Energy Harvesting Using the Rattleback: Theoretical Analysis and Simulations of Spin Resonance

2015 ◽  
Author(s):  
Aditya Nanda ◽  
M. Amin Karami ◽  
Puneet Singla
Keyword(s):  
Energy Harvesting ◽  
Closed Form Expression ◽  
Longitudinal Vibrations ◽  
Form Expression ◽  
Preferred Direction ◽  
Spin Resonance ◽  
Vibration Sensing ◽  
Inertia Parameters ◽  
Set Up ◽  
Linearized Model

This paper investigates the spin resonance of a rattleback subjected to base oscillations. The phenomenon of Spin resonance can transduce vibrations to rotations. The rattleback is an ellipsoidal top with a preferred direction of spin. If rotated anti to it, longitudinal vibrations are set up and spin direction is reversed. Simulations and results are presented which show that the rattleback has a mono-peak spin resonance with respect to base vibrations. Two frequencies that appear in the response are identified — the Coupled and Uncoupled frequencies. Spin resonance, it is deduced, occurs when the base frequency is twice the coupled frequency of the rattleback. A linearized model is developed and a closed form expression for the Resonant frequency in terms of the inertia parameters of the rattleback is derived. Novel ideas for applications in Energy harvesting and Vibration sensing that utilize the phenomenon of spin resonance are also included.

scholarly journals Outage probability analysis of dual energy harvesting relay network over rayleigh fading channel using SC and MRC technique

2019 ◽  
Vol 16 (2) ◽  
pp. 803
Author(s):  
Tan N. Nguyen ◽  
Minh Tran ◽  
Van-Duc Phan ◽  
Tran Thanh Trang
Keyword(s):  
Energy Harvesting ◽  
Outage Probability ◽  
Fading Channel ◽  
Rayleigh Fading ◽  
Dual Energy ◽  
Rayleigh Fading Channel ◽  
Maximal Ratio Combining ◽  
Relay Network ◽  
Closed Form Expression ◽  
Form Expression

<p><span>In this paper, the system model of dual-energy harvesting relay network over Rayleigh fading channel and the comparison between Selecting Combining (SC) and Maximal Ratio Combining (MRC) technique cases are proposed and investigated. The closed-form expression of the outage probability for the SC case and the integral-form expression of the outage probability for MRC case is derived. Moreover, the influence of the main parameters on the system performance is demonstrated entirely by the Monte Carlo simulation. From the results, we can see that all simulation and analytical results match well with each other.</span></p>

scholarly journals Energy Harvesting Enabled Full-Duplex Cooperative Relaying System over Fisher-Snedecor F-Distribution Fading Channel

2021 ◽  
pp. 82-90
Author(s):  
Kehinde O. Odeyemi ◽  
◽  
Pius A. Owolawi
Keyword(s):  
Energy Harvesting ◽  
Closed Form ◽  
System Performance ◽  
Fading Channel ◽  
Cooperative Relaying ◽  
Full Duplex ◽  
Closed Form Expression ◽  
Form Expression ◽  
The Impact ◽  
Relaying System

In this paper, the performance of an Energy Harvesting (EH) enabled full-duplex cooperative decode-and-forward (DF) relaying system is investigated over the Fisher-Snedecor F-fading channel. The system energy-constrained relay unit utilizes time-switching relay protocol for scavenging energy from the source signal and information transmission to the destination. To quantify the system performance, the exact analytical closed-form expression for the system outage probability is derived, and then used to obtain the analytical expression for the average throughput of delay-limited transmission mode. Moreover, the exact closed-form expression for the system Ergodic capacity is derived through which the average delay-tolerant throughput is determined for the system. In addition, the results demonstrate the impact of fading and shadowing severity on the system performance. It also is noticeable from the results that the performance of system is strongly affected by the loop back interference from the relay node. Finally, the accuracy of the derived analytical expressions is then validated through the Monte-Carlo simulation.

scholarly journals Optimal Energy Harvesting Scheme for Power Beacon-Assisted Wireless-Powered Networks

2017 ◽  
Vol 7 (3) ◽  
pp. 802
Author(s):  
Dinh-Thuan Do
Keyword(s):  
Energy Harvesting ◽  
Outage Probability ◽  
Relay Node ◽  
Relay Network ◽  
Closed Form Expression ◽  
Power Splitting ◽  
Amplify And Forward ◽  
Form Expression ◽  
Optimal Energy ◽  
Energy Harvesting System

In this paper, we consider one-way  relay with energy harvesting system based on power beacon (PB), in which the relay node harvests transmitted power from the PB station to forward signals to destination. We also analyse the relay network model with amplify-and-forward (AF) protocol for information cooperation and Power Splitting-based Relaying (PSR) protocol for power transfer. In particular, the outage probability and optimal energy harvesting (EH) power splitting fraction of novel scheme in are presented. We obtain analytical closed-form expression of  optimal energy harvesting (EH) power splitting fraction to minimize the outage probability of system. Using numerical and analytical simulations, the performances of different cases are presented and discussed.

scholarly journals Power-Splitting Scheme for Nonlinear Energy Harvesting AF Relaying with Direct Link

