Frequency-domain transient analysis of multitime partial differential equation systems

2011 ◽  
Author(s):  
Haotian Liu ◽  
Fengrui Shi ◽  
Yuanzhe Wang ◽  
Ngai Wong
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Frequency Domain ◽  
Transient Analysis ◽  
Partial Differential

scholarly journals Theory of differential offset continuation

Geophysics ◽  
2003 ◽  
Vol 68 (2) ◽  
pp. 718-732 ◽  
Author(s):  
Sergey Fomel
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Frequency Domain ◽  
Initial Value Problem ◽  
Data Transformation ◽  
Initial Value ◽  
Partial Differential ◽  
Reflection Data ◽  
Zero Offset

I introduce a partial differential equation to describe the process of prestack reflection data transformation in the offset, midpoint, and time coordinates. The equation is proved theoretically to provide correct kinematics and amplitudes on the transformed constant‐offset sections. Solving an initial‐value problem with the proposed equation leads to integral and frequency‐domain offset continuation operators, which reduce to the known forms of dip moveout operators in the case of continuation to zero offset.

Transient analysis of state-dependent queueing networks via cumulant functions

2001 ◽  
Vol 38 (04) ◽  
pp. 841-859 ◽  
Author(s):  
Timothy I. Matis ◽  
Richard M. Feldman
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Queueing Networks ◽  
Transient Analysis ◽  
Queueing Network ◽  
Partial Differential ◽  
Cumulant Generating Function ◽  
State Dependent ◽  
Intensity Functions ◽  
First Moment

A new procedure that generates the transient solution of the first moment of the state of a Markovian queueing network with state-dependent arrivals, services, and routeing is developed. The procedure involves defining a partial differential equation that relates an approximate multivariate cumulant generating function to the intensity functions of the network. The partial differential equation then yields a set of ordinary differential equations which are numerically solved to obtain the first moment.

Transient analysis of state-dependent queueing networks via cumulant functions

2001 ◽  
Vol 38 (4) ◽  
pp. 841-859 ◽  
Author(s):  
Timothy I. Matis ◽  
Richard M. Feldman
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Queueing Networks ◽  
Transient Analysis ◽  
Queueing Network ◽  
Partial Differential ◽  
Cumulant Generating Function ◽  
State Dependent ◽  
Intensity Functions ◽  
First Moment

A new procedure that generates the transient solution of the first moment of the state of a Markovian queueing network with state-dependent arrivals, services, and routeing is developed. The procedure involves defining a partial differential equation that relates an approximate multivariate cumulant generating function to the intensity functions of the network. The partial differential equation then yields a set of ordinary differential equations which are numerically solved to obtain the first moment.

Qxygen transfer in gravity flow sewers

2000 ◽  
Vol 42 (3-4) ◽  
pp. 417-422 ◽  
Author(s):  
T.Y. Pai ◽  
C.F. Ouyang ◽  
Y.C. Liao ◽  
H.G. Leu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dissolved Oxygen ◽  
Flow Velocity ◽  
Molecular Diffusion ◽  
Eddy Diffusion ◽  
Partial Differential ◽  
Diffusion Term ◽  
Sewer Pipes ◽  
Gravity Sewer

Oxygen diffused to water in gravity sewer pipes was studied in a 21 m long, 0.15 m diameter model sewer. At first, the sodium sulfide was added into the clean water to deoxygenate, then the pump was started to recirculate the water and the deoxygenated water was reaerated. The dissolved oxygen microelectrode was installed to measure the dissolved oxygen concentrations varied with flow velocity, time and depth. The dissolved oxygen concentration profiles were constructed and observed. The partial differential equation diffusion model that considered Fick's law including the molecular diffusion term and eddy diffusion term were derived. The analytic solution of the partial differential equation was used to determine the diffusivities by the method of nonlinear regression. The diffusivity values for the oxygen transfer was found to be a function of molecular diffusion, eddy diffusion and flow velocity.

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