The double Caldeira-Leggett model: Derivation and solutions of the master equations, reservoir-induced interactions and decoherence

In this paper we analyze the double Caldeira-Leggett model: the path integral approach to two interacting dissipative harmonic oscillators. Assuming a general form of the interaction between the oscillators, we consider two different situations: (i) when each oscillator is coupled to its own reservoir, and (ii) when both oscillators are coupled to a common reservoir. After deriving and solving the master equation for each case, we analyze the decoherence process of particular entanglements in the positional space of both oscillators. To analyze the decoherence mechanism we have derived a general decay function, for the off-diagonal peaks of the density matrix, which applies both to common and separate reservoirs. We have also identified the expected interaction between the two dissipative oscillators induced by their common reservoir. Such a reservoir-induced interaction, which gives rise to interesting collective damping effects, such as the emergence of relaxation- and decoherence-free subspaces, is shown to be blurred by the high-temperature regime considered in this study. However, we find that different interactions between the dissipative oscillators, described by rotating or counter-rotating terms, result in different decay rates for the interference terms of the density matrix. (C) 2010 Elsevier B.V. All rights reserved.

Interaction between the coating characteristics of galvanneal steel and forming parameters during flat die drawing

Galvanneal steel is considered to be better for automotive applications than its counterpart, galvanized steel, mainly because of its superior coating and surface properties. Galvanneal steel is produced by hot dipping sheet steel in a bath of molten zinc with small, controlled, levels of aluminium, followed by annealing which creates a Fe-Zn intermetallic layer. This intermetallic layer of the coating improves spot weldability and improves subsequent paint appearance. However, if the microstructure of the coating is not properly controlled and forming parameters are not properly selected, wear of the coating could occur during stamping. Frictional sliding of the sheet between the tool surfaces results in considerable amount of coating loss. An Interstitial Free steel with a Galvanneal coating of nominally 60g/m2 was used for the laboratory experiments. Flat Face Friction (FFF) tests were performed with different forming conditions and lubricants to simulate the frictional sliding in stamping. Glow-Discharge Optical Emission Spectrometry (DG-OES) was used to measure the change in the coating thickness during sliding. Optical microscopy was considered for imaging the surfaces as well as an optical method to compare the changes in the coating thickness during the forming. The change to the Galvanneal coating thickness was found to be a function of forming parameters.

Application of bending under tension test to determine the effect of tool radius and the contact pressure on the coefficient of friction in sheet metal forming

To quantify the frictional behaviour in sheet forming operations, several laboratory experiments which simulate the real forming conditions are performed. The Bending Under Tension Test is one such experiment which is often used to represent the frictional flow of sheet material around a die or a punch radius. Different mathematical representations are used to determine the coefficient of friction in the Bending Under Tension Test. In general the change in the strip thickness in passing over the die radius is neglected and the radius of curvature to thickness ratio is assumed to be constant in these equations. However, the effect of roller radius, sheet thickness and the surface pressure are also omitted in some of these equations. This work quantitatively determined the effect of roller radius and the tooling pressure on the coefficient of friction. The Bending Under Tension Test was performed using rollers with different radii and also lubricants with different properties. The tool radii were found to have a direct influence in the contact pressure. The effect of roller radius on friction was considerable and it was observed that there is a clear relationship between the contact pressure and the coefficient of friction.

Determination of drawbead contacts with variable bead penetration

In stamping operations, the sliding of the sheet metal over the drawbeads is of great importance. The geometry of the drawbead and the degree of penetration both influence material flow and alter the frictional effects between the work and the tool. The effect of drawbead penetration over drawbeads has been studied using the Drawbead Simulator (DBS) test. The contact phenomenon between the sheet and drawbeads was analysed by examining deformed samples with an image fitting technique. The results were compared with an FE simulation and with an approximate geometric analysis. The results give a useful relationship between the rates of change of the contact angle with increasing bead penetration.

