Von Zeipel method and the two-variable expansion procedure

1966 ◽  
Vol 71 ◽  
pp. 878 ◽  
Author(s):  
J. Kevorkian
Keyword(s):  
Expansion Procedure

scholarly journals Three-dimensional Maxwellian extended Newtonian gravity and flat limit

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Patrick Concha ◽  
Lucrezia Ravera ◽  
Evelyn Rodríguez ◽  
Gustavo Rubio
Keyword(s):  
Cosmological Constant ◽  
Three Dimensional ◽  
Expansion Method ◽  
Gravity Models ◽  
Newtonian Gravity ◽  
Newtonian Theory ◽  
Relativistic Limit ◽  
Expansion Procedure ◽  
Three Space ◽  
Chern Simons

Abstract In the present work we find novel Newtonian gravity models in three space-time dimensions. We first present a Maxwellian version of the extended Newtonian gravity, which is obtained as the non-relativistic limit of a particular U(1)-enlargement of an enhanced Maxwell Chern-Simons gravity. We show that the extended Newtonian gravity appears as a particular sub-case. Then, the introduction of a cosmological constant to the Maxwellian extended Newtonian theory is also explored. To this purpose, we consider the non-relativistic limit of an enlarged symmetry. An alternative method to obtain our results is presented by applying the semigroup expansion method to the enhanced Nappi-Witten algebra. The advantages of considering the Lie algebra expansion procedure is also discussed.

Effect of radiative heat loss on steady hypersonic flow past a blunt body

1967 ◽  
Vol 29 (3) ◽  
pp. 485-494 ◽  
Author(s):  
M. I. G. Bloor
Keyword(s):  
Numerical Solution ◽  
Heat Loss ◽  
Blunt Body ◽  
Radiative Heat ◽  
Constant Density ◽  
Axially Symmetric ◽  
Radiative Heat Loss ◽  
Stagnation Region ◽  
Expansion Procedure ◽  
Axis Of Symmetry

Using the grey gas approximation, the effect of radiative heat loss on axially symmetric flows is studied. Using an expansion procedure about the axis of symmetry, a numerical solution for the stagnation region is found taking the shock to be spherical. The results of this calculation are compared with the results of Lighthill's non-radiative constant density solution.

Strength Loss in Composite Cylinders Under Impact

1988 ◽  
Vol 110 (2) ◽  
pp. 180-184 ◽  
Author(s):  
A. P. Christoforou ◽  
S. R. Swanson
Keyword(s):  
Composite Structures ◽  
Composite Plates ◽  
Strength Loss ◽  
Pressure Vessels ◽  
Fourier Series Expansion ◽  
Lateral Impact ◽  
Low Velocity ◽  
Expansion Procedure ◽  
The Impact ◽  
Composite Cylinders

The problem of strength loss in composite structures due to impact appears to be important due to the sensitivity of advanced composites to these loadings. Although a number of studies have been carried out on impact of flat composite plates, relatively little work has been done on tubular geometries such as pressure vessels despite the usage in applications. We have addressed the problem of calculating strength loss due to low velocity, lateral impact of composite cylinders. In our model we use an existing Fourier Series expansion procedure to calculate ply stresses and strains, compare these values with allowables to predict fiber breakage during the impact, and finally use fracture mechanics to predict the strength loss due to the impact. Although the model is quite simplified, the general trends of experiments appear to be represented.

A Systematic Asymptotic Expansion Procedure for Slender Ships

1964 ◽  
Vol 8 (03) ◽  
pp. 15-23 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Asymptotic Expansion ◽  
Boundary Conditions ◽  
Arbitrary Shape ◽  
Careful Consideration ◽  
Wave Resistance ◽  
Expansion Procedure ◽  
Systematic Solution ◽  
The Individual ◽  
Correct Boundary Conditions

Inner and outer expansions are used to formulate a systematic solution to the problem of the steady translation of a slender ship of arbitrary shape. Careful consideration is givien to finding the correct boundary conditions to be satisfied by successive terms in the expansions, and certain of the individual terms are determined partly or completely as functions of hull shape. Some results are given concerning the second approximations to the potential and wave resistance.

Developed Plate Expansion Using Geodesics

1984 ◽  
Vol 21 (04) ◽  
pp. 384-388
Author(s):  
John C. Clements
Keyword(s):  
Differential Equation ◽  
Numerical Quadrature ◽  
Developable Surface ◽  
Accuracy Control ◽  
Isometric Mapping ◽  
Variable Stepsize ◽  
Mapping Algorithm ◽  
Equation Solving ◽  
Expansion Procedure ◽  
The Relationship

This work is concerned with the application of a new isometric mapping algorithm to hull plate expansion procedures for ships with all or portions of the hull consisting of developable surfaces. The expansion procedure is based on the relationship between the ruling lines r⇀(s) generating the developable surface S⇀(s,t) and one additional geodesic g⇀(s) constructed within the surface as the solution of the differential equation det(g⇀'g⇀"n⇀) = 0 where n⇀ is the unit normal to S⇀ at g⇀. Precise accuracy control is achieved through the use of adaptive numerical quadrature and a variable stepsize differential equation solving routine.

