Discrete artificial boundary conditions for nonlinear Schrödinger equations

In this work we construct and analyze discrete artificial boundary conditions (ABCs) for different finite difference schemes to solve nonlinear Schrödinger equations. These new discrete boundary conditions are motivated by the continuous ABCs recently obtained by the potential strategy of Szeftel. Since these new nonlinear ABCs are based on the discrete ABCs for the linear problem we first review the well-known results for the linear Schrödinger equation. We present our approach for a couple of finite difference schemes, including the Crank-Nicholson scheme, the Duran-Sanz-Serna scheme, the DuFort-Frankel method and several split-step (fractional step) methods such as the Lie splitting, the Strang splitting and the relaxation scheme of Besse. Finally, several numerical tests illustrate the accuracy and stability of our new discrete approach for the considered finite difference schemes

Discrete transparent boundary conditions for the mixed KDV-BBM equation

International audienceIn this paper, we consider artificial boundary conditions for the linearized mixed Korteweg-de Vries (KDV) Benjamin-Bona-Mahoney (BBM) equation which models water waves in the small amplitude, large wavelength regime. Continuous (respectively discrete) artificial boundary conditions involve non local operators in time which in turn requires to compute time convolutions and invert the Laplace transform of an analytic function (respectively the Z-transform of an holomor-phic function). In this paper, we propose a new, stable and fairly general strategy to carry out this crucial step in the design of transparent boundary conditions. For large time simulations, we also introduce a methodology based on the asymptotic expansion of coefficients involved in exact direct transparent boundary conditions. We illustrate the accuracy of our methods for Gaussian and wave packets initial data

Combined antitumor effects of bee venom and cisplatin on human cervical and laryngeal carcinoma cells and their drug resistant sublines

In the present study, we investigated the possible combined anticancer ability of bee venom (BV) and cisplatin towards two pairs of tumour cell lines: parental cervical carcinoma HeLa cells and their cisplatin-resistant HeLa CK subline, as well as laryngeal carcinoma HEp-2 cells and their cisplatin-resistant CK2 subline. Additionally, we identified several peptides of BV in the BV sample used in the course of the study and determined the exact concentration of MEL. BV applied alone in concentrations of 30 to 60 μg ml-1 displayed dose-dependent cytotoxicity against all cell lines tested. Cisplatin-resistant cervical carcinoma cells were more sensitive to BV than their parental cell lines (IC50 values were 52.50 μg ml-1 for HeLa vs. 47.64 μg ml-1 for HeLa CK cells), whereas opposite results were obtained for cisplatin-resistant laryngeal carcinoma cells (IC50 values were 51.98 μg ml-1 for HEp-2 vs. > 60.00 μg ml-1 for CK2 cells). Treatment with BV alone induced a necrotic type of cell death, as shown by characteristic morphological features, fast staining with ethidium-bromide and a lack of cleavage of apoptotic marker poly (ADP-ribose) polymerase (PARP) on Western blot. Combined treatment of BV and cisplatin induced an additive and/or weak synergistic effect towards tested cell lines, suggesting that BV could enhance the killing effect of selected cells when combined with cisplatin. Therefore, a greater anticancer effect could be triggered if BV was used in the course of chemotherapy. Our results suggest that combined treatment with BV could be useful from the point of minimizing the cisplatin concentration during chemotherapy, consequently reducing and/or postponing the development of cisplatin resistance

Altered localisation of the copper efflux transporters ATP7A and ATP7B associated with cisplatin resistance in human ovarian carcinoma cells

Metals in Catalysis, Biomimetics & Inorganic Material

MicroRNA-31 Regulates Chemosensitivity in Malignant Pleural Mesothelioma

YesMalignant pleural mesothelioma (MPM) is associated with an extremely poor prognosis, and most patients initially are or rapidly become unresponsive to platinum-based chemotherapy. MicroRNA-31 (miR-31) is encoded on a genomic fragile site, 9p21.3, which is reportedly lost in many MPM tumors. Based on previous findings in a variety of other cancers, we hypothesized that miR-31 alters chemosensitivity and that miR-31 reconstitution may influence sensitivity to chemotherapeutics in MPM. Reintroduction of miR-31 into miR-31 null NCI-H2452 cells significantly enhanced clonogenic resistance to cisplatin and carboplatin. Although miR-31 re-expression increased chemoresistance, paradoxically, a higher relative intracellular accumulation of platinum was detected. This was coupled to a significantly decreased intranuclear concentration of platinum. Linked with a downregulation of OCT1, a bipotential transcriptional regulator with multiple miR-31 target binding sites, we subsequently identified an indirect miR-31-mediated upregulation of ABCB9, a transporter associated with drug accumulation in lysosomes, and increased uptake of platinum to lysosomes. However, when overexpressed directly, ABCB9 promoted cellular chemosensitivity, suggesting that miR-31 promotes chemoresistance largely via an ABCB9-independent mechanism. Overall, our data suggest that miR-31 loss from MPM tumors promotes chemosensitivity and may be prognostically beneficial in the context of therapeutic sensitivity

Cisplatin resistance in non-small cell lung cancer cells is associated with an abrogation of cisplatin-induced G2/M cell cycle arrest

