Resonant Frequency and Sensitivity of an AFM Microcantilever Modeled by the Non-Local Theory

2011 ◽  
Author(s):  
E. Khosravani ◽  
M. H. Kahrobaiyan ◽  
M. T. Ahmadian
Keyword(s):  
Resonant Frequency ◽  
Classical Theory ◽  
Variational Approach ◽  
Contact Stiffness ◽  
Current Model ◽  
Equation Of Motion ◽  
Local Theory ◽  
Local Parameter ◽  
Non Local ◽  
The Difference

In this paper, utilizing the non-local theory, the resonant frequency and sensitivity of an AFM microcantilever are investigated. To that end, the governing equation of motion and corresponding boundary conditions are obtained using the variational approach. Afterwards, the resonant frequency and sensitivity of the AFM microcantilever are derived analytically and depicted in some figures versus the contact stiffness of the sampling surface. The results of the current model are compared to those of the classical theory. The comparison shows that the difference between the results of the non-local theory and those of the classical theory is significant when the non-local parameter is high but it diminishes as the non-local parameter decreases.

Resonant Frequency and Sensitivity of a Caliper Formed With Assembled Cantilever Probes Based on the Modified Strain Gradient Theory

2014 ◽  
Vol 20 (6) ◽  
pp. 1672-1681 ◽  
Author(s):  
Mohammad Abbasi ◽  
Seyed E. Afkhami
Keyword(s):  
Resonant Frequency ◽  
Strain Gradient ◽  
Couple Stress ◽  
Contact Stiffness ◽  
Current Model ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
The Difference ◽  
Material Length Scale ◽  
Beam Theories

AbstractThe resonant frequency and sensitivity of an atomic force microscope (AFM) with an assembled cantilever probe (ACP) is analyzed utilizing strain gradient theory, and then the governing equation and boundary conditions are derived by a combination of the basic equations of strain gradient theory and Hamilton’s principle. The resonant frequency and sensitivity of the proposed AFM microcantilever are then obtained numerically. The proposed ACP includes a horizontal cantilever, two vertical extensions, and two tips located at the free ends of the extensions that form a caliper. As one of the extensions is located between the clamped and free ends of the AFM microcantilever, the cantilever is modeled as two beams. The results of the current model are compared with those evaluated by both modified couple stress and classical beam theories. The difference in results evaluated by the strain gradient theory and those predicted by the couple stress and classical beam theories is significant, especially when the microcantilever thickness is approximately the same as the material length-scale parameters. The results also indicate that at the low values of contact stiffness, scanning in the higher cantilever modes decrease the accuracy of the proposed AFM ACP.

Study of internal stresses in rock massif within the framework of elastic layered block models with inclusions of the hierarchical structure of the L-rank.

2021 ◽  
Author(s):  
Olga Hachay ◽  
Andrey Khachay
Keyword(s):  
Hierarchical Structure ◽  
Classical Theory ◽  
Acoustic Waves ◽  
Degrees Of Freedom ◽  
Heterogeneous Media ◽  
Theory Of Elasticity ◽  
Rock Massif ◽  
Local Theory ◽  
Internal Stresses ◽  
Non Local

<p>In recent years, new models of continuum mechanics, generalizing the classical theory of elasticity, have been intensively developed. These models are used to describe composite and statistically heterogeneous media, new structural materials, as well as in complex massifs in mine conditions. The paper presents an algorithm for the propagation of longitudinal acoustic waves in the framework of active well monitoring of elastic layered block media with inclusions of hierarchical type of L-th rank. Relations for internal stresses and strains for each hierarchical rank are obtained, which constitute the non local theory of elasticity. The essential differences between the non local theory of elasticity and the classical one and the connection between them are investigated. A characteristic feature of the theory of media with a hierarchical structure is the presence of scale parameters in explicit or implicit form. This work focuses on the study of the effects of non locality and internal degrees of freedom, reflected in internal stresses, which are not described by the classical theory of elasticity and which can be potential precursors of the development of a catastrophic process in a rock massif. Thanks to the use of a model of a layered block medium with hierarchical inclusions, it is possible, using borehole acoustic monitoring, to determine the position of the highest values ​​of internal stresses and, with less effort, to implement the method of unloading the rock massif. If it is necessary to conduct short-term predictive monitoring of geodynamic regions and determine a more accurate position of the source of a dynamic phenomenon using borehole active acoustic observations, it is necessary to use the values ​​of the tensor of internal hierarchical stresses as a monitored parameter.</p>