Multiple Suture Synostosis and Increased Intracranial Pressure following Repair of Single Suture, Nonsyndromal Craniosynostosis

1998 ◽  
Vol 35 (2) ◽  
pp. 167-172 ◽  
Author(s):  
Roger J. Hudgins ◽  
Steven R. Cohen ◽  
Fernando D. Burstein ◽  
William R. Boydston
Keyword(s):  
Intracranial Pressure ◽  
Head Circumference ◽  
Cranial Sutures ◽  
Increased Intracranial Pressure ◽  
Common Multiple ◽  
Expansion Procedure ◽  
Delayed Closure ◽  
Single Suture ◽  
Less Common Multiple ◽  
Increased Icp

Objective Increased intracranial pressure, frequently associated with closure of multiple cranial sutures, has been reported to occur in 36% of cases following correction of syndromal craniosynostosis. Although much less common, multiple suture closure may occur following repair of single suture, non-syndromal craniosynostosis and we present cases that concern two such children. Results Two children with nonsyndromal craniosynostosis, one metopic and one left-coronal, underwent fronto-orbital advancement at age 3 months. At age 19 months and at age 5 years, respectively, both patients re-presented with headaches, decrease in head circumference percentile, and acceptable cosmetic outcome. Both had computerized tomographic evidence of multiple closed cranial sutures and increased intracranial pressure (ICP) (determined by monitoring). Both patients improved following a cranial expansion procedure. Conclusion Delayed closure of multiple sutures and resultant increased ICP may occur following correction of nonsyndromal, single suture craniosynos-tosis. This may be more likely when the initial suture is contiguous with the facial sutures. Children should be followed for many years following cranio-synostosis repair with cranial, neurologic, and possibly funduscopic examinations as well as head circumference measurements to detect delayed closure of cranial sutures.

The Scleral Expansion Procedure

2003 ◽  
pp. 219-235 ◽  
Author(s):  
Chris Phillips ◽  
Richard Yee
Keyword(s):  
Expansion Procedure

The retrieval of a surgical blade broken within the alveolar bone during minimally traumatic tooth extraction

2021 ◽  
Vol 14 (1) ◽  
pp. e240162
Author(s):  
Eldo Koshy ◽  
Lovely M Annamma ◽  
Biji Thomas George ◽  
Godfred Antony Menezes
Keyword(s):  
Dental Implant ◽  
Tooth Extraction ◽  
Alveolar Bone ◽  
Bone Destruction ◽  
Expansion Procedure ◽  
Bone Expansion ◽  
Scalpel Blade ◽  
Atraumatic Extraction ◽  
Tooth Removal

Minimally traumatic tooth removal is the norm for removing teeth when a dental implant is planned at that site. The quantity of available bone is the primary requisite to place an implant. The initial use of a scalpel blade to widen the periodontal space followed by the use of luxators is one of the techniques that is being followed for atraumatic extraction. A case of accidental breakage of a number 11 scalpel blade while attempting tooth removal and the method adopted in removing this portion of the blade without further bone destruction is reported here. The authors have not found any previously published cases, reporting the breakage of a scalpel blade during the bone expansion procedure and its management.

The effects of wall conductivity in magnetohydrodynamic duct flow at high Hartmann numbers

1971 ◽  
Vol 69 (2) ◽  
pp. 337-351 ◽  
Author(s):  
D. J. Temperley ◽  
L. Todd
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Applied Magnetic Field ◽  
Hartmann Number ◽  
Classical Model ◽  
Critical Discussion ◽  
Duct Flow ◽  
Rectangular Duct ◽  
Wall Conductivity ◽  
Expansion Procedure

AbstractLaminar motion of a conducting fluid in a rectangular duct is discussed. The applied magnetic field is uniform and parallel to one pair of sides of the duct. Classical theory is used and it is shown that the two successive limiting processes, lim (σwall → ∞; hσ wall → a finite, constant limit) and lim (M → ∞) are not always freely interchangeable; M being the Hartmann number, σwall the electrical conductivity of the duct wall and h the typical ratio of (wall thickness/duct width). A general expansion procedure for M ≫ 1, valid for all types of wall conductivities, is devised. A critical discussion of the deficiencies in the classical model is given.

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