An inverse problem in estimating the laser irradiance and thermal damage in laser-irradiated biological tissue with a dual-phase-lag model.

The aim of this study is to solve an inverse heat conduction problem to estimate the unknown time-dependent laser irradiance and thermal damage in laser-irradiated biological tissue from the temperature measurements taken within the tissue. The dual-phase-lag model is considered in the formulation of heat conduction equation. The inverse algorithm used in the study is based on the conjugate gradient method and the discrepancy principle. The effect of measurement errors and measurement locations on the estimation accuracy is also investigated. Two different examples of laser irradiance are discussed. Results show that the unknown laser irradiance and thermal damage can be predicted precisely by using the present approach for the test cases considered in this study.

Sensitivity analysis of rectangular atomic force microscope cantilevers immersed in liquids based on the modified couple stress theory.

The modified couple stress theory is adopted to study the sensitivity of a rectangular atomic force microscope (AFM) cantilever immersed in acetone, water, carbon tetrachloride (CCl4), and 1-butanol. The theory contains a material length scale parameter and considers the size effect in the analysis. However, this parameter is difficult to obtain via experimental measurements. In this study, a conjugate gradient method for the parameter estimation of the frequency equation is presented. The optimal method provides a quantitative approach for estimating the material length scale parameter based on the modified couple stress theory. The results show that the material length scale parameter of the AFM cantilever immersed in acetone, CCl4, water, and 1-butanol is 0, 25, 116.3, and 471 nm, respectively. In addition, the vibration sensitivities of the AFM cantilever immersed in these liquids are investigated. The results are useful for the design of AFM cantilevers immersed in liquids.

Estimation of surface heat flux and temperature distributions in a multilayer tissue based on the hyperbolic model of heat conduction.

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to solve the inverse hyperbolic heat conduction problem in estimating the unknown time-dependent surface heat flux in a skin tissue, which is stratified into epidermis, dermis, and subcutaneous layers, from the temperature measurements taken within the medium. Subsequently, the temperature distributions in the tissue can be calculated as well. The concept of finite heat propagation velocity is applied to the modeling of the bioheat transfer problem. The inverse solutions will be justified based on the numerical experiments in which two different heat flux distributions are to be determined. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The influence of measurement errors on the precision of the estimated results is also investigated. Results show that an excellent estimation on the time-dependent surface heat flux can be obtained for the test cases considered in this study.

Dynamic response of a cracked atomic force microscope cantilever used for nanomachining.

The vibration behavior of an atomic force microscope [AFM] cantilever with a crack during the nanomachining process is studied. The cantilever is divided into two segments by the crack, and a rotational spring is used to simulate the crack. The two individual governing equations of transverse vibration for the cracked cantilever can be expressed. However, the corresponding boundary conditions are coupled because of the crack interaction. Analytical expressions for the vibration displacement and natural frequency of the cracked cantilever are obtained. In addition, the effects of crack flexibility, crack location, and tip length on the vibration displacement of the cantilever are analyzed. Results show that the crack occurs in the AFM cantilever that can significantly affect its vibration response.PACS: 07.79.Lh; 62.20.mt; 62.25.Jk.

Frequency Shift of Carbon-Nanotube-Based Mass Sensor Using Nonlocal Elasticity Theory.

The frequency equation of carbon-nanotube-based cantilever sensor with an attached mass is derived analytically using nonlocal elasticity theory. According to the equation, the relationship between the frequency shift of the sensor and the attached mass can be obtained. When the nonlocal effect is not taken into account, the variation of frequency shift with the attached mass on the sensor is compared with the previous study. According to this study, the result shows that the frequency shift of the sensor increases with increasing the attached mass. When the attached mass is small compared with that of the sensor, the nonlocal effect is obvious and increasing nonlocal parameter decreases the frequency shift of the sensor. In addition, when the location of the attached mass is closer to the free end, the frequency shift is more significant and that makes the sensor reveal more sensitive. When the attached mass is small, a high sensitivity is obtained.

Vibration analysis of fluid-conveying double-walled carbon nanotubes based on nonlocal elastic theory.