Causality Violation and Non-local Generalization of the Lorentz-Dirac Equation

1977 ◽  
Vol 32 (3-4) ◽  
pp. 319-326
Author(s):  
P. Alber ◽  
W. Heudorfer ◽  
M. Sorg
Keyword(s):  
Dirac Equation ◽  
Equation Of Motion ◽  
Local Theory ◽  
Constant Force ◽  
Dirac Theory ◽  
Local Equation ◽  
Causality Violation ◽  
Finite Duration ◽  
Non Local

AbstractIt is demonstrated by a concrete example (constant force of finite duration) that the recently proposed, non-local equation of motion for the radiating electron does exhibit the effect of causality violation. This phenomenon, which occurs in the non-local theory in form of self-oscillations, is however less severe than in the Lorentz-Dirac theory, if only physically reasonable forces are admitted.

Study of the sensitivity and resonant frequency of the flexural modes of an atomic force microscopy microcantilever modeled by strain gradient elasticity theory

2013 ◽  
Vol 228 (8) ◽  
pp. 1299-1310 ◽  
Author(s):  
Mohammad Abbasi ◽  
Ardeshir Karami Mohammadi
Keyword(s):  
Atomic Force Microscopy ◽  
Resonant Frequency ◽  
Strain Gradient ◽  
Contact Stiffness ◽  
Current Model ◽  
Gradient Elasticity ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Force Microscopy ◽  
Atomic Force

In this study, the resonant frequency and sensitivity of an atomic force microscopy microcantilever are analyzed utilizing the strain gradient theory, and then the governing equation and boundary conditions are derived by a combination of the basic equations of the modified strain gradient theory and the Hamilton principle. Afterward, the resonant frequency and sensitivity of the proposed atomic force microscopy microcantilever are obtained numerically. The results of the current model are compared to those evaluated by both modified couple stress and classic beam theories. Results show that utilizing the strain gradient theory in the analysis of atomic force microscopy microcantilever dynamic behavior is necessary especially when the contact stiffness is high and the thickness of the microcantilever approaches the internal material length scale parameter.

On Free Vibration of Functionally Graded Euler-Bernoulli Beam Models Based on the Non-Local Theory

2012 ◽  
Author(s):  
Reza Moheimani ◽  
M. T. Ahmadian
Keyword(s):  
Free Vibration ◽  
Axial Load ◽  
Power Index ◽  
Theory Of Elasticity ◽  
Functionally Graded ◽  
Local Theory ◽  
Local Parameter ◽  
Bernoulli Beam ◽  
Non Local ◽  
Euler Bernoulli Beam

In this paper, the governing equations and boundary conditions of a functionally graded Euler-Bernoulli beam are developed based on the non-local theory of elasticity. Afterward, the free vibration is investigated and the effects of the axial load, the non-local parameter and the power index on the natural frequency of a hinged-hinged beam is assessed. The results indicate that the non-local parameter has a decreasing effect on the frequency while the power index has an increasing effect. It is also noted that the effect of the axial load is increasing too.

scholarly journals Measuring cost and affordability of current vs. healthy diets in Argentina: an application of linear programming and the INFORMAS protocol

