Modeling Brine Discharges from Multiple Marine Outfalls

Abstract When many marine outfalls are d ischarging brine to shallow coastal waters, the adverse long -term mutual impacts are strongly inter-dependent and of a capacity limit of the receiv ing waters. A mathematical model using a two-dimensional advection-diffusion equation based on a flat seabed is developed, and incorporates the effect of a coastal tidal current. The solutions are illustrat ed graphically to study the interaction of multip le brine plu mes, and then an asymptotic approximation will be made to the shoreline's concentration to evaluate the long -term salinity build-up in the coastal waters . An extension for calculat ing the co mpounded concentration following discharges from a modern marine outfall with a mu ltiport d iffuser is also considered. Keywords Brine discharge; far field model; long term impact assessment; multiport; tidal flow; two sea outfalls INTRODUCTION As desalinated water is indispensably required at all costs in hot and arid climate countries, there are intense seawater desalination activities in certa in coastlines of the Arabian Gulf, Red Sea, Mediterranean Sea, and the Gulf of Oman. In particular, more than half of the world's desalination plants are constructed along the coasts of the Arabian Gulf (a total capacity of 12 million m 3 /day), Gulf of Oman (1.1 million m 3 /day) and Red Sea (3.4 million m 3 /day

Quaternionic Root Systems and Subgroups of the Aut(F4)Aut(F_{4})

Cayley-Dickson doubling procedure is used to construct the root systems of some celebrated Lie algebras in terms of the integer elements of the division algebras of real numbers, complex numbers, quaternions and octonions. Starting with the roots and weights of SU(2) expressed as the real numbers one can construct the root systems of the Lie algebras of SO(4),SP(2)= SO(5),SO(8),SO(9),F_{4} and E_{8} in terms of the discrete elements of the division algebras. The roots themselves display the group structures besides the octonionic roots of E_{8} which form a closed octonion algebra. The automorphism group Aut(F_{4}) of the Dynkin diagram of F_{4} of order 2304, the largest crystallographic group in 4-dimensional Euclidean space, is realized as the direct product of two binary octahedral group of quaternions preserving the quaternionic root system of F_{4}.The Weyl groups of many Lie algebras, such as, G_{2},SO(7),SO(8),SO(9),SU(3)XSU(3) and SP(3)X SU(2) have been constructed as the subgroups of Aut(F_{4}). We have also classified the other non-parabolic subgroups of Aut(F_{4}) which are not Weyl groups. Two subgroups of orders192 with different conjugacy classes occur as maximal subgroups in the finite subgroups of the Lie group $G_{2}$ of orders 12096 and 1344 and proves to be useful in their constructions. The triality of SO(8) manifesting itself as the cyclic symmetry of the quaternionic imaginary units e_{1},e_{2},e_{3} is used to show that SO(7) and SO(9) can be embedded triply symmetric way in SO(8) and F_{4} respectively

Snub 24-Cell Derived from the Coxeter-Weyl Group W(D4)

Snub 24-cell is the unique uniform chiral polytope in four dimensions consisting of 24 icosahedral and 120 tetrahedral cells. The vertices of the 4-dimensional semi-regular polytope snub 24-cell and its symmetry group {(W(D_{4})\mathord{/{\vphantom {(W(D_{4}) C_{2}}}. \kern-\nulldelimiterspace} C_{2}}):S_{3} of order 576 are obtained from the quaternionic representation of the Coxeter-Weyl group \textbf{$W(D_{4}).$}The symmetry group is an extension of the proper subgroup of the Coxeter-Weyl group \textbf{$W(D_{4})$}by the permutation symmetry of the Coxeter-Dynkin diagram \textbf{$D_{4} .$} The 96 vertices of the snub 24-cell are obtained as the orbit of the group when it acts on the vector \textbf{$\Lambda =(\tau, 1, \tau, \tau)$}or\textbf{}on the vector\textbf{$\Lambda =(\sigma, 1, \sigma, \sigma)$}in the Dynkin basis with\textbf{$\tau =\frac{1+\sqrt{5}}{2} {\rm and}\sigma =\frac{1-\sqrt{5}}{2} {\rm .}$} The two different sets represent the mirror images of the snub 24-cell. When two mirror images are combined it leads to a quasi regular 4D polytope invariant under the Coxeter-Weyl group \textbf{$W(F_{4}).$}Each vertex of the new polytope is shared by one cube and three truncated octahedra. Dual of the snub 24 cell is also constructed. Relevance of these structures to the Coxeter groups \textbf{$W(H_{4}){\rm and}W(E_{8})$}has been pointed out.Comment: 15 pages, 8 figure

