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The majority of vehicle dynamics control systems currently in production utilize some form of brake or throttle intervention to generate a yaw moment and control wheel slip. Such control systems can be both intrusive and inefficient. The use of active driveline technology is therefore an attractive alternative and recent advances in controlled differential technology have served to make it a potentially viable one. Using simulation results, this paper will demonstrate the power of these devices to influence vehicle dynamics by first proposing a suitable control strategy. This is then used to illustrate how, with perfect actuation, a vehicle's handling characteristics may be modified. The actuator limitations imposed by the two main classes of contemporary controlled differentials are then discussed and imposed on the simulation model. Using the ideal results as a benchmark, the relative merits of each type are then assessed.

Gas struts are widely used in vehicle suspensions. However, they are highly non-linear and conventional linear models are not sufficient to describe their complex behaviour. In this paper, two non-linear gas strut models with different modelling approaches are presented. One is based on grey-box methods using the modular dynamic simulation package Bathfp, where both physical parameters and experimental data are used to model the strut. The other uses black-box methods in Matlab, where artificial neural networks are employed and experimental data are used to train the model. Simulation studies demonstrate that the neural network model is more suitable for real road vehicle simulations, whereas the Bathfp model is more appropriate for detailed system dynamics analysis, especially iso-frequency studies. Since the Bathfp model is able to predict the strut performance when certain parameters in the system are changed and can be easily integrated into different vehicle models, it is a useful design tool for both strut manufacturers and automotive original equipment manufacturers.

This paper demonstrates the use of an extended Kalman filter (KF) as a virtual sensor for non-measurable vehicle states and unknown vehicle parameters. The purpose of obtaining these values is to make them available within the control algorithms of the various automotive stability systems. Based on an extensive four-wheel vehicle model, an estimator is implemented on data from a test vehicle. Using available reference data, the suitability of the extended KF technique as a virtual sensor is demonstrated.

The article demonstrates the implementation of a model-based vehicle estimator, which can be used for combined estimation of vehicle states and parameters. The estimator is realised using the dual extended Kalman filter (DEKF) technique, which makes use of two Kalman filters running in parallel, thus ‘splitting’ the state and parameter estimation problems. Note that the two problems cannot be entirely separated due to their inherent interdependencies. This technique provides several advantages, such as the possibility to switch off the parameter estimator, once a sufficiently good set of estimates has been obtained. The estimator is based on a four-wheel vehicle model with four degrees of freedom, which accommodates the dominant modes only, and is designed to make use of several interchangeable tyre models. The paper demonstrates the appropriateness of the DEKF. Results to date indicate that this is an effective approach, which is considered to be of potential benefit to the automotive industry.

It is extremely difficult to maintain simultaneously a high standard of ride, handling, and body control in a vehicle with a conventional passive suspension. However, it is well known that active suspensions provide a possible solution to this problem, albeit with additional cost and weight. This paper describes the design and analysis of a hydropneumatic slow active suspension. The design is based on hydropneumatic suspension components taken from a commercial system. A non-linear quarter-car model is developed, which includes a gas strut model developed in a previous study and a non-linear dynamic flow control valve model. A hybrid control strategy is proposed for the disturbance rejection and self-levelling requirements. The disturbance rejection control is based on limited state feedbacks and the linear quadratic method plus a Kalman filter that is used to optimize the performance index. The self-levelling control employs a proportional, integral, and derivative (PID) control strategy. Practical issues, such as power consumption, controller robustness, and valve dynamics, are also investigated in this paper. Simulations show that the proposed system has good performance and robustness.

By electrical resistance tomography (ERT) the cross sectional profiles of gas hold-up in a o56mm bubble column are obtained with four designs of gas sparger. The effect of sparger geometry on the bubble distribution is revealed by applying a sensitivity conjugated gradients reconstruction method (SCG). Experimental results show that overall hold-up obtained by ERT is generally in good agreement with those measured with the pressure transducer and the ERT system produces informative evidence that the radial profiles of hold-up is very similar to the sparger design in the lower section of bubble column. Meanwhile, the rise velocity of bubble swarm and the Sauter mean bubble size are evaluated using ERT based on dynamic gas disengagement theory. The experimental results are in good agreement with correlations and conventional estimation obtained using pressure transmitter methods.

