scholarly journals Steady state of gradient echo sequences with radiofrequency phase cycling: Analytical solution, contrast enhancement with partial spoiling

2005 ◽  
Vol 55 (1) ◽  
pp. 98-107 ◽  
Author(s):  
Carl Ganter
Keyword(s):  
Steady State ◽  
Analytical Solution ◽  
Contrast Enhancement ◽  
Gradient Echo ◽  
Phase Cycling

Analytical Solution to Steady-State Heat-Conduction Problems With Irregularly Shaped Boundaries

1971 ◽  
Vol 93 (4) ◽  
pp. 449-454 ◽  
Author(s):  
D. M. France
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Analytical Solution ◽  
Least Squares ◽  
Series Solution ◽  
Point Matching ◽  
State Heat ◽  
Temperature Heat ◽  
Steady State Heat ◽  
Least Squares Approach

A method of obtaining an analytical solution to two-dimensional steady-state heat-conduction problems with irregularly shaped boundaries is presented. The technique of obtaining the coefficients to the series solution via a direct least-squares approach is compared to the “point-matching” scheme. The two methods were applied to problems with known solutions involving the three heat-transfer boundary conditions, temperature, heat flux, and convection coefficient specified. Increased accuracy with substantially fewer terms in the series solution was obtained via the least-squares technique.

scholarly journals The truncated Hyper-Poisson queues: Hk/Ma,b/C/N with balking, reneging and general bulk service rule

2008 ◽  
Vol 18 (1) ◽  
pp. 23-36 ◽  
Author(s):  
A.I. Shawky ◽  
M.S. El-Paoumy
Keyword(s):  
Steady State ◽  
Analytical Solution ◽  
Explicit Form ◽  
Recurrence Relations ◽  
Expected Number ◽  
Special Cases ◽  
Queue Discipline ◽  
Bulk Service ◽  
General Bulk Service Rule ◽  
Steady State Probabilities

The aim of this paper is to derive the analytical solution of the queue: Hk/Ma,b/C/N with balking and reneging in which (I) units arrive according to a hyper-Poisson distribution with k independent branches, (II) the queue discipline is FIFO; and (III) the units are served in batches according to a general bulk service rule. The steady-state probabilities, recurrence relations connecting various probabilities introduced are found and the expected number of units in the queue is derived in an explicit form. Also, some special cases are obtained. .

Steady-State Gradient-Echo Imaging

1996 ◽  
pp. 167-213
Author(s):  
Marinus T. Vlaardingerbroek ◽  
Jacques A. den Boer
Keyword(s):  
Steady State ◽  
Gradient Echo ◽  
Gradient Echo Imaging

scholarly journals Application of Analytical Solution to Steady-State Temperature Field by Double-Row-Pipe Freezing and Verification with Field Measurement: A Case Study of Connected Aisle

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Zequn Hong ◽  
Xiangdong Hu
Keyword(s):  
Temperature Field ◽  
Steady State ◽  
Analytical Solution ◽  
Wall Thickness ◽  
Field Measurement ◽  
Field Analysis ◽  
Shield Tunnel ◽  
Double Row ◽  
Steady State Temperature ◽  
Frozen Wall

In order to solve the problem of sealing water and bearing capacity of a connected aisle in an underwater shield tunnel, a double-circle horizontal freezing method was adopted for ground reinforcement in the connected aisle of Maliuzhou Tunnel, which is China’s first shield tunnel with superlarge diameter built in a composite stratum. This paper proposed a new double-row-pipe freezing model for the calculation of frozen wall thickness based on analytical solution to steady-state temperature field. Besides, field measurement and transient numerical studies of the active freezing period were also carried out to study the freeze-sealing effect. The results show that frozen wall thickness obtained by analytical solutions agrees well with numerical simulation results, which verifies the applicability of the newly proposed calculation method. Field analysis indicates that soil temperature gradually approaches a stable value which is far below the freezing point, and a reliable water-sealing curtain can be formed around the designed connected aisle. Maximum impact of soil excavation on the frozen wall is about 10°C, and reducing exposure time of excavation surface can effectively alleviate the weakening of frozen wall. To obtain comprehensive analysis for freezing wall thickness, a more reasonable arrangement of temperature-measuring holes is expected in future freezing engineering.

scholarly journals Geometric shape features extraction using a steady state partial differential equation system

2019 ◽  
Vol 6 (4) ◽  
pp. 647-656 ◽  
Author(s):  
Takayuki Yamada
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Steady State ◽  
Analytical Solution ◽  
Geometric Shape ◽  
Geometrical Shape ◽  
Shape Features ◽  
Partial Differential ◽  
Topological Constraint ◽  
Numerical Examples

Abstract A unified method for extracting geometric shape features from binary image data using a steady-state partial differential equation (PDE) system as a boundary value problem is presented in this paper. The PDE and functions are formulated to extract the thickness, orientation, and skeleton simultaneously. The main advantage of the proposed method is that the orientation is defined without derivatives and thickness computation is not imposed a topological constraint on the target shape. A one-dimensional analytical solution is provided to validate the proposed method. In addition, two-dimensional numerical examples are presented to confirm the usefulness of the proposed method. Highlights A steady state partial differential equation for extraction of geometrical shape features is formulated. The functions for geometrical shape features are formulated by the solution of the proposed PDE. Analytical solution is provided in one-dimension. Numerical examples are provided in two-dimension.

Prostate MR elastography with transperineal electromagnetic actuation and a fast fractionally encoded steady-state gradient echo sequence

2014 ◽  
Vol 27 (7) ◽  
pp. 784-794 ◽  
Author(s):  
Ramin Sebastian Sahebjavaher ◽  
Samuel Frew ◽  
Artem Bylinskii ◽  
Leon ter Beek ◽  
Philippe Garteiser ◽  
...  
Keyword(s):  
Steady State ◽  
Mr Elastography ◽  
Gradient Echo ◽  
Electromagnetic Actuation
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