A comparison of pilling results tested with the ICI pill box and a new perspex™ pill box

Identical single jersey wool knit fabrics produced inconsistent results when tested on the same type of ICI pill box in 4 independence testing laboratories.  The hypothesis formulated to investigate this event was that continued pilling testing in the ICI pill box changes the frictional properties of the cork liners, resulting in the difference pilling ratings.  The aim of this study was to decrease the inconsistencies in the pilling results by replacing the conventional cork lined pill box with a Perspex^TM pill box.  The smae or similar pilling results found for several of the knit facots tested in the two difference pill boxes, while for others there were some significant differences found.  In addition, while using the Perspex^TM pill box observations of the movement of the pilling tubes during testing provided evidence of greater fabric-to-fabric abrasion, rather the expected high degree of fabric-to-cork abrasion (or fabric-to-Perspex^TM) during pilling testing.

Artificial formation forces for stable aggregation of multi-agent system

This paper introduces, a robust and stable algorithm based on artificial formation forces, for multi-agent system (MAS) aggregation in 2D space. The MAS model with artificial forces; consists of inter-member collision avoidance element, formation generation element and a velocity based damping element; is analysed for stability and convergence. Computer simulations are used to illustrate stability and convergence, and to demonstrate effectiveness of the algorithm.

Kinematic modeling of a bio-inspired robotic fish

This paper proposes a kinematic modeling method for a bio-inspired robotic fish based on single joint. Lagrangian function of freely swimming robotic fish is built based on a simplified geometric model. In order to build the kinematic model, the fluid force acting on the robotic fish is divided into three parts: the pressure on links, the approach stream pressure and the frictional force. By solving Lagrange's equation of the second kind and the fluid force, the movement of robotic fish is obtained. The robotic fish's motion, such as propelling and turning are simulated, and experiments are taken to verify the model.

Lateral strength of zero bond masonry walls subjected to wind loads

Masonry walls are usually laid with the individual masonry units along a course overlapping units in the course below. Commonly, the perpend joints in the course occur above the mid-points of the units below to form a ‘half-bond’ or above a third point to form a ‘third-bond’. The amount of this overlap has a profound influence on the strength of a wall supported on three or four sides, where lateral pressures from wind cause combined vertical and horizontal flexure. Where masonry units are laid with mortar joints, the torsional shear bond resistance between the mortar and overlapping units largely determines the horizontal flexural strength. If there is zero bond strength between units, then the horizontal flexural strength is derived from the frictional resistance to torsion on the overlapping bed-faces of the units. This thesis reports a theoretical and experimental investigation into the frictional properties of overlapping units when subjected to combinations of vertical and horizontal moments and vertical axial compression. These basic properties were used to develop a theory to predict the lateral strength of walls supported on two, three or four sides. A plastic theory of behaviour was confirmed by experiment. The theory was then used to determine maximum unbraced panel sizes for particular boundary conditions. Design charts were developed to determine temporary bracing requirements for panels during construction.

