The Ghost Solid Methods for the Solid-Solid Interface

Ph.DDOCTOR OF PHILOSOPH

A Moving Boundary Flux Stabilization Method for Cartesian Cut-Cell Grids using Directional Operator Splitting

An explicit moving boundary method for the numerical solution of time-dependent hyperbolic conservation laws on grids produced by the intersection of complex geometries with a regular Cartesian grid is presented. As it employs directional operator splitting, implementation of the scheme is rather straightforward. Extending the method for static walls from Klein et al., Phil. Trans. Roy. Soc., A367, no. 1907, 4559-4575 (2009), the scheme calculates fluxes needed for a conservative update of the near-wall cut-cells as linear combinations of standard fluxes from a one-dimensional extended stencil. Here the standard fluxes are those obtained without regard to the small sub-cell problem, and the linear combination weights involve detailed information regarding the cut-cell geometry. This linear combination of standard fluxes stabilizes the updates such that the time-step yielding marginal stability for arbitrarily small cut-cells is of the same order as that for regular cells. Moreover, it renders the approach compatible with a wide range of existing numerical flux-approximation methods. The scheme is extended here to time dependent rigid boundaries by reformulating the linear combination weights of the stabilizing flux stencil to account for the time dependence of cut-cell volume and interface area fractions. The two-dimensional tests discussed include advection in a channel oriented at an oblique angle to the Cartesian computational mesh, cylinders with circular and triangular cross-section passing through a stationary shock wave, a piston moving through an open-ended shock tube, and the flow around an oscillating NACA 0012 aerofoil profile.Comment: 30 pages, 27 figures, 3 table

Phase-lagged formulation of quantum mechanics : application to ultra-fast processes of energy and information transport

In this report, a brief history of quantum mechanics and the major attempts and developments in the early days of quantum mechanics is presented. It is addressed that the Schrodinger equation, the corner stone in quantum mechanics, gives rise to the paradox of instantaneous propagation of energy. It is underlined that the Schrodinger equation is not a relativistic formula. Major attempts to overcome the paradox and to make the formulation relativistic are addressed. It is discussed that, despite of all the attempts, no unique and general formulation which removes the paradox and gives relativistic results in all cases is ever proposed.MASTER OF ENGINEERING (MAE

The ghost solid method for the elastic solid-solid interface

10.1016/j.jcp.2013.09.042Journal of Computational Physics257PA102-125JCTP

Effekterna av alendronat, denosumab och teriparatid på frakturrisk och bentäthet hos postmenopausala kvinnor med osteoporos

