Apparatus facilitates high-temperature tensile testing in vacuum

An apparutus for heating refractory materials to high temperatures during tensile testing includes a water-cooled stainless steel vacuum chamber. This contains a resistance heater consisting of a slit tube of tantalum or tungsten to enclose the tensile test rod

High temperature testing apparatus Patent

Test apparatus for determining mechanical properties of refractory materials at high temperatures in vacuum or inert atmosphere

Compton rockets and the minimum power of relativistic jets

The power of a relativistic jet depends on the number of leptons and protons carried by the jet itself. We have reasons to believe that powerful gamma-ray flat spectrum radio sources emit most of their radiation where radiative cooling is severe. This helps to find the minimum number of emitting leptons needed to explain the radiation we see. The number of protons is more uncertain. If there is one proton per electron, they dominate the jet power, but they could be unimportant if the emission is due to electron-positron pairs. In this case the total jet power could be much smaller. However, if the gamma-ray flux is due to inverse Compton scattering with seed photons produced outside the jet, the radiation is anisotropic also in the comoving frame, making the jet to recoil. This Compton rocket effect is strong for light, electron-positron jets, and negligible for heavy, proton dominated jets. No significant deceleration, required by fast superluminal motion, requires a minimum number of protons per lepton, and thus a minimum jet power. We apply these ideas to the blazar 3C 454.3, to find a robust lower limit to its total jet power: if the viewing angle theta_v ~ 1/Gamma the jet power is larger than the accretion luminosity L_d for any bulk Lorentz factor Gamma. For theta_v =0, instead, the minimum jet power can be smaller than L_d for Gamma<25. No more than ~10 pairs per proton are allowed.Comment: 5 pages, 2 figures, accepted for publication as a letter to MNRA

QPTAS and Subexponential Algorithm for Maximum Clique on Disk Graphs

A (unit) disk graph is the intersection graph of closed (unit) disks in the plane. Almost three decades ago, an elegant polynomial-time algorithm was found for Maximum Clique on unit disk graphs [Clark, Colbourn, Johnson; Discrete Mathematics '90]. Since then, it has been an intriguing open question whether or not tractability can be extended to general disk graphs. We show the rather surprising structural result that a disjoint union of cycles is the complement of a disk graph if and only if at most one of those cycles is of odd length. From that, we derive the first QPTAS and subexponential algorithm running in time 2^{O~(n^{2/3})} for Maximum Clique on disk graphs. In stark contrast, Maximum Clique on intersection graphs of filled ellipses or filled triangles is unlikely to have such algorithms, even when the ellipses are close to unit disks. Indeed, we show that there is a constant ratio of approximation which cannot be attained even in time 2^{n^{1-epsilon}}, unless the Exponential Time Hypothesis fails

Designing RNA secondary structures is hard

An RNA sequence is a word over an alphabet on four elements {A, C, G, U} called bases. RNA sequences fold into secondary structures where some bases match one another while others remain unpaired. Pseudoknot-free secondary structures can be represented as well-parenthesized expressions with additional dots, where pairs of matching parentheses symbolize paired bases and dots, unpaired bases. The two fundamental problems in RNA algorithmic are to predict how sequences fold within some model of energy and to design sequences of bases which will fold into targeted secondary structures. Predicting how a given RNA sequence folds into a pseudoknot-free secondary structure is known to be solvable in cubic time since the eighties and in truly subcubic time by a recent result of Bringmann et al. (FOCS 2016), whereas Lyngsø has shown it is NP-complete if pseudoknots are allowed (ICALP 2004). As a stark contrast, it is unknown whether or not designing a given RNA secondary structure is a tractable task; this has been raised as a challenging open question by Anne Condon (ICALP 2003). Because of its crucial importance in a number of fields such as pharmaceutical research and biochemistry, there are dozens of heuristics and software libraries dedicated to RNA secondary structure design. It is therefore rather surprising that the computational complexity of this central problem in bioinformatics has been unsettled for decades. In this paper we show that, in the simplest model of energy which is the Watson-Crick model the design of secondary structures is NP-complete if one adds natural constraints of the form: index i of the sequence has to be labeled by base b. This negative result suggests that the same lower bound holds for more realistic models of energy. It is noteworthy that the additional constraints are by no means artificial: they are provided by all the RNA design pieces of software and they do correspond to the actual practice (see for example the instances of the EteRNA project). Our reduction from a variant of 3-Sat has as main ingredients: arches of parentheses of different widths, a linear order interleaving variables and clauses, and an intended rematching strategy which increases the number of pairs iff the three literals of a same clause are not satisfied. The correctness of the construction is also quite intricate; it relies on the polynomial algorithm for the design of saturated structures – secondary structures without dots – by Haleš et al. (Algorithmica 2016), counting arguments, and a concise case analysis

Second-order operators with degenerate coefficients

We consider properties of second-order operators $H = -\sum^d_{i,j=1} \partial_i \, c_{ij} \, \partial_j$ on \Ri^d with bounded real symmetric measurable coefficients. We assume that $C = (c_{ij}) \geq 0$ almost everywhere, but allow for the possibility that $C$ is singular. We associate with $H$ a canonical self-adjoint viscosity operator $H_0$ and examine properties of the viscosity semigroup $S^{(0)}$ generated by $H_0$. The semigroup extends to a positive contraction semigroup on the $L_p$-spaces with $p \in [1,\infty]$. We establish that it conserves probability, satisfies $L_2$~off-diagonal bounds and that the wave equation associated with $H_0$ has finite speed of propagation. Nevertheless $S^{(0)}$ is not always strictly positive because separation of the system can occur even for subelliptic operators. This demonstrates that subelliptic semigroups are not ergodic in general and their kernels are neither strictly positive nor H\"older continuous. In particular one can construct examples for which both upper and lower Gaussian bounds fail even with coefficients in C^{2-\varepsilon}(\Ri^d) with $\varepsilon > 0$.Comment: 44 page

Dynamics and High Energy Emission of the Flaring HST-1 Knot in the M 87 Jet

Stimulated by recent observations of a radio-to-X-ray synchrotron flare from HST-1, the innermost knot of the M 87 jet, as well as by a detection of a very high energy gamma-ray emission from M 87, we investigated the dynamics and multiwavelength emission of the HST-1 region. We study thermal pressure of the hot interstellar medium in M 87 and argue for a presence of a gaseous condensation in its central parts. Interaction of the jet with such a feature is likely to result in formation of a converging reconfinement shock in the innermost parts of the M 87 jet. We show that for a realistic set of the outflow parameters, a stationary and a flaring part of the HST-1 knot located \~100 pc away from the active center can be associated with the decelerated portion of the jet matter placed immediately downstream of the point where the reconfinement shock reaches the jet axis. We discuss a possible scenario explaining a broad-band brightening of the HST-1 region related to the variable activity of the central core. We show that assuming a previous epoch of the high central black hole activity resulting in ejection of excess particles and photons down along the jet, one may first expect a high-energy flare of HST-1 due to inverse-Comptonisation of the nuclear radiation, followed after a few years by an increase in the synchrotron continuum of this region. If this is the case, then the recently observed increase in the knot luminosity in all spectral bands could be regarded as an unusual echo of the outburst that had happened previously in the active core of the M 87 radio galaxy.Comment: 30 pages, 7 figures included. Accepted for publication in MNRA