On the origin of the Korteweg-de Vries equation

The Korteweg-de Vries equation has a central place in a model for waves on shallow water and it is an example of the propagation of weakly dispersive and weakly nonlinear waves. Its history spans a period of about sixty years, starting with experiments of Scott Russell in 1834, followed by theoretical investigations of, among others, Lord Rayleigh and Boussinesq in 1871 and, finally, Korteweg and De Vries in 1895. In this essay we compare the work of Boussinesq and Korteweg-de Vries, stressing essential differences and some interesting connections. Although there exist a number of articles, reviewing the origin and birth of the Korteweg-de Vries equations, connections and differences, not generally known, are reported.Comment: minor corrections; 25 pages, 3 figure

Probing the Nature of the Vela X Cocoon

Vela X is a pulsar wind nebula (PWN) associated with the active pulsar B0833-45 and contained within the Vela supernova remnant (SNR). A collimated X-ray filament ("cocoon") extends south-southwest from the pulsar to the center of Vela X. VLA observations uncovered radio emission coincident with the eastern edge of the cocoon and H.E.S.S. has detected TeV $\gamma$-ray emission from this region as well. Using XMM-\textit{Newton} archival data, covering the southern portion of this feature, we analyze the X-ray properties of the cocoon. The X-ray data are best fit by an absorbed nonequilibrium plasma model with a powerlaw component. Our analysis of the thermal emission shows enhanced abundances of O, Ne, and Mg within the cocoon, indicating the presence of ejecta-rich material from the propagation of the SNR reverse shock, consistent with Vela X being a disrupted PWN. We investigate the physical processes that excite the electrons in the PWN to emit in the radio, X-ray and $\gamma$-ray bands. The radio and non-thermal X-ray emission can be explained by synchrotron emission. We model the $\gamma$-ray emission by Inverse Compton scattering of electrons off of cosmic microwave background (CMB) photons. We use a 3-component broken power law to model the synchrotron emission, finding an intrinsic break in the electron spectrum at $\sim5 \times 10^{6}$ keV and a cooling break at $\sim$ 5.5 $\times 10^{10}$ keV. This cooling break along with a magnetic field strength of 5 $\times 10^{-6}$ G indicate that the synchrotron break occurs at $\sim$1 keV.Comment: accepted for publication to ApJ

Physics Opportunities for Vector-Boson Scattering at a Future 100 TeV Hadron Collider

Vector-boson scattering (VBS) processes provide particularly promising means for probing the mechanism of electroweak symmetry breaking and to search for new physics in the weak sector. In the environment of a future proton-proton collider operating at a center-of-mass energy of 100 TeV, unprecedented opportunities arise for the investigation of this important class of reactions. We highlight the prominent features of VBS processes in this energy regime and discuss how the VBS signal can be isolated in the presence of a priori large QCD backgrounds. We find excellent opportunities for the analysis of VBS reactions in a kinematic range that is inaccessible to present colliders.Comment: 26 pages, 14 figures; matches version published by Phys. Rev.

Security analysis of the micro transport protocol with a misbehaving receiver

BitTorrent is the most widely used Peer-to-Peer (P2P) protocol and it comprises the largest share of traffic in Europe. To make BitTorrent more Internet Service Provider (ISP) friendly, BitTorrent Inc. invented the Micro Transport Protocol (uTP). It is based on UDP with a novel congestion control called Low Extra Delay Background Transport (LEDBAT). This protocol assumes that the receiver always gives correct feedback, since otherwise this deteriorates throughput or yields to corrupted data. We show through experimental investigation that a misbehaving uTP receiver, which is not interested in data integrity, can increase the bandwidth of the sender by up to five times. This can cause a congestion collapse and steal large share of a victim’s bandwidth. We present three attacks, which increase the bandwidth usage significantly. We have tested these attacks in a real world environment and show its severity both in terms of number of packets and total traffic generated. We also present a countermeasure for protecting against the attacks and evaluate the performance of that defence strategy

Universal Unitarity Triangle and Physics Beyond the Standard Model

We make the simple observation that there exists a universal unitarity triangle for all models, like the SM, the Two Higgs Doublet Models I and II and the MSSM with minimal flavour violation, that do not have any new operators beyond those present in the SM and in which all flavour changing transitions are governed by the CKM matrix with no new phases beyond the CKM phase. This universal triangle can be determined in the near future from the ratio (Delta M)_d/(Delta M)_s and sin(2 beta) measured first through the CP asymmetry in B_d^0 to psi K_S and later in K to pi nu nubar decays. Also suitable ratios of the branching ratios for B to X_{d,s} nu nubar and B_{d,s} to mu^+ mu^- and the angle gamma measured by means of CP asymmetries in B decays can be used for this determination. Comparison of this universal triangle with the non-universal triangles extracted in each model using epsilon, (Delta M)_d and various branching ratios for rare decays will allow to find out in a transparent manner which of these models, if any, is singled out by experiment. A virtue of the universal triangle is that it allows to separate the determination of the CKM parameters from the determination of new parameters present in the extensions of the SM considered here.Comment: 12 pages, 1 figur