Epihypocurves and epihypocyclic surfaces with arbitrary base curve

If a circle rolls around another motionless circle then a point bind with the rolling circle forms a curve. It is called epicycloid, if a circle is rolling outside the motionless circle; it is called hypocycloid if the circle is rolling inside the motionless circle. The point bind to the rolling circle forms a space curve if the rolling circle has the constant incline to the plane of the motionless circle. The cycloid curve is formed when the circle is rolling along a straight line. The geometry of the curves formed by the point bind to the circle rolling along some base curve is investigated at this study. The geometry of the surfaces formed when the circle there is rolling along some curve and rotates around the tangent to the curve is considered as well. Since when the circle rotates in the normal plane of the base curve, a point rigidly connected to the rotating circle arises the circle, then an epihypocycloidal cyclic surface is formed. The vector equations of the epihypocycloid curve and epihypocycloid cycle surfaces with any base curve are established. The figures of the epihypocycloids with base curves of ellipse and sinus are got on the base of the equations obtained. These figures demonstrate the opportunities of form finding of the surfaces arised by the cycle rolling along different base curves. Unlike epihypocycloidal curves and surfaces with a base circle, the shape of epihypocycloidal curves and surfaces with a base curve other than a circle depends on the initial rolling point of the circle on the base curve.

Study of Asphalt-Concrete Pavement Fatigue Modeling

Deterioration of asphalt pavements due to fatigue cracking is one of the most common highway pavement failure types. If the fatigue cracks are allowed to develop and grow, the driving comfort and safety, i.e., serviceability of the pavement, decreases. Pavement fatigue behaviour is not a straightforward mechanism and involves many factors and effects, thus computational methods are developed in order to help understand how the pavement works. This paper explores the accuracy and applicability of a less computational resource demanding procedure that uses transient material mechanical behaviour to model the long-term behaviour of a pavement structure. First, the mechanical and fatigue properties of asphalt were determined at the laboratory. Then a four-layer finite-element model was created using Ansys software. Two different models – with and without infinity elements – and two different fatigue simulation procedures – full and simplified – were considered. Material parameters were obtained by the laboratory tests and material properties degraded over time. Cyclic surface loading was applied to simulate the passing of a truck – 6 million fatigue cycles were simulated.

Simultanous Transient Surface Temperature and Heat Flux Measurements in a Large Bore Two-Stroke Diesel Engine

Surface temperature measurements were performed in a large bore two-stroke diesel engine used for ship propulsion. A specially designed fast-response surface thermocouple was used together with an embedded standard K-type thermocouple to measure surface temperature and heat flux with high temporal resolution. Heat flux calculations were carried out both analytically and numerically showing good agreement between the results. Measurements were carried out at three different engine load conditions (25%, 30% and 50% load) in one of the fuel atomizers in the cylinder head. Cyclic surface temperature variations of up to approximately 80 K with a peak temperature of 860 K were observed. The magnitude of the perturbation of the temperature field due to the presence of the thermocouples was investigated by three dimensional CFD simulations.

Geomorphological consequences of weak lower continental crust, and its significance for studies of uplift, landscape evolution, and the interpretation of river terrace sequences

Effects of flow in the lower continental crust have often been ignored in the geomorphological literature on the growth of topography during the Quaternary. However, the ability of the lower crust to flow in response to horizontal pressure gradients, caused by lateral variations in the depth of the base of the brittle upper crust, results in two mechanisms for the growth of topography, which can occur either separately or in combination. First, an increase in the rate of erosion in a region will result in a progressive reduction in the depth of the base of the brittle layer, which will drive inflow of lower crust to beneath the region, which will increase the crustal thickness and thus the altitude of the Earth’s surface. It is important to note that this mechanism can increase the mean altitude of the Earth’s surface, not just the altitude of summits formed of erosion-resistant rock or other features that are not eroding, which will rise faster than the surrounding eroding landscape. Second, repeated cyclic surface loading by ice sheets or fluctuations in global sea-level will cause net flow from areas of relatively cool lower crust to beneath areas of warmer crust. This process will thus usually result in net flow of lower crust from beneath offshore areas to beneath land areas, thinning the crust and increasing the bathymetry offshore but adding to the crustal thickness and so uplifting the land surface onshore. Although these two processes have different mechanisms, the time scale over which both operate is governed by the time required for heat diffusion, resulting from lower-crustal flow (which is concentrated near the Moho), to affect the position of the base of the brittle layer. As a result, the uplift responses for both processes can be very similar. This means that to resolve the physical cause of uplift at any locality requires knowledge of the regional conditions before uplift began, not just evidence (such as river terrace sequences) from during the course of uplift. This study illustrates the complexities and practical difficulties that can result from these issues, using case studies of localities that have been modelled in detail. It also points out that, although the ability to carry out quantitative calculations involving lower-crustal flow is new, the idea that such flow provides a general mechanism for the growdi of topography was first suggested in the early 19th century, but was later abandoned - apparently mistakenly. An early Middle Pleistocene increase in uplift rates is widely-recognised from river terrace records, and typically marks a transition from broad valleys in areas of low relief to narrower, more deeply incised gorges. It is suggested that the isostatic response to cyclic surface loading, caused by the growth and decay of continental ice sheets and the associated sea-level fluctuations, is the main cause of this change, following the increase in scale of ice sheet development from oxygen isotope stage 22 (~0.9 Ma) onwards. The less well resolved earlier increase in uplift rates, evident in some river terrace records at ~3 Ma, is more likely to result from the isostatic response to increased rates of erosion linked to the contemporaneous deterioration in climate.