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Consequently, the expression for the spring nodal forces F s p I 1 and F s p I 2 for nodes I 1 and I 2 connected by the spring are given by. A beam b associated with three nodes I 1 , I 2 , and I 3 , provides resistance to bending and sets a preferred possibly a time-dependent curvature of the fiber.
We approximate the second derivative in eq. This implies small bending deformation. For the case of uniform distance between neighboring nodes of a beam in the reference configuration, i. As a first test case, we consider the problem of flow past a rigid circular cylinder. This problem has been the subject of many theoretical, experimental, and numerical studies, and the hydrodynamic force on the cylinder at various Reynolds numbers are readily available for comparison. Here, we conduct two-dimensional simulation of cases at Reynolds numbers 20, 40, and In these simulations, instead of modeling the rigid cylinder as a 2D circular disk, we model only the circular boundary of the disk as a rigid boundary immersed in a fluid.
Specifically, we consider a cylinder of diameter D centered at the origin of the domain. The circular boundary i. The zero-velocity condition along Lagrangian node s i is enforced using the penalty method:. The circle is immersed in a large fluid domain. To resolve the boundary layer and shed vortex structures, we perform simulations on an adaptively refined grid Griffith et al.
Consequently, the drag and lift coefficients become periodic as shown in Fig. They are all found to be in good agreement with results from previous studies.
For the fiber-based IB scheme, Griffith [ 21 , 33 ] has studied convergence properties for various 2D cases. Here we present a test case of a 3D elastic cylindrical tube undergoing dilation to verify the solution methodology. A cylindrical tube composed of three families of continuous fibers i. We nondimensionalize the system based on the inner radius of the cylindrical tube and the density and viscosity of the fluid. The dilation process includes two phases.
The first phase is an inflation phase. This is modeled by adding fluid in the domain from the top end while keeping its bottom end closed. The second phase is the relaxation phase. The relaxation phase continues until a stationary state is reached, at which the inertial and viscous terms are approximately three orders of magnitude smaller than the pressure term.
Thus, the pressure force from the constraint of fluid incompressibility is balanced by the elastic force in the tube. The simulations are carried by specifying the following boundary conditions for the fluid domain: traction normal and tangential free boundary conditions for the four lateral surfaces of the domain; zero-velocity boundary condition for the bottom surface; and a time-dependent velocity boundary condition for the top surface.
Here, h t is a decreasing function of time which vanishes at the end of the inflation process. We assume a plain strain state for this relatively long tube at the final equilibrium state. Let U r denote the radial displacement field of the tube in the middle region, then by assuming plane strain conditions i.
We use the observed U r i in our simulations, and compare the numerical and predicted analytic values of the inner pressure, denoted as P numerical and P analytic , respectively. Here, we conduct test cases with different tube thickness and dilation levels, where higher dilation level is simulated by adding more fluid into the tube during the dilation phase. To prevent the fluid from leaking out of the structure, we keep the grid size of Lagrangian mesh smaller than that of Eulerian mesh.
The grid number for cases with different tube thickness is listed in Table 2. Error in the inner pressure for different tube thickness T. U r i and P numerical are radial displacement of the inner surface and inner pressure in the middle section of the tube, respectively. Higher dilation level is simulated by adding more fluid in the tube, as shown by the increase of U r i. In the previous section, we showed that our IB formulation for an elastic tube is able to capture the analytical trend of a dilation process.
In this section, we extend the elastic tube model to describe esophageal transport. The anatomy of the human esophagus is illustrated in Fig. Depending on its content, the bolus is generally considered as a Newtonian fluid, with its viscosity varying from one centipoise cP to several hundred centipoise [ 36 ]. The overall volume of the bolus is on the order of a few milliliters [ 37 ].
Studies of Pouderoux et al. The multiple layers of the esophagus. The inner most layer is the mucosal layer including mucosa and submucosa , which is highly folded at rest; the outer layers are muscle layers including circular muscle layer and longitudinal muscle layer reproduced with permission from Kahrilas [ 34 ].
The reference configuration of the esophagus model is taken to be a long straight cylindrical tube made up of elastic fibers. There are five important components in our esophagus model: 1 inner layer of mucosa IM ; 2 outer layer of mucosa OM ; 3 interfacial IF layer; 4 circular muscle CM ; and 5 longitudinal muscle LM. The IM and OM layers together represent the mucosal layer of the esophagus, which we split into two layers for numerical purposes see Sec. The length of the esophagus tube is taken to be mm, as the typical human esophagus length is in the range of — mm [ 38 ].