The efficacy of cisplatin-based chemotherapy in cancer is limited by the occurrence of innate and acquired drug resistance. In order to better understand the mechanisms underlying acquired cisplatin resistance, we have compared the adenocarcinoma-derived non-small cell lung cancer (NSCLC) cell line A549 and its cisplatin-resistant sub-line A549rCDDP2000 with regard to cisplatin resistance mechanisms including cellular platinum accumulation, DNA-adduct formation, cell cycle alterations, apoptosis induction and activation of key players of DNA damage response. In A549rCDDP2000 cells, a cisplatin-induced G2/M cell cycle arrest was lacking and apoptosis was reduced compared to A549 cells, although equitoxic cisplatin concentrations resulted in comparable platinum-DNA adduct levels. These differences were accompanied by changes in the expression of proteins involved in DNA damage response. In A549 cells, cisplatin exposure led to a significantly higher expression of genes coding for proteins mediating G2/M arrest and apoptosis (mouse double minute 2 homolog (MDM2), xeroderma pigmentosum complementation group C (XPC), stress inducible protein (SIP) and p21) compared to resistant cells. This was underlined by significantly higher protein levels of phosphorylated Ataxia telangiectasia mutated (pAtm) and p53 in A549 cells compared to their respective untreated control. The results were compiled in a preliminary model of resistance-associated signaling alterations. In conclusion, these findings suggest that acquired resistance of NSCLC cells against cisplatin is the consequence of altered signaling leading to reduced G2/M cell cycle arrest and apoptosis

Diskrete transparente Randbedingungen für Evolutionsgleichungen

Die vorliegende Doktorarbeit befasst sich mit der Herleitung und Implementierung von diskreten transparenten Randbedingungen für Systeme von Evolutionsgleichungen. Transparente Randbedingungen (TRBen) sind spezielle künstliche Randbedingungen, durch die die Lösung der Gleichung auf beschränktem und mit TRBen versehenem Gebiet mit der exakten Lösung des Ganzraumproblems (auf diesem beschränkten Gebiet) übereinstimmt. Die Differentialgleichungen werden durch ein Finite-Differenzen-Verfahren (theta-Schema) diskretisiert. Für die entstandene diskrete Gleichung werden diskrete transparente Randbedingungen (DTRBen) hergeleitet, wodurch die DTRBen besonders gut an das numerische Verfahren angepasst sind. Für skalare Gleichungen sind diese DTRBen bereits länger bekannt und man weiß, dass im Gegensatz zur ad-hoc Diskretisierung der analytischen TRBen Stabilitätsprobleme und künstliche Reflektionen am Rand vermieden werden können. Wir werden uns hier mit Systemen von Differentialgleichungen (parabolisch und Schrödinger Typ) befassen. Für diese Systeme ist der Ansatz der DTRBen gänzlich neu und wirft zusätzliche Probleme auf, die für skalare Gleichungen nicht auftreten. Nachdem wir uns eingehend mit den TRBen und DTRBen für schwach gekoppelte Systeme von parabolischen Differentialgleichungen beschäftigt haben, die das Verhalten von fluiden stochastischen Petri-Netzen beschreiben, verallgemeinern wir unser Vorgehen auf ein beliebiges lineares parabolisches System. Im Anschluss daran betrachten wir ein System von Schrödinger-Gleichungen, wie es z.B. in der Halbleiterphysik als sogenannte k·p-Schrödinger Gleichung der Quantenmechanik auftritt. Die angeführten numerischen Beispiele zeigen, dass sowohl für parabolische als auch für Systeme von Schrödinger Gleichungen die DTRBen nur sehr kleine Fehler verursachen.This dissertation is concerned with the derivation and implementation of discrete transparent boundary conditions for systems of evolution equations. Transparent boundary conditions (TBCs) are a special kind of artificial boundary conditions, that are constructed in such a way, that the solution on a bounded domain with TBCs is equal to the solution of the whole-space problem restricted to the bounded (computational) domain. The partial differential equations are discretised by finite differences (theta-scheme) and discrete transparent boundary conditions (DTBCs) are constructed for the discrete equation. Therefore, the DTBCs are well adapted to the numerical scheme. For scalar equations these DTBCs are well established. Compared to discretising the analytical TBC, in the scalar case it is known that these DTBCs have the advantage, not to destroy the stability properties of the underlying discrete scheme and to avoid any numerical reflections. In this dissertation we will deal with systems of partial differ ential equations (parabolic and Schrödinger type). For these systems the approach of DTBCs is completely new and involves additional problems not encountered in the scalar case. Since the numerical computation of these DTBCs is very costly, we give an approximation which greatly reduces the effort. After a concise construction of the TBCs and DTBCs for the weakly coupled system of parabolic equations arising from the mathematical description of fluid stochastic Petri nets, we proceed to extend the results to a system of general parabolic equations. Finally we will consider DTBCs for a system of Schrödinger-type equations, which arise e.g. in the physics of layered semiconductor devices as the so called k·p-Schrödinger equation of quantum mechanics. For both kinds of systems we will give numerical examples, which show the very small error caused by the DTBC

Fast Calculation of Energy and Mass preserving solutions of Schrödinger-Poisson systems on unbounded domains

This paper deals with the numerical solution of the time–dependent Schrödinger–Poisson system in the spherically symmetric case. Since the problem is posed on an unbounded domain one has to introduce artificial boundary conditions to confine the computational domain. The main topic of this work is the construction of a so–called discrete transparent boundary condition (TBC) for a Crank–Nicolsontype predictor–corrector scheme for solving the Schrödinger–Poisson system. This scheme has the property of mass and energy conservation exactly on the discrete level. We propose different strategies for the discrete TBC and present an efficient implementation. Finally, a numerical example illustrate the findings and shows the comparison results between the different approaches