Effect of wind gusts on the motion of a balloon-borne observation platform

The effect of wind gusts on the magnitude of the pendulation angles of a balloon-borne observation platform is determined. A system mathematical model is developed and the solution of this model is used to determine the magnitude of the observation platforms pendulation angles

The Influence of Bureau Scores, Customized Scores and Judgmental Review on the Bank Underwriting Decision-Making Process

In recent years commercial banks have moved toward automated forms of underwriting. This study employs unique bank loan-level data from a scoring lender to determine whether automated underwriting exhibits a potential ‘‘disparate impact’’ across income strata. The findings indicate that strict application of this custom scoring model leads to higher denial rates for low- to moderate-income borrowers when compared with both a naý¨ve judgmental system and a bureau scoring approach. These results suggest that financial regulators should focus more resources on the evaluation and study of customized scoring models.

Resonant Characteristics of Rectangular Microcantilevers Vibrating Torsionally in Viscous Liquid Media

The resonant characteristics of rectangular microcantilevers vibrating in the torsional mode in viscous liquid media are investigated. The hydrodynamic load (torque per unit length) on the vibrating beam due to the liquid was first determined using a finite element model. An analytical expression of the hydrodynamic function in terms of the Reynolds number and aspect ratio, h/b (with thickness, h, and width, b) was then obtained by fitting the numerical results. This allowed for the resonance frequency and quality factor to be investigated as functions of both beam geometry and medium properties. Moreover, the effects of the aspect ratio on the cross-section\u27s torsional constant, K, which affects the microcantilever\u27s torsional stiffness, and on its polar moment of inertia, Jp, which is associated with the beam\u27s rotational inertia, are also considered when obtaining the resonance frequency and quality factor. Compared with microcantilevers under out-of-plane (transverse) flexural vibration, the results show that microcantilevers that vibrate in their 1st torsional or 1st in-plane (lateral) flexural resonant modes have higher resonance frequency and quality factor. The increase in resonance frequency and quality factor results in higher mass sensitivity and reduced frequency noise, respectively. The improvement in the sensitivity and quality factor are expected to yield much lower limits of detection in liquid-phase chemical sensing applications

Resonant Characteristics of Rectangular Hammerhead Microcantilevers Vibrating Laterally in Viscous Liquid Media

The resonant characteristics of laterally vibrating rectangular hammerhead microcantilevers in viscous liquid media are investigated. The rectangular hammerhead microcantilever is modeled as an Euler-Bernoulli beam (stem) and a rigid body (head). A modified semi-analytical expression for the hydrodynamic function in terms of the Reynolds number, Re, and aspect ratio, h/b, is proposed to rapidly evaluate the sensing characteristics. Using this expression, the resonance frequency, quality factor and normalized surface mass sensitivity are investigated as a function of the dimensions of the microcantilever and liquid properties. Guidelines for design of hammerhead microcantilever geometry are proposed to achieve efficient sensing platforms for liquid-phase operation. The improvement in the sensing area and characteristics are expected to yield higher sensitivity of detection and improved signal-to-noise ratio in liquid-phase chemical sensing applications

Analytical Modeling of a Novel High-\u3cem\u3eQ\u3c/em\u3e Disk Resonator for Liquid-Phase Applications

To overcome the detrimental effects of liquid environments on microelectromechanical systems resonator performance, the in-fluid vibration of a novel disk resonator supported by two electrothermally driven legs is investigated through analytical modeling and the effects of the system’s geometric/material parameters on the dynamic response are explored. The all-shear interaction device (ASID) is based on engaging the surrounding fluid primarily through shearing action. The theory comprises a continuous-system, multimodal model, and a single-degree-of-freedom model, the latter yielding simple formulas for the fundamental-mode resonant characteristics that often furnish excellent estimates to the results based on the more general model. Comparisons between theoretical predictions and previously published liquid-phase quality factor (Q) data (silicon devices in heptane) show that the theoretical results capture the observed trends and also give very good quantitative estimates, particularly for the highest Q devices. Moreover, the highest Q value measured in the earlier study (304) corresponded to a specimen whose disk radius-to-thickness ratio was 2.5, a value that compares well with the optimal value of 2.3 predicted by the present model. The insight furnished by the proposed theory is expected to lead to further improvements in ASID design to achieve unprecedented levels of performance for a wide variety of liquid-phase resonator applications