Elastic behaviour in mechanical draw presses

This thesis explores the elastic behaviour of the mechanical double action press and draw die system commonly used to draw sheet metal components in the automotive industry. High process variability in production and excessive time spent in die try-out are significant problems in automotive stamping. It has previously been suggested that the elastic behaviour of the system may contribute to these problems. However, the mechanical principles that cause the press system to affect the forming process have not been documented in detail. Due to a poor understanding of these problems in industry, the elasticity of the press and tools is currently not considered during the die design. The aim of this work was to explore the physical principles of press system elasticity and determine the extent to which it contributes to problems in try-out and production. On the basis of this analysis methods were developed for controlling or accounting for problems during the design process. The application of frictional restraining force to the edges of the blank during forming depends on the distribution and magnitude of the clamping force between the binders surfaces of the draw die. This is an important control parameter for the deep drawing process. It has been demonstrated in this work that the elasticity of the press and draw die can affect clamping force in two ways. The response of the press system, to the forces produced in the press during forming, causes the magnitude of clamping force to change during the stroke. This was demonstrated using measured data from a production press. A simple linear elastic model of the press system was developed to illustrate a definite link between the measured force variation and the elasticity of the press and tools. The simple model was extended into a finite element model of the complete press system, which was used to control a forming simulation. It was demonstrated that stiffness variation within the system could influence the final strains in a drawn part. At the conclusion of this investigation a method is proposed for assessing the sensitivity of a part to clamping force variation in the press during die design. A means of reducing variation in the press through the addition of a simple linear spring element is also discussed. The second part of the work assessed the influence of tool structure on the distribution of frictional restraining forces to the blank. A forming simulation showed that tool stiffness affects the distribution of clamping pressure between the binders. This was also shown to affect the final strains in a drawn part. However, the most significant influence on restraining force was the tendency of the blank to increase in thickness between the binders during forming. Using a finite element approximation of the try-out process it was shown that the structure of the tool would also contribute to the problems currently experienced in try-out where uneven contact pressure distributions are addressed by manually adjusting the tool surfaces. Finally a generalised approach to designing draw die structures was developed. Simple analysis methods were combined with finite element based topology optimisation techniques to develop a set of basic design guidelines. The aim of the guidelines was to produce a structure with uniform stiffness response to a pressure applied at the binder surface. The work concludes with a recommendation for introducing the methods developed in this thesis into the standard production process.

Adhesion performance of polymer nanofibres under shear loading

Geckos have extraordinary wall-climbing ability because of the millions of hairs with micro/nano fibrillar structures on their feet. Mimicking gecko's feet is of scientific and engineering importance for development of physical adhesion materials and devices. The design of gecko-inspired physical adhesives seems to be geometry dominated. In this study, Finite Element Method (FEM) has been used to analyse the vertical peel-off force of polyporpylene (PP) nanofibres having different fibre dimensions, inclining angels and contact areas on a flat glass substrate. It has been found that the main parameters affecting the frictional adhesion are fibre diameter and fibre aspect ratio, the inclining angle between the fibre and the substrate surface, and the intimate contact areas. Our analysis has shown that PP nanofibres with a diameter of less than 200nm can generate less peel-off force than fibres of larger diameters, indicating more stable adhesion with the glass substrate for thinner fibres. A bent fibre with more intimate contact area can bear more shear force than a straight fibre with less contact area. Also, under the same shear loading, fibres with an inclining angle of less than 30° provide a low peel off force.

Three dimensional stability charts for slopes based on limit analysis methods

This paper uses finite element upper and lower bound limit analysis to produce chart solutions for three-dimensional (3D) natural slopes for both short- and long-term stability. The presented chart solutions are convenient tools that can be used for preliminary design purposes. The rigorous limit analysis results in this paper were found to bracket the true factor of safety within ±10% or better, which can be used as a benchmark for the solutions from other methods. The depth of the slip surfaces is observed to be generally shallow for most analyzed cases, particularly for the long-term slope stability problem. In addition, it was found that using a two-dimensional (2D) analysis may lead to significant differences in estimating safety factors, which can differ by 2%–60% depending on the slope geometry and soil properties. Therefore, great care and judgement are required when applying 2D analyses to 3D slope problems.

Flexible multibody approach in forward dynamic simulation of locomotive strains in human skeleton with flexible lower body bones

A method for bone strain estimation is examined in this article. The flexibility of a single bone in an otherwise rigid human skeleton model has been studied previously by various authors. However, in the previous studies, the effect of the flexibility of multiple bones on the musculoskeletal model behavior was ignored. This study describes a simulation method that can be used to estimate the bone strains at both tibias and femurs of a 65-year old Caucasian male subject. The verification of the method is performed by the comparison of the results with other studies available in literature. The results of the study show good correlation with the results of previous empirical studies. A damping effect of the flexible bones on the model is also studied in this paper.

Effects of temperature in relation to sheet metal stamping

The demand to reduce the use of lubricants and increase tool life in sheet metal stamping has resulted in increased research on the sliding contact between the tool and the sheet materials. Unlubricated sliding wear tests for soft carbon steel sliding on D2 tool steel were performed using a pin-on-disk tribometer. The results revealed that temperature has an influencing role in the wear of tool steel and that material transfer between tool and sheet can be minimized at a certain temperature range in sheet metal stamping.

