Continuous dynamical systems that realize discrete optimization on the hypercube

We study the problem of finding a local minimum of a multilinear function E over the discrete set {0,1}n. The search is achieved by a gradient-like system in [0,1]n with cost function E. Under mild restrictions on the metric, the stable attractors of the gradient-like system are shown to produce solutions of the problem, even when they are not in the vicinity of the discrete set {0,1}n. Moreover, the gradient-like system connects with interior point methods for linear programming and with the analog neural network studied by Vidyasagar (IEEE Trans. Automat. Control 40 (8) (1995) 1359), in the same context. © 2004 Elsevier B.V. All rights reserved.

Plane-strain discrete dislocation plasticity with climb-assisted glide motion of dislocations

A small-strain two-dimensional discrete dislocation plasticity (DDP) framework is developed wherein dislocation motion is caused by climb-assisted glide. The climb motion of the dislocations is assumed to be governed by a drag-type relation similar to the glide-only motion of dislocations: such a relation is valid when vacancy kinetics is either diffusion limited or sink limited. The DDP framework is employed to predict the effect of dislocation climb on the uniaxial tensile and pure bending response of single crystals. Under uniaxial tensile loading conditions, the ability of dislocations to bypass obstacles by climb results in a reduced dislocation density over a wide range of specimen sizes in the climb-assisted glide case compared to when dislocation motion is only by glide. A consequence is that, at least in a single slip situation, size effects due to dislocation starvation are reduced. By contrast, under pure bending loading conditions, the dislocation density is unaffected by dislocation climb as geometrically necessary dislocations (GNDs) dominate. However, climb enables the dislocations to arrange themselves into lower energy configurations which significantly reduces the predicted bending size effect as well as the amount of reverse plasticity observed during unloading. The results indicate that the intrinsic plasticity material length scale associated with GNDs is strongly affected by thermally activated processes and will be a function of temperature. © 2013 IOP Publishing Ltd.

The impact of sand slugs against beams and plates: Coupled discrete particle/finite element simulations

The impact of a slug of dry sand particles against a metallic sandwich beam or circular sandwich plate is analysed in order to aid the design of sandwich panels for shock mitigation. The sand particles interact via a combined linear-spring-and-dashpot law whereas the face sheets and compressible core of the sandwich beam and plate are treated as rate-sensitive, elastic-plastic solids. The majority of the calculations are performed in two dimensions and entail the transverse impact of end-clamped monolithic and sandwich beams, with plane strain conditions imposed. The sand slug is of rectangular shape and comprises a random loose packing of identical, circular cylindrical particles. These calculations reveal that loading due to the sand is primarily inertial in nature with negligible fluid-structure interaction: the momentum transmitted to the beam is approximately equal to that of the incoming sand slug. For a slug of given incoming momentum, the dynamic deflection of the beam increases with decreasing duration of sand-loading until the impulsive limit is attained. Sandwich beams with thick, strong cores significantly outperform monolithic beams of equal areal mass. This performance enhancement is traced to the "sandwich effect" whereby the sandwich beams have a higher bending strength than that of the monolithic beams. Three-dimensional (3D) calculations are also performed such that the sand slug has the shape of a circular cylindrical column of finite height, and contains spherical sand particles. The 3D slug impacts a circular monolithic plate or sandwich plate and we show that sandwich plates with thick strong cores again outperform monolithic plates of equal areal mass. Finally, we demonstrate that impact by sand particles is equivalent to impact by a crushable foam projectile. The calculations on the equivalent projectile are significantly less intensive computationally, yet give predictions to within 5% of the full discrete particle calculations for the monolithic and sandwich beams and plates. These foam projectile calculations suggest that metallic foam projectiles can be used to simulate the loading by sand particles within a laboratory setting. © 2013 Elsevier Ltd.

Study on small-strain behaviours of methane hydrate sandy sediments using discrete element method

Methane hydrate bearing soil has attracted increasing interest as a potential energy resource where methane gas can be extracted from dissociating hydrate-bearing sediments. Seismic testing techniques have been applied extensively and in various ways, to detect the presence of hydrates, due to the fact that hydrates increase the stiffness of hydrate-bearing sediments. With the recognition of the limitations of laboratory and field tests, wave propagation modelling using Discrete Element Method (DEM) was conducted in this study in order to provide some particle-scale insights on the hydrate-bearing sandy sediment models with pore-filling and cementation hydrate distributions. The relationship between shear wave velocity and hydrate saturation was established by both DEM simulations and analytical solutions. Obvious differences were observed in the dependence of wave velocity on hydrate saturation for these two cases. From the shear wave velocity measurement and particle-scale analysis, it was found that the small-strain mechanical properties of hydrate-bearing sandy sediments are governed by both the hydrate distribution patterns and hydrate saturation. © 2013 AIP Publishing LLC.

