A THEORETICAL PREDICTION OF SALT DOME PATTERNS

Geophysics ◽  
1965 ◽  
Vol 30 (4) ◽  
pp. 633-643 ◽  
Author(s):  
Franz Selig
Keyword(s):  
Mathematical Formulation ◽  
Three Dimensional ◽  
Salt Dome ◽  
Geometrical Parameters ◽  
Explicit Solutions ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Rate Of Growth ◽  
And Control

Z. F. Daneš’s mathematical formulation of salt dome dynamics was modified to the extent that explicit solutions can be obtained. For both the two‐dimensional and three‐dimensional model, a formula is derived relating the rate of growth and the wavenumber of a fundamental mode with the physical and geometrical parameters. It is shown that there exists one wavenumber for which the rate of growth reaches a maximum. In time this component will dominate and control the final pattern.

Clinical experience of using virtual 3D modelling for pre and intraoperative guidance during robotic-assisted partial nephrectomy

2021 ◽  
pp. 205141582110002
Author(s):  
Lorenz Berger ◽  
Aziz Gulamhusein ◽  
Eoin Hyde ◽  
Matt Gibb ◽  
Teele Kuusk ◽  
...  
Keyword(s):  
Computed Tomography ◽  
Partial Nephrectomy ◽  
Surgical Outcome ◽  
Prospective Cohort ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Robotic Assisted ◽  
Robotic Assisted Partial Nephrectomy

Objective: Surgical planning for robotic-assisted partial nephrectomy is widely performed using two-dimensional computed tomography images. It is unclear to what extent two-dimensional images fully simulate surgical anatomy and case complexity. To overcome these limitations, software has been developed to reconstruct three-dimensional models from computed tomography data. We present the results of a feasibility study, to explore the role and practicality of virtual three-dimensional modelling (by Innersight Labs) in the context of surgical utility for preoperative and intraoperative use, as well as improving patient involvement. Methods: A prospective study was conducted on patients undergoing robotic-assisted partial nephrectomy at our high volume kidney cancer centre. Approval from a research ethics committee was obtained. Patient demographics and tumour characteristics were collected. Surgical outcome measures were recorded. The value of the three-dimensional model to the surgeon and patient was assessed using a survey. The prospective cohort was compared against a retrospective cohort and cases were individually matched using RENAL (radius, exophytic/endophytic, nearness to collecting system or sinus, anterior/posterior, location relative to polar lines) scores. Results: This study included 22 patients. Three-dimensional modelling was found to be safe for this prospective cohort and resulted in good surgical outcome measures. The mean (standard deviation) console time was 158.6 (35) min and warm ischaemia time was 17.3 (6.3) min. The median (interquartile range) estimated blood loss was 125 (50–237.5) ml. Two procedures were converted to radical nephrectomy due to the risk of positive margins during resection. The median (interquartile range) length of stay was 2 (2–3) days. No postoperative complications were noted and all patients had negative surgical margins. Patients reported improved understanding of their procedure using the three-dimensional model. Conclusion: This study shows the potential benefit of three-dimensional modelling technology with positive uptake from surgeons and patients. Benefits are improved perception of vascular anatomy and resection approach, and procedure understanding by patients. A randomised controlled trial is needed to evaluate the technology further. Level of evidence: 2b

Blast load simulation using conical shock tube systems

2019 ◽  
Vol 11 (2) ◽  
pp. 135-158 ◽  
Author(s):  
Ahmed Ismail ◽  
Mohamed Ezzeldin ◽  
Wael El-Dakhakhni ◽  
Michael Tait
Keyword(s):  
Shock Tube ◽  
Three Dimensional ◽  
Design Parameters ◽  
Civil Infrastructure ◽  
Two Dimensional ◽  
Blast Loads ◽  
Dimensional Model ◽  
Tube System ◽  
Three Dimensional Model ◽  
Conical Shock

