The purpose of this paper is to design a stabilizing controller for a car with n connected trailers. The proposed control algorithm is constructed on the Lyapunov theory. In this paper, the purpose of navigating the system toward the desired point considering the slip phenomenon as a main source of uncertainty is analyzed. First mathematical models are presented. Then, a stabilizing control approach based on the Lyapunov theory is presented. Subsequently, an uncertainty estimator is taken into account to overcome the wheel slip effects. Obtained results show the convergence properties of the proposed control algorithm against the slip phenomenon.

High-purity niobium single crystals of five different orientations were compressed at 77 K to 2–4% plastic strain to investigate the mechanisms operative in the initial stage of yielding. The crystals deformed in the direction close to the [001] axis exhibit predominant slip on the high-stressed (101) and a much lower stressed $\left( {0\bar{1}1} \right)$ plane. The expected slip on the $\left( {\bar{1}01} \right)$ plane is nearly homogeneously distributed with only a few sharp slip traces corresponding to localized slip. The samples compressed along center-triangle orientations and those close to the $\left[ {011} \right] - \left[ {\bar{1}11} \right]$ edge deform predominantly by twinning on {112}〈111〉 systems with some contribution from slip on the $\left( {\bar{1}01} \right)\left[ {\bar{1}\bar{1}\bar{1}} \right]$ system with the highest Schmid factor. A majority of twins exhibit internal contrast due to alternating slip on $\left( {\bar{1}01} \right)$ and $\left( {0\bar{1}1} \right)$ planes. No slip traces are observed in the matrix adjacent to the twin, which implies that twin boundaries are impenetrable obstacles for the motion of dislocations.

The twinning and slip modes of a rolled magnesium alloy sheet were investigated through quasi-in-situ tensile tests that were carried out along the rolling direction at room temperature with a constant strain rate. Scanning electron microscopy and electron backscattered diffraction observations were used to identify activated twinning and slip systems. Schmid factors were calculated to analyze different deformation modes. The analyses show that a small number of {10-12} tensile twins were present during deformation, and these twins resulted from the accommodation of compression along the tensile direction. Post-deformation examination revealed the dominance of prismatic <a> slip.

In recent days, nanofluids have derived the attention of researchers, scientists and engineers due to their abundant applications in Engineering and technology and specific applications such as Electronics cooling, vehicle cooling, medical applications including cancer therapy and so on. Motivated by these applications of nanofluids, this work is mainly concerned with the convective heat transfer of nanofluids. MHD slip flow of nanofluids with heat absorption over a rotating disk subjected to suction has been analyzed. Two types of nanofluids such as copper-water nanofluid and silver-water nanofluid are considered for the present study. The system of axisymmetric nonlinear partial differential equations governing the hydromagnetic steady flow and heat transfer are reduced to nonlinear ordinary differential equations by introducing suitable similarity transformations. The resulting non-linear ordinary differential equations are solved numerically by most efficient Nachtsheim-Swigert shooting iteration technique for satisfaction of asymptotic boundary conditions along with Runge – Kutta Fehlberg Method. The flow field is affected by the presence of physical parameters, such as magnetic interaction parameter, suction parameter, slip parameter and solid volume fraction, whereas the temperature field is addionally affected by magnetic interaction parameter, suction parameter, internal heat absorption parameter and solid volume fraction. With the amplifying effect in magnetic interaction parameter, suction parameter, slip parameter and solid volume fraction, the radial and tangential velocities decline. Axial velocity gets decelerated for increasing magnetic interaction parameter and slip parameter whereas it gets accelerated for growing effect of suction parameter and solid volume fraction. The temperature of the fluid within the boundary layer enhances with the increasing effect of magnetic interaction parameter and solid volume fraction while it reduces for increasing values of the suction parameter and internal heat absorption parameter. Also the values of radial and tangential skin friction coefficients and Nusselt number are obtained numerically and are tabulated.

A theoretical investigation of the unsteady flow of a Newtonian fluid through a channel is presented using an alternative boundary condition to the standard no-slip condition, namely the Navier boundary condition, independently proposed over a hundred years ago by both Navier and Maxwell. This boundary condition contains an extra parameter called the slip length, and the most general case of a constant but different slip length on each channel wall is studied. An analytical solution for the velocity distribution through the channel is obtained via a Fourier series, and is used as a benchmark for numerical simulations performed utilizing a finite element analysis modified with a penalty method to implement the slip boundary condition. Comparison between the analytical and numerical solution shows excellent agreement for all combinations of slip lengths considered.

