Stability analysis and observer design for discrete-time SEIR epidemic models

This paper applies Micken's discretization method to obtain a discrete-time SEIR epidemic model. The positivity of the model along with the existence and stability of equilibrium points is discussed for the discrete-time case. Afterwards, the design of a state observer for this discrete-time SEIR epidemic model is tackled. The analysis of the model along with the observer design is faced in an implicit way instead of obtaining first an explicit formulation of the system which is the novelty of the presented approach. Moreover, some sufficient conditions to ensure the asymptotic stability of the observer are provided in terms of a matrix inequality that can be cast in the form of a LMI. The feasibility of the matrix inequality is proved, while some simulation examples show the operation and usefulness of the observer.

Novel fluid grid and voidage calculation techniques for a discrete element model of a 3D cylindrical fluidized bed

A discrete element model (DEM) combined with computational fluid dynamics (CFD) was developed to model particle and fluid behaviour in 3D cylindrical fluidized beds. Novel techniques were developed to (1) keep fluid cells, defined in cylindrical coordinates, at a constant volume in order to ensure the conditions for validity of the volume-averaged fluid equations were satisfied and (2) smoothly and accurately measure voidage in arbitrarily shaped fluid cells. The new technique for calculating voidage was more stable than traditional techniques, also examined in the paper, whilst remaining computationally-effective. The model was validated by quantitative comparison with experimental results from the magnetic resonance imaging of a fluidised bed analysed to give time-averaged particle velocities. Comparisons were also made between theoretical determinations of slug rise velocity in a tall bed. It was concluded that the DEM-CFD model is able to investigate aspects of the underlying physics of fluidisation not readily investigated by experiment. © 2014 The Authors.

instability of standing wave, global existence and blowup for the klein-gordon-zakharov system with different-degree nonlinearities

This paper discusses the Klein–Gordon–Zakharov system with different-degree nonlinearities in two and three space dimensions. Firstly, we prove the existence of standing wave with ground state by applying an intricate variational argument. Next, by introducing an auxiliary functional and an equivalent minimization problem, we obtain two invariant manifolds under the solution flow generated by the Cauchy problem to the aforementioned Klein–Gordon–Zakharov system. Furthermore, by constructing a type of constrained variational problem, utilizing the above two invariant manifolds as well as applying potential well argument and concavity method, we derive a sharp threshold for global existence and blowup. Then, combining the above results, we obtain two conclusions of how small the initial data are for the solution to exist globally by using dilation transformation. Finally, we prove a modified instability of standing wave to the system under study.

A global shallow water model using high order multi-moment constrained finite volume method and icosahedral grid

A novel accurate numerical model for shallow water equations on sphere have been developed by implementing the high order multi-moment constrained finite volume (MCV) method on the icosahedral geodesic grid. High order reconstructions are conducted cell-wisely by making use of the point values as the unknowns distributed within each triangular cell element. The time evolution equations to update the unknowns are derived from a set of constrained conditions for two types of moments, i.e. the point values on the cell boundary edges and the cell-integrated average. The numerical conservation is rigorously guaranteed. in the present model, all unknowns or computational variables are point values and no numerical quadrature is involved, which particularly benefits the computational accuracy and efficiency in handling the spherical geometry, such as coordinate transformation and curved surface. Numerical formulations of third and fourth order accuracy are presented in detail. The proposed numerical model has been validated by widely used benchmark tests and competitive results are obtained. The present numerical framework provides a promising and practical base for further development of atmospheric and oceanic general circulation models. (C) 2009 Elsevier Inc. All rights reserved.

An extended variable-grid global ocean circulation model and its preliminary results of the equatorial Pacific circulation

To investigate the interaction between the tropical Pacific and China seas a variable-grid global ocean circulation model with fine grid[(1/6)degrees] covering the area from 20degreesS to 50degreesN and from 99degrees to 150degreesE is developed. Numerical computation of the annually cyclic circulation fields is performed. The results of the annual mean zonal currents and deep to abyssal western boundary currents in the equatorial Pacific Ocean are reported. The North Equatorial Current,the North Equatorial Countercurrent, the South Equatorial Current and the Equatorial Undercurrent are fairly well simulated. The model well reproduces the northward flowing abyssal western boundary current. From the model results a lower deep western boundary current east of the Bismarck-Solomon-New Hebrides Island chain at depths around 2 000 in has been found. The model results also show that the currents in the equatorial Pacific Ocean have multi-layer structures both in zonal currents and western boundary currents, indicating that the global ocean overturning thermohaline circulation appears of multi-layer pattern.

