Maximum principle preserving high order schemes for convection-dominated diffusion equations

The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO scheme, and then propose a new parametrized MPP high order finite difference(FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains the third order accuracy without extra CFL constraint when the low order monotone flux is chosen appropriately. Numerical tests in both one and two dimensional cases are performed on the simulation of the incompressible Navier-Stokes equations in vorticity stream-function formulation and several other problems to show the effectiveness of the proposed method.

TYPE I INSULIN-LIKE GROWTH FACTOR RECEPTOR TYROSINE KINASE AS A MOLECULAR TARGET IN MANTLE CELL LYMPHOMA

Mantle cell lymphoma (MCL) is an aggressive B-cell lymphoid malignancy representing 5-10% of all non-Hodgkin’s lymphomas. It is distinguished by the t(11;14)(q13;q32) chromosomal translocation that juxtaposes the proto-oncogene CCND1, which encodes cyclin D1 at 11q13 to the IgH gene at 14q32. MCL patients represent about 6% of all new cases of Non-Hodgkin’s lymphomas per year or about 3,500 new cases per year. MCL occurs more frequently in older adults – the average age at diagnosis is the mid-60s with a male-to-female ratio of 2-3:1. It is typically characterized by the proliferation of neoplastic B-lymphocytes in the mantle zone of the lymph node follicle that have a prominent inclination to disseminate to other lymphoid tissues, bone marrow, peripheral blood and other organs. MCL patients have a poor prognosis because they develop resistance/relapse to current non-specific therapeutic regimens. It is of note that the exact molecular mechanisms underlying the pathogenesis of MCL are not completely known. It is reasonable to anticipate that better characterization of these mechanisms could lead to the development of specific and likely more effective therapeutics to treat this aggressive disease. The type I insulin-like growth factor receptor (IGF-IR) is thought to be a key player in several different solid malignancies such as those of the prostate, breast, lung, ovary, skin and soft tissue. In addition, recent studies in our lab showed evidence to support a pathogenic role of IGF-IR in some types of T-cell lymphomas and chronic myeloid leukemia. Constitutively active IGF-IR induces its oncogenic effects through the inhibition of apoptosis and induction of transformation, metastasis, and angiogenesis. Previous studies have shown that signaling through IGF-IR leads to the vi activation of multiple signaling transduction pathways mediated by the receptor-associated tyrosine kinase domain. These pathways include PI3K/Akt, MAP kinase, and Jak/Stat. In the present study, we tested the possible role of IGF-IR in MCL. Our results demonstrate that IGF-IR is over-expressed in mantle cell lymphoma cell lines compared with normal peripheral blood B- lymphocytes. Furthermore, inhibition of IGF-IR by the cyclolignan picropodophyllin (PPP) decreased cell viability and cell proliferation in addition to induction of apoptosis and G2/M cell cycle arrest. Screening of downstream oncogenes and apoptotic proteins that are involved in both IGF-IR and MCL signaling after treatment with PPP or IGF-IR siRNA showed significant alterations that are consistent with the cellular changes observed after PPP treatment. Therefore, our findings suggest that IGF-IR signaling contributes to the survival of MCL and thus may prove to be a legitimate therapeutic target in the future.

Magma Extraction from the Mantle Wedge at Convergent Margins Through Dikes: A Parametric Sensitivity Analysis

We address under what conditions a magma generated by partial melting at 100 km depth in the mantle wedge above a subduction zone can reach the crust in dikes before stalling. We also address under what conditions primitive basaltic magma (Mg # >60) can be delivered from this depth to the crust. We employ linear elastic fracture mechanics with magma solidification theory and perform a parametric sensitivity analysis. All dikes are initiated at a depth of 100 km in the thermal core of the wedge, and the Moho is fixed at 35 km depth. We consider a range of melt solidus temperatures (800-1100 degrees C), viscosities (10-100 Pa s), and densities (2400-2700 kg m(-3)). We also consider a range of host rock fracture toughness values (50-300 MPa m(1/2)) and dike lengths (2-5 km) and two thermal structures for the mantle wedge (1260 and 1400 degrees C at 100 km depth and 760 and 900 degrees C at 35 km depth). For the given parameter space, many dikes can reach the Moho in less than a few hundred hours, well within the time constraints provided by U series isotope disequilibria studies. Increasing the temperature in the mantle wedge, or increasing the dike length, allows additional dikes to propagate to the Moho. We conclude that some dikes with vertical lengths near their critical lengths and relatively high solidus temperatures will stall in the mantle before reaching the Moho, and these may be returned by corner flow to depths where they can melt under hydrous conditions. Thus, a chemical signature in arc lavas suggesting partial melting of slab basalts may be partly influenced by these recycled dikes. Alternatively, dikes with lengths well above their critical lengths can easily deliver primitive magmas to the crust, particularly if the mantle wedge is relatively hot. Dike transport remains a viable primary mechanism of magma ascent in convergent tectonic settings, but the potential for less rapid mechanisms making an important contribution increases as the mantle temperature at the Moho approaches the solidus temperature of the magma.