The thin liquid layer confined in the narrow esophageal lumen is assumed to have a circular cross section in the reference configuration with a radius of 0. The thickness of each esophageal wall component is obtained based on the clinical data of human esophagus at non-rest state i.
The thickness of each layer at rest is listed in Table 4 and is based on the clinical data of Mittal et al. On the six surfaces of the fluid box, we impose stress-free boundary conditions. We also fix the esophageal top end, which, in the physiological situation, is constrained by the upper esophageal sphincter.
A schematic of the overall model is shown in Fig. Here, we consider the transport of an initially filled bolus in the upper end of esophagus. Schematic not drawn to scale of the computational domain consisting of the elastic esophagus and a viscous fluid. The elastic esophagus, a cylindrical tube with its top end fixed, is immersed in the background fluid in our 3D computational model.
The upper esophagus is initially filled with a bolus, and the lower part is filled with a thin liquid layer in the lumen. Traction-free boundary conditions are applied to all surfaces of the rectangular computational domain. Thickness of each esophageal layer: clinical data [ 39 ] and data used in our model. Note that the clinical test obtains the thickness of each layer at its non-rest state, with esophageal lumen dilated by the intruded catheter.
Computer model adopts the thickness of each layer at its rest state. The thickness of mucosal layer measured based on the ultrasound image is much lower than the thickness at rest, as the intruded catheter will distend the mucosal layer significantly and reduce the layer thickness.
The esophageal tissue is generally modeled as a nonlinear anisotropic elastic or pseudo-elastic material. The reported material properties, such as the modulus of the muscle layers in the circumferential and longitudinal orientations, are substantially different [ 5 , 6 , 7 , 8 , 9 , 10 ]. Here we assume an elastic behavior of each fibrous esophageal layer. Such models have been used to estimate the muscle tension [ 14 ].
For the mucosal layer, Stavropoulou [ 10 ] characterized the elasticity of the mucosal layer in their axial and circumferential directions, which can be represented by axially-circumferentially-radially arranged fiber network.
By contrast, Natali et al. Thus, to demonstrate the capabilities of our modeling approach, we consider both fiber arrangements of the mucosal layer in Sections 5.
In vivo experiments [ 2 , 3 ] show that during normal esophageal transport, there is well-coordinated circular muscle CM contraction and longitudinal muscle LM shortening. A quantitative model to characterize the contraction and shortening process in terms of neuronal firing or reaction kinetics in muscles is not available; however, experiments show that there is a precise synchrony between the two types of muscle activation patterns [ 2 , 3 ]. In our model, this sequential activation is implemented by dynamically changing the rest lengths of the fibers.
Then an active spring representing a section of one active muscle fiber has its rest length r z, t given by. The variation of muscle activation along this contracting segment will likely influence bolus transport. To understand this influence, we propose two muscle activation models, namely uniform muscle activation and nonuniform muscle activation.
The common parameters of muscle activation model used in all the cases of esophageal transport are listed in Table 5.
Model parameters for the circular muscle CM contraction and longitudinal muscle LM shortening used in all the cases. The muscle activation model is based on eq. Esophageal transport involves multiple length scales, which is evidenced by the fact that the esophageal length is mm, while the lumen radius at rest is only 0. The requirement of resolving the narrow lumen dictates the grid size of the problem. More challenging in terms of computational modeling is the large deformation of the inner lumen, which results from the dilation caused by bolus movement.
This can be seen in Fig. The choice of the Lagrangian mesh size must also address the issues of large deformations of lumen and the external fluid leaking into the tube, which could occur when the Lagrangian mesh becomes coarser than its Eulerian counterpart [ 15 ].
For the outer layers with relatively small dilation, a relatively coarser Lagrangian mesh is used to reduce the computational cost. The mesh sizes for various esophageal components are listed in Table 6.
The axial beams included in the model provide resistance to curvature changes in the axial direction that are associated with buckling of the tube. The total time for the transport is about 2. The relative change in the bolus volume is within 0. Because of complex kinematics of the esophageal structure, the apparently overlapping or missing springs in the above figures are actually a consequence of out-of-plane motions.
Here we report a case study of the esophageal transport that considers the mucosal layer to be composed of axially-circumferentially-radially arranged fibers. Experiments show the intact mucosal layer is highly folded at rest see Fig. We use uniform activation model as described in eq. The reduction ratio a 0 for CM contraction and LM shortening are chosen to be 0.