The strut is one of the most important components in a vehicle suspension system; however, it is also one of the most difficult elements to model owing to its highly nonlinear characteristics. In this paper a non-linear gas strut model built in the software package Bath fp is presented. Both analytical and parametric modelling methods were used in the representation of different components in the strut. Simulations at various frequencies showed good agreement with experimental results. A sensitivity analysis of strut performance is presented at the end of the paper. It was found that the damper valve characteristics, the rod diameter, the temperature, and the user-defined polytropic index significantly affect the strut performance.

Two actuation mechanisms are considered for the comparison of performance capabilities in improving the yaw-sideslip handling characteristics of a road vehicle. Yaw moments are generated either by the use of single-wheel braking or via driveline torque distribution using an overdriven active rear differential. For consistency, a fixed reference vehicle system is used, and the two controllers are synthesized via a single design methodology. Performance measures relate to both open-loop and closed-loop driving demands, and include both on-centre and limit handling manoeuvres.

Other than the Crittenden County fault zone (CCFZ), little is known about the seismic hazard from earthquake faults within 50 km of Memphis, Tennessee, a city that contains a large inventory of older buildings that are vulnerable to moderate and strong earthquake ground shaking. To address this lack of knowledge about faulting near Memphis, we acquired a 4.5 km long Mini-Sosie seismic-reflection profile across the boundary between the loess-covered bluffs and modern Mississippi River flood plain in Meeman-Shelby Forest State Park north of Memphis. We imaged a previously unknown reverse/thrust fault that displaces Paleozoic and Cretaceous rocks and upwarps Tertiary deposits on the floodplain portion of the profile about 25 km north of downtown Memphis. The Paleozoic and Cretaceous rocks are vertically faulted about 70 and 40 m, respectively, in an up-to-the-west sense of displacement. The fault displacement apparently terminates in the basal portion of the Paleocene section and causes only an upwarping of the overlying deposits. The overlying Paleocene and Eocene deposits, which are probably the youngest deposits imaged, are upwarped about 50–60 m with the same sense of displacement as the underlying older units. The sense of displacement, amplitude, and appearance of the fault in the seismic data are very similar to that observed in the seismic reflection images of the CCFZ 15 km west of this profile. Although we have imaged this new fault in only one location, its proximity to Memphis and similarities to the CCFZ, leads us to speculate that it may be a parallel structure to the CCFZ and thus warrants further study.

This paper reviews a collaborative research programme aimed at improving vehicle performance using adaptive control techniques. Initially the design of active suspension systems is considered, and the benefits of using a non-linear controller model with an adaptive control scheme are discussed. Adaptive schemes for active roll control are then considered, and the merits of incorporating a Smith predictor to accommodate for system delays are high-lighted. Preliminary research in adaptive cruise control and collision avoidance is discussed and plans for further developments are outlined.

Part 1 of the paper demonstrated the compromises required in suspension design brought about by the conflicting demands of ride and handling, and the constraints applied by the need to minimize body acceleration within a limited suspension travel. It then went on to show how a state feedback controller can be used to provide improvements in ride which are not achievable with standard passive components. This second part discusses the hardware employed, which ranges from simple switched dampers, through semi-active dampers, and low-bandwidth/soft active suspensions, to high-bandwidth/stiff active suspensions. The benefits to be derived from each of the technologies is assessed, together with the practical implications.

Automotive suspension design is a compromise brought about by the conflicting demands of ride and handling. The past few years have seen the introduction of increasingly sophisticated, electronically controlled, components into automotive suspensions which redefine the boundaries of the compromise. The paper has been written in two parts. This first part reviews the compromises which are required in the design of a conventional passive suspension. It then goes on to show how those compromises can be changed by the inclusion of active components. The second part discusses the hardware employed which ranges from simple switched dampers, through semi-active dampers, and low bandwidth/soft active suspensions, to high bandwidth/stiff active suspensions. The benefits to be derived from each of the technologies will be assessed, together with their strengths and weaknesses.

The paper presents the results of investigative studies involving the performance of full linear and non-linear suspension models configured in a low bandwidth active suspension form. The non-linear model includes non-linear spnng stiffness, bilinear damping rates, saturation in the control valve, friction and bilinear bump stops. Initial results compare the two models when making use of a multi-modal controller with fixed gains. It is shown that the non-linear model is able to replicate the actual system more closely and the performance of the non-linear system is then evaluated using an adaptive controller. Results demonstrate that when adaptation is incorporated into the controller the power required to achieve satisfactory performance is reduced.