Combustion simulations for a self controlling variable compression ratio connecting rod

Variable compression ratio enables an engine to achieve increased efficiency at part loads, where the majority of driving occurs, without sacrificing full load power requirements or increasing the risk of engine knock. Although over 100 patents and patent applications exist none of these systems has been commercialized yet due to issues related to feasibility, cost and frictional loss. A new approach of a self controlling variable compression ratio connecting rod is presented that does not need a friction intensive external activation and that could even be retrofitted. The potential in fuel consumption and exhaust emission reduction as well as increased power and torque output for this concept has been verified in combustion simulations utilizing the latest research results related to the dynamic heat transfer in the combustion chamber from Professor Kleinschmidt from the University of Siegen, Germany. The self controlling variable compression ratio connecting rod allows the con rod to compress at high load conditions thereby increasing cylinder volume to alleviate combustion pressures and temperatures and therefore limit knock onset. The biggest efficiency gains can be achieved at medium load where the reduction of heat loss during the compression of the connecting rod plays a major role additional to the well known efficiency gains of an increased compression ratio. The combustion simulation results shows fuel consumption can be reduced by between 3% and 5% during part load and wide open throttle operation at various engine speeds. Emissions are also reduced significantly; particularly NOx and CO emissions were reduced by up to 35%.The self controlling variable compression ratio connecting rod allows the con rod to compress at high load conditions thereby increasing cylinder volume to alleviate combustion pressures and temperatures and therefore limit knock onset. The biggest efficiency gains can be achieved at medium load where the reduction of heat loss during the compression of the connecting rod plays a major role additional to the well known efficiency gains of an increased compression ratio.The combustion simulation results shows fuel consumption can be reduced by between 3% and 5% during part load and wide open throttle operation at various engine speeds. Emissions are also reduced significantly; particularly NOx and CO emissions were reduced by up to 35%.

A novel exhaust heat recovery system to reduce fuel consumption

Internal combustion engines release about 1/3 of the energy bound in the fuel as exhaust waste gas energy and another 1/3 energy is wasted through heat transfer into the ambient. On the other hand losses through friction are the third largest root cause for energy loss in internal combustion engines. During city driving frictional losses can be of the same size as the effective work, and during cold start these losses are even bigger. Therefore it is obvious to utilise wasted exhaust energy to warm up the engine oil directly. Frictional losses of any engine can be reduced during part load. Sensitivity analyses have been conducted for different concepts that utilise exhaust energy to reduce engine viscosity and friction. For a new system with an exhaust gas/oil heat exchanger the following benefits have been demonstrated:

• Fuel consumption reductions of over 7% measured as an average over 5 NEDC tests
compared to the standard system configuration.
• Significant reductions in exhaust emissions, mainly CO and NOx have been achieved
• Significantly higher oil temperatures during cold start indicate large potential to
reduce engine wear through reduced water condensation in the crankcase
• Fuel consumption reductions of further 3.3% to 4.6% compared to the 7% measured
over the NEDC test can be expected under real world customer usage conditions at
lower ambient temperatures.

Oil temperature measurements and analysis resulted in the idea of a novel system with further potential to reduce fuel consumption. This Oil Viscosity Energy Recovery System (OVER 7™) consists of 3 key features that add significant synergies if combined in a certain way: an oil warm up circuit/bypass, including oil pressure control and Exhaust Gas/Oil Heat Exchanger. The system separates the thermal inertias of the oil in the engine galleries and the oil pan, reduces hydraulic pumping losses, increases the heat transfer from the cylinder head to the oil, and utilises the exhaust heat to reduce oil friction.

The project demonstrated that sensitivity analysis is an important tool for the evaluation of different concepts. Especially for new concepts that include transient heat transfer such a qualitative approach in combination with accurate experiments and measurements can be faster and more efficient in leading to the desired improvements compared to time consuming detailed simulations.