scholarly journals Dynamic Viscoelastic Effects on Sound Wave Diffraction by Spherical and Cylindrical Shells Submerged in and Filled with Viscous Compressible Fluids

2003 ◽  
Vol 10 (5-6) ◽  
pp. 339-363 ◽  
Author(s):  
Seyyed M. Hasheminejad ◽  
Naemeh Safari
Keyword(s):  
Viscoelastic Properties ◽  
Scattering Problem ◽  
Acoustic Scattering ◽  
Closed Form Solution ◽  
Directivity Pattern ◽  
Form Solution ◽  
Fluid Viscosity ◽  
Sound Scattering ◽  
Force Magnitude ◽  
Viscoelastic Effects

An analysis for sound scattering by fluid-filled spherical and cylindrical viscoelastic shells immersed in viscous fluids is outlined. The dynamic viscoelastic properties of the scatterer and the viscosity of the surrounding and core fluids are rigorously taken into account in the solution of the acoustic scattering problem. The novel features of Havriliak-Negami model for viscoelastic material dynamic behaviour description along with the appropriate wave-harmonic field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in form of infinite series. Subsequently, the associated acoustic field quantities such as the scattered far-field pressure directivity pattern, form function amplitude, transmitted intensity ratio, and acoustic force magnitude are evaluated for given sets of medium physical properties. Numerical results clearly indicate that in addition to the traditional fluid viscosity-related mechanisms, the dynamic viscoelastic properties of the shell material as well as its thickness can be of major significance in sound scattering. Limiting cases are examined and fair agreements with well-known solutions are established.

Acoustic Scattering by a Fluid-Encapsulating Spherical Viscoelastic Membrane Including Thermoviscous Effects

2005 ◽  
Vol 21 (4) ◽  
pp. 205-215 ◽  
Author(s):  
Seyyed M. Hasheminejad
Keyword(s):  
Viscoelastic Material ◽  
Viscoelastic Properties ◽  
Scattering Problem ◽  
Acoustic Scattering ◽  
Closed Form Solution ◽  
Practical Interest ◽  
Directivity Pattern ◽  
Form Solution ◽  
Heat Conducting ◽  
Harmonic Field

AbstractThis study provides a general analysis for scattering of a planar monochromatic compressional sound wave by a fluid-filled viscoelastic spherical membrane immersed in an unbounded viscous heat-conducting compressible fluid. The thermoviscous effects in the fluid are incorporated by application of a thin boundary layer model. The dynamic viscoelastic properties of the spherical membrane are rigorously taken into account in the solution of the acoustic-scattering problem. Havriliak-Negami model for viscoelastic material behaviour along with the appropriate wave-harmonic field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in form of infinite series. Subsequently, the basic acoustic quantities, such as the scattered far-field pressure directivity pattern, and the scattering cross section are evaluated for given sets of viscoelastic material properties. Numerical results clearly indicate that, in addition to the traditional fluid thermoviscosity-related mechanisms, dynamic viscoelastic properties of the obstacle can be of significance in sound scattering. The presented analysis is of practical interest in development of contrast agents for echocardiographic research with potential clinical applications.

Nanoelectromechanics of Piezoresponse Force Microscopy: Contact Properties, Fields Below the Surface and Polarization Switching

2003 ◽  
Vol 784 ◽  
Author(s):  
S. V. Kalinin ◽  
Junsoo Shin ◽  
M. Kachanov ◽  
E. Karapetian ◽  
A. P. Baddorf
Keyword(s):  
Strain Distribution ◽  
Point Charge ◽  
Closed Form Solution ◽  
Piezoresponse Force Microscopy ◽  
Polarization Switching ◽  
Ferroelectric Material ◽  
Form Solution ◽  
Force Microscopy ◽  
Force Magnitude ◽  
Resolution Limits

ABSTRACTTo achieve quantitative interpretation of Piezoresponse Force Microscopy (PFM), including resolution limits, tip bias- and strain-induced phenomena and spectroscopy, knowledge of elastic and electrostatic field distributions below the tip is required. The exact closed form solution of the coupled electroelastic problem for piezoelectric indentation is derived and used to obtain the tip-induced electric field and strain distribution in the ferroelectric material. This establishes a complete continuum mechanics description of the PFM imaging mechanism. These solutions are reduced to the point charge/force behavior for large separations from contact, and the applicability limits and charge/force magnitude for these models are established. The implications of these results for ferroelectric polarization switching processes are analyzed.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

Capacity Analysis for Correlated Multi-Hop MIMO Channels under Colored Noise

2015 ◽  
Vol 1 ◽  
pp. 41
Author(s):  
Nguyen N. Tran ◽  
Ha X. Nguyen
Keyword(s):  
Computational Complexity ◽  
Mutual Information ◽  
Closed Form Solution ◽  
Optimal Solution ◽  
Form Solution ◽  
Maximization Problem ◽  
Capacity Analysis ◽  
Mimo Channels ◽  
Average Mutual Information ◽  
Channel Output

A capacity analysis for generally correlated wireless multi-hop multi-input multi-output (MIMO) channels is presented in this paper. The channel at each hop is spatially correlated, the source symbols are mutually correlated, and the additive Gaussian noises are colored. First, by invoking Karush-Kuhn-Tucker condition for the optimality of convex programming, we derive the optimal source symbol covariance for the maximum mutual information between the channel input and the channel output when having the full knowledge of channel at the transmitter. Secondly, we formulate the average mutual information maximization problem when having only the channel statistics at the transmitter. Since this problem is almost impossible to be solved analytically, the numerical interior-point-method is employed to obtain the optimal solution. Furthermore, to reduce the computational complexity, an asymptotic closed-form solution is derived by maximizing an upper bound of the objective function. Simulation results show that the average mutual information obtained by the asymptotic design is very closed to that obtained by the optimal design, while saving a huge computational complexity.

scholarly journals Geometric Average Asian Option Pricing with Paying Dividend Yield under Non-Extensive Statistical Mechanics for Time-Varying Model

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 828 ◽  
Author(s):  
Jixia Wang ◽  
Yameng Zhang
Keyword(s):  
Statistical Mechanics ◽  
Option Pricing ◽  
Asset Price ◽  
Closed Form Solution ◽  
Real Data ◽  
Form Solution ◽  
Asian Option ◽  
Time Varying ◽  
Dividend Yield ◽  
Geometric Average

This paper is dedicated to the study of the geometric average Asian call option pricing under non-extensive statistical mechanics for a time-varying coefficient diffusion model. We employed the non-extensive Tsallis entropy distribution, which can describe the leptokurtosis and fat-tail characteristics of returns, to model the motion of the underlying asset price. Considering that economic variables change over time, we allowed the drift and diffusion terms in our model to be time-varying functions. We used the I t o ^ formula, Feynman–Kac formula, and P a d e ´ ansatz to obtain a closed-form solution of geometric average Asian option pricing with a paying dividend yield for a time-varying model. Moreover, the simulation study shows that the results obtained by our method fit the simulation data better than that of Zhao et al. From the analysis of real data, we identify the best value for q which can fit the real stock data, and the result shows that investors underestimate the risk using the Black–Scholes model compared to our model.

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