Manufacturing systems generally encompass processes that are discrete in time and space. Among the variety of real-time supervisory control techniques reported in the literature, controlled-automata-based discrete event system (DES) theory is one of the few with mathematical formalism. However, the control of even a moderately complex system using this theory may require a very large control strategy. To attempt to cope with this problem, a hybrid supervisory controller was developed that splits operations between a DES-theory-based supervisory controller and an alternate mechanism. The alternate mechanism reroutes part production in real time whenever a priori unmodeled events occur. This modified approach provides a significantly more efficient controller than could be attained using solely a DES-theory-based supervisory controller.

The paper presents results of investigative studies involving non-linear pitch/bounce and roll half car models in order to assess the performance of fixed gain controllers within a low bandwidth active suspension configuration. The vehicle is subjected to acceleration, braking and cornering manoeuvres. The results highlight the compromise that exists between the body acceleration and strut deflection loops and it is concluded that an element of adaptivity within the scheme could be used to advantage.

Automotive suspension design is a compromise brought about by the conflicting demands of ride and handling. We have seen the introduction of increasingly sophisticated, electronically controlled components which redefine the boundaries of the compromise. The major elements of a motor car suspension are summarised by the author. The technology employed in automotive suspension design covers a wide range of sophistication, performance and cost and can be categorised as: adaptive suspension, semi-active suspension, low-bandwidth active suspension, and four wheel steering systems. The author considers each of these categories.

The function of an automotive suspension system is to maintain passenger comfort and vehicle road handling capabilities whilst supporting the body mass of the vehicle and operating within the constraints of the suspension working space. In order to satisfy these criteria the overall suspension system is required to be ‘tuned’ to provide a satisfactory compromise; the point at which this compromise is made is an important design parameter and varies from vehicle to vehicle depending upon its application and may also be required to vary depending upon operating conditions. The paper presents results of an extensive sensitivity analysis aimed at assessing the effectiveness of an optimal control law design which is based on a low order generalised minimum variance approach applied to a low bandwidth slow active suspension system. The control law design is assessed when subjected to an increase in the body mass of the vehicle as well as variations in the tyre spring rate and the conventional suspension elements; the base vehicle under consideration being a large luxury saloon car. The results of the sensitivity analysis highlight the need for flexibility in the controller cost weightings and reinforce the appropriateness and practicability of using a fixed low order model structure in order to achieve further improvements in overall ride quality.

Various sensor technologies require a monolayer of tightly bound proteins. Five methods for protein immobilization were evaluated, comprising two methods of linker attachment to a silicon nitride surface (CNBr, silanization) and three methods of linker attachment to the protein (via primary amines, carboxyl groups, and the aromatic rings of tyrosine and histidine). These covalent binding methods were evaluated by immobilization of the enzyme alkaline phosphatase and with monoclonal antibodies tagged with 125I. It was determined that approximately 75% of the protein on the "covalently" immobilized samples was simply adsorbed. Adsorption was reduced by varying the pH and ionic strength of the wash buffers as well as by adding chaotropes and competitors to the wash buffer. A more efficient method of reducing adsorption was to perform the immobilization in the presence of a detergent; 0.5% Tween 60 was the most effective detergent studied. The optimized procedure gives a surface loading of 1.20 x 10(12) MAb/cm2. of which approximately 10% was adsorbed protein. This surface density is consistent with a monolayer of immobilized protein. This protein was shown to be active by challenging immobilized antibodies with 35S-labelled antigen; only the antibody/antigen pair released radioactive material upon elution.

A general formal transient solution to the linear boundary value problem which governs the transport of interstitials injected into an arbitrary bounded domain from oxidizing segments on the surface is presented. An explicit expression for the Green's function which appears as the kernel in the integral representation of the general transient solution is given for a simple domain of interest in the study of oxidation-enhanced diffusion (OED). By combining this explicit expression for the Green's function with the general formal solution, a transient analytical model for predicting the redistribution of interstitials injected into the simple domain from a single oxidizing segment is obtained. An illustrated example important to OED is considered and results obtained with the model and by approximations to the model are compared. Also, the results obtained with the SUPREM-IV program are presented for comparison. >

This paper demonstrates the implementation of a comprehensive vehicle model combined with a driver model in closed loop for the purpose of developing and testing of vehicle stability systems. As an example of such a stability system, a model of an active front steering controller is considered. The operation of this controller is based on vehicle states available my means of a state estimator. The functional efficiency of these combined models is demonstrated using a double-lane change manoeuvre. The use of the stability controller shows clear improvement in terms of the vehicle dynamical stability.