This paper presents an analytical solution to a coupled vibration problem of fluid-conveying double-walled carbon nanotubes (DWCNTs) and analyzes the influences of nonlocal effect, aspect ratio and van der Waals interaction on the fundamental frequency. According to the analysis, the results show that the vibration frequencies of the first three modes of DWCNTs are lower than those of single-walled carbon nanotubes (SWCNTs). The trend is more obvious when the flow velocity is high. It can also be found that the velocity of vibration-induced flutter instability for DWCNTs is lower than that of SWCNTs. In addition, the frequency of mode 1 of DWCNTs decreases with increasing nonlocal parameter. However, the frequency increases as the aspect ratio and the van der Waals interaction increased, especially at higher flow velocities.

Coupled lateral bending-torsional vibration sensitivity of atomic force microscope cantilever.

We study the influence of the contact stiffness and the ration between cantilever and tip lengths on the resonance frequencies and sensitivities of lateral cantilever modes. We derive expressions to determine both the effective resonance frequency and the mode sensitivity of an atomic force microscope (AFM) rectangular cantilever. Once the contact stiffness is given, the resonance frequency and the sensitivity of the vibration modes can be obtained from the expression. The results show that each mode has a different resonant frequency to variations in contact stiffness and each frequency increased until it eventually reached a constant value at very high contact stiffness. The low-order vibration modes are more sensitive to vibration than the high-order mode when the contact stiffness is low. However, the situation is reversed when the lateral contact stiffness became higher. Furthermore, increasing the ratio of tip length to cantilever length increases the vibration frequency and the sensitivity of AFM cantilever.

Study of the sensitivity of the first four flexural modes of an AFM cantilever with a sidewall probe.

The resonant frequency and sensitivity of flexural vibration for an atomic force microscope (AFM) cantilever with a sidewall probe have been analyzed. A closed-form expression for the sensitivity of vibration modes has been obtained using the relationship between the resonant frequency and contact stiffness of cantilever and sample. The results show that a sidewall scanning AFM is more sensitive when the contact stiffness is lower and that the first mode is the most sensitive. However, the high-order modes become more sensitive than the low-order modes as the contact stiffness increases. The resonance frequency of an AFM cantilever is low when contact stiffness is small. However, the frequency rapidly increases as contact stiffness increases. In addition, it can be found that the effects of the vertical extension on the sensitivity and the resonant frequency of an AFM cantilever are significant. Decreasing the length of vertical extension can increase the resonance frequency and sensitivity of mode 1 when the contact stiffness is small. However, the situation is reverse when the contact stiffness becomes large.

An inverse problem of estimating the heat source in tapered optical fibers for scanning near-field optical microscopy.

A conjugate gradient method based on inverse algorithm is applied in this study to estimate the unknown space- and time-dependent heat source in aluminum-coated tapered optical fibers for scanning near-field optical microscopy, by reading the transient temperature data at the measurement positions. No prior information is available on the functional form of the unknown heat source in the present study; thus, it is classified as the function estimation in inverse calculation. The accuracy of the inverse analysis is examined by using the simulated exact and inexact temperature measurements. Results show that an excellent estimation on the heat source and temperature distributions in the tapered optical fiber can be obtained for all the test cases considered in this study.

Vibration sensitivity of the scanning near-field optical microscope with a tapered optical fiber probe.

In this paper the Rayleigh-Ritz method was used to study the scanning near-field optical microscope (SNOM) with a tapered optical fiber probe's flexural and axial sensitivity to vibration. Not only the contact stiffness but also the geometric parameters of the probe can influence the flexural and axial sensitivity to vibration. According to the analysis, the lateral and axial contact stiffness had a significant effect on the sensitivity of vibration of the SNOM's probe, each mode had a different level of sensitivity and in the first mode the tapered optical fiber probe was the most acceptive to higher levels of flexural and axial vibration. Generally, when the contact stiffness was lower, the tapered probe was more sensitive to higher levels of both axial and flexural vibration than the uniform probe. However, the situation was reversed when the contact stiffness was larger. Furthermore, the effect that the probe's length and its tapered angle had on the SNOM's probe axial and flexural vibration were significant and these two conditions should be incorporated into the design of new SNOM probes.