An integrated 2-D model of a lithium ion battery: The effect of material parameters and morphology on storage particle stress

An integrated 2-D model of a lithium ion battery is developed to study the mechanical stress in storage particles as a function of material properties. A previously developed coupled stress-diffusion model for storage particles is implemented in 2-D and integrated into a complete battery system. The effect of morphology on the stress and lithium concentration is studied for the case of extraction of lithium in terms of previously developed non-dimensional parameters. These non-dimensional parameters include the material properties of the storage particles in the system, among other variables. We examine particles functioning in isolation as well as in closely-packed systems. Our results show that the particle distance from the separator, in combination with the material properties of the particle, is critical in predicting the stress generated within the particle. © 2012 Springer-Verlag.

Models and algorithms for tracking of maneuvering objects using variable rate particle filters

Standard algorithms in tracking and other state-space models assume identical and synchronous sampling rates for the state and measurement processes. However, real trajectories of objects are typically characterized by prolonged smooth sections, with sharp, but infrequent, changes. Thus, a more parsimonious representation of a target trajectory may be obtained by direct modeling of maneuver times in the state process, independently from the observation times. This is achieved by assuming the state arrival times to follow a random process, typically specified as Markovian, so that state points may be allocated along the trajectory according to the degree of variation observed. The resulting variable dimension state inference problem is solved by developing an efficient variable rate particle filtering algorithm to recursively update the posterior distribution of the state sequence as new data becomes available. The methodology is quite general and can be applied across many models where dynamic model uncertainty occurs on-line. Specific models are proposed for the dynamics of a moving object under internal forcing, expressed in terms of the intrinsic dynamics of the object. The performance of the algorithms with these dynamical models is demonstrated on several challenging maneuvering target tracking problems in clutter. © 2006 IEEE.

Uniform stability of a particle approximation of the optimal filter derivative

Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity, or derivative, of the optimal filter with respect to the static parameters of the state-space model; for instance, in order to obtain maximum likelihood model parameters of interest, or to compute the optimal controller in an optimal control problem. In Poyiadjis et al. [2011] an original particle algorithm to compute the filter derivative was proposed and it was shown using numerical examples that the particle estimate was numerically stable in the sense that it did not deteriorate over time. In this paper we substantiate this claim with a detailed theoretical study. Lp bounds and a central limit theorem for this particle approximation of the filter derivative are presented. It is further shown that under mixing conditions these Lp bounds and the asymptotic variance characterized by the central limit theorem are uniformly bounded with respect to the time index. We demon- strate the performance predicted by theory with several numerical examples. We also use the particle approximation of the filter derivative to perform online maximum likelihood parameter estimation for a stochastic volatility model.

Convergence of the auxiliary particle implementation of the PHD filter

Optimal Bayesian multi-target filtering is in general computationally impractical owing to the high dimensionality of the multi-target state. The Probability Hypothesis Density (PHD) filter propagates the first moment of the multi-target posterior distribution. While this reduces the dimensionality of the problem, the PHD filter still involves intractable integrals in many cases of interest. Several authors have proposed Sequential Monte Carlo (SMC) implementations of the PHD filter. However, these implementations are the equivalent of the Bootstrap Particle Filter, and the latter is well known to be inefficient. Drawing on ideas from the Auxiliary Particle Filter (APF), a SMC implementation of the PHD filter which employs auxiliary variables to enhance its efficiency was proposed by Whiteley et. al. Numerical examples were presented for two scenarios, including a challenging nonlinear observation model, to support the claim. This paper studies the theoretical properties of this auxiliary particle implementation. $\mathbb{L}_p$ error bounds are established from which almost sure convergence follows.

Auxiliary particle implementation of the probability hypothesis density filter

Optimal Bayesian multi-target filtering is, in general, computationally impractical owing to the high dimensionality of the multi-target state. The Probability Hypothesis Density (PHD) filter propagates the first moment of the multi-target posterior distribution. While this reduces the dimensionality of the problem, the PHD filter still involves intractable integrals in many cases of interest. Several authors have proposed Sequential Monte Carlo (SMC) implementations of the PHD filter. However, these implementations are the equivalent of the Bootstrap Particle Filter, and the latter is well known to be inefficient. Drawing on ideas from the Auxiliary Particle Filter (APF), we present a SMC implementation of the PHD filter which employs auxiliary variables to enhance its efficiency. Numerical examples are presented for two scenarios, including a challenging nonlinear observation model.

Poroviscoelastic characterization of particle-reinforced gelatin gels using indentation and homogenization.