Interbasin freshwater, heat and salt transport through the boundaries of the East and South China Seas from a variable-grid global ocean circulation model

The monthly and annual mean freshwater, heat and salt transport through the open boundaries of the South and East China Seas derived from a variable-grid global ocean circulation model is reported. The model has 1/6degrees resolution for the seas adjacent to China and 30 resolution for the global ocean. The model results are in fairly good agreement with the existing estimates based on measurements. The computation shows that the flows passing through the South China Sea contribute volume, heat and salt transport of 5.3 Sv, 0.57 PW and 184 Ggs(-1), respectively (about 1/4) to the Indonesian Throughflow, indicating that the South China Sea is an important pathway of the Pacific to Indian Ocean throughflow. The volume, heat and salt transport of the Kuroshio in the East China Sea is 25.6 Sv, 2.32 PW and 894 Ggs(-1), respectively. Less than 1/4 of this transport passes through the passage between Iriomote and Okinawa. The calculation of heat balance indicates that the South China Sea absorbs net heat flux from the sun and atmosphere with a rate of 0.08 PW, while the atmosphere gains net heat flux from the Baohai, Yellow and East China Seas with a rate of 0.05 PW.

Sea surface height and transport stream function of the South China Sea from a variable-grid global ocean circulation model

A fine-grid model (1/6degrees) covering the South China Sea (SCS), East China Sea and Japan/East Sea, which is embedded into a coarse-grid (3degrees) global model, was established to study the SCS circulation. In the present paper, we report the model-produced monthly and annual mean transport stream functions and sea surface heights(SSH) and their anomalies of the SCS. Comparison to the TOPEX/Poseidon data shows that the model-produced monthly sea surface height anomalies (SSHA) are in good agreement with altimeter measurements. Based on the results, the circulation of the SCS, especially the upper layer circulation, is discussed. In the surface layer, the western Philippine Sea water intrudes into the SCS through the Luzon Strait in autumn, winter and spring, but not in summer. However, as far as the whole water column is concerned, the water intrudes into the SCS through the Luzon Strait all the year round. This indicates that in summer the water still intrudes into the SCS in the subsurface and intermediate layers. The area near the northern continental slope of the SCS is dominated by a cyclonic circulation all the year round. The SCS Southern Anticyclonic Gyre, SE Vietnam Off-Shore Current in summertime and SCS Southern Cyclonic Gyre in wintertime are reproduced reasonably. The difference between the monthly averaged SSH and SSHA is significant, indicating the importance of the mean SSH in the SCS circulation.

Grid integration of wave energy & generic modelling of ocean devices for power system studies

The work presented in this thesis covers four major topics of research related to the grid integration of wave energy. More specifically, the grid impact of a wave farm on the power quality of its local network is investigated. Two estimation methods were developed regarding the flicker level Pst generated by a wave farm in relation to its rated power as well as in relation to the impedance angle ψk of the node in the grid to which it is connected. The electrical design of a typical wave farm design is also studied in terms of minimum rating for three types of costly pieces of equipment, namely the VAr compensator, the submarine cables and the overhead line. The power losses dissipated within the farm's electrical network are also evaluated. The feasibility of transforming a test site into a commercial site of greater rated power is investigated from the perspective of power quality and of cables and overhead line thermal loading. Finally, the generic modelling of ocean devices, referring here to both wave and tidal current devices, is investigated.

Tectonic and magmatic segmentation of the Global Ocean Ridge System: A synthesis of observations

© 2016 The Author(s).Mid-ocean ridges display tectonic segmentation defined by discontinuities of the axial zone, and geophysical and geochemical observations suggest segmentation of the underlying magmatic plumbing system. Here, observations of tectonic and magmatic segmentation at ridges spreading from fast to ultraslow rates are reviewed in light of influential concepts of ridge segmentation, including the notion of hierarchical segmentation, spreading cells and centralized v. multiple supply of mantle melts. The observations support the concept of quasi-regularly spaced principal magmatic segments, which are 30-50 km long on average at fast- to slow-spreading ridges and fed by melt accumulations in the shallow asthenosphere. Changes in ridge properties approaching or crossing transform faults are often comparable with those observed at smaller offsets, and even very small discontinuities can be major boundaries in ridge properties. Thus, hierarchical segmentation models that suggest large-scale transform fault-bounded segmentation arises from deeper level processes in the asthenosphere than the finer-scale segmentation are not generally supported. The boundaries between some but not all principal magmatic segments defined by ridge axis geophysical properties coincide with geochemical boundaries reflecting changes in source composition or melting processes. Where geochemical boundaries occur, they can coincide with discontinuities of a wide range of scales.