Integrals of Motion for Critical Dense Polymers and Symplectic Fermions

We consider critical dense polymers ${\cal L}(1,2)$. We obtain for this model the eigenvalues of the local integrals of motion of the underlying Conformal Field Theory by means of Thermodynamic Bethe Ansatz. We give a detailed description of the relation between this model and Symplectic Fermions including the indecomposable structure of the transfer matrix. Integrals of motion are defined directly on the lattice in terms of the Temperley Lieb Algebra and their eigenvalues are obtained and expressed as an infinite sum of the eigenvalues of the continuum integrals of motion. An elegant decomposition of the transfer matrix in terms of a finite number of lattice integrals of motion is obtained thus providing a reason for their introduction.Comment: 53 pages, version accepted for publishing on JSTA

Lateral-Mode Vibration of Microcantilever-Based Sensors in Viscous Fluids Using Timoshenko Beam Theory

To more accurately model microcantilever resonant behavior in liquids and to improve lateral-mode sensor performance, a new model is developed to incorporate viscous fluid effects and Timoshenko beam effects (shear deformation, rotatory inertia). The model is motivated by studies showing that the most promising geometries for lateral-mode sensing are those for which Timoshenko effects are most pronounced. Analytical solutions for beam response due to harmonic tip force and electrothermal loadings are expressed in terms of total and bending displacements, which correspond to laser and piezoresistive readouts, respectively. The influence of shear deformation, rotatory inertia, fluid properties, and actuation/detection schemes on resonant frequencies ( ) and quality factors ( ) are examined, showing that Timoshenko beam effects may reduce and by up to 40% and 23%, respectively, but are negligible for width-to-length ratios of 1/10 and lower. Comparisons with measurements (in water) indicate that the model predicts the qualitative data trends, but underestimates the softening that occurs in stiffer specimens, indicating that support deformation becomes a factor. For thinner specimens, the model estimates quite well, but exceeds the observed values for thicker specimens, showing that the Stokes resistance model employed should be extended to include pressure effects for these geometries.[2014-0157

Timoshenko Beam Model for Lateral Vibration of Liquid-Phase Microcantilever-Based Sensors

Dynamic-mode microcantilever-based devices are potentially well suited to biological and chemical sensing applications. However, when these applications involve liquid-phase detection, fluid-induced dissipative forces can significantly impair device performance. Recent experimental and analytical research has shown that higher in-fluid quality factors (Q) are achieved by exciting microcantilevers in the lateral flexural mode. However, experimental results show that, for microcantilevers having larger width-to-length ratios, the behaviors predicted by current analytical models differ from measurements. To more accurately model microcantilever resonant behavior in viscous fluids and to improve understanding of lateral-mode sensor performance, a new analytical model is developed, incorporating both viscous fluid effects and “Timoshenko beam” effects (shear deformation and rotatory inertia). Beam response is examined for two harmonic load types that simulate current actuation methods: tip force and support rotation. Results are expressed in terms of total beam displacement and beam displacement due solely to bending deformation, which correspond to current detection methods used with microcantilever-based devices (optical and piezoresistive detection, respectively). The influences of the shear, rotatory inertia, and fluid parameters, as well as the load/detection scheme, are investigated. Results indicate that load/detection type can impact the measured resonant characteristics and, thus, sensor performance, especially at larger values of fluid resistance

Timoshenko Beam Effects in Lateral-mode Microcantilever-based Sensors in Liquids

Recent experimental and analytical research has shown that higher in-fluid quality factors (Q) are achieved by actuating microcantilevers in the lateral flexural mode, especially for microcantilevers having larger width-to-length ratios. However, experimental results show that for these geometries the resonant characteristics predicted by the existing analytical models differ from the measurements. A recently developed analytical model to more accurately predict the resonant behaviour of these devices in viscous fluids is described. The model incorporates viscous fluid effects via a Stokes-type fluid resistance assumption and `Timoshenko beam\u27 effects (shear deformation and rotatory inertia). Unlike predictions based on Euler-Bernoulli beam theory, the new theoretical results for both resonant frequency and Q exhibit the same trends as seen in the experimental data for in-water measurements as the beam slenderness decreases. An analytical formula for Q is also presented to explicitly illustrate how Q depends on beam geometry and on beam and fluid properties. Beam thickness effects are also examined and indicate that the analytical results yields good numerical estimates of Q for the thinner (5 μm) specimens tested, but overestimate Q for the thicker (20 μm) specimens, thus suggesting that a more accurate fluid resistance model should be introduced in the future for the latter case