of data. The UMsim can be used to simulate the microclimates, in particular the surface temperatures of urban blocks, therefore it can be used to assess the impact of urban surfaces properties on urban microclimates. The UMsim will be able to produce robust data and images of urban environments for sustainable urban design.

The comfort, energy and health implications of London’s urban heat island

The urban heat island (UHI) is a well-known effect of urbanisation and is particularly important in world megacities. Overheating in such cities is expected to be exacerbated in the future as a result of further urban growth and climate change. Demonstrating and quantifying the impact of individual design interventions on the UHI is currently difficult using available software tools. The tools developed in the LUCID (‘The Development of a Local Urban Climate Model and its Application to the Intelligent Design of Cities’) research project will enable the related impacts to be better understood, quantified and addressed. This article summarises the relevant literature and reports on the ongoing work of the project.

Applying the extended Kalman filter to systems described by nonlinear differential-algebraic equations

This paper describes a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation models using the extended Kalman filter. The method involves the use of a time-varying linearisation of a semi-explicit index one differential-algebraic equation. The estimation technique consists of a simplified extended Kalman filter that is integrated with the differential-algebraic equation model. The paper describes a simulation study using a model of a batch chemical reactor. It also reports a study based on experimental data obtained from a mixing process, where the model of the system is solved using the sequential modular method and the estimation involves a bank of extended Kalman filters.

Optimal control of nonlinear systems represented by differential algebraic equations

An iterative procedure is described for solving nonlinear optimal control problems subject to differential algebraic equations. The procedure iterates on an integrated modified simplified model based problem with parameter updating in such a manner that the correct solution of the original nonlinear problem is achieved.

Long-term effect of volcanic forcing on ocean heat content

Explosive volcanic eruptions cause episodic negative radiative forcing of the climate system. Using coupled atmosphere-ocean general circulation models (AOGCMs) subjected to historical forcing since the late nineteenth century, previous authors have shown that each large volcanic eruption is associated with a sudden drop in ocean heat content and sea-level from which the subsequent recovery is slow. Here we show that this effect may be an artefact of experimental design, caused by the AOGCMs not having been spun up to a steady state with volcanic forcing before the historical integrations begin. Because volcanic forcing has a long-term negative average, a cooling tendency is thus imposed on the ocean in the historical simulation. We recommend that an extra experiment be carried out in parallel to the historical simulation, with constant time-mean historical volcanic forcing, in order to correct for this effect and avoid misinterpretation of ocean heat content changes

Vertical heat transports in the ocean and their effect on time-dependent climate change

In response to increasing atmospheric con- centrations of greenhouse gases, the rate of time- dependent climate change is determined jointly by the strength of climate feedbacks and the e�ciency of pro- cesses which remove heat from the surface into the deep ocean. This work examines the vertical heat transport processes in the ocean of the HADCM2 atmosphere± ocean general circulation model (AOGCM) in experi- ments with CO2 held constant (control) and increasing at 1% per year (anomaly). The control experiment shows that global average heat exchanges between the upper and lower ocean are dominated by the Southern Ocean, where heat is pumped downwards by the wind- driven circulation and di�uses upwards along sloping isopycnals. This is the reverse of the low-latitude balance used in upwelling±di�usion ocean models, the global average upward di�usive transport being against the temperature gradient. In the anomaly experiment, weakened convection at high latitudes leads to reduced diffusive and convective heat loss from the deep ocean, and hence to net heat uptake, since the advective heat input is less a�ected. Reduction of deep water produc- tion at high latitudes results in reduced upwelling of cold water at low latitudes, giving a further contribution to net heat uptake. On the global average, high-latitude processes thus have a controlling in¯uence. The impor- tant role of di�usion highlights the need to ensure that the schemes employed in AOGCMs give an accurate representation of the relevant sub-grid-scale processes.

Generalised Dirichelt-to-Neumann map in time dependent domains

We study the heat, linear Schrodinger and linear KdV equations in the domain l(t) < x < ∞, 0 < t < T, with prescribed initial and boundary conditions and with l(t) a given differentiable function. For the first two equations, we show that the unknown Neumann or Dirichlet boundary value can be computed as the solution of a linear Volterra integral equation with an explicit weakly singular kernel. This integral equation can be derived from the formal Fourier integral representation of the solution. For the linear KdV equation we show that the two unknown boundary values can be computed as the solution of a system of linear Volterra integral equations with explicit weakly singular kernels. The derivation in this case makes crucial use of analyticity and certain invariance properties in the complex spectral plane. The above Volterra equations are shown to admit a unique solution.