A heat conduction problem of 2D unbounded composites with imperfect contact conditions

We consider a steady-state heat conduction problem in 2D unbounded doubly periodic composite materials with temperature independent conductivities of their components. Imperfect contact conditions are assumed on the boundaries between the matrix and inclusions. By introducing complex potentials, the corresponding boundary value problem for the Laplace equation is transformed into a special R-linear boundary value problem for doubly periodic analytic functions. The method of functional equations is used for obtaining a solution. Thus, the R-linear boundary value problem is transformed into a system of functional equations which is analysed afterwards. A new improved algorithm for solving this system is proposed. It allows to compute the average property and reconstruct the temperature and the flux at an arbitrary point of the composite. Computational examples are presented

Effective conductivity of a composite material with stiff imperfect contact conditions

We present an analytic and numerical analysis of several properties of a composite material with stiff imperfect interface conditions. Spaces of functions are identified where we can guarantee existence and uniqueness of solutions. In particular, formulas for the temperature distribution and flux are exhibited. Numerical calculations of the material characteristics such as temperature, flux and the effective conductivity are also performed and interpreted

The prolonged X-ray flaring activity of Mrk 501 in 2014

The X-ray variability of the BL Lacertae source Mrk 501 was studied during 11.5 yr of monitoring with Swift. Here, we report the results of this study pertaining to the epoch of 2014 March-October, when our target showed the most powerful and long-lasting X-ray flaring activity. This epoch was characterized by X-ray flares varying in amplitude by factors of 2-5 on time-scales of a few weeks or shorter. We detected 35 instances of the intraday variability, sometimes occurring within the 1 ks observational runs. The X-ray flux was generally correlated with the TeV flux, while the 0.3-300 GeV and optical-UV fluxes did not show a significant correlation. Some notable incidences of more complicated variability patterns could also be recognized, indicating that the high-energy emission in Mrk 501 arose from an emission region more complex than a single zone. The best fits of the 0.3-10 keV spectra were mainly obtained using the logparabola model. Strong spectral variability was detected, affecting the slope but not the curvature of the spectrum. In strong flares, the spectral index became harder than 1.70. The spectral evolution was characterized by a harder-when-brighter behaviour, shifting the peak of the spectral energy distribution by about 20 keV that happens rarely in blazars

Bounded H∞\mathbf{H_\infty}-Calculus for Differential Operators on Conic Manifolds with Boundary

We derive conditions that ensure the existence of a bounded $H_\infty$-calculus in weighted $L_p$-Sobolev spaces for closed extensions $\underline{A}_T$ of a differential operator $A$ on a conic manifold with boundary, subject to differential boundary conditions $T$. In general, these conditions ask for a particular pseudodifferential structure of the resolvent $(\lambda-\underline{A}_T)^{-1}$ in a sector $\Lambda\subset\mathbf{C}$. In case of the minimal extension they reduce to parameter-ellipticity of the boundary value problem $(A,T)$. Examples concern the Dirichlet and Neumann Laplacians.Comment: 23 page

The WEBT Campaign on the Blazar 3C279 in 2006

The quasar 3C279 was the target of an extensive multiwavelength monitoring campaign from January through April 2006, including an optical-IR-radio monitoring campaign by the Whole Earth Blazar Telescope (WEBT) collaboration. In this paper we focus on the results of the WEBT campaign. The source exhibited substantial variability of optical flux and spectral shape, with a characteristic time scale of a few days. The variability patterns throughout the optical BVRI bands were very closely correlated with each other. In intriguing contrast to other (in particular, BL Lac type) blazars, we find a lag of shorter- behind longer-wavelength variability throughout the RVB ranges, with a time delay increasing with increasing frequency. Spectral hardening during flares appears delayed with respect to a rising optical flux. This, in combination with the very steep IR-optical continuum spectral index of ~ 1.5 - 2.0, may indicate a highly oblique magnetic field configuration near the base of the jet. An alternative explanation through a slow (time scale of several days) acceleration mechanism would require an unusually low magnetic field of < 0.2 G, about an order of magnitude lower than inferred from previous analyses of simultaneous SEDs of 3C279 and other FSRQs with similar properties.Comment: Accepted for publication in Ap

Maximal L p -regularity for the Laplacian on Lipschitz domains

We consider the Laplacian with Dirichlet or Neumann boundary conditions on bounded Lipschitz domains ?, both with the following two domains of definition:D1(?) = {u ? W1,p(?) : ?u ? Lp(?), Bu = 0}, orD2(?) = {u ? W2,p(?) : Bu = 0}, where B is the boundary operator.We prove that, under certain restrictions on the range of p, these operators generate positive analytic contraction semigroups on Lp(?) which implies maximal regularity for the corresponding Cauchy problems. In particular, if ? is bounded and convex and 1 < p ? 2, the Laplacian with domain D2(?) has the maximal regularity property, as in the case of smooth domains. In the last part,we construct an example that proves that, in general, the Dirichlet–Laplacian with domain D1(?) is not even a closed operator

Comparing the genetic typing methods for effective surveillance and rabies control in Georgia

A full nucleoprotein gene sequencing of 68 isolates collected from passive rabies surveillance system in Georgia between 2015 and 2016 identified two distinct dog rabies phylogroups, GEO_V1 and GEO_V2, which both belonged to the cosmopolitan dog clade. GEO_V1 was found throughout the country and was further divided into four sub-phylogroups that overlapped geographically; GEO_V2 was found in the southeast region and was closely related to dog rabies in Azerbaijan. A sequence analysis of the full N gene, partial nucleoprotein gene of N-terminal and C-terminal, and the amplicon sequences of pan-lyssavirus RT-qPCR LN34 showed that all four sequencing approaches provided clear genetic typing results of canine rabies and could further differentiate GEO_V1 and GEO_V2. The phylogenetic analysis results vary and were affected by the length of the sequences used. Amplicon sequencing of the LN34 assay positive samples provided a rapid and cost-effective method for rabies genetic typing, which is important for improving rabies surveillance and canine rabies eradication globally