Thin-film Rayleigh–Taylor instability in the presence of a deep periodic corrugated wall

Rayleigh–Taylor instability of a thin liquid film overlying a passive fluid is examined when the film is attached to a periodic wavy deep corrugated wall. A reduced-order long-wave model shows that the wavy wall enhances the instability toward rupture when the interface pattern is sub-harmonic to the wall pattern. An expression that approximates the growth constant of instability is obtained for any value of wall amplitude for the special case when the wall consists of two full waves and the interface consists of a full wave. Nonlinear computations of the interface evolution show that sliding is arrested by the wavy wall if a single liquid film residing over a passive fluid is considered but not necessarily when a bilayer sandwiched by a top wavy wall and bottom flat wall is considered. In the latter case interface tracking shows that primary and secondary troughs will evolve and subsequently slide along the flat wall due to symmetry-breaking. It is further shown that this sliding motion of the interface can ultimately be arrested by the top wavy wall, depending on the holdup of the fluids. In other words, there exists a critical value of the interface position beyond which the onset of the sliding motion is observed and below which the sliding is always arrested.

Molecular Dynamics: A Study on Slip, Drops, and Graphene

<p>Molecular dynamics (MD) is a computational tool used to study physical systems by modeling the atomic-scale interactions between atoms. MD can accurately predict the properties of materials where models are well developed. For new materials, models may be in their early stages and may lack the ability to produce accurate results; however, MD can still provide insight into the physical properties of these new materials. This thesis will use MD to study two different systems. First, the Lennard-Jones (L-J) liquid is used to study how the intrinsic slip lengths of atomic sized surfaces add to produce an effective slip of a larger surface made up of these atomic constituents. The results show that the effective slip of a surface is dominated by its smallest slip, and these results show good agreement with a theory that predicts effective slip given the intrinsic slip and roughness of a surface. The L-J model is also used to investigate the rolling and sliding motion of viscous drops on super-hydrophobic surfaces. The effects of drop size, slip length, and gravity on drop velocities are investigated, and a model that predicts drop speed given the characteristics of a drop and a surface is proposed. The model shows good agreement with simulation results, especially for certain regimes. Second, graphene is studied with MD using various atomistic models. The energies of layers of graphene are reproduced using an Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential, and the energies required to exfoliate graphene from crystal graphite and nickel nano-particles are calculated. The calculations from MD show good agreement with literature and experiment, and these results demonstrate how simple models in MD can produce useful results to aid research and experiment. Finally, the formation of nano-bubbles in graphene grown on platinum is studied using the AIREBO and L-J potentials. The basic formation of graphene nano-bubbles is demonstrated by compressing the edges of graphene flakes. The simulations highlight the importance of proper boundary conditions, such as atom pinning, in order to produce tall, smooth nano-bubbles. The results also suggest that accurate models will be required to effectively demonstrate bubble formation.</p>

Molecular Dynamics: A Study on Slip, Drops, and Graphene

<p>Molecular dynamics (MD) is a computational tool used to study physical systems by modeling the atomic-scale interactions between atoms. MD can accurately predict the properties of materials where models are well developed. For new materials, models may be in their early stages and may lack the ability to produce accurate results; however, MD can still provide insight into the physical properties of these new materials. This thesis will use MD to study two different systems. First, the Lennard-Jones (L-J) liquid is used to study how the intrinsic slip lengths of atomic sized surfaces add to produce an effective slip of a larger surface made up of these atomic constituents. The results show that the effective slip of a surface is dominated by its smallest slip, and these results show good agreement with a theory that predicts effective slip given the intrinsic slip and roughness of a surface. The L-J model is also used to investigate the rolling and sliding motion of viscous drops on super-hydrophobic surfaces. The effects of drop size, slip length, and gravity on drop velocities are investigated, and a model that predicts drop speed given the characteristics of a drop and a surface is proposed. The model shows good agreement with simulation results, especially for certain regimes. Second, graphene is studied with MD using various atomistic models. The energies of layers of graphene are reproduced using an Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential, and the energies required to exfoliate graphene from crystal graphite and nickel nano-particles are calculated. The calculations from MD show good agreement with literature and experiment, and these results demonstrate how simple models in MD can produce useful results to aid research and experiment. Finally, the formation of nano-bubbles in graphene grown on platinum is studied using the AIREBO and L-J potentials. The basic formation of graphene nano-bubbles is demonstrated by compressing the edges of graphene flakes. The simulations highlight the importance of proper boundary conditions, such as atom pinning, in order to produce tall, smooth nano-bubbles. The results also suggest that accurate models will be required to effectively demonstrate bubble formation.</p>

Robust sliding mode preview control for uncertain discrete-time systems with time-varying delay

This article focuses on the problem of robust sliding mode preview control for a class of non-linear delayed systems. It is assumed that the reference signal is previewed with a fixed length ahead and the norm of uncertainty is bounded. A model transformation is introduced to approximate the time-varying delay such that augmented error systems can be constructed. Conditions of asymptotic stability of sliding motion are established via the small gain theorem. The sliding mode preview controller is designed such that the controlled system state can be attracted to the switching surface and keep on it thereafter. A numerical example is presented to illustrate the effectiveness of the proposed control design.