Other parameters are listed in Table 5. As shown in the Fig. The running bolus, indicated by the negative axial velocity, is confined by the inner layer of mucosa IM. This underlines the role of mucosal layers in preparing the tear-drop shape of the bolus.
The pressure distribution shown in Fig. This is consistent with reported experimental observations [ 3 ]. This is different from previous models for bolus transport [ 4 , 12 , 14 ] where the bolus shape was pre-defined. Only the inner layer of mucosa IM of the esophagus white is shown to better visualize the inside bolus. Detailed information on the deformation of each esophageal layer is illustrated in Fig. It can be seen that a typical esophageal segment at each axial location passes through four distinct stages: a the segment is at rest; b the segment is dilated by the incoming bolus; c the segment contracts as a result of the incoming activation wave; and d the segment relaxes after the activation wave passes.
First, mucosal layer shapes the running bolus by dynamically closing or narrowing the lumen above the bolus region while opening the lumen from below. Previous studies on bolus transport excluded mucosal layers, and did not capture this important feature of bolus movement [ 4 , 12 , 14 ]. At the contraction region behind the bolus, a pressure peak and an increased muscle CSA i.
In this case, we use the same geometry and material model of esophagus as of Case 1 in Section 5. Other parameters used in the muscle activation model are listed in Table 5. The transport phenomenon is shown in Figs. It is clear that the nonuniform muscle activation results in more pronounced contraction, as illustrated in Fig.
We remark that a distinctive muscle CSA peak overlaps with the pressure peak in this case, as shown in Fig. This is different from Case 1 in Section 5. A coexisting muscle CSA and pressure peak is also observed in the clinical test of Mittal et al. Natali et al. Here we present a case with such a helical mucosal fiber arrangement. Highly recommended, highly approachable, extremely friendly and genuinly caring about buyers and sellers alike. We found John to be very straightforward, no surprises and very supportive, he gave us space when we needed it and also provided all the support we needed by answering all our questions.
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The 16th and 17th centuries witnessed profound cultural, social and economic change in Ireland, which saw the older feudal lordships being assimilated into a more expansive centralised state under the Tudor and Stuart dynasties.
Periodic rebellions by the old Catholic order, both Anglo-Irish and Gaelic-Irish, were followed by the widespread confiscation of lands and their resettlement by English,Welsh and Scottish settlers who were largely Protestant and whose loyalty to the Crown was more assured. Outside the planted areas, older social and economic relationships were also transformed by the Reformation and Counter-Reformation, the development of mercantile capitalism and the influence of the Renaissance. People were reassessing the world around them and their place in the greater cosmological order.
Such processes impacted upon the way people interacted with each other and the physical environment, leading to changes in the consumption of goods and materials, in the management of the surrounding landscape and in the types of buildings erected. Changes in the latter can be seen with the rise of the 16th—17th-century manor house, where New English landlords and their families would reside at the centre of large estates, producing a surplus that would supply the demands of a newly emerging mercantile economy.
Across the country, and bridging cultural divides, the new architecture was also being embraced by the Old English and by the Gaelic-Irish.
A fine example of an architecture in transition is to be seen at Leamanagh Castle, Co. Besides manor houses, this cultural and social transformation manifested itself in other ways, aspects of which have come to light during archaeological investigations carried out in advance of road development by the NRA.
Farmsteads and outhouses of timber-framed and stone construction, field boundaries, limekilns and military sites have been identified. The reuse of earlier sites for more contemporary purposes can also be seen in the subsequent occupation of dissolved monasteries and circular enclosed sites ringforts. The excavation of such sites is very important, as the bulk of the population of early modern Ireland c. The Irish countryside was undergoing fundamental change from the 16th century onwards with the enclosure of agricultural land, a process that is evident in the large number of field boundaries uncovered on road schemes by archaeologists.
The first systematic enclosure of fields took place following the imposition of English landholding norms across the whole country. A map of an estate at Mogeely, Co. Writing in , Sir Henry Piers gave an account of local farming practices in County Westmeath, where tillage ground was enclosed and pastoral land left open Feehan , As late as , however,Thomas Molyneux described open countryside without enclosures between Kilconnell and Athenry in east County Galway, suggesting that the process of enclosing the Irish countryside was a prolonged affair that was not finally concluded until the 18th century ibid.
Ordinary dwellings of the 17th century Along the route of the M8 motorway, the ephemeral remains of three late 17th-century houses and three outhouses were uncovered at Ballinvinny South, Co. Cork, situated by an earlier medieval moated site Illus 2. Encounters between Peoples Illus.
