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Item Steady boundary layer slip flow along with heat and mass transfer over a flat porous plate embedded in a porous medium.(Public Library of Science, 2014-12) Aziz, A.; Siddique, J.I.; Aziz, T.Show more In this paper, a simplified model of an incompressible fluid flow along with heat and mass transfer past a porous flat plate embedded in a Darcy type porous medium is investigated. The velocity, thermal and mass slip conditions are utilized that has not been discussed in the literature before. The similarity transformations are used to transform the governing partial differential equations (PDEs) into a nonlinear ordinary differential equations (ODEs). The resulting system of ODEs is then reduced to a system of first order differential equations which was solved numerically by using Matlab bvp4c code. The effects of permeability, suction/ injection parameter, velocity parameter and slip parameter on the structure of velocity, temperature and mass transfer rates are examined with the aid of several graphs. Moreover, observations based on Schmidt number and Soret number are also presented. The result shows, the increase in permeability of the porous medium increase the velocity and decrease the temperature profile. This happens due to a decrease in drag of the fluid flow. In the case of heat transfer, the increase in permeability and slip parameter causes an increase in heat transfer. However for the case of increase in thermal slip parameter there is a decrease in heat transfer. An increase in the mass slip parameter causes a decrease in the concentration field. The suction and injection parameter has similar effect on concentration profile as for the case of velocity profile.Show more Item Self-Similar Unsteady Flow of a Sisko Fluid in a Cylindrical Tube Undergoing Translation.(Hindawi Publishing Corporation, 2015) Khan, M.; Abelman, S.; Mahomed, F.M.Show more The governing nonlinear equation for unidirectional flow of a Sisko fluid in a cylindrical tube due to translation of the tube wall is modelled in cylindrical polar coordinates.The exact steady-state solution for the nonlinear problem is obtained.Thereduction of the nonlinear initial value problem is carried out by using a similarity transformation.The partial differential equation is transformed into an ordinary differential equation, which is integrated numerically taking into account the influence of the exponent n and the material parameter b of the Sisko fluid. The initial approximation for the fluid velocity on the axis of the cylinder is obtained by matching inner and outer expansions for the fluid velocity. A comparison of the velocity, vorticity, and shear stress of Newtonian and Sisko fluids is presented.Show more Item A partial Lagrangian approach to mathematical models of epidemiology.(Hindawi Publishing Corporation, 2015) Naz, R.; Naeem, I; Mahomed, F.M.Show more This paper analyzes the first integrals and exact solutions of mathematical models of epidemiology via the partial Lagrangian approach by replacing the three first-order nonlinear ordinary differential equations by an equivalent system containing one second order equation and a first-order equation. The partial Lagrangian approach is then utilized for the second-order ODE to construct the first integrals of the underlying system.We investigate the SIR and HIV models.We obtain two first integrals for the SIR model with and without demographic growth. For the HIV model without demography, five first integrals are established and two first integrals are deduced for the HIV model with demography. Then we utilize the derived first integrals to construct exact solutions to the models under investigation. The dynamic properties of these models are studied too. Numerical solutions are derived for SIR models by finite difference method and are compared with exact solutions.Show more Item Dynamic Euler-Bernoulli Beam Equation: Classification and Reductions.(Hindawi Publishing Corporation, 2015) Naz, R.; Mahomed, F.M.Show more We study a dynamic fourth-order Euler-Bernoulli partial differential equation having a constant elastic modulus and area moment of inertia, a variable lineal mass density g(x), and the applied load denoted by f(u), a function of transverse displacement u(t,x). The complete Lie group classification is obtained for different forms of the variable lineal mass density g(x) and applied load f(u). The equivalence transformations are constructed to simplify the determining equations for the symmetries. The principal algebra is one-dimensional and it extends to two- and three-dimensional algebras for an arbitrary applied load, general power-law, exponential, and log type of applied loads for different forms of g(x). For the linear applied load case, we obtain an infinite-dimensional Lie algebra. We recover the Lie symmetry classification results discussed in the literature when g(x) is constant with variable applied load f(u). For the general power-law and exponential case the group invariant solutions are derived. The similarity transformations reduce the fourth-order partial differential equation to a fourth-order ordinary differential equation. For the power-law applied load case a compatible initial-boundary value problem for the clamped and free end beam cases is formulated. We deduce the fourth-order ordinary differential equation with appropriate initial and boundary conditions.Show more Item Use of wood anatomy to identify poisonous plants: Charcoal of Spirostachys africana.