Climb-enabled discrete dislocation plasticity

A small strain two-dimensional discrete dislocation plasticity framework coupled to vacancy diffusion is developed wherein the motion of edge dislocations is by a combination of glide and climb. The dislocations are modelled as line defects in a linear elastic medium and the mechanical boundary value problem is solved by the superposition of the infinite medium elastic fields of the dislocations and a complimentary non-singular solution that enforces the boundary conditions. Similarly, the climbing dislocations are modelled as line sources/sinks of vacancies and the vacancy diffusion boundary value problem is also solved by a superposition of the fields of the line sources/sinks in an infinite medium and a complementary non-singular solution that enforces the boundary conditions. The vacancy concentration field along with the stress field provides the climb rate of the dislocations. Other short-range interactions of the dislocations are incorporated via a set of constitutive rules. We first employ this formulation to investigate the climb of a single edge dislocation in an infinite medium and illustrate the existence of diffusion-limited and sink-limited climb regimes. Next, results are presented for the pure bending and uniaxial tension of single crystals oriented for single slip. These calculations show that plasticity size effects are reduced when dislocation climb is permitted. Finally, we contrast predictions of this coupled framework with an ad hoc model in which dislocation climb is modelled by a drag-type relation based on a quasi steady-state solution. © 2013 Elsevier Ltd. All rights reserved.

Adapting data processing to compare model and experiment accurately: A discrete element model and magnetic resonance measurements of a 3d cylindrical fluidized bed

Discrete element modeling is being used increasingly to simulate flow in fluidized beds. These models require complex measurement techniques to provide validation for the approximations inherent in the model. This paper introduces the idea of modeling the experiment to ensure that the validation is accurate. Specifically, a 3D, cylindrical gas-fluidized bed was simulated using a discrete element model (DEM) for particle motion coupled with computational fluid dynamics (CFD) to describe the flow of gas. The results for time-averaged, axial velocity during bubbling fluidization were compared with those from magnetic resonance (MR) experiments made on the bed. The DEM-CFD data were postprocessed with various methods to produce time-averaged velocity maps for comparison with the MR results, including a method which closely matched the pulse sequence and data processing procedure used in the MR experiments. The DEM-CFD results processed with the MR-type time-averaging closely matched experimental MR results, validating the DEM-CFD model. Analysis of different averaging procedures confirmed that MR time-averages of dynamic systems correspond to particle-weighted averaging, rather than frame-weighted averaging, and also demonstrated that the use of Gaussian slices in MR imaging of dynamic systems is valid. © 2013 American Chemical Society.

Novel fluid grid and voidage calculation techniques for a discrete element model of a 3D cylindrical fluidized bed

A discrete element model (DEM) combined with computational fluid dynamics (CFD) was developed to model particle and fluid behaviour in 3D cylindrical fluidized beds. Novel techniques were developed to (1) keep fluid cells, defined in cylindrical coordinates, at a constant volume in order to ensure the conditions for validity of the volume-averaged fluid equations were satisfied and (2) smoothly and accurately measure voidage in arbitrarily shaped fluid cells. The new technique for calculating voidage was more stable than traditional techniques, also examined in the paper, whilst remaining computationally-effective. The model was validated by quantitative comparison with experimental results from the magnetic resonance imaging of a fluidised bed analysed to give time-averaged particle velocities. Comparisons were also made between theoretical determinations of slug rise velocity in a tall bed. It was concluded that the DEM-CFD model is able to investigate aspects of the underlying physics of fluidisation not readily investigated by experiment. © 2014 The Authors.

