'It Has to Go Down A Little, In Order to Go Around'- Following Feynman on the Gyroscope

In this paper we show that with the help of accessible, teaching quality equipment, some interesting details of the motion of a gyroscope, typically overlooked in introductory courses, can be measured and compared to theory. We begin by deriving a simple relation between the asymptotic dip angle of a gyroscope released from rest and its precession velocity. We then describe an experiment which measures these parameters. The data gives excellent agreement with the model. The idea for this project was suggested by the discussion of gyroscopic motion in The Feynman Lectures on Physics. Feynman's conclusion (stated in colloquial terms and quoted in the title) is confirmed and, in addition, conservation of angular momentum, which underlies this effect, is quantitatively demonstrated.Comment: 6 pages, 4 figure

Explicit asymptotic modelling of transient Love waves propagated along a thin coating

The official published version can be obtained from the link below.An explicit asymptotic model for transient Love waves is derived from the exact equations of anti-plane elasticity. The perturbation procedure relies upon the slow decay of low-frequency Love waves to approximate the displacement field in the substrate by a power series in the depth coordinate. When appropriate decay conditions are imposed on the series, one obtains a model equation governing the displacement at the interface between the coating and the substrate. Unusually, the model equation contains a term with a pseudo-differential operator. This result is confirmed and interpreted by analysing the exact solution obtained by integral transforms. The performance of the derived model is illustrated by numerical examples.This work is sponsored by the grant from Higher Education of Pakistan and by the Brunel University’s “BRIEF” research award

Electromechanical finite element modelling for dynamic analysis of a cantilevered piezoelectric energy harvester with tip mass offset under base excitations

A new electromechanical finite element modelling of a vibration power harvester and its validation with experimental studies are presented in this paper. The new contributions for modelling the electromechanical finite element piezoelectric unimorph beam with tip mass offset under base excitation encompass five major solution techniques. These include the electromechanical discretization, kinematic equations, coupled field equations, Lagrangian electromechanical dynamic equations, and orthonormalised global matrix and scalar forms of electromechanical finite element dynamic equations. Such techniques have not been rigorously modelled previously by other researchers. There are also benefits to presenting the numerical techniques proposed in this paper. First, the proposed numerical techniques can be used for Q1 applications in many different geometrical models, including MEMS power harvesting devices. Second, applying tip mass offset located after the end of the piezoelectric beam length can result in a very practical design, which avoids direct contact with piezoelectric material because of its brittle nature.Since the surfaces of actual piezoelectric material are covered evenly with thin conducting electrodes for generating single voltage, we introduce the new electromechanical discretization, consisting of the mechanical and electrical discretised elements. Moreover, the reduced electromechanical finite element dynamic equations can be further formulated to obtain the series form of new multimode electromechanical frequency response functions (FRFs) of the displacement, velocity, voltage, current, and power, including optimal power harvesting. The normalized numerical strain node and eigenmode shapes are also further formulated using numerical discretization. Finally, the parametric numerical case studies of the piezoelectric unimorph beam under a resistive shunt circuit show good agreement with the experimental studies

Endocrine-Sensitive Disease Rate in Postmenopausal Patients With Estrogen Receptor–Rich/ERBB2-Negative Breast Cancer Receiving Neoadjuvant Anastrozole, Fulvestrant, or Their Combination: A Phase 3 Randomized Clinical Trial

Importance: Adding fulvestrant to anastrozole (A+F) improved survival in postmenopausal women with advanced estrogen receptor (ER)–positive/ERBB2 (formerly HER2)–negative breast cancer. However, the combination has not been tested in early-stage disease. Objective: To determine whether neoadjuvant fulvestrant or A+F increases the rate of pathologic complete response or ypT1-2N0/N1mic/Ki67 2.7% or less residual disease (referred to as endocrine-sensitive disease) over anastrozole alone. Design, Setting, and Participants: A phase 3 randomized clinical trial assessing differences in clinical and correlative outcomes between each of the fulvestrant-containing arms and the anastrozole arm. Postmenopausal women with clinical stage II to III, ER-rich (Allred score 6-8 or >66%)/ERBB2-negative breast cancer were included. All analyses were based on data frozen on March 2, 2023. Interventions: Patients received anastrozole, fulvestrant, or a combination for 6 months preoperatively. Tumor Ki67 was assessed at week 4 and optionally at week 12, and if greater than 10% at either time point, the patient switched to neoadjuvant chemotherapy or immediate surgery. Main Outcomes and Measures: The primary outcome was the endocrine-sensitive disease rate (ESDR). A secondary outcome was the percentage change in Ki67 after 4 weeks of neoadjuvant endocrine therapy (NET) (week 4 Ki67 suppression). Results: Between February 2014 and November 2018, 1362 female patients (mean [SD] age, 65.0 [8.2] years) were enrolled. Among the 1298 evaluable patients, ESDRs were 18.7% (95% CI, 15.1%-22.7%), 22.8% (95% CI, 18.9%-27.1%), and 20.5% (95% CI, 16.8%-24.6%) with anastrozole, fulvestrant, and A+F, respectively. Compared to anastrozole, neither fulvestrant-containing regimen significantly improved ESDR or week 4 Ki67 suppression. The rate of week 4 or week 12 Ki67 greater than 10% was 25.1%, 24.2%, and 15.7% with anastrozole, fulvestrant, and A+F, respectively. Pathologic complete response/residual cancer burden class I occurred in 8 of 167 patients and 17 of 167 patients, respectively (15.0%; 95% CI, 9.9%-21.3%), after switching to neoadjuvant chemotherapy due to week 4 or week 12 Ki67 greater than 10%. PAM50 subtyping derived from RNA sequencing of baseline biopsies available for 753 patients (58%) identified 394 luminal A, 304 luminal B, and 55 nonluminal tumors. A+F led to a greater week 4 Ki67 suppression than anastrozole alone in luminal B tumors (median [IQR], −90.4% [−95.2 to −81.9%] vs −76.7% [−89.0 to −55.6%]; P  Conclusions and Relevance: In this randomized clinical trial, neither fulvestrant nor A+F significantly improved the 6-month ESDR over anastrozole in ER-rich/ERBB2-negative breast cancer. Aromatase inhibition remains the standard-of-care NET. Differential NET response by PAM50 subtype in exploratory analyses warrants further investigation. Trial Registration: ClinicalTrials.gov Identifier: NCT01953588</p