One of these houses was a three-roomed cottage approximately 11 m by 5 m. The building is thought to have been timber-framed, with the walls possibly covered with clay packing. Gun money was a temporary currency, first issued by James II in , consisting of coins struck from cheap metals, including melted-down cannons.
This hoard of seven half-crowns, 27 shillings and 33 sixpences was probably deposited and forgotten about when devaluation rendered the brass coinage worthless after the victory of William III in Hanley , ; Cotter Another example of a 17th-century timber-framed house was uncovered at Danesfort 4, Co.
The cottage was represented by the remnants of a low stone wall-footing only surviving to an extent of 3. E; Ministerial Direction No. A; Excavation Director Richard Jennings. Kilkenny, showing the remains of the 17th- century house in blue Richard Jennings. Kilkenny Richard Jennings. The timber frames of the houses at Ballinvinny South and Danesfort had long since decayed, but their general appearance and layout may be ascertained from contemporary cartographic sources. In Thomas Raven drew maps that recorded in detail the appearance and layout of the villages and manor houses that were established by a number of London-based guilds and companies in County Derry under the auspices of the Ulster Plantation Illus.
These maps feature rather attractive depictions of timber-framed houses, 50 in number all together, with a central chimneystack, two dormer windows in the front elevation and almost all roofs slated or tiled. The timber box frames possessed both diagonal braces and horizontal ties, with no apparent evidence of cruck construction crucks are pairs of curved timbers that extend from the ground or from low wall-footings to support roofs Robinson , 17— Comparison of these drawings with other documents and proposed plans in the archives of the London Companies suggests that Raven, and Captain Nicholas Pynnar in an earlier survey of , represented actual buildings on the ground with moderate accuracy Jope , The Civil Survey of records that most of the examples in County Derry were destroyed in the troubles of the mid-century with the outbreak of an uprising in late , followed by eight years of civil war and the subsequent reconquest of Ireland by Oliver Cromwell and his generals by , while the disappearance of woodlands in the region would also have brought about their demise Robinson , 17— Hence the investigation of similar post-medieval timber-framed buildings on development schemes such as roads is very important, as these buildings have not survived either as relic buildings or as part of the vernacular building tradition.
Stone-built houses were also a feature of the built environment of the post-medieval period. On the route of the M6 motorway, the remains of a stone-built house with associated structures were uncovered at Annagh Hill 3, Co.
It has been suggested by the excavator that the house may have possessed a direct entry plan as opposed to a lobby entry, given the popularity of the former plan in 18th- and 19th-century vernacular housing in the region. A single fragment of a possible roof tile suggests that some of the buildings may have been roofed in slate, although it is likely that thatch was also used. Derry, illustrating the manor house and village, the latter containing houses of different styles and traditions: timber-framed, stone-built and clay-built Trustees of Lambeth Palace Library, MS , ff 85v— The roofs were covered in slate or tile, although several examples were thatched.
Few houses were equipped with gable hearths, most being provided with chimneys in a central position. The entry was also usually in a central position, which may have relevance for the interpretation of the house at Annagh Hill. The houses were gabled, with gable windows at a raised level indicating the presence of lofts Robinson , Typifying the challenges posed to archaeologists working on this period, however, no remains of these houses recorded by Raven in County Derry can be identified Jope , , which makes the identification of 17th-century houses at Annagh Hill 3 and elsewhere all the more significant.
Relatively few upstanding examples can be found in Ireland, unlike the situation in England and Wales, where substantial numbers of homesteads dating from the 16th and 17th centuries are still standing both of timber frame and stone construction. The more stable political conditions across the Irish Sea encouraged greater continuity of landownership, with landlords and their tenants able to sustain the continued maintenance of dwellings over time.
A tobacco pipe bowl of 17th-century form was recovered from the primary fill of the ditch, as was a charcoal sample that produced a date of AD — Beta A clay tobacco pipe stem and a sherd of North Devon Gravel-Tempered Ware were also retrieved from tertiary fills of the ditch, and such finds, along with the lack of early medieval material, suggest that the enclosure was occupied and possibly even laid out in the 17th century.
Later in the century a gabled stone building was erected; the metalled surface on which it was built overlay the ditch, which had been filled in at this stage Illus. The walls were built of roughly dressed, clay-bonded masonry.
Features within the interior of the building included hearths or fire- spots and a stone-capped drain. While early medieval circular enclosures ringforts have seen subsequent activity in the late medieval and early modern periods, the significance of the Newcastle enclosure is that it may illustrate the construction of a ringfort-type monument by a Gaelic-Irish family in the 17th century.