Dynamic output feedback sliding mode control for uncertain linear systems

In this paper, a class of uncertain linear systems with unmatched disturbances is considered, where the nominal system representation is allowed to be non-minimum phase. A sliding surface is designed which is dependent on the system output, observed state, and estimated uncertain parameters. A linear coordinate transformation is introduced so that the stability analysis of the reduced-order sliding mode dynamics can be conveniently performed. A robust output feedback sliding mode control (OFSMC) is then designed to drive the considered system state to reach the sliding surface in finite time and maintain a sliding motion thereafter. A simulation example for a high incidence research model (HIRM) aircraft is used to demonstrate the effectiveness of the proposed method.

A Study of Support Characteristics of Collaborative Reinforce System of U-Steel Support and Anchored Cable for Roadway under High Dynamic Stress

This paper presents a comprehensive study of the support effect and characteristics of a collaborative reinforce system of U-steel support and anchored cable (USS-AC) for roadway under high dynamic stress in a coal mine in China. The deformational behavior of the roadway and the load characteristics of reinforcing elements were measured in real time and analyzed. A numerical simulation study has also been conducted to identify the interaction of the reinforcing elements to the surrounding rock under dynamic load. The research results suggest that the stress distribution of roadway surrounding rock could be changed and that residual strength of the surrounding rock near opening could be increased by using USS-AC. Based on the action of anchored cable, the moment distribution of U-steel support is optimized. The load capacity and nondeformability of the U-steel support are promoted. And the global stability of U-steel support is enhanced so as to achieve the goal of high supporting resistance. When the deformation stress of the surrounding rock is higher, the U-steel support deforms as the surrounding rock. The two side beams and the overlapping parts of U-steel support suffer the highest deformation stress. As a result, the anchored cable provides higher reaction force for the previous locations of the U-steel support in order to prevent deformation of support towards to excavation. As an integral structure, the U-steel support is confined to a limited deformation space under the action of anchored cable. The larger deformation is released through sliding motion of the overlapping parts so as to reach the ultimate of high supporting resistance of USS-AC.

Fatigue of full crown monolithic CAD/CAM restorations for posterior teeth

Objective The purpose of this study is to estimate the fatigue life of five polycrystalline zirconia CAD/CAM ceramic materials used for posterior restoration. This study presents the first time methodology to translate raw data obtained from laboratory test into useful data to predict the clinical life of dental restoration. Methods A typical model for the first molar restored crown is built and transferred into finite element software ANSYS 18.1 flor execution FEA. The materials are: two Y-TZP zirconia (LAVA (LVs), and EVEREST (KVs); IPS e.max CAD; Suprinity PC; and Celtra Duo. Two types of loads are applied, axial load and axial load followed by the sliding motion of lower jaw. The fatigue resistance of various restorative materials is determined. Results Experimental findings show that all the samples have fractured between cusps at the same location, which is slightly off the symmetry fissure plane. For crowns made of LAVA and EVEREST, the life is longer than 10 years under an axial load of 1000 N, while the lives for IPS e.max CAD; Suprinity PC; and Celtra Duo were longer than 10 years under an axial load of 185 N. The life of all-ceramic crown materials was predicted by FEA and found to conform to previous experimental and clinical observations. Conclusion Crowns made of Y-TZP zirconia has superior fatigue resistance compared to other ceramic CAD/CAM materials.

Sliding repetitive control with adaptive bound estimation for motion systems liable to periodic exogenous signals

Periodic exogenous signals often exist in motion systems, especially those involving one or more rotating elements. These periodic exogenous signals deteriorate the performance of motion systems, and these adverse effects cannot be practically eliminated by straightforwardly increasing feedback control gains due to sensor noise, actuator saturation, and unmodeled plant dynamics. This paper describes a sliding repetitive controller for motion systems subject to periodic exogenous signals. Moreover, an adaptive law for bound estimation is devised to ensure the presence of a sliding motion for both repetitive learning and disturbance observation. The tracking motion system of a disk drive is considered in practice, and a traditional repetitive controller is also implemented for performance comparisons with the proposed scheme. Experimental results are reported in this paper, showing the efficacy of the proposed scheme.