The hyperfine properties of a hydrogenated Fe/V superlattice

: We study the effect of hydrogen on the electronic, magnetic and hyperfine structures of an iron-vanadium superlattice consisting of three Fe monolayers and nine V monolayers. The contact charge density ({\rho}), the contact hyperfine field (Bhf) and the electronic field gradient (EFG) at the Fe sites for different H locations and H fillings are calculated using the first principle full-potential linear-augmented-plane-wave (FP-LAPW) method . It is found that sizeable changes in the hyperfine properties are obtained only when H is in the interface region.Comment: 6 pages, 2 figures, 3 tables, ICAME 2011 conference (Kobe, Japan

Non-Isothermal Model for Nematic Spherulite Growth

A computational study of the growth of two-dimensional nematic spherulites in an isotropic phase was performed using a Landau-de Gennes type quadrupolar ensor order parameter model for the first-order isotropic/nematic transition of 5CB (pentyl-cyanobiphenyl). An energy balance, taking anisotropy into account, was derived and incorporated into the time-dependent model. Growth laws were determined for two different spherulite morphologies of the form tn, with and without the inclusion of thermal effects. Results show that incorporation of the thermal energy balance correctly predicts the transition of the growth law exponent from the volume driven regime (n=1) to the thermally limited regime (approaching n=0.5), agreeing well with experimental observations. An interfacial nemato-dynamic model is used to gain insight into the interactions that result in the progression of different spherulite growth regimes

Propagation of fronts with gradient and curvature dependent velocities

SIGLEAvailable from British Library Document Supply Centre-DSC:DXN010396 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Simple Monte Carlo Cellular Models for Surface Evolution

Monte Carlo cellular simulations are described for some simple surface evolution models. Surface growth is simulated by adding new cells to the surface. The bonding of a new cell arriving to a site on the surface depends on the number of cells present around that site; new cells are more likely to stick at sites with the fewest missing surrounding cells. Applications are given for simulating the propagation of a flame front and the formation of surface landforms; and the (anisotropic) growth of a crystal, where the surface may grow more rapidly in one direction than others

Atomistic simulation and <i>ab initio</i> study of the defect structure of spinel-related Li_0.5-0.5xMg_xFe_2-0.5xO₄

The position of magnesium ions in Mg2+ -doped lithium ferrite of the composition Li0.5 0.5xMgxFe2.5- 0.5xO4, which has been a matter of uncertainty among some experimentalists, is investigated using interatomic potential and ab initio DFT calculations. Among possible 19 defect structure models, some of which have been reported experimentally, the lowest energy is found for Mg2+ ions evenly replacing Li+ and Fe3+ ion on octahedral sites. This gives a decrease in magnetisation for the Mg2+ -doped ferrite relative to the un-doped lithium ferrite. The results suggest that some experimental observations of increased magnetisation of spinel lithium ferrite on Mg2+-doping could be due to substitution of Mg2+ or Li+ on tetrahedral sites at the high temperatures used in preparation of the solid and/or as the presence of undetected defects in the initial precursors

Age, growth, population dynamics and stock status of Perna perna in Omani waters

Aim: Population parameters such as growth, recruitment pattern, mortality, exploitation rate and the length-weight relationship were investigated for the brown mussel, Perna pernain Omani waters. Methodology: Monthly shell-length frequency of P. perna were collected from three different locations, namely, Mirbat, Ra's Al-Had and Ra's Madrakah for one year from December 2010 to November 2011. The data were analysed using the FiSAT (FAO-ICLARM Stock Assessment Tools) software to estimate population parameters. Results: The length of individuals ranged from 10.34 to 104.03 mm and the weight from 0.12 to 52.45 g. The estimated relative growth coefficient (b) was 3.079(?0.019), and the 95% confidence levelof branged from 3.045 to 3.116. The annual recruitment pattern of P. perna showed a continuous trend throughout the year. The peak recruitment at Mirbat (19%) and Ra'sAl Had (21%) was observed in June, whereas at Ra's Madrakah (24%)it was observedinJuly. The estimated total mortality values ofP. pernawere 2.84 yr-1, 3.28 yr-1 and 2.48 yr-1 at Mirbat, Ra's Al Had and Ra's Madrakah, respectively, while the natural mortality rates were 1.25 yr-1 at Mirbat, 1.29 yr-1 at Ra'sAl Had, and 1.23 yr-1 at Ra's Madrakah. The fishing mortality rates were 1.59 yr-1 at Mirbat, 1.99 yr-1 at Ra'sAlHad and 1.25 yr-1 at Ra's Madrakah. The Perna perna attained an approximate length of 53.5 mm at the end of one year. Exploitation rate (E) was 0.56, 0.60 and 0.50 at Mirbat, Ra'sAlHad and Ra's Madrakah, respectively. Interpretation : The results revealed that the stock of P. perna at Mirbat and Ra's Al Had areas was over exploited. However, currentlyatRa's Madrakah the stock ofP. pernais currently optimally exploited.The authors would like to express their sincere gratitude to the Agriculture and Fisheries Development Fund for funding thisstudy.WealsothanksDr.HusseinAl-MasrooriandDr.Ahmed Al-Maskri for this help in running this project