Calibration of the spring constant of cantilevers of arbitrary shape using the phase signal in an atomic force microscope.

The measurement of cantilever parameters is an essential part of performing a calibrated measurement with an atomic force microscope (AFM). The thermal motion method is a widely used technique for calibrating the spring constant of an AFM cantilever, which can be applied to non-rectangular cantilevers. Given the trend towards high frequency scanning, calibration of non-rectangular cantilevers is of increasing importance. This paper presents two results relevant to cantilever calibration via the thermal motion method. We demonstrate the possibility of using the AFM's phase signal to acquire the thermal motion. This avoids the challenges associated with connecting the raw photodiode signal to a separate spectrum analyser. We also describe how numerical calculations may be used to calculate the parameters needed in a thermal motion calibration of a non-rectangular cantilever. Only accurate knowledge of the relative size of the in-plane dimensions of the cantilever is needed in this computation. We use this pair of results in the calibration of a variety of rectangular and non-rectangular cantilevers. We observe an average difference between the Sader and thermal motion values of cantilever stiffness of 10%.

A simple bioconjugate attachment protocol for use in single molecule force spectroscopy experiments based on mixed self-assembled monolayers.

Single molecule force spectroscopy is a technique that can be used to probe the interaction force between individual biomolecular species. We focus our attention on the tip and sample coupling chemistry, which is crucial to these experiments. We utilised a novel approach of mixed self-assembled monolayers of alkanethiols in conjunction with a heterobifunctional crosslinker. The effectiveness of the protocol is demonstrated by probing the biotin-avidin interaction. We measured unbinding forces comparable to previously reported values measured at similar loading rates. Specificity tests also demonstrated a significant decrease in recognition after blocking with free avidin.

A body force-based method for prediction of multiple-pure-tone noise: Validation

Emissions, fuel burn, and noise are the main drivers for innovative aircraft design. Embedded propulsion systems, such as for example used in hybrid-wing body aircraft, can offer fuel burn and noise reduction benefits but the impact of inlet flow distortion on the generation and propagation of turbomachinery noise has yet to be assessed. A novel approach is used to quantify the effects of non-uniform flow on the creation and propagation of multiple pure tone (MPT) noise. The ultimate goal is to conduct a parametric study of S-duct inlets to quantify the effects of inlet design parameters on the acoustic signature. The key challenge is that the effects of distortion transfer, noise source generation and propagation through the non-uniform flow field are inherently coupled such that a simultaneous computation of the aerodynamics and acoustics is required to capture the mechanisms at play. The technical approach is based on a body force description of the fan blade row that is able to capture the distortion transfer and the blade-to-blade flow variations that cause the MPT noise while reducing computational cost. A single, 3-D full-wheel CFD simulation, in which the Euler equations are solved to second-order spatial and temporal accuracy, simultaneously computes the MPT noise generation and its propagation in distorted inlet flow. A new method of producing the blade-to-blade variations in the body force field for MPT noise generation has been developed and validated. The numerical dissipation inherent to the solver is quantified and used to correct for non-physical attenuation in the far-field noise spectra. Source generation, acoustic propagation and acoustic energy transfer between modes is examined in detail. The new method is validated on NASA's Source Diagnostic Test fan and inlet, showing good agreement with experimental data for aerodynamic performance, acoustic source generation, and far-field noise spectra. The next steps involve the assessment of MPT noise in serpentine inlet ducts and the development of a reduced order formulation suitable for incorporation into NASA's ANOPP framework. © 2010 by Jeff Defoe, Alex Narkaj & Zoltan Spakovszky.

Measurement of the Interaction Between Recombinant I-domain from Integrin alpha 2 beta 1 and a Triple Helical Collagen Peptide with the GFOGER Binding Motif Using Molecular Force Spectroscopy.

The role of the collagen-platelet interaction is of crucial importance to the haemostatic response during both injury and pathogenesis of the blood vessel wall. Of particular interest is the high affinity interaction of the platelet transmembrane receptor, alpha 2 beta 1, responsible for firm attachment of platelets to collagen at and around injury sites. We employ single molecule force spectroscopy (SMFS) using the atomic force microscope (AFM) to study the interaction of the I-domain from integrin alpha 2 beta 1 with a synthetic collagen related triple-helical peptide containing the high-affinity integrin-binding GFOGER motif, and a control peptide lacking this sequence, referred to as GPP. By utilising synthetic peptides in this manner we are able to study at the molecular level subtleties that would otherwise be lost when considering cell-to-collagen matrix interactions using ensemble techniques. We demonstrate for the first time the complexity of this interaction as illustrated by the complex multi-peaked force spectra and confirm specificity using control blocking experiments. In addition we observe specific interaction of the GPP peptide sequence with the I-domain. We propose a model to explain these observations.

Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach

We apply adjoint-based sensitivity analysis to a time-delayed thermo-acoustic system: a Rijke tube containing a hot wire. We calculate how the growth rate and frequency of small oscillations about a base state are affected either by a generic passive control element in the system (the structural sensitivity analysis) or by a generic change to its base state (the base-state sensitivity analysis). We illustrate the structural sensitivity by calculating the effect of a second hot wire with a small heat-release parameter. In a single calculation, this shows how the second hot wire changes the growth rate and frequency of the small oscillations, as a function of its position in the tube. We then examine the components of the structural sensitivity in order to determine the passive control mechanism that has the strongest influence on the growth rate. We find that a force applied to the acoustic momentum equation in the opposite direction to the instantaneous velocity is the most stabilizing feedback mechanism. We also find that its effect is maximized when it is placed at the downstream end of the tube. This feedback mechanism could be supplied, for example, by an adiabatic mesh. We illustrate the base-state sensitivity by calculating the effects of small variations in the damping factor, the heat-release time-delay coefficient, the heat-release parameter, and the hot-wire location. The successful application of sensitivity analysis to thermo-acoustics opens up new possibilities for the passive control of thermo-acoustic oscillations by providing gradient information that can be combined with constrained optimization algorithms in order to reduce linear growth rates. © Cambridge University Press 2013.

Transducer and base compliance alter the in situ 6 dof force measured from muscle during an isometric contraction in a multi-joint limb.

Although musculoskeletal models are commonly used, validating the muscle actions predicted by such models is often difficult. In situ isometric measurements are a possible solution. The base of the skeleton is immobilized and the endpoint of the limb is rigidly attached to a 6-axis force transducer. Individual muscles are stimulated and the resulting forces and moments recorded. Such analyses generally assume idealized conditions. In this study we have developed an analysis taking into account the compliances due to imperfect fixation of the skeleton, imperfect attachment of the force transducer, and extra degrees of freedom (dof) in the joints that sometimes become necessary in fixed end contractions. We use simulations of the rat hindlimb to illustrate the consequences of such compliances. We show that when the limb is overconstrained, i.e., when there are fewer dof within the limb than are restrained by the skeletal fixation, the compliances of the skeletal fixation and of the transducer attachment can significantly affect measured forces and moments. When the limb dofs and restrained dofs are matched, however, the measured forces and moments are independent of these compliances. We also show that this framework can be used to model limb dofs, so that rather than simply omitting dofs in which a limb does not move (e.g., abduction at the knee), the limited motion of the limb in these dofs can be more realistically modeled as a very low compliance. Finally, we discuss the practical implications of these results to experimental measurements of muscle actions.

Code-specific policy gradient rules for spiking neurons

Although it is widely believed that reinforcement learning is a suitable tool for describing behavioral learning, the mechanisms by which it can be implemented in networks of spiking neurons are not fully understood. Here, we show that different learning rules emerge from a policy gradient approach depending on which features of the spike trains are assumed to influence the reward signals, i.e., depending on which neural code is in effect. We use the framework of Williams (1992) to derive learning rules for arbitrary neural codes. For illustration, we present policy-gradient rules for three different example codes - a spike count code, a spike timing code and the most general "full spike train" code - and test them on simple model problems. In addition to classical synaptic learning, we derive learning rules for intrinsic parameters that control the excitability of the neuron. The spike count learning rule has structural similarities with established Bienenstock-Cooper-Munro rules. If the distribution of the relevant spike train features belongs to the natural exponential family, the learning rules have a characteristic shape that raises interesting prediction problems.

Alternating spatial patterns for coordinated group motion

Motivated by recent observations of fish schools, we study coordinated group motion for individuals with oscillatory speed. Neighbors that have speed oscillations with common frequency, amplitude and average but different phases, move together in alternating spatial patterns, taking turns being towards the front, sides and back of the group. We propose a model and control laws to investigate the connections between these spatial dynamics, communication when sensing is range or direction limited, and convergence of coordinated group motions. ©2007 IEEE.

The inverse problem in magnetic force microscopy--inferring sample magnetization from MFM images.

Nanomagnetic structures have the potential to surpass silicon's scaling limitations both as elements in hybrid CMOS logic and as novel computational elements. Magnetic force microscopy (MFM) offers a convenient characterization technique for use in the design of such nanomagnetic structures. MFM measures the magnetic field and not the sample's magnetization. As such the question of the uniqueness of the relationship between an external magnetic field and a magnetization distribution is a relevant one. To study this problem we present a simple algorithm which searches for magnetization distributions consistent with an external magnetic field and solutions to the micromagnetic equations' qualitative features. The algorithm is not computationally intensive and is found to be effective for our test cases. On the basis of our results we propose a systematic approach for interpreting MFM measurements.