Nonlinear surface waves on the plasma-vacuum interface

In this paper we study the propagation of weakly nonlinear surface waves on a plasma-vacuum interface. In the plasma region we consider the equations of incompressible magnetohydrodynamics, while in vacuum the magnetic and electric fields are governed by the Maxwell equations. A surface wave propagate along the plasma-vacuum interface, when it is linearly weakly stable. Following the approach of Ali and Hunter, we measure the amplitude of the surface wave by the normalized displacement of the interface in a reference frame moving with the linearized phase velocity of the wave, and obtain that it satisfies an asymptotic nonlocal, Hamiltonian evolution equation. We show the local-in-time existence of smooth solutions to the Cauchy problem for the amplitude equation in noncanonical variables, and we derive a blow up criterion.Comment: arXiv admin note: text overlap with arXiv:1305.5327 by other author

On the amplitude equation of approximate surfacewaves on the plasma-vacuum interface

In this paper we present a recent result about the propagation of weakly nonlinear surface waves on a plasma-vacuum interface. In the plasma region we consider the equations of incompressible magnetohydrodynamics, while in vacuum the magnetic and electric fields are governed by the Maxwell equations. A surface wave propagate along the plasma-vacuum interface, when it is linearly weakly stable. Following the approach of Alì and Hunter, we measure the amplitude of the surface wave by the normalized displacement of the interface in a reference frame moving with the linearized phase velocity of the wave, and obtain that it satisfies an asymptotic nonlocal, Hamiltonian evolution equation with quadratic nonlinearity. We show the local-in-time existence of smooth solutions to the Cauchy problem for the amplitude equation in noncanonical variables, and we derive the regularity of the first order corrections of the asymptotic expansion

Response to erlotinib in a patient with lung adenocarcinoma harbouring the EML4-ALK translocation: A case report.

Lung cancer is the leading cause of cancer-associated mortality worldwide, and the mainstay of treatment remains to be personalised therapy. Tyrosine kinase inhibitors of the epidermal growth factor receptor (EGFR-TKIs) have been reported to exert a significant impact in the treatment of non-small cell lung cancer (NSCLC), particularly in patients harbouring mutations in the EGFR gene. The echinoderm microtubule-associated protein-like 4-anaplastic lymphoma kinase (EML4-ALK) gene translocation has been described in a subset of patients with NSCLC and possesses potent oncogenic activity. This translocation represents one of the most novel molecular targets in the treatment of NSCLC. Patients who harbour the EML4-ALK rearrangement possess lung tumours that lack EGFR or K-ras mutations. The present study reports the case of a patient possessing the EML4-ALK rearrangement that was initially treated with erlotinib and achieved a lasting clinical response. To the best of our knowledge, the current study is the first report of a clinical response to EGFR-TKI in a patient with lung adenocarcinoma harbouring the EML4-ALK fusion gene, but no EGFR mutations. However, as the disease progressed, the ALK gene status of the tumour was investigated, and based upon a positive result, the patient was treated with crizotinib and achieved a complete response. In conclusion, the present study suggests that the EML4-ALK rearrangement is not always associated with resistance to EGFR-TKIs. Further studies are required to clarify the biological features of these tumours and to investigate the mechanisms underlying the primary resistance to EGFR-TKIs when the EML4-ALK rearrangement is present

Let-7g and miR-21 expression in non-small cell lung cancer: correlation with clinicopathological and molecular features