Thermal Convection in Ice Sheets: We Look But Do Not See

Thermal convection in the Antarctic and Greenland ice sheets has been dismissed on the grounds that radio-echo stratigraphy is undisturbed for long distances. However, the undisturbed stratigraphy lies, for the most part, above the density inversion in polar ice sheets and therefore does not disprove convection. An echo-free zone is widespread below the density inversion, yet nobody has cited this as a strong indication that convection is indeed present at d�pth. A generalized Rayleigh criterion for thermal convection in e1astic-viscoplastic polycrystalline solids heated from below is developed and applied to ice-sheet convection. An infinite Rayleigh number at the onset of primary creep decreases with time and becomes constant when secondary creep dominates, suggesting that any thermal buoyancy stress can initiate convection but convection cannot be sustained below a buoyancy stress of about 3 kPa. An analysis of the temperature profile down the Byrd Station core hole suggests that about 1000 m of ice below the density inversion will sustain convection. Creep along the Byrd Station strain network, radar sounding in East Antarctica, and seismic sounding in West Antarctica are examined for evidence of convective creep superimposed on advective creep. It is concluded that the evidence for convection is there, if we look for it with the intention offinding it.

Tertiary Minette and Melanephelinite Dikes, Wasatch Plateau, Utah - Records of Mantle Heterogeneities and Changing Tectonics

A swarm of minette and melanephelinite dikes is exposed over 2500 km2 in and near the Wasatch Plateau, central Utah, along the western margin of the Colorado Plateaus in the transition zone with the Basin and Range province. To date, 110 vertical dikes in 25 dike sets have been recognized. Strikes shift from about N80-degrees-W for 24 Ma dikes, to about N60-degrees-W for 18 Ma, to due north for 8-7 m.y. These orientations are consistent with a shift from east-west Oligocene compression associated with subduction to east-west late Miocene crustal extension. Minettes are the most common rock type; mica-rich minette and mica-bearing melanephelinite occurs in 24 Ma dikes, whereas more ordinary minette is found in 8-7 Ma dikes. One melanephelinite dike is 18 Ma. These mafic alkaline rocks are transitional to one another in modal and major element composition but have distinctive trace element patterns and isotopic compositions; they appear to have crystallized from primitive magmas. Major, trace element, and Nd-Sr isotopic data indicate that melanephelinite, which has similarities to ocean island basalt, was derived from small degree melts of mantle with a chondritic Sm/Nd ratio probably located in the asthenosphere, but it is difficult to rule out a lithospheric source. In contrast, mica-bearing rocks (mica melanephelinite and both types of minette) are more potassic and have trace element patterns with strong Nb-Ta depletions and Sr-Nd isotopic compositions caused by involvement with a component from heterogeneously enriched lithospheric mantle with long-term enrichment of Rb or light rare earth elements (REE) (epsilon Nd as low as - 15 in minette). Light REE enrichment must have occurred anciently in the mid-Proterozoic when the lithosphere was formed and is not a result of Cenozoic subduction processes. After about 25 Ma, foundering of the subducting Farallon plate may have triggered upwelling of warm asthenospheric mantle to the base of the lithosphere. Melanephelinite magma may have separated from the asthenosphere and, while rising through the lithosphere, provided heat for lithospheric magma generation. Varying degrees of interaction between melanephelinite and small potassic melt fractions derived from the lithospheric mantle can explain the gradational character of the melanephelinite to minette suite.

Thermal Convection and the Origin of Ice Streams

Ice streams are a fact of ice-sheet dynamics, draining up to 90% of the ice. Thermal convection in ice below the density inversion is a speculation. An attempt is made to meld the two in such a way that the speculation becomes an explanation for the fact.

Zevalin and BEAM (Z-BEAM) versus rituximab and BEAM (R-BEAM) conditioning chemotherapy prior to autologous stem cell transplantation in patients with mantle cell lymphoma.

Early relapse is common in patients with mantle cell lymphoma (MCL) highlighting the unmet need for further improvement of therapeutic options for these patients. CD20 inhibition combined with induction chemotherapy as well as consolidation with high-dose chemotherapy (HDCT) is increasingly considered cornerstones within current therapy algorithms of MCL whereas the role of radioimmunotherapy is unclear. This retrospective single center study compared 46 consecutive MCL patients receiving HDCT in first or second remission. Thirty-five patients had rituximab and BEAM (R-BEAM), and 11 patients received ibritumomab tiuxetan (Zevalin®), an Yttrium-90 labeled CD20 targeting antibody, prior to BEAM (Z-BEAM) followed by autologous stem cell transplantation (ASCT). We observed that the 5-year overall survival (OS) in the R-BEAM and Z-BEAM groups was 55% and 71% (p = 0.288), and the 4-year progression free survival (PFS) was 32% and 41%, respectively (p = 0.300). There were no treatment related deaths in both groups, and we observed no differences in toxicities, infection rates or engraftment. Our data suggest that the Z-BEAM conditioning regimen followed by ASCT is well tolerated, but was not associated with significantly improved survival compared to R-BEAM. Copyright © 2015 John Wiley & Sons, Ltd.