Background Osteoporosis is a disease with reduced bone mass and deterioration of bone structure, which leads to increased risk of fractures (1.9). Approximately one in four men and one in two women will at some time in life suffer a fracture due to osteoporosis. Supplemental calcium and vitamin D have long been a cornerstone of osteoporosis treatment. Drugs that are also used clinically for the treatment of osteoporosis include bisphosphonates, denosumab, selective estrogen receptor modulators (SERM), and strontium (3). Bisphosphonates are the most used osteoporosis drugs (4). The bisphosphonates alendronate, risedronate and zoledronic acid are interchangeable as first choice treatment of osteoporosis in postmenopausal women. Denosumab is another drug with antiresorptive effects that has been registered for the treatment of postmenopausal osteoporosis in recent years. Teriparatide (PTH) is an anabolic drug used for osteoporosis (3.6). Objective: The objective of this study was to examine the efficacy of alendronate, denosumab and teriparatide on fracture risk and bone mineral density in postmenopausal women with osteoporosis with the help of published meta-analyses and clinical trials. Result: Examined articles showed that alendronate treatment for at least one year reduces the risk of vertebral fractures with NNT = 17-50 and the risk of non-vertebral fractures with NNT = 50. PTH reduced the risk of vertebral fractures with NNT = 9.8 and non-vertebral fractures with NNT = 29. A statistically significant increase in BMD was also observed with an increase in BMD of 8.14% in the spine and 2.48% in the hip. PTH treatment compared with alendronate treatment was found to have a statistically significant difference (P=0.004) in the reduction of non-vertebral fracture risk with NNT = 10,4. Teriparatid treatment also showed more positive effects as compared to alendronate on BMD increases. Denosumab treatment for 36 months reduced the risk of fractures with a relative reduction of 68% for vertebral fractures and a relative reduction of 20% for non-vertebral fractures. Denosumab treatment for 12 months compared with alendronate therapy in postmeopausala women showed no statistically significant difference in fracture risk (p=0,19). The increase in BMD was, however, greater in the denosumab group than in the alendronate group, with 0.53% in the distal radius, 1.14% in the hip , 0.77% in the lumbar spine and 0.79% in the femoral neck.   Conclusion: These studies show that all three drugs, alendronate, PTH and denosumab, have good effects on reducing the risk of fractures in postmenopausal women. All drugs lead to increases in BMD in different parts of the skeleton. Reduction of fracture risk was greater for both denosumab treatment and PTH treatment compared to alendronate treatment, also BMD increased more with denosumab or PTH treatment compared with alendronate treatment.Bakgrund Osteoporos är ett sjukdomstillstånd med reducerad benmassan och försämringar i benvävnadens struktur, som leder till att man lättare kan få benbrott. Ungefär var fjärde man och varannan kvinna drabbas någon gång i livet av en fraktur på grund av osteoporos. Tillägg av kalcium och vitamin D har länge varit en grundval inom osteoporosbehandlingen. Läkemedel som också används kliniskt för osteoporosbehandling inkluderar bisfosfonater, denosumab, selektiva östrogenreceptormodulatorer (SERM), samt strontiumsalt. Bisfosfonater är den mest använda gruppen av osteoporosläkemedel. Bisfosfonater som alendronate, risedronat och zoledronsyra vilka är utbytbara mot varandra räknas som förstahandsval i behandling av osteoporos hos postmenopausala kvinnor. Denosumab är ett annat osteoporosläkemedel med antiresorptiv effekt som registrerats för behandling av postmenopausal osteoporos de senaste åren. Teriparatid (PTH) är ett anabolt läkemedel som också används mot osteoporos. Syftet: Syftet med detta arbete var att med hjälp av publicerade meta-analyser och kliniska studier undersöka effekterna av alendronat, denosumab och teriparatid på frakturrisk och bentäthet hos postmenopausala kvinnor med osteoporos. Resultat: Granskade artiklar på postmenopausala kvinnor visar att alendronatbehandling under minst ett år minskar risken för vertebrala frakturer med NNT =17-50 och för icke-vertebrala frakturer med NNT=50. PTH minskade risken för vertebrala frakturer med NNT=9,8 och icke-vertebrala frakturer med NNT= 29. Statistiskt signifikant ökning i BMD förelåg också med 8.14% i ryggrad och 2,48% i höften. PTH behandling jämfört med alendronat visade en statistiskt signifikant skillnad (p=0.004) för minskning av icke-vertebrala frakturer med NNT=10,4. Teriparatidbehandling visade också mer positiva effekter jämfört med alendronat avseende ökningar i BMD. Denosumabbehandling i 36 månader minskade risken för frakturer med en relativ minskning på 68 % för vertebrala frakturer och en relativ minskning på 20% för icke-vertebrala frakturer. Denosumabbehandling under 12 månader jämfört med alendronatbehandling hos postmenopausala kvinnor gav ingen statistiskt signifikant skillnad (p =0.19) i frakturrisk. Ökning av BMD var dock större i denosumabgruppen än i alendronatgruppen, 0.53%  i distala radius, 1.14 % i höften, 0.77% i ländryggen  och 0.79% i lårbenhalsen. Slutsats: Studierna visade att alla tre undersökta läkemedel, alendronat, PTH och denosumab, har goda effekter på minskning av frakturrisk hos postmenopausala kvinnor. Samtliga läkemedel leder till ökning av BMD i olika delar av skelettet. Minskningen av frakturrisk var större för både denosumabbehandling och PTH-behandling jämfört med alendronat, även BMD ökade mer vid denosumab- eller PTH-behandling jämfört med alendronatbehandling

The ghost solid methods for the elastic–plastic solid–solid interface and the ϑ-criterion

Two variants of the Ghost Solid Method (GSM), namely the Original GSM (OGSM) and Modified GSM (MGSM), are proposed for the elastic–plastic solid–solid interactions in a Lagrangian framework. It is shown that the OGSM is highly problem related and can lead to large numerical errors under certain material combinations or in the presence of the wave propagation through the solid–solid interface. The ϑ-criterion, previously developed for the elastic–elastic solid–solid interactions [1], has been applied to the OGSM for the elastic–plastic interactions. It is shown that this criterion can successfully detect the onset of these large errors. Moreover, it is shown that it can be used to determine the reliability of the results obtained using the OGSM. The MGSM has been shown to be able to remove the large numerical errors that would normally arise due to the OGSM. Next, the extension of the two variants of the GSM, to two-dimensional settings, is presented for two idealized interface conditions, namely the no-slip condition, and the perfect-slip conditions. Numerous numerical experiments are provided attesting to the effectiveness and viability of the GSMs, for simulating wave propagation at the elastic–plastic solid–solid interface. The applicability of the ϑ-criterion is also studied in the numerical experiments