(Academy of Science of South Africa (ASSAf), 2015-03-01) Lennox, S.J.; Bamford, M.Show more Spirostachys africana Sond. (tamboti/tambotie) is a woodland tree that is often found near water. It has a poisonous and purgative latex. The archaeological site of Sibudu, a rock shelter in KwaZulu-Natal, has evidence, from well-preserved charcoal and seeds, of past environments and wood use from approximately 77-38 thousand years ago (ka). As their uses and environmental indicators are different, it is critical to confidently distinguish among the three anatomically similar woods of the Euphorbiaceae: Spirostachys africana, Sclerocroton integerrimus and Shirakiopsis elliptica. A detailed anatomical study of reference and archaeological charcoal shows that xylem vessel width increases proportionally as vessel frequency decreases, from Spirostachys africana, Sclerocroton integerrimus to Shirakiopsis elliptica. Crystals of calcium oxalate are present in ray cells of Spirostachys africana, whereas silica bodies are present in ray cells of Sclerocroton integerrimus and Shirakiopsis elliptica. Using these features, the presence of Spirostachys africana was confirmed amongst hearth charcoal of the Spotty Camel layer, with an age of approximately 58 ka and of the Mottled Deposit occupational layer, with an age of approximately 49 ka. The presence of this charcoal, collected from ancient fireplaces or sieved from surrounding sediments, implies that people at Sibudu understood and used this poisonous tree to their advantage. We are encouraged in this view by the presence of many Cryptocarya woodii leaves found on the surface of 77-ka sedge bedding at Sibudu (Wadley L et al., Science. 2011;334:1388-1391). Cryptocarya woodii has insecticidal and larvacidal properties and members of the Laurel family are well known for their medicinal properties.Show more Item Study of nonlinear MHD tribological squeeze film at generalized magnetic reynolds numbers using DTM.(Public Library of Science, 2015-08-12) Rashidi, M.M.; Freidoonimehr, N.; Momoniat, E.; Rostami, B.Show more In the current article, a combination of the differential transform method (DTM) and Padé approximation method are implemented to solve a system of nonlinear differential equations modelling the flow of a Newtonian magnetic lubricant squeeze film with magnetic induction effects incorporated. Solutions for the transformed radial and tangential momentum as well as solutions for the radial and tangential induced magnetic field conservation equations are determined. The DTM-Padé combined method is observed to demonstrate excellent convergence, stability and versatility in simulating the magnetic squeeze film problem. The effects of involved parameters, i.e. squeeze Reynolds number (N1), dimensionless axial magnetic force strength parameter (N2), dimensionless tangential magnetic force strength parameter (N3), and magnetic Reynolds number (Rem) are illustrated graphically and discussed in detail. Applications of the study include automotive magneto-rheological shock absorbers, novel aircraft landing gear systems and biological prosthetics.Show more Item Heat transfer analysis for stationary boundary layer slip flow of a power-law fluid in a Darcy porous medium with plate suction/injection.(Public Library of Science, 2015-09-25) Aziz, A.; Ali, Y.; Aziz, T.; Siddique, J.I.Show more In this paper, we investigate the slip effects on the boundary layer flow and heat transfer characteristics of a power-law fluid past a porous flat plate embedded in the Darcy type porous medium. The nonlinear coupled system of partial differential equations governing the flow and heat transfer of a power-law fluid is transformed into a system of nonlinear coupled ordinary differential equations by applying a suitable similarity transformation. The resulting system of ordinary differential equations is solved numerically using Matlab bvp4c solver. Numerical results are presented in the form of graphs and the effects of the powerlaw index, velocity and thermal slip parameters, permeability parameter, suction/injection parameter on the velocity and temperature profiles are examined.Show more Item Traditional glue, adhesive and poison used for composite weapons by ju/'hoan san in nyae nyae, Namibia. implications for the evolution of hunting equipment in prehistory.