Hydrogels are promising materials for bioengineering applications, and are good model materials for the study of hydrated biological tissues. As these materials often have a structural function, the measurement of their mechanical properties is of fundamental importance. In the present study gelatin gels reinforced with ceramic microspheres are produced and their poroviscoelastic response in spherical indentation is studied. The constitutive responses of unreinforced gels are determined using inverse finite element modeling in combination with analytical estimates of material parameters. The behavior of composite gels is assessed by both analytical and numerical homogenization. The results of the identification of the constitutive parameters of unreinforced gels show that it is possible to obtain representative poroviscoelastic parameters by spherical indentation without the need for additional mechanical tests. The agreement between experimental results on composite gelatin and the predictions from homogenization modeling show that the adopted modeling tools are capable of providing estimates of the poroviscoelastic response of particle-reinforced hydrogels.

A zero-stiffness elastic shell structure

A remarkable shell structure is described that, due to a particular combination of geometry and initial stress, has zero stiffness for any finite deformation along a twisting path; the shell is in a neutrally stable state of equilibrium. Initially the shell is straight in a longitudinal direction, but has a constant, nonzero curvature in the transverse direction. If residual stresses are induced in the shell by, for example, plastic deformation, to leave a particular resultant bending moment, then an analytical inextensional model of the shell shows it to have no change in energy along a path of twisted configurations. Real shells become closer to the inextensional idealization as their thickness is decreased; experimental thin-shell models have confirmed the neutrally stable configurations predicted by the inextensional theory. A simple model is described that shows that the resultant bending moment that leads to zero stiffness gives the shell a hidden symmetry, which explains this remarkable property.

A model for the erosive wear of rubber at oblique impact angles

A model has been developed to predict the erosive wear behaviour of elastomers under conditions of glancing impact by small hard particles. Previous work has shown the erosive wear mechanism of elastomers under these conditions to be similar in nature to that of abrasive wear by a sharp blade. The model presented here was developed from the model of Southern and Thomas for sliding abrasion, by combining their treatment of the growth of surface cracks with a model for particle impact in which the force - displacement relationship for an idealized flat-ended punch on a semi-infinite elastic solid was assumed. In this way an expression for the erosive wear rate was developed, and compared with experimental measurements of wear rate for natural rubber, styrene - butadiene rubber and a highly crosslinked polybutadiene rubber. Good qualitative agreement was found between the predictions of the model and the experimental measurements. The variation of erosion rate with impact velocity, impact angle, particle size, elastic modulus of the material, coefficient of friction and fatigue properties were all well accounted for. Quantitative agreement was less good, and the effects of erosive particle shape could not be accounted for. The reasons for these discrepancies are discussed. © 1992 IOP Publishing Ltd.

A three-dimensional tunnel model for calculation of train-induced ground vibration

The frequency range of interest for ground vibration from underground urban railways is approximately 20 to 100 Hz. For typical soils, the wavelengths of ground vibration in this frequency range are of the order of the spacing of train axles, the tunnel diameter and the distance from the tunnel to nearby building foundations. For accurate modelling, the interactions between these entities therefore have to be taken into account. This paper describes an analytical three-dimensional model for the dynamics of a deep underground railway tunnel of circular cross-section. The tunnel is conceptualised as an infinitely long, thin cylindrical shell surrounded by soil of infinite radial extent. The soil is modelled by means of the wave equations for an elastic continuum. The coupled problem is solved in the frequency domain by Fourier decomposition into ring modes circumferentially and a Fourier transform into the wavenumber domain longitudinally. Numerical results for the tunnel and soil responses due to a normal point load applied to the tunnel invert are presented. The tunnel model is suitable for use in combination with track models to calculate the ground vibration due to excitation by running trains and to evaluate different track configurations. © 2006 Elsevier Ltd. All rights reserved.

Effect of particle concentration on erosion rate of mild steel bends in a pneumatic conveyor

Particle concentration is known as a main factor that affects erosion rate of pipe bends in pneumatic conveyors. With consideration of different bend radii, the effect of particle concentration on weight loss of mild steel bends has been investigated in an industrial scale test rig. Experimental results show that there was a significant reduction of the specific erosion rate for high particle concentrations. This reduction was considered to be as a result of the shielding effect during the particle impacts. An empirical model is given. Also a theoretical study of scaling on the shielding effect, and comparisons with some existing models, are presented. It is found that the reduction in specific erosion rate (relative to particle concentration) has a stronger relationship in conveying pipelines than has been found in the erosion tester. © 2004 Elsevier B.V. All rights reserved.

