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A specific family of spanwise-localised invariant solutions of plane Couette flow exhibits homoclinic snaking, a process by which spatially localised invariant solutions of a nonlinear partial differential equation smoothly grow additional structure at their fronts while undergoing a sequence of saddle-node bifurcations. Homoclinic snaking is well understood in the context of simpler pattern-forming systems such as the one-dimensional Swift–Hohenberg equation with cubic-quintic nonlinearity. The Swift–Hohenberg solutions closely resemble the snaking solutions of plane Couette flow, yet this remarkable resemblance and the mechanisms supporting homoclinic snaking within the three-dimensional Navier–Stokes equations remain to be fully understood. Studies of Swift–Hohenberg revealed the central importance of discrete symmetries for homoclinic snaking to be supported by an equation. We therefore study the structural stability of the characteristic snakes-and-ladders structure associated with homoclinic snaking in three-dimensional plane Couette flow for flow modifications that break symmetries of the flow. We demonstrate that wall-normal suction modifies the bifurcation structure of three-dimensional plane Couette solutions in the same way a symmetry-breaking quadratic term modifies solutions of the one-dimensional Swift–Hohenberg equation. These modifications are related to the breaking of the discrete rotational symmetry. At large amplitudes of the symmetry-breaking wall-normal suction the connected snakes-and-ladders structure is destroyed. Previously unknown solution branches are created and can be parametrically continued to vanishing suction. This yields new localised solutions of plane Couette flow that exist in a wide range of Reynolds numbers.
At sufficiently high Reynolds numbers, shear-flow turbulence close to a wall acquires universal properties. When length and velocity are rescaled by appropriate characteristic scales of the turbulent flow and thereby measured in inner units, the statistical properties of the flow become independent of the Reynolds number. We demonstrate the existence of a wall-attached non-chaotic exact invariant solution of the fully nonlinear three-dimensional Navier–Stokes equations for a parallel boundary layer that captures the characteristic self-similar scaling of near-wall turbulent structures. The branch of travelling wave solutions can be followed up to
. Combined theoretical and numerical evidence suggests that the solution is asymptotically self-similar and exactly scales in inner units for Reynolds numbers tending to infinity. Demonstrating the existence of invariant solutions that capture the self-similar scaling properties of turbulence in the near-wall region is a step towards extending the dynamical systems approach to turbulence from the transitional regime to fully developed boundary layers.
The difficulties of transporting heavy mobile robots limit robotic experiments in agriculture. Virtual reality however, offers an alternative to conduct experiments in agriculture. This paper presents an application of virtual reality in a robot navigational experiment using SolidWorks and simulated into MATLAB. Trajectories were initiated using Probabilistic Roadmap and compared based on travel time, distance and tracking error, and the efficiency was calculated. The simulation results showed that the proposed method was able to conduct the navigational experiment inside the virtual environment. U-turn trajectory was chosen as the best trajectory for crop inspection with 82.7% efficiency.
Silicon nanowires are becoming more important because of increasing requirements of the small scale and dense integration of devices. We report a top-down fabrication method for silicon nanowires using high-energy ion beam irradiation of bulk p-type silicon followed by electrochemical etching. Silicon nanowires with a diameter of ∼50nm have been fabricated and densely patterned nanowire arrays fabricated in different resistivity silicon wafers. With a suitable support structure, free standing silicon nanowires are also achieved. We investigate results depending on silicon wafer resistivity and location within the irradiated area.
We report a modified deep reactive ion etching method to realize high aspect
ratio features and nano-grasses on silicon substrates. This etching
technique uses sequential etching and passivation sub-cycles and it is based
on three gases of H2, O2 and SF6 in the presence of rf-plasma. By adjusting the etching parameters such as the flows of various
gases, the plasma power and duration of each cycle, the process can be
controlled to obtain high aspect ratio vertical structures on silicon
substrates. Features with aspect ratios of the order of 30–50 and heights of
the order of 25–30 μm are obtained. On the other hand, one can program
the etching parameters to achieve grass-full structures in desired places
and with pre-designed patterns. The formation of nano-grass on silicon
surface, improves its wetability with water and oil spills. This property
has been used to entrap carbon nanotubes onto nano-structured surfaces in
This paper describes the results of extensive performance and reliability characterization of a silicon-based surface micro-machined tunable optical filter. The device comprises a high-finesse Fabry-Perot etalon with one flat and one curved dielectric mirror. The curved mirror is mounted on an electrostatically actuated silicon nitride membrane tethered to the substrate using silicon nitride posts. A voltage applied to the membrane allows the device to be tuned by adjusting the length of the cavity. The device is coupled optically to an input and an output single mode fiber inside a hermetic package. Extensive performance characterization (over operating temperature range) was performed on the packaged device. Parameters characterized included tuning characteristics, insertion loss, filter line-width and side mode suppression ratio. Reliability testing was performed by subjecting the MEMS structure to a very large number of actuations at an elevated temperature both inside the package and on a test board. The MEMS structure was found to be extremely robust, running trillions of actuations without failures. Package level reliability testing conforming to Telcordia standards indicated that key device parameters including insertion loss, filter line-width and tuning characteristics did not change measurably over the duration of the test.
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