scholarly journals A Computer Program for a Canonical Problem in Underwater Shock

1994 ◽  
Vol 1 (4) ◽  
pp. 331-337 ◽  
Author(s):  
Thomas L. Geers ◽  
Teh-Hua Ju
Keyword(s):  
Computer Program ◽  
Closed Form Solution ◽  
Form Solution ◽  
Marine Structures ◽  
Underwater Explosions ◽  
Generalized Fourier Series ◽  
Method Of Solution ◽  
Underwater Shock ◽  
Acoustic Fluid ◽  
Element Boundary

Finite-element/boundary-element codes are widely used to analyze the response of marine structures to underwater explosions. An important step in verifying the correctness and accuracy of such codes is the comparison of code-generated results for canonical problems with corresponding analytical or semianalytical results. At the present time, such comparisons rely on hardcopy results presented in technical journals and reports. This article describes a computer program available from SAVIAC that produces user-selected numerical results for a step-wave-excited spherical shell submerged in and (optionally) filled with an acoustic fluid. The method of solution employed in the program is based on classical expansion of the field quantities in generalized Fourier series in the meridional coordinate. Convergence of the series is enhanced by judicious application of modified Cesàro summation and partial closed-form solution.

Configuring Marine Riser Tapered Stress Joints Used in Top-Supported Applications

2004 ◽  
Vol 126 (3) ◽  
pp. 201-207 ◽  
Author(s):  
Cormack C. Gordon ◽  
Don W. Dareing
Keyword(s):  
Differential Equation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Marine Riser ◽  
Cross Sectional ◽  
Marine Risers ◽  
Dynamic Analyses ◽  
Stress Levels ◽  
Method Of Solution ◽  
Type Differential Equation

The objective of this paper is to present a direct and useful method for establishing the configuration of tapered stress joints for marine risers so that stress levels are fairly balanced over the length of the stress joint and within acceptable stress levels. The method of solution approximates straight tapered stress joints with one, whose cross sectional moment of inertia varies parabolically along the stress joint. This approximation leads to the classic Euler type differential equation, which can be solved directly giving a closed form solution. The formulation of deflection and stresses should be of use to designers of marine tubulars. Even though the focus of the study is on a static analysis of top located stress joints, the method of solution can be adapted to mudline attachment locations as well as dynamic analyses.

Calculation of the Equilibrium Configuration of Shopping Facility Sizes

1980 ◽  
Vol 12 (9) ◽  
pp. 983-1000 ◽  
Author(s):  
P A Phiri
Keyword(s):  
Closed Form ◽  
Nonlinear Equations ◽  
Gradient Method ◽  
Equilibrium Configuration ◽  
Closed Form Solution ◽  
Theoretical Framework ◽  
Form Solution ◽  
Method Of Solution ◽  
Special Case ◽  
General Method

This paper presents a range of methods for computing the equilibrium configuration of shopping facility sizes. First, the presently available range of quasi-balancing factor methods is considered and built into a theoretical framework in which further algorithms may be defined. Then the use of the gradient method is considered, which is a general method of solution of nonlinear equations. Last, it is shown that a special case exists in which a closed form solution may be obtained.

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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