2,289 research outputs found
When is a Stokes line not a Stokes line?
No full textDuring the course of a Stokes phenomenon, an asymptotic expansion can change its form as a further series, prefactored by an exponentially small term and a Stokes multiplier, appears in the representation. The initially exponentially small contribution may nevertheless grow to dominate the behaviour for other values of the asymptotic or associated parameters.We introduce the concept of a higher order Stokes phenomenon, at which a Stokes multiplier itself can change value. We show that the higher order Stokes phenomenon can be used to explain the apparent sudden birth of Stokes lines at regular points, why some Stokes lines are irrelevant to a given problem and why it is indispensible to the proper derivation of expansions that involve three or more possible asymptotic contributions. We provide an example of how the higher order Stokes phenomenon can have important effects on the large time behaviour of linear partial differential equations.Subsequently we apply these techniques to Burgers equation, a non-linear partial differential equation developed to model turbulent fluid flow. We find that the higher order Stokes phenomenon plays a major, yet very subtle role in the smoothed shock wave formation of this equation
Biography of Mary Jane Oliver
No full textTypescript of a sketch biography about Mary Jane (Oliver) Barlow, who came came from England around 1851 and with her husband, Oswald Barlow, helped to settle Saint George. Author unknown, but copied on January 13, 1937 by Virginia M. Lee of the Federal Writers Project, WPA, at Ogden, Uta
Percutaneous suction and irrigation for the treatment of recalcitrant pyogenic spondylodiscitis
No full textAbstract Background The primary management of pyogenic spondylodiscitis is conservative. Once the causative organism has been identified, by blood culture or biopsy, administration of appropriate intravenous antibiotics is started. Occasionally patients do not respond to antibiotics and surgical irrigation and debridement is needed. The treatment of these cases is challenging and controversial. Furthermore, many affected patients have significant comorbidities often precluding more extensive surgical intervention. The aim of this study is to describe early results of a novel, minimally invasive percutaneous technique for disc irrigation and debridement in pyogenic spondylodiscitis. Materials and methods A series of 10 consecutive patients diagnosed with pyogenic spondylodiscitis received percutaneous disc irrigation and debridement. The procedure was performed by inserting two Jamshidi needles percutaneously into the disc space. Indications for surgery were poor response to antibiotic therapy (8 patients) and the need for more extensive biopsy (2 patients). Pre- and postoperative white blood cell count (WBC), C-reactive protein (CRP), erythrocyte sedimentation rate (ESR), Oswestry disability index (ODI), and visual analogue score (VAS) for back pain were collected. Minimum follow-up was 18 months, with regular interval assessments. Results There were 7 males and 3 females with a mean age of 67 years. The mean WBC before surgery was 14.63 × 109/L (10.9–26.4) and dropped to 7.48 × 109/L (5.6–9.8) after surgery. The mean preoperative CRP was 188 mg/L (111–250) and decreased to 13.83 mg/L (5–21) after surgery. Similar improvements were seen with ESR. All patients reported significant improvements in ODI and VAS scores after surgery. The average hospital stay after surgery was 8.17 days. All patients had resolution of the infection, and there were no complications associated with the procedure. Conclusions Our study confirms the feasibility and safety of our percutaneous technique for irrigation and debridement of pyogenic spondylodiscitis. Percutaneous irrigation and suction offers a truly minimally invasive option for managing recalcitrant spondylodiscitis or for diagnostic purposes. The approach used is very similar to discography and can be easily adapted to different hospital settings. Level of Evidence Level II
Socially Engaged: The Author\u27s Guide to Social Media
No full textToday\u27s successful author needs a strong online presence, but how do you choose which social media platforms work best for your books while building your readership?