(Public Library of Science, 2015-10) Wadley, L.; Trower, G.; Backwell, L.; D'Errico, F.Show more Ju/'hoan hunters from Nyae Nyae, near Tsumkwe in Namibia, demonstrate the manufacture of three fixative pastes made from plant extracts, and poison made from grubs and plant extracts. Ammocharis coranica and Terminalia sericea produce simple glue. Ozoroa schinzii latex mixed with carbonized Aristeda adscensionis grass is a compound adhesive. Composite poison is made from Chrysomelid grub viscera mixed with salivary extracts of Acacia mellifera inner bark and the tuber sap of Asparagus exuvialis. In order to document potential variability in the chaîne opératoire, and to eliminate inherent biases associated with unique observations, we studied manufacturing processes in three separate Nyae Nyae villages. Although there are methodological similarities in the Nyae Nyae area, we observed a few differences in contemporary traditions of poison manufacture. For example, some hunters make powder from Asparagus exuvialis tuber sap by boiling, reducing, hardening and grinding it, while others simply use heated sap. The Ju/'hoan hunting kit provides insights for archaeologists, but we must exercise caution when looking for continuity between prehistoric and historical technical systems. Some traditions have been lost to modern hunters, while others are new. We should also expect variability in the Stone Age because of geographically restricted resources. Simple glue, compound adhesive, and poison recipes identified in the Stone Age have no modern equivalents. By about 60,000 years ago at Diepkloof, simple glue was used for hafting tools, but at similarly-aged Sibudu there are recipes that combine red ochre powder with plant and/or animal ingredients. At Border Cave, novel poisons and compound adhesives were used in the Early Later Stone Age. It is possible that the complexity that we record in the manufacture of fixative pastes and poison used by Ju/'hoan hunters represents a hafting system both similar to and different from that observed at the Stone Age sites of Diepkloof, Sibudu, and Border Cave.Show more Item Dental microwear differences between eastern and southern African fossil bovids and hominins.(Academy of Science of South Africa (ASSAf), 2016-03) Ungar, P.S.; Scott, J.R.; Steininger, C.M.Show more Dental microwear has proven to be a valuable tool for reconstructing diets of fossil vertebrates. However, recent studies have suggested that the pattern of microscopic scratches and pits on teeth may be more reflective of environmental grit than of food preferences. Could differences in dental microwear between early hominins, for example, therefore be a result of dust level rather than of diet? We investigated this possibility using a palaeocommunity approach. We compared microwear texture differences between eastern and southern African Hominini, along with Plio-Pleistocene specimens representing two tribes of bovids, Alcelaphini and Antilopini, from the same deposits as the early hominins. If exogenous grit swamps diet signals, we would expect community-wide microwear patterns separating samples by region. Results indicate that each of the three tribes shows a different pattern of variation of microwear textures between eastern and southern Africa. These results imply that differences in microwear reflect diet rather than grit load, and that microwear can provide valuable information not just about environmental dust level, but about food preferences of fossil vertebrates.Show more Item Analytical modeling of MHD flow over a permeable rotating disk in the presence of soret and dufour effects: Entropy analysis.(MDPI AG, 2016-04-26) Freidoonimehr, N.; Rashidi, M.M.; Abelman, S.; Lorenzini, G.Show more The main concern of the present article is to study steady magnetohydrodynamics (MHD) flow, heat transfer and entropy generation past a permeable rotating disk using a semi numerical/analytical method named Homotopy Analysis Method (HAM). The results of the present study are compared with numerical quadrature solutions employing a shooting technique with excellent correlation in special cases. The entropy generation equation is derived as a function of velocity, temperature and concentration gradients. Effects of flow physical parameters including magnetic interaction parameter, suction parameter, Prandtl number, Schmidt number, Soret and Dufour number on the fluid velocity, temperature and concentration distributions as well as entropy generation number are analysed and discussed in detail. Results show that increasing the Soret number or decreasing the Dufour number tends to decrease the temperature distribution while the concentration distribution is enhanced. The averaged entropy generation number increases with increasing magnetic interaction parameter, suction parameter, Prandtl number, and Schmidt number.Show more Item A hominin first rib discovered at the Sterkfontein Caves, South Africa.(Academy of Science of South Africa (ASSAf), 2016-05) Tawane, G.; Garcia-Martinez, D.; Eyre, J.; Bastir, M.; Berger, L.R.; Schmid, P.; Nalla, S.; Williams, S.A.Show more First ribs - the first or most superior ribs in the thorax - are rare in the hominin fossil record, and when found, have the potential to provide information regarding the upper thorax shape of extinct hominins. Here, we describe a partial first rib from Member 4 of the Sterkfontein Caves, South Africa. The rib shaft is broken away, so only the head and neck are preserved. The rib is small, falling closest to small-bodied Australopithecus first ribs (AL 288-1 and MH1). Given that it was recovered near the StW 318 femur excavation, which also represents a small individual, we suggest that the two may be associated. Three-dimensional geometric morphometric analyses were used to quantify the rib fragment morphology and compare it to extant hominoid and other fossil hominin ribs. While only the proximal end is preserved, our analyses show that South African Australopithecus share derived features of the proximal first rib more closely resembling A. afarensis and later hominins than great apes.Show more Item An early instance of upper palaeolithic personal ornamentation from China: The freshwater shell bead from Shuidonggou 2.