This paper proposes a novel shuffle turning method for a humanoid robot that controls the load distribution of the soles of the robot's feet. Turning motions of a humanoid robot are conventionally performed through a repeated foot stepping motion. However, this motion is inefficient and time-consuming. In our method, the feet are slid along the floor without a stepping movement. In order to reduce the friction with the floor and to achieve the correct shuffle turning motion, a non-uniform load distribution of the soles is controlled. Experiments using a humanoid robot were conducted on two floors with differing friction amounts, and the validity of the proposed method was verified.

The shape and velocity of a sliding droplet are computed by solving the Navier-Stokes equation with free interface boundary conditions. The Galerkin finite element methodis implemented in a 2D computation domain discretized using an unstructured mesh withtriangular elements. The mesh is refined recursively at the corners (contact points). Thestationary sliding velocity is found to be strongly dependent on grid refinement, which isa consequence of the contact line singularity resolved through the effective slip across thefinite elements adjacent to the contact point. For small droplets, this dependence is wellapproximated by a theoretical estimates obtained using multiscale expansion and matchingtechnique in lubrication approximation, where the corner element size is used as a microscaleparameter. For larger droplets, the shape is also dependent on grid refinement. This questions the validity of numerous computations of flows with moving contact line where gridsare invariably much more coarse than molecular scales on which the singularity is resolved. Itis suggested that extrapolation to molecular scales should be used to obtain realistic results.

This study investigates experimentally the velocity of the center of mass with respect to the base of support while subjects step on slippery flooring. The moments of the joints of both legs are also investigated to gain further insights into the source of any correlation found in reacting to slippery perturbation. Twenty-two healthy subjects dressed with safety harness walked first without and then with slippery perturbation, guided by a metronome at 120 steps/min and 90 steps/min cadence. Data were collected from a motion analysis system and force plates. Subjects falling had distinguishably slower velocity of center of mass with respect to the lead stance foot compared to the subjects maintaining balance at contralateral toe off. Larger knee flexion moment and ankle plantar flexion moment in the perturbed leg were found among subjects regaining balance. Faster velocity of center of mass with respect to base of support is noteworthy in subjects regaining balance from slippery perturbation. The response of lower extremities, especially about the thigh and leg in the lead stance limb, were important to improve the velocity of the center of mass with respect to base of support.

Upon encountering a wet or contaminated floor, people often modify their gait and posture to prevent themselves from slipping. This study was conducted to investigate the modification of gait patterns in healthy young adults as they approached and stepped on a slippery floor. Ten females and twelve males were instructed to walk at two different pacer speeds, 90 and 120steps/min, guided by a metronome, on a walkway with two forceplates placed at the center. During the step immediately prior to stepping on a forceplate with or without slippery disturbance, temporo-spatial parameters, selected kinematic parameters, and foot-floor reaction forces were evaluated in each cadence. The results showed that modifications of gait patterns for slip perturbation included shorter step length, increases of flexion angles of hip and knee joints,increases of plantarflexion angles of ankle joint with flattened foot, and decreases of the forward and backward groundreaction forces. However, it was found that such modifications for slip perturbation did not seem to efficiently prevent people from falling.

Four balanced cross sections, supported by longitudinal sections, structure contour maps, stratigraphic separation diagrams and hangingwall sequence diagrams are keys to this interpretation of the Moine thrust, which forms the western margin of the Caledonides in NW Scotland. New basement and cover correlations between foreland and thrust belt give new slip estimates for the Moine thrust (∼ 77 km), the Loch More klippe (≥ 43 km), Glencoul sheet (20–25 km), Ben More sheet (∼28 km), Achall and Dundonnell ‘sheet II’ (∼28 km).

Like other major thrusts the Moine thrust moved in a smooth or rough fashion at different places and times, and many structures are a footwall response to its passage. Widely developed duplexes vary in thickness so that the roof thrust is folded and occasionally faulted; many late Caledonian folds in the Moine metasediments are of this origin. The presence of igneous bodies with contact aureoles increased the propensity to rough slip and this, by causing thickening in the footwall to the Moine thrust, is partly responsible for the Assynt culmination.

The previously accepted sequence of thrusting from foreland to hinterland, which has been deduced from the concept of ‘overstep’ of the Moine thrust across lower thrusts, is considered to be a misconception of thrust geometry. Instead, a ‘piggy-back’ sequence of thrusts, from higher to lower, is proposed.