Effect of shunted piezoelectric control for tuning piezoelectric power harvesting system responses – Analytical techniques

This paper presents new analytical modelling of shunt circuit control responses for tuning electromechanical piezoelectric vibration power harvesting structures with proof mass offset. For this combination, the dynamic closed-form boundary value equations reduced from strong form variational principles were developed using the extended Hamiltonian principle to formulate the new coupled orthonormalised electromechanical power harvesting equations showing combinations of the mechanical system (dynamical behaviour of piezoelectric structure), electromechanical system (electrical piezoelectric response) and electrical system (tuning and harvesting circuits). The reduced equations can be further formulated to give the complete forms of new electromechanical multi-mode FRFs and time waveform of the standard AC-DC circuit interface. The proposed technique can demonstrate self-adaptive harvesting response capabilities for tuning the frequency band and the power amplitude of the harvesting devices. The self-adaptive tuning strategies are demonstrated by modelling the shunt circuit behaviour of the piezoelectric control layer in order to optimise the harvesting piezoelectric layer during operation under input base excitation. In such situations, with proper tuning parameters the system performance can be substantially improved. Moreover, the validation of the closed-form technique is also provided by developing the Ritz method-based weak form analytical approach giving similar results. Finally, the parametric analytical studies have been explored to identify direct and relevant contributions for vibration power harvesting behaviours

Hair Cell Bundles: Flexoelectric Motors of the Inner Ear

Microvilli (stereocilia) projecting from the apex of hair cells in the inner ear are actively motile structures that feed energy into the vibration of the inner ear and enhance sensitivity to sound. The biophysical mechanism underlying the hair bundle motor is unknown. In this study, we examined a membrane flexoelectric origin for active movements in stereocilia and conclude that it is likely to be an important contributor to mechanical power output by hair bundles. We formulated a realistic biophysical model of stereocilia incorporating stereocilia dimensions, the known flexoelectric coefficient of lipid membranes, mechanical compliance, and fluid drag. Electrical power enters the stereocilia through displacement sensitive ion channels and, due to the small diameter of stereocilia, is converted to useful mechanical power output by flexoelectricity. This motor augments molecular motors associated with the mechanosensitive apparatus itself that have been described previously. The model reveals stereocilia to be highly efficient and fast flexoelectric motors that capture the energy in the extracellular electro-chemical potential of the inner ear to generate mechanical power output. The power analysis provides an explanation for the correlation between stereocilia height and the tonotopic organization of hearing organs. Further, results suggest that flexoelectricity may be essential to the exquisite sensitivity and frequency selectivity of non-mammalian hearing organs at high auditory frequencies, and may contribute to the “cochlear amplifier” in mammals

Power efficiency of outer hair cell somatic electromotility

© 2009 Rabbitt et al. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in PLoS Computational Biology 5 (2009): e1000444, doi:10.1371/journal.pcbi.1000444.Cochlear outer hair cells (OHCs) are fast biological motors that serve to enhance the vibration of the organ of Corti and increase the sensitivity of the inner ear to sound. Exactly how OHCs produce useful mechanical power at auditory frequencies, given their intrinsic biophysical properties, has been a subject of considerable debate. To address this we formulated a mathematical model of the OHC based on first principles and analyzed the power conversion efficiency in the frequency domain. The model includes a mixture-composite constitutive model of the active lateral wall and spatially distributed electro-mechanical fields. The analysis predicts that: 1) the peak power efficiency is likely to be tuned to a specific frequency, dependent upon OHC length, and this tuning may contribute to the place principle and frequency selectivity in the cochlea; 2) the OHC power output can be detuned and attenuated by increasing the basal conductance of the cell, a parameter likely controlled by the brain via the efferent system; and 3) power output efficiency is limited by mechanical properties of the load, thus suggesting that impedance of the organ of Corti may be matched regionally to the OHC. The high power efficiency, tuning, and efferent control of outer hair cells are the direct result of biophysical properties of the cells, thus providing the physical basis for the remarkable sensitivity and selectivity of hearing.This work was supported by NIDCD R01 DC04928 (Rabbitt), NIDCD R01 DC00384 (Brownell) and NASA Ames GSRA56000135 (Breneman)