(Public Library of Science, 2016-05) Wei, Y.; D'Errico, F.; Vanhaeren, M.; Li, F.; Gao, X.Show more We report the discovery and present a detailed analysis of a freshwater bivalve from Shuidonggou Locality 2, layer CL3. This layer is located c. 40 cm below layer CL2, which has yielded numerous ostrich eggshell beads. The shell is identified as the valve of a Corbicula fluminea. Data on the occurrence of this species in the Shuidonggou region during Marine Isotope Stage 3 and taphonomic analysis, conducted in the framework of this study, of a modern biocoenosis and thanatocoenosis suggest that the archeological specimen was collected at one of the numerous fossil or sub-fossil outcrops where valves of this species were available at the time of occupation of level CL3. Experimental grinding and microscopic analysis of modern shells of the same species indicate that the Shuidonggou shell was most probably ground on coarse sandstone to open a hole on its umbo, attach a thread, and use the valve as a personal ornament. Experimental engraving of freshwater shells and microscopic analysis identify an incision crossing the archaeological valve outer surface as possible deliberate engraving. Reappraisal of the site chronology in the light of available radiocarbon evidence suggests an age of at least 34-33 cal kyr BP for layer CL3. Such estimate makes the C. fluminea recovered from CL3 one of the earliest instances of personal ornamentation and the earliest example of a shell bead from China.Show more Item The stable isotope setting of Australopithecus sediba at Malapa, South Africa.(Academic of Science of South Africa (ASSAf), 2016-07) Holt, E.; Dirks, P.; PLaczek, C.; Berger, L.R.Show more We report delta C-13 and delta O-18 results from carbonate-cemented cave sediments at Malapa in South Africa. The sediments were deposited during a short-period magnetic reversal at 1.977±0.003 Ma, immediately preceding deposition of Facies D sediments that contain the type fossils of Australopithecus sediba. Values of delta C-13 range between -5.65 and -2.09 with an average of -4.58±0.54% (Vienna Pee Dee Belemnite, VPDB) and values of delta O-18 range between -6.14 and -3.84 with an average of -4.93±0.44% (VPDB). Despite signs of diagenetic alteration from metastable aragonite to calcite, the Malapa isotope values are similar to those obtained in two previous studies in South Africa for the same relative time period. Broadly, the Malapa delta C-13 values provide constraints on the palaeovegetation at Malapa. Because of the complex nature of the carbonate cements and mixed mineralogy in the samples, our estimates of vegetation type (C4-dominant) must be regarded as preliminary only. However, the indication of a mainly C4 landscape is in contrast to the reported diet of A. sediba, and suggests a diverse environment involving both grassland and riparian woodland.Show more Item Earliest hominin cancer: 1.7-million-year- old osteosarcoma from Swartkrans Cave, South Africa(Academy of Science of South Africa (ASSAf), 2016-07) Odes, E.J.; Randolph-Quinney, P.S.; Steyn, M.; Thockmorton, Z.; Smilg, J.S.; Zipfel, B.; Augustine, T.N.; de Beer, F.; Hoffman, J.W.; Franklin, R.D.; Berger, L.R.Show more The reported incidence of neoplasia in the extinct human lineage is rare, with only a few confirmed cases of Middle or Later Pleistocene dates reported. It has generally been assumed that premodern incidence of neoplastic disease of any kind is rare and limited to benign conditions, but new fossil evidence suggests otherwise. We here present the earliest identifiable case of malignant neoplastic disease from an early human ancestor dated to 1.8–1.6 million years old. The diagnosis has been made possible only by advances in 3D imaging methods as diagnostic aids. We present a case report based on re-analysis of a hominin metatarsal specimen (SK 7923) from the cave site of Swartkrans in the Cradle of Humankind, South Africa. The expression of malignant osteosarcoma in the Swartkrans specimen indicates that whilst the upsurge in malignancy incidence is correlated with modern lifestyles, there is no reason to suspect that primary bone tumours would have been any less frequent in ancient specimens. Such tumours are not related to lifestyle and often occur in younger individuals. As such, malignancy has a considerable antiquity in the fossil record, as evidenced by this specimen.Show more Item Osteogenic tumour in Australopithecus sediba: Earliest hominin evidence for neoplastic disease(Academy of Science of South Africa (ASSAf)., 2016-07) Randolph-Quinney, P.S.; Williams, S.A.; Steyn, M.; Meyer, M.R.; Smilg, J.S.; Churchill, S.E.; Odes, E.J.; Augustine, T.; Tafforeau, P.; Berger, L.R.Show