This raises the issue of the late construction and use of the monument type, which has been examined recently by Fitzpatrick No evidence for a tower-house was detected within the grounds of the enclosure, suggesting that the castle lay elsewhere in the townland.
The limited extent of the archaeological excavations, however, does not preclude the possibility that the tower- house lies elsewhere within the enclosure. It is not uncommon for a tower-house to be built on a pre-existing site, the earlier enclosures being used as bawns enclosed 4 NGR , ; height 93 m OD; Excavation Reg.
Earthwork defences of curvilinear plan, however, could be constructed from scratch as well, their layout not being governed by a pre-existing ringfort. A tower-house was built on the northern shores of Pallas Lough, Co. Could the reuse or construction of the circular enclosure suggest a conscious revival of past cultural accomplishments in the face of great social and cultural changes? One site associated with 17th-century military activity was a subcircular enclosure at Castlecranna, Co.
Tipperary, on the M7, which was initially thought to be early medieval in date. Excavation uncovered the remains of a subcircular enclosure 24 m by 27 m in extent defined by a ditch, though no traces of a bank were found Illus. Inside the enclosure was a trapezoidal structure along with slot-trenches, pits, post- and stake-holes. External features included a possible post- and stake-built structure, pits, stone- lined drains and furrows.
One of the pits in the interior of the enclosure yielded a medieval date. No datable artefacts were recovered in situ; finds were recovered, however, during the metal-detection of removed soil but, instead of detailing early medieval activity, items such as shot of varying calibre, high-quality buttons, possible parts of firearms and 17th-century coinage spoke of a different time and purpose. Eight coins were found, including three silver Elizabeth I shillings —1 , a silver James I sixpence and a silver Charles I coin pre McNamara Only three sherds of post-medieval pottery were retrieved, suggesting that this site was not used for domestic purposes McNamara , 36—7.
The enclosure is without known parallel but may have been occupied as a temporary defensive position during either the troubles of —53 or the Williamite War of — Tipperary AirShots Ltd.
The use of post-dissolution monasteries Another aspect of settlement in the post-medieval period was the continued use of monastic sites following their formal dissolution in the midth century.
Given that there is no record that the abbey was adopted as a parish church, it is likely that this was a mortuary 6 NGR , ; height 6 m OD; Excavation Reg. Clare, with distinctive chimneystack of 17th-century date top right erected in southern claustral range, looking north-west James Lyttleton. This building still exists today, with a chimneystack of rather massive proportions that is characteristic of 17th-century vernacular architecture Illus. The lower fill of the cesspit was radiocarbon-dated to AD — This suggests that the post-dissolution occupants of the building at the south-western corner of the cloister were of a certain social standing that allowed them to avail of expensive consumer goods.
Castles bore witness to the tragic consequences of this, one example being Carrickmines Castle on the outskirts of Dublin, which was attacked during the troubles of the s.
Archaeological excavation of the castle and an associated village settlement, in advance of the construction of the M50 motorway, uncovered two mass burials containing the articulated remains of 15 individuals, including men, women and children. The individuals, aged between three and 45 years, had been placed within two shallow pits. In addition, the remains of a juvenile aged between nine and 12 years were recovered from between these multiple interments, as well as the remains of a young male buried face down nearly 8 m north-east of the mass burials.
The remains revealed evidence of unhealed blade trauma, while one individual bore unhealed blunt force trauma to the head. Closely associated with the skeletal remains in the mass burial was a musket ball, suggesting that at least one individual had been shot.
The nature of the burials and the associated artefacts suggest that these deaths occurred in the aftermath of the siege of Carrickmines Castle Fibiger et al. Battlefields have also attracted the interest of archaeologists, who seek material traces of these military engagements in order to question the documented accounts of battles.
The M6 motorway passed just to the north of the site of the Battle of Aughrim, one of the more important engagements that took place between the Jacobite and Williamite forces in At a critical stage in the battle, this troop, under the command of Colonel Henry Luttrell, fled the field, leaving the infantry to the mercy of enemy attack on the northern flank.
Such work is important in developing understandings of how military engagements developed and in situating the sites of battles within their historical and archaeological context, as has been proposed by Shiels R; Ministerial Direction No. Dublin Valerie J Keeley Ltd. Galway Rubicon Heritage Services Ltd. Conclusion This paper is only a synopsis of certain 16th- and 17th-century sites uncovered in advance of road developments by the NRA. Nevertheless, many of these sites demonstrate that encounters between natives and newcomers did bring about change in various spheres such as architecture, agriculture, religious practice and the patterns of consumption.