On the Generalization of Displacement-Based Laminate Theories

1989 ◽  
Vol 42 (11S) ◽  
pp. S213-S222 ◽  
Author(s):  
J. N. Reddy
Keyword(s):  
Analytical Solution ◽  
Elasticity Theory ◽  
Shear Deformation ◽  
Single Layer ◽  
Numerical Results ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Laminate Theory ◽  
Displacement Based

A review and generalization of the displacement-based two-dimensional plate theories is presented. The classical and shear deformation single–layer theories up to the third-order are presented in a single theory through tracers. The layer–wise laminate theory developed by the author is reviewed. Numerical results are presented to illustrate the accuracy of the layer–wise theory by comparison with the analytical solution of the 3–D elasticity theory.

Exact third-order structure functions for two-dimensional turbulence

2018 ◽  
Vol 851 ◽  
pp. 672-686 ◽  
Author(s):  
Jin-Han Xie ◽  
Oliver Bühler
Keyword(s):  
Structure Functions ◽  
Spectral Energy ◽  
Order Structure ◽  
Two Dimensional ◽  
Third Order ◽  
Transfer Rates ◽  
The Third ◽  
Random Forcing ◽  
Asymptotic Expressions ◽  
Special Case

We derive and investigate exact expressions for third-order structure functions in stationary isotropic two-dimensional turbulence, assuming a statistical balance between random forcing and dissipation both at small and large scales. Our results extend previously derived asymptotic expressions in the enstrophy and energy inertial ranges by providing uniformly valid expressions that apply across the entire non-dissipative range, which, importantly, includes the forcing scales. In the special case of white noise in time forcing this leads to explicit predictions for the third-order structure functions, which are successfully tested against previously published high-resolution numerical simulations. We also consider spectral energy transfer rates and suggest and test a simple robust diagnostic formula that is useful when forcing is applied at more than one scale.

A Two-Dimensional Potential Flow Model of the Wave Field Generated by a Semisubmerged Body in Heaving Motion

1988 ◽  
Vol 32 (02) ◽  
pp. 83-91
Author(s):  
X. M. Wang ◽  
M. L. Spaulding
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Model ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Potential Flow Model ◽  
Good Agreement

A two-dimensional potential flow model is formulated to predict the wave field and forces generated by a sere!submerged body in forced heaving motion. The potential flow problem is solved on a boundary fitted coordinate system that deforms in response to the motion of the free surface and the heaving body. The full nonlinear kinematic and dynamic boundary conditions are used at the free surface. The governing equations and associated boundary conditions are solved by a second-order finite-difference technique based on the modified Euler method for the time domain and a successive overrelaxation (SOR) procedure for the spatial domain. A series of sensitivity studies of grid size and resolution, time step, free surface and body grid redistribution schemes, convergence criteria, and free surface body boundary condition specification was performed to investigate the computational characteristics of the model. The model was applied to predict the forces generated by the forced oscillation of a U-shaped cylinder. Numerical model predictions are generally in good agreement with the available second-order theories for the first-order pressure and force coefficients, but clearly show that the third-order terms are larger than the second-order terms when nonlinearity becomes important in the dimensionless frequency range 1≤ Fr≤ 2. The model results are in good agreement with the available experimental data and confirm the importance of the third order terms.

An analytical solution to separate P‐waves and S‐waves in VSP wavefields

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 955-967 ◽  
Author(s):  
Hiroshi Amano
Keyword(s):  
Analytical Solution ◽  
Formal Solution ◽  
Seismic Profile ◽  
Synthetic Seismograms ◽  
Third Order ◽  
P Waves ◽  
Practical Applications ◽  
S Waves ◽  
The Third ◽  
Z Domain

An analytical solution to separate P‐waves and S‐waves in vertical seismic profile (VSP) wavefields is derived using combinations of certain terms of the formal solution for forward VSP modeling. Some practical applications of this method to synthetic seismograms and field data are investigated and evaluated. Little wave distortion is recognized, and the weak wavefield masked by dominant wavetrains can be extracted with this method. The decomposed wavefield is expressed in the frequency‐depth (f-z) domain as a linear combination of up to the third‐order differential of traces, which is approximated by trace differences in the practical separation process. In general, five traces with single‐component data are required in this process, but the same process is implemented with only three traces in the acoustic case. Two‐trace extrapolation is applied to each edge of the data gather to enhance the accuracy of trace difference. Since the formulas are developed in the f-z domain, the influence of anelasticity can be taken into account, and the calculation is carried out fast enough with the benefit of the fast Fourier transform (FFT).

A note on Kolmogorov's third-order structure-function law, the local isotropy hypothesis and the pressure–velocity correlation

1996 ◽  
Vol 326 ◽  
pp. 343-356 ◽  
Author(s):  
Erik Lindborg
Keyword(s):  
Structure Function ◽  
Strain Tensor ◽  
Inertial Range ◽  
Order Structure ◽  
Two Dimensional ◽  
Mean Flow ◽  
Velocity Correlation ◽  
Third Order ◽  
The Third ◽  
Point Pressure

We show that Kolmogorov's (1941b) inertial-range law for the third-order structure function can be derived from a dynamical equation including pressure terms and mean flow gradient terms. A new inertial-range law, relating the two-point pressure–velocity correlation to the single-point pressure–strain tensor, is also derived. This law shows that the two-point pressure–velocity correlation, just like the third-order structure function, grows linearly with the separation distance in the inertial range. The physical meaning of both this law and Kolmogorov's law is illustrated by a Fourier analysis. An inertial-range law is also derived for the third-order velocity–enstrophy structure function of two-dimensional turbulence. It is suggested that the second-order vorticity structure function of two-dimensional turbulence is constant and scales with$\epsilon ^{2/3}_\omega$in the enstrophy inertial range, εωbeing the enstrophy dissipation. Owing to the constancy of this law, it does not imply a Fourier-space inertial-range law, and therefore it is not equivalent to thek−1law for the enstrophy spectrum, suggested by Kraichnan (1967) and Batchelor (1969).

scholarly journals ON BORWEIN’S CONJECTURES FOR PLANAR UNIFORM RANDOM WALKS

2019 ◽  
Vol 107 (3) ◽  
pp. 392-411 ◽  
Author(s):  
YAJUN ZHOU
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Random Walks ◽  
Euclidean Plane ◽  
Feynman Diagrams ◽  
Quantum Field ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Uniformly Convergent

Let $p_{n}(x)=\int _{0}^{\infty }J_{0}(xt)[J_{0}(t)]^{n}xt\,dt$ be Kluyver’s probability density for $n$-step uniform random walks in the Euclidean plane. Through connection to a similar problem in two-dimensional quantum field theory, we evaluate the third-order derivative $p_{5}^{\prime \prime \prime }(0^{+})$ in closed form, thereby giving a new proof for a conjecture of J. M. Borwein. By further analogies to Feynman diagrams in quantum field theory, we demonstrate that $p_{n}(x),0\leq x\leq 1$ admits a uniformly convergent Maclaurin expansion for all odd integers $n\geq 5$, thus settling another conjecture of Borwein.

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