Marketing professor Tyra Burton and international bestselling author Jana Oliver tackle tough Social Media questions with real-world examples and insights to help you build your brand and expand your fanbase.https://digitalcommons.kennesaw.edu/facbooks2014/1009/thumbnail.jp
Discontinuous Galerkin methods for computational aerodynamics - 3D adaptive flow simulation with the DLR PADGE code
No full textOver the last years, the discontinuous Galerkin method (DGM) has demonstrated its excellence in accurate, high-order numerical simulations for a wide range of applications in computational physics. However, the development of practical, computationally efficient flow solvers for industrial applications is still in the focus of active research. This paper deals with solving the Navier-Stokes equations describing the motion of three-dimensional, viscous compressible fluids. We present details of the PADGE code under development at the German Aerospace Center (DLR) that is aimed at large-scale applications in aerospace engineering. The discussion covers several advanced aspects like the solution of the Reynolds-averaged Navier-Stokes and k-ω turbulence model equations, a curved boundary representation, anisotropic mesh adaptation for reducing output error and techniques for solving the nonlinear algebraic equations. The performance of the solver is assessed for a set of test cases
First evidence of marine turtle gastroliths in a fossil specimen: Paleobiological implications in comparison to modern analogues
No full textSemi-articulated remains of a large chelonioid turtle from the Turonian strata (Upper Cretaceous; ca. 93.9–89.8 Myr) near Sant’Anna d’Alfaedo (Verona province, northeastern Italy) are described for the first time. Together with the skeletal elements, the specimen also preserves pebbles inside the thoracic area which are lithologically distinct from the surrounding matrix. These allochthonous clasts are here interpreted as geo-gastroliths, in-life ingested stones that resided in the digestive tract of the animal. This interpretation marks the first reported evidence of geophagy in a fossil marine turtle. SEM-EDS analysis, together with macroscopic petrological characterization, confirm the presence of both siliceous and carbonatic pebbles. These putative geo-gastroliths have morphometries and size ranges more similar to those of gastroliths in different taxa (fossils and extant) than allochthonous “drop-stone” clasts from the same deposit that were carried by floating vegetation A dense pitted pattern of superficial erosion is microscopically recognizable on the carbonatic gastroliths, consistent with surface etching due to gastric acids. The occurrence of a similar pattern was demonstrated by the experimental etching of carbonatic pebbles with synthetic gastric juice. Gut contents of modern green sea turtles (Chelonia mydas) were surveyed for substrate ingestion, providing direct evidence of geophagic behavior in extant chelonioids. Comparison with modern turtle dietary habits may suggests that the pebbles were ingested as a way to supplement calcium after or in preparation for egg deposition, implying that the studied specimen was possibly a gravid female
Oliver C. Hampton and other Shaker teacher-musicians of Ohio and Kentucky
No full textThe purpose of this study is to present an example of a Shaker teacher-musician whose thinking and activities exemplified those Shakers living in the "western" Shaker societies of Ohio and-Kentucky. Oliver C. Hampton is that person. Hampton was a teacher, musician, composer, poet, writer of prose, elder, and trustee of the Union Village, Whitewater, and North Union, Ohio societies. Historians do not rank Hampton and his several teacher-musician friends as highly as other, better-known Shaker leaders. Nevertheless, Hampton and his colleagues contributed much to the betterment of their fellow Shakers' lives through their considerable efforts.Chapter Two gives the reader a brief historical background to enable him better to understand the beginnings of this unique religious movement.Chapter.Three deals with Shaker attitudes on religion, education, and music. The philosophy of these facets of Shaker life are explored because these attitudes affected everything the Shakers did.Chapter Four gives details of the life of Oliver C. Hampton. His personality is set forth. His responsibilities as elder, teacher, and musician are discussed. Thirty examples of Oliver Hampton's hymns and laboring songs are briefly analyzed from the singer's perspective.Chapter Five discusses Susanna M. Brady, the Rupes, and other musicians and teachers of the Ohio and Kentucky societies.Chapter Six gives a brief summary of the contributions of Oliver Hampton and his friends in the Ohio and Kentucky Shaker societies.Appendices further illustrate the musical, poetic, and prose efforts of Hampton, the Rupes, Brady, and others. Appendix A lists all Shaker teachers and musicians found by the writer. Appendix B is an article by Hampton as published in The Shaker. Appendix C contains the thirty musical examples of Hampton as copied from the originals and then transcribed by the author. Appendix D lists the musical examples contained in the paper and where they may be found. Appendix E contains music attributed to the Rupes and Brady. Appendix F is a set of three photographs, including one of Hampton.Thesis (D.A.