more We describe the earliest evidence for neoplastic disease in the hominin lineage. This is reported from the type specimen of the extinct hominin Australopithecus sediba from Malapa, South Africa, dated to 1.98 million years ago. The affected individual was male and developmentally equivalent to a human child of 12 to 13 years of age. A penetrating lytic lesion affected the sixth thoracic vertebra. The lesion was macroscopically evaluated and internally imaged through phase-contrast X-ray synchrotron microtomography. A comprehensive differential diagnosis was undertaken based on gross- and micro-morphology of the lesion, leading to a probable diagnosis of osteoid osteoma. These neoplasms are solitary, benign, osteoid and bone-forming tumours, formed from well-vascularised connective tissue within which there is active production of osteoid and woven bone. Tumours of any kind are rare in archaeological populations, and are all but unknown in the hominin record, highlighting the importance of this discovery. The presence of this disease at Malapa predates the earliest evidence of malignant neoplasia in the hominin fossil record by perhaps 200 000 years.Show more Item A decorated raven bone from the Zaskalnaya VI (Kolosovskaya) Neanderthal site, Crimea(Public Library of Science, 2017-03) Majkic, A.; Evans, S.; Stepanchuk, V.; Tsvelykh, A.; D'Errico, F.Show more We analyze a radius bone fragment of a raven (Corvus corax) from Zaskalnaya VI rock shelter, Crimea. The object bears seven notches and comes from an archaeological level attributed to a Micoquian industry dated to between 38 and 43 cal kyr BP. Our study aims to examine the degree of regularity and intentionality of this set of notches through their technological and morphometric analysis, complemented by comparative experimental work. Microscopic analysis of the notches indicate that they were produced by the to-and-fro movement of a lithic cutting edge and that two notches were added to fill in the gap left between previously cut notches, probably to increase the visual consistency of the pattern. Multivariate analysis of morphometric data recorded on the archaeological notches and sets of notches cut by nine modern experimenters on radii of domestic turkeys shows that the variations recorded on the Zaskalnaya set are comparable to experimental sets made with the aim of producing similar, parallel, equidistant notches. Identification of the Weber Fraction, the constant that accounts for error in human perception, for equidistant notches cut on bone rods and its application to the Zaskalnaya set of notches and thirty-six sets of notches incised on seventeen Upper Palaeolithic bone objects from seven sites indicate that the Zaskalnaya set falls within the range of variation of regularly spaced experimental and Upper Palaeolithic sets of notches. This suggests that even if the production of the notches may have had a utilitarian reason the notches were made with the goal of producing a visually consistent pattern. This object represents the first instance of a bird bone from a Neanderthal site bearing modifications that cannot be explained as the result of butchery activities and for which a symbolic argument can be built on direct rather than circumstantial evidence.Show more Item Patterns of change and continuity in ochre use during the late Middle Stone Age of the Horn of Africa: The Porc-Epic Cave record(Public Library of Science, 2017-05) Rosso, D. E.; D'Errico, F.; Queffelec, A.Show more Ochre is found at numerous Middle Stone Age (MSA) sites and plays a key role in early modern human archaeology. Here we analyse the largest known East African MSA ochre assemblage, comprising 40 kg of ochre, found at Porc-Epic Cave, Ethiopia, spanning a period of at least 4,500 years. Visual characterisation of ochre types, microscopic identification of traces of modification, morphological and morphometric analysis of ochre pieces and modified areas, experimental reproduction of grinding processes, surface texture analysis of archaeological and experimentally ground ochre facets, laser granulometry of ochre powder produced experimentally on different grindstones and by Hamar and Ovahimba women from Ethiopia and Namibia respectively, were, for the first time, combined to explore diachronic shifts in ochre processing technology. Our results identify patterns of continuity in ochre acquisition, treatment and use reflecting both persistent use of the same geological resources and similar uses of iron-rich rocks by late MSA Porc-Epic inhabitants. Considering the large amount of ochre processed at the site, this continuity can be interpreted as the expression of a cohesive cultural adaptation, largely shared by all community members and consistently transmitted through time. A gradual shift in preferred processing techniques and motions is interpreted as reflecting cultural drift within this practice. Evidence for the grinding of ochre to produce small quantities of powder throughout the sequence is consistent with a use in symbolic activities for at least part of the ochre assemblage from Porc-Epic Cave.Show more