The main purpose of this paper is to document the findings of a study tasked by the joint staff regarding the potential supportability of the Global Hawk (GH) high data rate requirements using the Wideband Gapfiller Satellite (WGS). The joint staff tasking was based upon an intelligence program decision memorandum (IPDM) tasking investigating options for the support of the Global Hawk unmanned aerial vehicle beyond line of sight requirements. DISA conducted the study with support from the Space and Missile Systems Center MILSATCOM Joint Program Office (SMC/MJPO) and from ARMYSpace the WGSSATCOM System Expert (SSE). SMC/MJPO provided the WGS payload specification as proposed by Boeing and ARMYSpace provided operational and technical input into the study. WGS will provide up to nineteen 125-MHz digital transponders to meet tactical user requirements. These segments can be flexibly connected between Ka and X-band and can route subsegments of these 125-MHz band segments between X- and Ka-band coverages. Analyses are based on Ka-band connectivity between the satellite and the Global Hawk platform, with hub to satellite connectivity at either Ka-band or X-band. In addition to bandwidth considerations, the analysis examines required power budgets and coverages expected to serve the Global Hawk mission.

The purpose of this paper is to summarize the findings of an assessment tasked by the joint staff regarding the broadcast ground segment architecture for the Wideband Gapfiller Satellite (WGS). WGS has the capability to permit Global Broadcast Service (GBS) injection at either Ka-band (30 GHz) or X-band (8-GHz), and be cross-banded and received by current GBS receive-only suites at 20-GHz. Original plans were to buy three new GBS Ka-band injection terminals to support GBS on WGS; however, to save costs, one alternative is to use existing DSCS X-band terminals to perform the GBS injection on WGS with crossbanding to the current Ka-band GBS receive suites. Then, as UHF Follow-On (UFO) GBS satellites reach their end of life, the existing Ka-band GBS injection terminals will replace the X-band injection, freeing the latter for other missions. This paper examines various options and provides recommendations for GBS injection on WGS in consideration of the available Xand Ka-band bandwidth and the corresponding antenna coverage issues. This paper also discusses an option for GBS reception at X-band for sites with existing X-band two-way services. Based on this capability, the paper shows options for a Ka-only GBS, cross-banded Ka-to-X band GBS, X-to-Ka-band GBS, and X-to-X-band GBS. Planned use of these options will provide coverage flexibility and ease the current planning burden and will minimize the amount of beam movement to achieve desired worldwide coverage goals.

Dipole Magnets is one of a set of self-paced interactive training tutorials on particle accelerators that target a broad audience. It covers the bending and focusing properties of dipole magnets. The tutorial contains five sections, four of which are accessible to undergraduate science majors and accelerator technicians.

Severe hot-carrier degradation has been observed in deep-submicron N-MOSFETs, and is shown to be caused by several advanced device processing steps. These processing steps can also introduce significant changes in other device parameters, such as the threshold voltage and transconductance, etc., for devices without any hot-carrier stress. The two major achievements of this work are that: (1) we systematically illustrate that the process-induced lifetime degradation is most sensitive to details of back-end wafer processing, particularly when it involves high density plasma (HDP-CVD) oxide deposition and H/sub 2/ annealing; (2) we demonstrate experimentally, for the first time, that using a properly designed SiN pre-metal-dielectric (PMD) liner process can most effectively stop the back-end process-induced lifetime degradation. This result is different from previous reports which indicated that an additional SiN liner could further degrade the device lifetime (Tokitoh et al., 1995 and 1997; Cheek et al., 1997). We show that this apparent inconsistency is partly because one must be very careful in designing the liner process to make it work properly, and partly because the previous studies did not cover back-end process-induced hot-carrier effects.

The paper describes an oleo-pneumatic active suspension which has been developed using a linear multivariable controller. In order to optimise the performance of the system it has been necessary to address the nonlinearities of the system, such as those inherent in the gas spring, bump and rebound stops, dampers and flow control valves. A description is given of the nonlinearities and effects encountered under changing load, manoeuvre and ride inputs. Results are presented which demonstrate the benefits of using a nonlinear controller model within an adaptive control scheme.