Numerical Analysis of Higher Order Discontinuous Galerkin Finite Element Methods
No full textAfter the introduction in Section 1 this lecture starts off with
recalling well-known results from the numerical analysis of the
continuous finite element methods. In particular, we recall a
priori error estimates in the energy norm and the
L2-norm including their proofs for higher order standard
finite element methods of Poisson's equation in Section 2 and for the
standard and the streamline diffusion finite element method of the
linear advection equation in Section 3.
We then introduce the discontinuous Galerkin discretization of the
linear advection equation in Section 4. Following
[Brezzi-Marini-Süli-2004] we consider two numerical flux
functions, the mean-value flux and the upwind flux, and derive the
corresponding a priori error estimates. Whereas the standard
Galerkin discretization of the linear advection equation is unstable
and requires e.g. streamline diffusion for stabilization, we will see
in Section 4 that the discontinuous Galerkin discretization of the
linear advection based on upwind is stable without addition of
streamline diffusion.
Then in Section 5, we follow [Arnold-Brezzi-Cockburn-Marini-2002] and
derive and analyze a variety of discontinuous Galerkin discretizations
of Poisson's equations. In particular, we derive the symmetric and
non-symmetric interior penalty Galerkin method (SIPG and NIPG), the
method of Baumann-Oden (BO) and the first and second method of Bassi
and Rebay (BR1 and BR2). The analysis of the methods includes the
consistency and adjoint consistency of the schemes, continuity and
coercivity of the respective bilinear forms and a priori
error estimates for the interior penalty methods. In particular, we
will see that the adjoint consistent SIPG scheme is of optimal order
in the L2-norm whereas the adjoint inconsistent NIPG scheme
is not.
Motivated by the connection of adjoint consistency of DG
discretizations to the availability of optimal order error estimates
in the L2-norm we concentrate on the adjoint consistency
property in Section 6. In particular, here we follow [Hartmann-2007]
and give a general framework for analyzing the consistency and adjoint
consistency of DG discretizations for linear problems with
inhomogeneous boundary conditions. This includes the derivation of
continuous adjoint problems associated to specific target quantities,
the derivation of primal and adjoint residual forms of the
discretizations and the discussion whether the discretizations in
combination with specific target quantities J(.) are adjoint
consistent or not. This analysis is performed in Sections 6.3 and 6.4
for the interior penalty DG discretization of the Dirichlet-Neumann
boundary value problem of Poisson's equations and for the upwind DG
discretization of the linear advection equation, respectively.
Then in Section 7 the previously shown properties and estimates for
the interior penalty and the upwind DG discretization are used to
derive a priori estimates for the error measured in terms of
target quantities J(.). Here again, we will see that a discretization
must be consistent and adjoint consistent in order to provide optimal
error estimates in J(.).
This lecture is finalized with the Sections 8 and 9 which introduce
the DG discretizations of the compressible Euler and Navier-Stokes
equations. Additionally, the consistency and adjoint consistency
analysis which has been introduced in Section 6 for linear problems is
now generalized to nonlinear problems in Section 8.5. This analysis is
performed for the compressible Euler and Navier-Stokes equations in
Sections 8.6 and 9.3, respectively. This includes the derivation of an
adjoint consistent discretization of boundary conditions and of target
functionals. Here particular emphasis is placed on the aerodynamic
force coefficients like the drag, lift and moment coefficients.
Various examples in Sections 5.6, 7.3, 8.7 and 9.4 illustrate the
numerical methods described.