MicroRNAs (miRNAs) play a key role in cancer pathogenesis and are involved in several human cancers, including non-small cell lung cancer (NSCLC). This study evaluated Let-7g and miR-21 expression by quantitative real-time PCR in 80 NSCLC patients and correlated the results with their main clinicopathological and molecular features. MiR-21 expression was significantly higher in NSCLC tissues compared to non-cancer lung tissues (p<0.0001), while no significant changes in Let-7g expression were observed between the tumor and normal lung tissues. Target prediction analysis led to the identification of 26 miR-21 and 24 Let-7g putative target genes that play important roles in cancer pathogenesis and progression. No significant association was observed between the analysed miRNAs and the main clinicopathological or molecular characteristics of the NSCLC patients, although both miRNAs were downregulated in squamous cell carcinomas compared to adenocarcinomas. Noteworthy, we observed a significant association between low Let-7g expression and metastatic lymph nodes at diagnosis (p=0.046), as well as between high miR-21 expression and K-Ras mutations (p=0.0003). Survival analysis did not show any significant correlation between prognosis and the analysed miRNAs, although the patients with a high Let-7g and miR-21 expression showed a significantly lower short-term progression-free survival (p=0.01 and p=0.0003, respectively) and overall survival (p=0.023 and p=0.0045, respectively). In conclusion, we showed that Let-7g and miR-21 expression was deregulated in NSCLC and we demonstrated a strong relationship between miR-21 overexpression and K-Ras mutations. Our data indicate that Let-7g and miR-21 profiling combined with the determination of K-Ras mutational status may be considered a useful biomarker for a more effective molecular characterization and clinical management of NSCLC patients

On the vanishing electron-mass limit in plasma hydrodynamics in unbounded media

We consider the zero-electron-mass limit for the Navier-Stokes-Poisson system in unbounded spatial domains. Assuming smallness of the viscosity coefficient and ill-prepared initial data, we show that the asymptotic limit is represented by the incompressible Navier-Stokes system, with a Brinkman damping, in the case when viscosity is proportional to the electron-mass, and by the incompressible Euler system provided the viscosity is dominated by the electron mass. The proof is based on the RAGE theorem and dispersive estimates for acoustic waves, and on the concept of suitable weak solutions for the compressible Navier-Stokes system

A priori estimates for 3D incompressible current-vortex sheets

We consider the free boundary problem for current-vortex sheets in ideal incompressible magneto-hydrodynamics. It is known that current-vortex sheets may be at most weakly (neutrally) stable due to the existence of surface waves solutions to the linearized equations. The existence of such waves may yield a loss of derivatives in the energy estimate of the solution with respect to the source terms. However, under a suitable stability condition satisfied at each point of the initial discontinuity and a flatness condition on the initial front, we prove an a priori estimate in Sobolev spaces for smooth solutions with no loss of derivatives. The result of this paper gives some hope for proving the local existence of smooth current-vortex sheets without resorting to a Nash-Moser iteration. Such result would be a rigorous confirmation of the stabilizing effect of the magnetic field on Kelvin-Helmholtz instabilities, which is well known in astrophysics

Treatment with interleukin-2 in malignant pleural mesothelioma: immunological and angiogenetic assessment and prognostic impact

BACKGROUND: Administration of interleukin-2 (IL-2) has shown some effects on malignant pleural mesothelioma (MPM) tumour regression. The purpose of this study was to investigate the ability of IL-2 to modify immunological effector cells and angiogenesis in MPM patients and their prognostic value. METHODS: Tumour-infiltrating lymphocytes (CD4, CD8, Foxp3), mast cells (MCs) (tryptase and chymase), microvessel count (MVC) and VEGF were determined by immunohistochemistry in two series of MPM patients: 60 patients treated with intra-pleural preoperative IL-2 and 33 patients untreated. RESULTS: Tryptase MCs, and CD8 and Foxp3 lymphocytes were significantly increased in the IL-2-treated group, whereas MVC was significantly lower in the same group. Moreover, in the IL-2-treated group, greater tryptase + MCs and greater Foxp3 lymphocytes were associated with improved and poorer clinical outcomes, respectively. Notably, when these two immunological parameters were combined, they predicted outcomes more effectively. CONCLUSIONS: This study showed that IL-2 treatment leads to a significant increase of immunological parameters, concomitantly with a reduction in vasculature, providing new insight into the cancer mechanisms mediated by IL-2. Moreover, these results suggest that tryptase-positive MCs and Foxp3 + lymphocytes predict clinical outcomes in IL-2-treated patients, highlighting the critical role of the inflammatory response in mesothelioma cancer progression. British Journal of Cancer (2009) 101, 1869-1875. doi:10.1038/sj.bjc.6605438 www.bjcancer.com (C) 2009 Cancer Research U