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Xiaobo Bai ◽  
Jingfeng Shao ◽  
Jiangang Tian ◽  
Liqin Shi
Keyword(s):  
Energy Harvesting ◽  
Logistic Function ◽  
System Capacity ◽  
Closed Form Expression ◽  
Power Splitting ◽  
Direct Link ◽  
Form Expression ◽  
Relay Systems ◽  
Model Based ◽  
Energy Constrained

Simultaneous wireless information and power transfer (SWIPT) is a promising technique to prolong the lifetime of energy-constrained relay systems. Most previous works optimize power-splitting (PS) scheme based on a linear or a simple two-piecewise linear energy harvesting (EH) model, while the employed EH model may not characterize the properties of practical EH harvesters well. This leads to a mismatch between the existing PS scheme and the practical EH harvester available for relay systems. Motivated by this, this paper is devoted to the design of PS scheme in a nonlinear EH amplify-and-forward energy-constrained relay system in the presence of a direct link between the source and the destination. In particular, we formulate an optimization problem to maximize the system capacity according to the instantaneous channel state information, subject to a nonlinear EH model based on the logistic function. The objective function of the formulated problem is proven to be unimodal and there is no closed-form expression for the optimal PS ratio due to the complexity of logistic function. In order to reduce overhead cost of optimizing PS ratio, a simpler nonlinear EH model based on the inverse proportional function is employed to replace the nonlinear EH model based on the logistic function and we further derive the closed-form expression for the optimal PS ratio. Simulation results reveal that a higher system capacity can be achieved when the PS scheme is optimized based on nonlinear EH models instead of the linear EH model, and that there is only a marginal difference between the capacity under the two optimal PS schemes optimized for two different nonlinear EH models.

scholarly journals Synthesizing of Planar and Conformal Double-Sided Parallel-Cross Dipoles FSS Based on Closed-Form Expression

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Yassine Zouaoui ◽  
Larbi Talbi ◽  
Khelifa Hettak ◽  
Naresh K. Darimireddy
Keyword(s):  
Closed Form ◽  
Closed Form Expression ◽  
Form Expression

Distribution of Consensus in a Broadcasting-based Consensus-forming Algorithm

2021 ◽  
Vol 48 (3) ◽  
pp. 91-96
Author(s):  
Shigeo Shioda
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Closed Form ◽  
Probability Density ◽  
Infinite Number ◽  
Stable Distribution ◽  
Random Variable ◽  
Cauchy Distribution ◽  
Closed Form Expression ◽  
Form Expression

The consensus achieved in the consensus-forming algorithm is not generally a constant but rather a random variable, even if the initial opinions are the same. In the present paper, we investigate the statistical properties of the consensus in a broadcasting-based consensus-forming algorithm. We focus on two extreme cases: consensus forming by two agents and consensus forming by an infinite number of agents. In the two-agent case, we derive several properties of the distribution function of the consensus. In the infinite-numberof- agents case, we show that if the initial opinions follow a stable distribution, then the consensus also follows a stable distribution. In addition, we derive a closed-form expression of the probability density function of the consensus when the initial opinions follow a Gaussian distribution, a Cauchy distribution, or a L´evy distribution.

scholarly journals Colored HOMFLY-PT for hybrid weaving knot $$ {\hat{\mathrm{W}}}_3 $$(m, n)

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Vivek Kumar Singh ◽  
Rama Mishra ◽  
P. Ramadevi
Keyword(s):  
Closed Form ◽  
Topological Strings ◽  
Chebyshev Polynomials ◽  
Fibonacci Numbers ◽  
Infinite Family ◽  
Closed Form Expression ◽  
Two Dimensional ◽  
Laurent Polynomials ◽  
Form Expression ◽  
Torus Knots

Abstract Weaving knots W(p, n) of type (p, n) denote an infinite family of hyperbolic knots which have not been addressed by the knot theorists as yet. Unlike the well known (p, n) torus knots, we do not have a closed-form expression for HOMFLY-PT and the colored HOMFLY-PT for W(p, n). In this paper, we confine to a hybrid generalization of W(3, n) which we denote as $$ {\hat{W}}_3 $$ W ̂ 3 (m, n) and obtain closed form expression for HOMFLY-PT using the Reshitikhin and Turaev method involving $$ \mathrm{\mathcal{R}} $$ ℛ -matrices. Further, we also compute [r]-colored HOMFLY-PT for W(3, n). Surprisingly, we observe that trace of the product of two dimensional $$ \hat{\mathrm{\mathcal{R}}} $$ ℛ ̂ -matrices can be written in terms of infinite family of Laurent polynomials $$ {\mathcal{V}}_{n,t}\left[q\right] $$ V n , t q whose absolute coefficients has interesting relation to the Fibonacci numbers $$ {\mathrm{\mathcal{F}}}_n $$ ℱ n . We also computed reformulated invariants and the BPS integers in the context of topological strings. From our analysis, we propose that certain refined BPS integers for weaving knot W(3, n) can be explicitly derived from the coefficients of Chebyshev polynomials of first kind.

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