In particular, the contents of this lecture is given as follows
1) Introduction
1.1) Higher order discretization methods
1.2) Discontinuous Galerkin discretizations
1.3) Numerical analysis of finite element methods
1.4) Outline
2) Higher order continuous FE methods for Poisson's equation
2.1) Poisson's equation
2.1.1) The homogeneous Dirichlet problem
2.1.2) The inhomogeneous Dirichlet problem
2.1.3) The Neumann problem
2.2) The standard finite element method for Poisson's equation
2.2.1) Consistency
2.2.2) Existence and uniqueness of discrete solutions
2.2.3) Best approximation property
2.2.4) Interpolation estimates
2.2.5) A priori error estimates in the H1- and L2-norm
3) Higher order continuous FE methods for the linear advection equation
3.1) The linear advection equation
3.1.1) Variational formulation with strong boundary conditions
3.1.2) Variational formulation with weak boundary conditions
3.2) The standard Galerkin method with weak boundary conditions
3.3) The streamline diffusion method with weak boundary conditions
4) Higher order DG discretizations of the linear advection equation
4.1) Mesh related function spaces
4.2) A variational formulation of the linear advection equation
4.3) Consistency, conservation property, coercivity and stability
4.4) The discontinuous Galerkin discretization
4.5) The local L2-projection and approximation estimates
4.6) A priori error estimates
4.7) The discontinuous Galerkin discretization based on upwind
4.7.1) The importance of the inter-element jump terms
4.7.2) The global and local conservation property
4.7.3) Consistency
5) Higher order DG discretizations of Poisson's equation
5.1) The system and primal flux formulation
5.2) The DG discretization: Consistency and adjoint consistency
5.3) Derivation of various DG discretization methods
5.3.1) The SIPG and NIPG methods and the method of Baumann-Oden
5.3.2) The original DG discretization of Bassi and Rebay (BR1)
5.3.3) The modified DG discretization of Bassi and Rebay (BR2)
5.4) Consistency, adjoint consistency, continuity and coercivity
5.5) A priori error estimates
5.6) Numerical results
6) Consistency and adjoint consistency for linear problems
6.1) Definition of consistency and adjoint consistency
6.2) The consistency and adjoint consistency analysis
6.3) Adjoint consistency analysis of the IP discretization
6.3.1) The continuous adjoint problem to Poisson's equation
6.3.2) Primal residual form of the interior penalty DG discretization
6.3.3) Adjoint residual form of the interior penalty DG discretization
6.4) Adjoint consistency analysis of the upwind DG discretization
6.4.1) The continuous adjoint problem to the linear advection equation
6.4.2) Primal residual form of the DG discretization based on upwind
6.4.3) Adjoint residual form of the DG discretization based on upwind
7) A priori error estimates for target functionals J(.)
7.1) Upwind DG of the linear advection equation: Estimates in J(.)
7.2) IP DG discretization for Poisson's equation: Estimates in J(.)
7.3) Numerical results
8) Discontinuous Galerkin discretizations of the compressible Euler equations
8.1) Hyperbolic conservation equations
8.2) The compressible Euler equations
8.3) The DG discretization of the compressible Euler equations
8.4) Boundary conditions
8.5) Consistency and adjoint consistency for nonlinear problems
8.5.1) The consistency and adjoint consistency analysis
8.6) Adjoint consistency analysis of DG for the compressible Euler equations
8.6.1) The continuous adjoint problem to the compressible Euler equations
8.6.2) Primal residual form of DG for the compressible Euler equations
8.6.3) Adjoint residual form of DG for the compressible Euler equations
8.7) Numerical results
9) DG discretizations of the compressible Navier-Stokes equations
9.1) The compressible Navier-Stokes equations
9.2) DG discretizations of the compressible Navier-Stokes equations
9.3) Adjoint consistency analysis of DG for the compressible Navier-Stokes equations
9.3.1) The continuous adjoint problem to the compressible NS equations
9.3.2) Primal residual form of DG for the compressible NS equations
9.3.3) Adjoint residual form of DG for the compressible NS equations
9.4) Numerical results
Acknowledgements
Bibliograph
Answer to the Letter to the Editor of L. Denteneer et al. concerning “Do we have the right PROMs for measuring outcomes in lumbar spinal surgery?” by O.M. Stokes et al., Eur Spine J (2017) 26:816–824
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