Discrete multicomponent model for biodiesel spray combustion simulation

An important first step in spray combustion simulation is an accurate determination of the fuel properties which affects the modelling of spray formation and reaction. In a practical combustion simulation, the implementation of a multicomponent model is important in capturing the relative volatility of different fuel components. A Discrete Multicomponent (DM) model is deemed to be an appropriate candidate to model a composite fuel like biodiesel which consists of four components of fatty acid methyl esters (FAME). In this paper, the DM model is compared with the traditional Continuous Thermodynamics (CTM) model for both diesel and biodiesel. The CTM model is formulated based on mixing rules that incorporate the physical and thermophysical properties of pure components into a single continuous surrogate for the composite fuel. The models are implemented within the open-source CFD code OpenFOAM, and a semi-quantitative comparison is made between the predicted spray-combustion characteristics and optical measurements of a swirl-stabilised flame of diesel and biodiesel. The DM model performs better than the CTM model in predicting a higher magnitude of heat release rate in the top flame brush region of the biodiesel flame compared to that of the diesel flame. Using both the DM and CTM models, the simulation successfully reproduces the droplet size, volume flux, and droplet density profiles of diesel and biodiesel. The DM model predicts a longer spray penetration length for biodiesel compared to that of diesel, as seen in the experimental data. Also, the DM model reproduces a segregated biodiesel fuel vapour field and spray in which the most abundant FAME component has the longest vapour penetration. In the biodiesel flame, the relative abundance of each fuel component is found to dominate over the relative volatility in terms of the vapour species distribution and vice versa in the liquid species distribution. © 2014 Elsevier Ltd. All rights reserved.

Linear multimodal actuation through discrete coupling

Due to technological limitations, robot actuators are often designed for specific tasks with narrow performance goals, whereas a wide range of behaviors is necessary for autonomous robots in uncertain complex environments. In an effort to increase the versatility of actuators, we introduce a new concept of multimodal actuation (MMA) that employs dynamic coupling in the form of clutches and brakes to change its mode of operation. The dynamic coupling allows motors and passive elements such as springs to be engaged and disengaged within a single actuator. We apply the concept to a linear series elastic actuator which uses friction brakes controlled online for the dynamic coupling. With this prototype, we are able to demonstrate several modes of operation including stiff position control, series elastic actuation as well as the possibility to store and release energy in a controlled manner for explosive tasks such as jumping. In this paper, we model the proposed concept of actuation and show a systematic performance analysis of the physical prototype that we developed in our laboratory. © 1996-2012 IEEE.

Linear multi-modal actuation through discrete coupling

Due to technological limitations robot actuators are often designed for specific tasks with narrow performance goals, whereas a wide range of output and behaviours is necessary for robots to operate autonomously in uncertain complex environments. We present a design framework that employs dynamic couplings in the form of brakes and clutches to increase the performance and diversity of linear actuators. The couplings are used to switch between a diverse range of discrete modes of operation within a single actuator. We also provide a design solution for miniaturized couplings that use dry friction to produce rapid switching and high braking forces. The couplings are designed so that once engaged or disengaged no extra energy is consumed. We apply the design framework and coupling design to a linear series elastic actuator (SEA) and show that this relatively simple implementation increases the performance and adds new behaviours to the standard design. Through a number of performance tests we are able to show rapid switching between a high and a low impedance output mode; that the actuator's spring can be charged to produce short bursts of high output power; and that the actuator has additional passive and rigid modes that consume no power once activated. Robots using actuators from this design framework would see a vast increase in their behavioural diversity and improvements in their performance not yet possible with conventional actuator design. © 2012 IEEE.

Trajectory control based on discrete full-range dynamics

There has been an increasing interest in the use of mechanical dynamics, (e.g., assive, Elastic, And viscous dynamics) for energy efficient and agile control of robotic systems. Despite the impressive demonstrations of behavioural performance, The mechanical dynamics of this class of robotic systems is still very limited as compared to those of biological systems. For example, Passive dynamic walkers are not capable of generating joint torques to compensate for disturbances from complex environments. In order to tackle such a discrepancy between biological and artificial systems, We present the concept and design of an adaptive clutch mechanism that discretely covers the full-range of dynamics. As a result, The system is capable of a large variety of joint operations, including dynamic switching among passive, actuated and rigid modes. The main innovation of this paper is the framework and algorithm developed for controlling the trajectory of such joint. We present different control strategies that exploit passive dynamics. Simulation results demonstrate a significant improvement in motion control with respect to the speed of motion and energy efficiency. The actuator is implemented in a simple pendulum platform to quantitatively evaluate this novel approach.