Because of their nondeterministic nature of behaviour, the supervisory control of manufacturing systems must be carried out in closed loop. This trait greatly increases the size and complexity of the discrete-event system (DES)-based supervisory-controllers of manufacturing systems. In an attempt to cope with this complexity, a hybrid supervisory controller (HSC) is proposed. It splits operations between its three elements: (i) a DES supervisory controller, which contains the nominal control strategy, (ii) a diagnostic system, which monitors the workcell, and (iii) an alternate strategy driver (ASD), that asserts control by revising the nominal strategy of the DES supervisory controller, whenever events diverge from the states of the DES supervisory controller. This modified approach to DES control provides a more efficient controller than could reasonably be attained using solely a DES supervisory controller. >

In this paper, we report a physically based interpretation of the MOSFET effective channel length, L/sub eff/. L/sub eff/ of a MOSFET is usually extracted from measurements of the linear region current gain (1/K method) or the linear region resistance (resistance method) on transistors with different gate lengths. We find that the extracted L/sub eff/ of a submicron lightly doped drain/source (LDD) MOSFET is strongly influenced by diffusion of minority carriers (electrons for NMOSFETs) from the gate-controlled LDD overlap region into the inversion layer. This changes the resistance of the inversion layer at the source/drain ends and thus causes the extracted L/sub eff/ to deviate from the metallurgical channel length, L/sub met/. The impact of minority carrier diffusion is stronger for shorter channel lengths; therefore, the extracted /spl Delta/L(=L/sub gate/-L/sub eff/ where L/sub gate/ is the drawn gate length) increases with decreasing gate length. The choice of gate lengths used in L/sub eff/ extraction will, thus, influence the value for L/sub eff/. MINIMOS 2D simulations have been used to study this effect. The results have been confirmed by actual measurements on submicron LDD MOSFETs. This analysis has been used to select the best choices of L/sub gate/ and bias condition to minimize errors in the measurement of L/sub eff/. >

Since the designation in the 1970s of a military satellite communications Ka-band (30-31 GHz uplink, 20.2-21.2 GHz downlink), these frequencies have held great potential to support US forces and requirements. In 1995, the Ka-band was chosen for the Global Broadcast Service (GBS) which will be operational on the UFO satellites beginning in 1998. However, only a small percentage of the allocated 1 GHz of bandwidth will be used by GBS. During the MILSATCOM architecture reviews, the Ka-band was again considered for the Advanced Wideband System (AWS) and the Gapfiller satellites. This paper discusses the potential uses of the Ka-band for the AWS and Gapfiller satellites. Included is a technical discussion of the potential applications for both tactical and fixed infrastructure requirements in the 2005-to-2010 timeframe.

The paper outlines simulation studies and investigations of a hydraulic actuated brake (HAB) and an alternative electromechanically actuated brake (EMB) system on a half-car model using the Simulink environment. The vehicle simulation model used is briefly explained as follows. Both implementations build on a brake by wire technology, which is essentially an interface for driver assistance. The input is obtained from 0-100% brake actuation converted into pressure applied to the brake system. This gives scope for further development, for example increasing brake pressure in emergency situations and traction control. Additionally, it covers safety aspects in design and implementation. For example, a design for a hydraulic based brake-by-wire pedal emulator with failed power braking requirements may be found in Zehnder et al. (1999). In the paper various ABS control strategies utilizing HAB and EMB technologies are evaluated and compared. The ABS control strategies are outlined and comparisons of the results are discussed.

A very important goal of mechatronics in system development is the integration of mechanical, electronic and software subsystems in order to increase functionality, minimize weight, and reduce production costs. In this work, industry demands on methods and tools for mechatronic vehicle development are addressed from the current product development in industry. The development of a mechatronic car door concept and dynamic stability control are used as examples to identify strong and weak parts of the current processes. Railway vehicle development aspects are also discussed. It is shown that a very important aspect for a successful mechatronic design is co-operation in an interdisciplinary design team. In terms of design methodology, the systematic identification of mechatronic potential based on function analysis is a main issue. Computer tools and technology for concept simulation, co-simulation, managing of models with different complexity as well as model exchange are identified as important demands for future effective development of mechatronic vehicles.

