H. Thomas Banks

Estimation of distributed parameters in permittivity models of composite dielectric materials using reflectance

Abstract We investigate the feasibility of quantifying properties of a composite dielectric material through the reflectance, where the permittivity is described by the Lorentz model in which an unknown probability measure is placed on the model parameters. We summarize the computational and theoretical framework (the Prohorov metric framework) developed by our group in the past two decades for nonparametric estimation of probability measures using a least-squares method, and point out the limitation of the existing computational algorithms for this particular application. We then improve the algorithms, and demonstrate the feasibility of our proposed methods by numerical results obtained for both simulated data and experimental data for inorganic glass when considering the resonance wavenumber as a distributed parameter. Finally, in the case where the distributed parameter is taken as the relaxation time, we show using simulated data how the addition of derivative measurements improves the accuracy of the method.

Analysis of variability in estimates of cell proliferation parameters for cyton-based models using CFSE-based flow cytometry data

Abstract In this article we assess variability in cell proliferation dynamics observed for CD4+ and CD8+ T cells collected from two healthy donors. We review a recently developed class of models that incorporates the so-called “cyton model” for cell numbers into a conservation-based PDE model for cell population dynamics and describe a statistical model that relates CFSE-based flow cytometry data to such models. A parameter estimation scheme is summarized and then applied to a large body of data to assess experimental variability (variation in parameter estimates as identical experiments are replicated) and biological variability (differences in parameter estimates obtained for different donors and cell types) in the context of these models. Variability in the data obtained from replicated experiments is also discussed. The results of this study indicate that many of the cyton model parameters for describing cell proliferation can be reliably estimated using our approach; however, they also show that substantial changes to our mathematical model and/or experimental procedures may be required to ensure identifiability of the remaining cell proliferation parameters.

Modeling aspects concerning THUNDER actuators

This paper summarizes techniques for modeling geometric properties of THUNDER actuators which arise in the fabrication process. These actuators are high performance composites comprised of layers of piezoceramics in combination with aluminum, stainless steel, brass or titanium bonded with hot- melt adhesive. During the construction process, the assembly is heated under pressure to high temperatures, cooled and repoled to restore the actuator capabilities. This process provides the actuators with the robustness necessary to withstand the high voltages required for large displacement and force outputs. The process also provides the actuators with their characteristic curved shape. In this paper, relations between the thermal and electrostatic properties of the material and the final geometric configuration are quantified. This provides an initial model that can be employed in control applications which employ THUNDER actuators.

Evaluation criteria for THUNDER actuators

THUNDERTM (thin-layer composite unimorph ferroelectric driver and sensor) represents a new class of piezoceramic- based actuators capable of generating significant displacements and forces in response to input voltages. The performance capabilities of THUNDERTM actuators are due to the component materials and process used in their construction. A typical THUNDERTM actuator is composed of metallic backing materials (e.g., aluminum or stainless steel), a piezoceramic wafer, and adhesive in spray or film form. The materials are bonded under high pressures and temperatures and then cooled to room temperature after the adhesive has solidified. Due to the prestresses which result from the differing thermal properties of the component materials under cooling, the actuator is highly durable with respect to mechanical impacts and voltage levels. As a result of this construction voltages in excess of 800 V can be applied to new actuator models without causing damage. This provides the actuators with significant displacement and force capabilities. In this paper, we discuss the development of evaluation criteria which are suitable for characterizing the actuator capabilities and provide a legitimate methodology for comparing THUNDERTM properties with those of other smart material actuators. For example, the concept of blocked force is often used to quantify the force capabilities of an actuator. However due to the inherent curvature and mode of operation, standard techniques for measuring blocked forces are inappropriate for THUNDERTM actuators. Furthermore, changing operating conditions, frequency, etc., often make blocked force measurements ambiguous. We will discuss techniques for evaluating THUNDERTM properties in a manner which limits such ambiguities when comparing with other smart materials. We note that the evaluation issues discussed here are germane to a variety of high performance smart material transducers.