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Gabriel Giacobone ◽  
Maria Victoria Tiscornia ◽  
Leila Guarnieri ◽  
Luciana Castronuovo ◽  
Sally Mackay ◽  
...  
Keyword(s):  
Linear Programming ◽  
Energy Intake ◽  
Current Model ◽  
Food Product ◽  
Poor Households ◽  
Average Household Income ◽  
Healthy Diets ◽  
Diet Cost ◽  
The Difference ◽  
Optimal Approach

Abstract Background Food cost and affordability is one of the main barriers to improve the nutritional quality of diets of the population. However, in Argentina, where over 60% of adults and 40% of children and adolescents are overweight or obese, little is known about the difference in cost and affordability of healthier diets compared to ordinary, less healthy ones. Methods We implemented the “optimal approach” proposed by the International Network for Food and Obesity/non-communicable diseases Research, Monitoring and Action Support (INFORMAS). We modelled the current diet and two types of healthy diets, one equal in energy with the current diet and one 6.3% lower in energy by linear programming. Cost estimations were performed by collecting food product prices and running a Monte Carlo simulation (10,000 iterations) to obtain a range of costs for each model diet. Affordability was measured as the percentage contribution of diet cost vs. average household income in average, poor and extremely poor households and by income deciles. Results On average, households must spend 32% more money on food to ensure equal energy intake from a healthy diet than from a current model diet. When the energy intake target was reduced by 6.3%, the difference in cost was 22%. There are no reasonably likely situations in which any of these healthy diets could cost less or the same than the current unhealthier one. Over 50% of households would be unable to afford the modelled healthy diets, while 40% could not afford the current diet. Conclusions Differential cost and affordability of healthy vs. unhealthy diets are germane to the design of effective public policies to reduce obesity and NCDs in Argentina. It is necessary to implement urgent measures to transform the obesogenic environment, making healthier products more affordable, available and desirable, and discouraging consumption of nutrient-poor, energy-rich foods.

Performance Analysis of Different Modulation Formats in Optical Communication

2016 ◽  
Vol 37 (2) ◽  
Author(s):  
Kulwinder Singh ◽  
Maninder Singh ◽  
Kamaljit Singh Bhatia ◽  
Hardeep Singh Ryait
Keyword(s):  
Performance Analysis ◽  
Phase Shift ◽  
Resonant Frequency ◽  
Optical Communication ◽  
Data Transmission ◽  
Modulation Formats ◽  
Differential Phase Shift ◽  
Eye Diagram ◽  
The Difference ◽  
Sequence Generator

AbstractIn this paper, we demonstrated the variation of different parameters with quadrature amplitude modulation (QAM) and differential phase shift key (DPSK) sequence generator, which generates modulated signals, in data transmission for communication and analysed that how the difference of these sequence generators effect its resonant frequency (RF) value, eye diagram and electrical constellation representation of the system.

scholarly journals Diluted mass gap in strongly coupled non-local Yang-Mills

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Marco Frasca ◽  
Anish Ghoshal
Keyword(s):  
Field Theory ◽  
Particle Physics ◽  
Mass Scale ◽  
Local Theory ◽  
Quantum Field ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Mass Gap ◽  
Non Local ◽  
Non Locality

Abstract We investigate the non-perturbative regimes in the class of non-Abelian theories that have been proposed as an ultraviolet completion of 4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an infinite series of higher-order derivatives inspired by string field theory. We prove that, at the non-perturbative level, the physical spectrum of the theory is actually corrected by the “infinite number of derivatives” present in the action. We derive a set of Dyson-Schwinger equations in differential form, for correlation functions till two-points, the solution for which are known in the local theory. We obtain that just like in the local theory, the non-local counterpart displays a mass gap, depending also on the mass scale of non-locality, and show that it is damped in the deep UV asymptotically. We point out some possible implications of our result in particle physics and cosmology and discuss aspects of non-local QCD-like scenarios.

scholarly journals Non-Local Theory of Nucleon-Meson Field

1952 ◽  
Vol 8 (1) ◽  
pp. 133-134
Author(s):  
N. Shono
Keyword(s):  
Local Theory ◽  
Meson Field ◽  
Non Local
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