Asymptotic parabolicity for strongly damped wave equations

For $S$ a positive selfadjoint operator on a Hilbert space, $$\frac{d^2u}{dt}(t) + 2 F(S)\frac{du}{dt}(t) + S^2u(t)=0$$ describes a class of wave equations with strong friction or damping if $F$ is a positive Borel function. Under suitable hypotheses, it is shown that $$u(t)=v(t)+ w(t)$$ where $v$ satisfies $$2F(S)\frac{dv}{dt}(t)+ S^2v(t)=0$$ and $$\frac{w(t)}{\|v(t)\|} \rightarrow 0, \; \text{as} \; t \rightarrow +\infty.$$ The required initial condition $v(0)$ is given in a canonical way in terms of $u(0)$, $u'(0)$

Illuminating Massive Black Holes With White Dwarfs: Orbital Dynamics and High Energy Transients from Tidal Interactions

White dwarfs (WDs) can be tidally disrupted only by massive black holes (MBHs) with masses less than $\sim10^5 M_\odot$. These tidal interactions feed material to the MBH well above its Eddington limit, with the potential to launch a relativistic jet. The corresponding beamed emission is a promising signpost to an otherwise quiescent MBH of relatively low mass. We show that the mass transfer history, and thus the lightcurve, are quite different when the disruptive orbit is parabolic, eccentric, or circular. The mass lost each orbit exponentiates in the eccentric-orbit case leading to the destruction of the WD after several tens of orbits. We examine the stellar dynamics of clusters surrounding MBHs to show that single-passage WD disruptions are substantially more common than repeating encounters. The $10^{49}$ erg s$^{-1}$ peak luminosity of these events makes them visible to cosmological distances. They may be detectible at rates of as many as tens per year by instruments like Swift. In fact, WD-disruption transients significantly outshine their main-sequence star counterparts, and are the most likely tidal interaction to be detected arising from MBHs with masses less than $10^5 M_\odot$. The detection or non-detection of such WD-disruption transients by Swift is, therefore, a powerful tool to constrain lower end of the MBH mass function. The emerging class of ultra-long gamma ray bursts all have peak luminosities and durations reminiscent of WD disruptions, offering a hint that WD-disruption transients may already be present in existing datasets.Comment: Revised following response from refere

Nonsymmetric elliptic operators with wentzell boundary conditions in general domains

We study nonsymmetric second order elliptic operators with Wentzell boundary conditions in general domains with sufficiently smooth boundary. The ambient space is a space of Lp-type, 1 ≤ p ≤ ∞. We prove the existence of analytic quasicontractive (C0)-semigroups generated by the closures of such operators, for any 1 ≤ p ≤ ∞. Moreover, we extend a previous result concerning the continuous dependence of these semigroups on the coefficients of the boundary condition. We also specify precisely the domains of the generators explicitly in the case of bounded domains and 1 ≤ p ≤ ∞, when all the ingredients of the problem, including the boundary of the domain, the coefficients, and the initial condition, are of class C∞

Sphere rolling on the surface of a cone

We analyse the motion of a sphere that rolls without slipping on a conical surface having its axis in the direction of the constant gravitational field of the Earth. This nonholonomic system admits a solution in terms of quadratures. We exhibit that the only circular of the system orbit is stable and furthermore show that all its solutions can be found using an analogy with central force problems. We also discuss the case of motion with no gravitational field, that is, of motion on a freely falling cone.Comment: 12 pages, 2 figures, to be published in Eur J Phy

Magnetic correlation functions in the slow and fast solar wind in the Eulerian reference frame

Simultaneous multiple point measurements of the magnetic field from seven spacecraft are employed to estimate the Eulerian correlation function and decorrelation time scales in the near Earth solar wind for two different solar wind speed ranges. We find that the Eulerian decorrelation time scale differs significantly in the slow solar wind (600 km/s) wind, where slab-type turbulence dominates. In slow solar wind, the decorrelation time is 215 ± 43 min, and in fast solar wind, the decorrelation time scale is 114 ± 23 min, which indicates thatdecorrelation times vary with the nature of the turbulence. The values reported here are comparable to estimates of decorrelation times based on a number of different models, but do not clearly support or refute any specific solar wind turbulence model. These results may be useful in magnetohydrodynamic modeling of the solar wind and can contribute to our understanding of solar and galactic cosmic ray diffusion in the heliosphere.Fil: Weygand, James M.. University of California; Estados UnidosFil: Matthaeus, W. H.. University of Delaware; Estados UnidosFil: Kivelson M. G.. University of California; Estados UnidosFil: Dasso, Sergio Ricardo. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentin

Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions

In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the Kelvin-Voigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained

HPV transcript expression affects cervical cancer response to chemoradiation

Persistent HPV infection is causative for the majority of cervical cancer cases; however, current guidelines do not require HPV testing for newly diagnosed cervical cancer. Using an institutional cohort of 88 patients with cervical cancer treated uniformly with standard-of-care chemoradiation treatment (CRT) with prospectively collected clinical outcome data, we observed that patients with cervical tumors containing HPV genotypes other than HPV 16 have worse survival outcomes after CRT compared with patients with HPV 16+ tumors, consistent with previously published studies. Using RNA sequencing analysis, we quantified viral transcription efficiency and found higher levels of E6 and the alternative transcript E6*I in cervical tumors with HPV genotypes other than HPV 16. These findings were validated using whole transcriptome data from The Cancer Genome Atlas (n = 304). For the first time to our knowledge, transcript expression level of HPV E6*I was identified as a predictive biomarker of CRT outcome in our complete institutional data set (n = 88) and within the HPV 16+ subset (n = 36). In vitro characterization of HPV E6*I and E6 overexpression revealed that both induce CRT resistance through distinct mechanisms dependent upon p53-p21. Our findings suggest that high expression of E6*I and E6 may represent novel biomarkers of CRT efficacy, and these patients may benefit from alternative treatment strategies