Dynamic simulations and nonlinear homogenization study for magnetorheological fluids

We first present a summary of results obtained with a numerical code to perform particle dynamics simulations of magnetorheological (MR) fluids upon application of an external magnetic field. These simulations, for the first time, account fully for all linear (long-range) magnetic interactions and are made feasible by recent developments of the Fast Multipole Method. In addition, we present some numerical and theoretical studies for the overall magnetic response in MR fluids based on nonlinear homogenization theory. We show that these results can be effectively used to study a number of experimental findings such as effective magnetic permeabilities (from the linear through saturation regimes) and response time scales, all of which are of crucial importance in the design of MR fluids.

Distributed parameter system models for damage detection and location in smart material structures

Nondestructive damage detection is an important issue in aging civil engineering, aerospace structures, and several other areas. This study presents an attempt to use parameterized partial differential equations and Galerkin approximation techniques to detect and locate damage. Dynamical analysis is carried out using structure bonded piezoceramic patches as both sensors and actuators. Our presentation demonstrates the flexibility and accuracy of this approach. It is mode independent and can sense the presence of damage and locate certain damages to a satisfactory precision. As an example, a beam with a pair of piezoceramic patches bonded to it is used as the test structure; several computational examples with holes of different size, shape, and location in the beam are investigated.

Ecosystem function in predator–prey food webs—confronting dynamic models with empirical data

Most ecosystem functions and related services involve species interactions across trophic levels, for example, pollination and biological pest control. Despite this, our understanding of ecosystem function in multitrophic communities is poor, and research has been limited to either manipulation in small communities or statistical descriptions in larger ones. Recent advances in food web ecology may allow us to overcome the trade-off between mechanistic insight and ecological realism. Molecular tools now simplify the detection of feeding interactions, and trait-based approaches allow the application of dynamic food web models to real ecosystems. We performed the first test of an allometric food web models ability to replicate temporally nonaggregated abundance data from the field and to provide mechanistic insight into the function of predation. We aimed to reproduce and explore the drivers of the population dynamics of the aphid herbivore Rhopalosiphum padi observed in ten Swedish barley fields. We used a dynamic food web model, taking observed interactions and abundances of predators and alternative prey as input data, allowing us to examine the role of predation in aphid population control. The inverse problem methods were used for simultaneous model fit optimization and model parameterization. The model captured >70% of the variation in aphid abundance in five of ten fields, supporting the model-embodied hypothesis that body size can be an important determinant of predation in the arthropod community. We further demonstrate how in-depth model analysis can disentangle the likely drivers of function, such as the communitys abundance and trait composition. Analysing the variability in model performance revealed knowledge gaps, such as the source of episodic aphid mortality, and general method development needs that, if addressed, would further increase model success and enable stronger inference about ecosystem function. The results demonstrate that confronting dynamic food web models with abundance data from the field is a viable approach to evaluate ecological theory and to aid our understanding of function in real ecosystems. However, to realize the full potential of food web models, in ecosystem function research and beyond, trait-based parameterization must be refined and extended to include more traits than body size.

Ultrasonic attenuation spectroscopy and dispersion characteristics in cortical bone

A mathematical model to predict the ultrasonic attenuation coefficient as a function of frequency in cortical bone is proposed, and the effects of micro-architectural changes on model parameters are studied in this work. Spectroscopy was performed in numerical finite differences time domain simulations to study the individual effects of pore diameter on ultrasonic attenuation. The attenuation coefficient was calculated by measuring the wave amplitude of the wave propagated in simulated bone slabs. Data obtained from numerical simulations show an acceptable match with the proposed model, and the model parameters varied consistently with increasing pore diameter in the cortical bone slabs. Results of this research indicate the potential of a mathematical model to predict the dispersion of attenuation in cortical bone as a function of frequency, pore size and pore density.

Modeling of the structural acoustic coupling inside a thin cylindrical shell

A fully coupled mathematical model describing the dynamics of a cylindrical structural acoustics problem is presented. The geometry of interest consists of an acoustic field lying inside a vibrating thin cylindrical shell. In this model, the shell dynamics are coupled to the interior acoustic field through pressure and momentum conditions. Because the model will ultimately be used in control applications involving piezoceramic actuators, the loads and material contributions resulting from bonded piezoceramic patches are also included in the discussion. Strong and weak forms of the modeling set of coupled partial differential equations (PDEs) are presented, thus yielding a framework which is amenable to the application of various approximation techniques to the problem of developing schemes for forward simulations, parameter estimation, and application of PDE-based control strategies.