The imaging of phase distributions in vessels using tomographic techniques offers benefits in relation to improved and more efficient control schemes arising from comprehensive data acquisition. However, such image measurements are multivariate in nature and require statistical treatment. Therefore, the modelling of a multiphase process by tomography is different from the conventional process modelling where the measurements are univariate. In this paper, principal component analysis is used to extract useful information from tomographic images and to estimate the dynamic behaviour of mixing processes.

The paper presents the results of investigative studies involving the performance of a full nonlinear vehicle suspension system configured in a low bandwidth active suspension form. By using a multi-modal control technique the benefits of using an online adaptive scheme are explored and compared to a fixed multi-modal scheme. The vehicle is subjected to differing load conditions and temperatures and is simulated whilst undergoing various manoeuvres and road input conditions. Results in this paper suggest that potential improvement using an adaptive approach can be achieved, particularly in terms of a reduction in total fluid flow.

This chapter illustrates the application of fundamental theories of particle deposition to the modeling of particulate removal in packed-bed filters. Filtration theories that describe the capture (or removal) of particles in packed-bed filters can be classified into two types—phenomenological (macroscopic) and fundamental (microscopic). The ultimate aim of filtration models is to predict removal of particles as a function of suspension characteristics, physical and chemical properties of the filter, and flow conditions. Important suspension characteristics are density, size, size distribution, and surface chemistry of the particles; and temperature, viscosity, and solution chemistry of the suspending medium. The parameters that describe the properties of packed-bed filters are bed depth, grain size, grain shape, grain surface chemistry, and porosity. Another important parameter in packed-bed filtration is the approach (superficial) velocity. The approach velocity is defined as the ratio of the volumetric flow rate to the filter cross-section area.

This chapter illustrates the principles of simulating the behavior of colloidal systems by using practical examples showing the application of selected simulation methods. Compared with ordinary colloids, magnetic particle dispersions have distinctive properties and behave quite differently. This is because, in addition to the usual isotropic colloidal forces such as electrostatic and van der Waals forces, magnetic particles are also subject to magnetic interactions, which are uniaxial by nature. As the magnetic interactions, and hence, the total interaction energy, depend not only on the separation distance but also on the orientation of the particles, aggregates of magnetic particles tend to have an anisotropic chain-like structure. By applying Monte Carlo (MC) simulation methods, it is possible to study the influence of process variables on the structural properties of magnetic particle dispersions. Hence, if aggregation through van der Waals force is dominant, the flocs formed will be more isotropic; if magnetic aggregation becomes more dominant, chains with relatively few side-arms or branches will form.

Electrical interaction among colloidal particles (especially in aqueous systems) is one of the most important influences on particle stability, aggregation, and deposition. In an electrolyte solution, the distribution of ions around a charged particle is not uniform, and it gives rise to an electrical double layer. The essential point is that the charge on, say, a particle surface is balanced by an equivalent number of oppositely charged counterions in solution. These counterions are subject to two opposing influences: electrostatic attraction tending to localize the counterions close to the particles, and the tendency of ions to diffuse randomly throughout the solution, owing to their thermal energy. The surface charge on a particle and the associated counterion charged together constitute the electrical double layer. The surface charge and the distribution of counterions near to the surface depend greatly on the nature and concentration of salts in solution, giving a relatively simple means of modifying colloid interactions. In most cases, the only practical means of manipulating the stability of particles and their tendency to deposit on surfaces is by changing the electrical interaction through changes in the solution chemistry. For this reason, this chapter outlines the important properties of the electrical double layer, and shows how physical models can be applied.

This chapter discusses about a fundamental assumption regarding aggregation. It states that aggregation is a second-order rate process in which the rate of collision is proportional to the product of concentrations of two colliding species. With regard to the rate of aggregation, all collisions may not be successful in producing aggregates. The fraction of successful collisions is called the collision efficiency and given the symbol α. If there is strong repulsion among particles, practically no collision gives an aggregate and α=0. When there is no significant net repulsion or when there is an attraction among particles, the collision efficiency can approach unity. Although there are some theoretical difficulties, it is usual to assume that the collision rate is independent of colloid interactions and depends only on particle transport. This assumption can often be justified on the basis of the short-range nature of interparticle forces, which operate over a range which is usually much less than the particle size, so that particles are nearly in contact before these forces come into play. The “decoupling” of transport and attachment steps greatly simplifies the analysis of aggregation kinetics and a similar assumption is common in simple treatments of particle deposition. A very important case where this approach is not justified is that of hydrodynamic or viscous interaction, which involves much longer-range effects.