With the increased frequency of accidental and deliberate explosions, evaluating the response of civil infrastructure systems to blast loading has been attracting the interests of the research and regulatory communities. However, with the high cost and complex safety and logistical issues associated with field explosives testing, North American blast-resistant construction standards (e.g. ASCE 59-11 and CSA S850-12) recommend the use of shock tubes to simulate blast loads and evaluate relevant structural response. This study first aims at developing a simplified two-dimensional axisymmetric shock tube model, implemented in ANSYS Fluent, a computational fluid dynamics software, and then validating the model using the classical Sod’s shock tube problem solution, as well as available shock tube experimental test results. Subsequently, the developed model is compared to a more complex three-dimensional model and the results show that there is negligible difference between the two models for axisymmetric shock tube performance simulation; however, the three-dimensional model is necessary to simulate non-axisymmetric shock tubes. Following the model validation, extensive analyses are performed to evaluate the influences of shock tube design parameters (e.g. the driver section pressure and length and the expansion section length) on blast wave characteristics to facilitate a shock tube design that would generate shock waves similar to those experienced by civil infrastructure components under blast loads. The results show that the peak reflected pressure increases as the driver pressure increases, while a decrease in the expansion length increases the peak reflected pressure. In addition, the positive phase duration increases as both the driver length and expansion length are increased. Finally, the developed two-dimensional axisymmetric model is used to optimize the dimensions of a physical large-scale conical shock tube system constructed for civil infrastructure component blast response evaluation applications. The capabilities of such shock tube system are further investigated by correlating its design parameters to a range of explosion threats identified by different hemispherical TNT charge weight and distance scenarios.

Eclectic modelling of the North Atlantic. II. Transient tracers and the ventilation of the Eastern Basin thermocline

1988 ◽  
Vol 325 (1583) ◽  
pp. 201-236 ◽  
Keyword(s):  
North Atlantic ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Ekman Pumping ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Oxygen Utilization ◽  
The North ◽  
Time Histories ◽  
Weak Constraints

Renewal rates of the waters of the thermocline in the eastern North Atlantic are estimated by combining linear quasi-geostrophic dynamics with steady and transient tracers into a unified eclectic, reservoir model. The two-dimensional model first employed is finally rejected when it is found that it generates oxygen-utilization rates (OUR) that are, by conventional biological wisdom, too high. The three-dimensional model that replaces the two-dimensional one shows that the our is indeterminate, with possible ranges from zero to unacceptably high values. The region is flushed primarily from the north and east. The problem of using transient tracers is mathematically equivalent to that of distributed-system boundary-control theory, the open-ocean boundary conditions playing the role of the unknown control variables. The missing time histories of this new set of unknowns means that tritium and helium-3 distributions are only comparatively weak constraints on the flow field, but do set upper bounds on the vertical exchange with surface waters. Surface Ekman pumping is adequate to explain the interior distributions without additional buoyancy ventilation, although this latter process is possible. Some speculation is made about conditions under which transient tracers might play a more definitive role.

Static three-dimensional modelling of pneumatic tyres using the technique of element overlaying

2002 ◽  
Vol 216 (9) ◽  
pp. 709-716 ◽  
Author(s):  
J Pelc
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Vertical Load ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Tyre Model ◽  
Radial Stiffness ◽  
Rubber Composite ◽  
Stiffness Characteristics ◽  
Incompressible Rubber

The aim of the paper is to propose and verify an effective method for the realistic modelling of pneumatic tyres. A static, three-dimensional model of a pneumatic tyre, based on the finite element (FE) program MARC, is presented. The cord-rubber composite was modelled by overlaying the elements characterizing the cord and those representing incompressible rubber. A two-dimensional model was used to simulate the tyre mounting and inflation process. The model was then developed into a three-dimensional one. The displacements, radial stiffness and delamination stresses caused by the vertical load were determined. The shape of the tyre footprint and the pressure distribution in this zone were also predicted. Good correlation between measured and computed stiffness characteristics was observed. The proposed technique of element overlaying yields a tyre model that is numerically more stable than that using only orthotropic elements (very stiff cord merged with compliant rubber).

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