Discrete element calculations of the impact of a sand column against rigid structures

Discrete particle simulations of column of an aggregate of identical particles impacting a rigid, fixed target and a rigid, movable target are presented with the aim to understand the interaction of an aggregate of particles upon a structure. In most cases the column of particles is constrained against lateral expansion. The pressure exerted by the particles upon the fixed target (and the momentum transferred) is independent of the co-efficient of restitution and friction co-efficient between the particles but are strongly dependent upon the relative density of the particles in the column. There is a mild dependence on the contact stiffness between the particles which controls the elastic deformation of the densified aggregate of particles. In contrast, the momentum transfer to a movable target is strongly sensitive to the mass ratio of column to target. The impact event can be viewed as an inelastic collision between the sand column and the target with an effective co-efficient of restitution between 0 and 0.35 depending upon the relative density of the column. We present a foam analogy where impact of the aggregate of particles can be modelled by the impact of an equivalent foam projectile. The calculations on the equivalent projectile are significantly less intensive computationally and yet give predictions to within 5% of the full discrete particle calculations. They also suggest that "model" materials can be used to simulate the loading by an aggregate of particles within a laboratory setting. © 2012 Elsevier Ltd. All rights reserved.

A simple prediction model for asphalt surface texture incorporating mix gradation and air voids

This paper presents the results of a preliminary study that seeks to show how asphalt grading and air voids are related to the texture depth of asphalt. The fiftieth percentile particle size (D50) is shown to be a good predictor of texture depth measurements from a collected database of field and laboratory studies. The D50 is used to normalise collected texture data and this 'relative texture' is shown to correlate with air voids. Regression analyses confirm that air voids should be included along with a measure of gradation in the interpretation of asphalt surface texture.The derived formulae are used to develop correlation charts.

Validation of a lattice Boltzmann model for gas-solid reactions with experiments

A lattice Boltzmann method is used to model gas-solid reactions where the composition of both the gas and solid phase changes with time, while the boundary between phases remains fixed. The flow of the bulk gas phase is treated using a multiple relaxation time MRT D3Q19 model; the dilute reactant is treated as a passive scalar using a single relaxation time BGK D3Q7 model with distinct inter- and intraparticle diffusivities. A first-order reaction is incorporated by modifying the method of Sullivan et al. [13] to include the conversion of a solid reactant. The detailed computational model is able to capture the multiscale physics encountered in reactor systems. Specifically, the model reproduced steady state analytical solutions for the reaction of a porous catalyst sphere (pore scale) and empirical solutions for mass transfer to the surface of a sphere at Re=10 (particle scale). Excellent quantitative agreement between the model and experiments for the transient reduction of a single, porous sphere of Fe 2O 3 to Fe 3O 4 in CO at 1023K and 10 5Pa is demonstrated. Model solutions for the reduction of a packed bed of Fe 2O 3 (reactor scale) at identical conditions approached those of experiments after 25 s, but required prohibitively long processor times. The presented lattice Boltzmann model resolved successfully mass transport at the pore, particle and reactor scales and highlights the relevance of LB methods for modelling convection, diffusion and reaction physics. © 2012 Elsevier Inc.

The Gaussian mixture MCMC particle algorithm for dynamic cluster tracking

We present a novel filtering algorithm for tracking multiple clusters of coordinated objects. Based on a Markov chain Monte Carlo (MCMC) mechanism, the new algorithm propagates a discrete approximation of the underlying filtering density. A dynamic Gaussian mixture model is utilized for representing the time-varying clustering structure. This involves point process formulations of typical behavioral moves such as birth and death of clusters as well as merging and splitting. For handling complex, possibly large scale scenarios, the sampling efficiency of the basic MCMC scheme is enhanced via the use of a Metropolis within Gibbs particle refinement step. As the proposed methodology essentially involves random set representations, a new type of estimator, termed the probability hypothesis density surface (PHDS), is derived for computing point estimates. It is further proved that this estimator is optimal in the sense of the mean relative entropy. Finally, the algorithm's performance is assessed and demonstrated in both synthetic and realistic tracking scenarios. © 2012 Elsevier Ltd. All rights reserved.

A unifying resolution-independent formulation for early vision

We present a model for early vision tasks such as denoising, super-resolution, deblurring, and demosaicing. The model provides a resolution-independent representation of discrete images which admits a truly rotationally invariant prior. The model generalizes several existing approaches: variational methods, finite element methods, and discrete random fields. The primary contribution is a novel energy functional which has not previously been written down, which combines the discrete measurements from pixels with a continuous-domain world viewed through continous-domain point-spread functions. The value of the functional is that simple priors (such as total variation and generalizations) on the continous-domain world become realistic priors on the sampled images. We show that despite its apparent complexity, optimization of this model depends on just a few computational primitives, which although tedious to derive, can now be reused in many domains. We define a set of optimization algorithms which greatly overcome the apparent complexity of this model, and make possible its practical application. New experimental results include infinite-resolution upsampling, and a method for obtaining subpixel superpixels. © 2012 IEEE.