Non-integrability of a fifth order equation with integrable two-body dynamics

We consider the fifth order partial differential equation (PDE) u4x,t?5uxxt+4ut+uu5x+2uxu4x?5uu3x?10uxuxx+12uux=0, which is a generalization of the integrable Camassa-Holm equation. The fifth order PDE has exact solutions in terms of an arbitrary number of superposed pulsons, with geodesic Hamiltonian dynamics that is known to be integrable in the two-body case N=2. Numerical simulations show that the pulsons are stable, dominate the initial value problem and scatter elastically. These characteristics are reminiscent of solitons in integrable systems. However, after demonstrating the non-existence of a suitable Lagrangian or bi-Hamiltonian structure, and obtaining negative results from Painlev\'{e} analysis and the Wahlquist-Estabrook method, we assert that the fifth order PDE is not integrable

A class of equations with peakon and pulson solutions (with an Appendix by Harry Braden and John Byatt-Smith)

We consider a family of integro-differential equations depending upon a parameter $b$ as well as a symmetric integral kernel $g(x)$. When $b=2$ and $g$ is the peakon kernel (i.e. $g(x)=\exp(-|x|)$ up to rescaling) the dispersionless Camassa-Holm equation results, while the Degasperis-Procesi equation is obtained from the peakon kernel with $b=3$. Although these two cases are integrable, generically the corresponding integro-PDE is non-integrable. However,for $b=2$ the family restricts to the pulson family of Fringer & Holm, which is Hamiltonian and numerically displays elastic scattering of pulses. On the other hand, for arbitrary $b$ it is still possible to construct a nonlocal Hamiltonian structure provided that $g$ is the peakon kernel or one of its degenerations: we present a proof of this fact using an associated functional equation for the skew-symmetric antiderivative of $g$. The nonlocal bracket reduces to a non-canonical Poisson bracket for the peakon dynamical system, for any value of $b\neq 1$.Comment: Contribution to volume of Journal of Nonlinear Mathematical Physics in honour of Francesco Caloger

A lattice model of hydrophobic interactions

Hydrogen bonding is modeled in terms of virtual exchange of protons between water molecules. A simple lattice model is analyzed, using ideas and techniques from the theory of correlated electrons in metals. Reasonable parameters reproduce observed magnitudes and temperature dependence of the hydrophobic interaction between substitutional impurities and water within this lattice.Comment: 7 pages, 3 figures. To appear in Europhysics Letter

A new dromaeosaurid (Dinosauria: Theropoda) from the Upper Cretaceous Wulansuhai Formation of Inner Mongolia, China

We describe a new dromaeosaurid theropod from the Upper Cretaceous Wulansuhai Formation of Bayan Mandahu, Inner Mongolia. The new taxon, Linheraptor exquisitus gen. et sp. nov., is based on an exceptionally well-preserved, nearly complete skeleton. This specimen represents the fifth dromaeosaurid taxon recovered from the Upper Cretaceous Djadokhta Formation and its laterally equivalent strata, which include the Wulansuhai Formation, and adds to the known diversity of Late Cretaceous dromaeosaurids. Linheraptor exquisitus closely resembles the recently reported Tsaagan mangas. Uniquely among dromaeosaurids, the two taxa share a large, anteriorly located maxillary fenestra and a contact between the jugal and the squamosal that excludes the postorbital from the infratemporal fenestra. These features suggest a sister-taxon relationship between L. exquisitus and T. mangas, which indicates the presence of a unique dromaeosaurid lineage in the Late Cretaceous of Asia. A number of cranial and dental features seen in L. exquisitus and T. mangas, and particularly some postcranial features of L. exquisitus, suggest that these two taxa are probably intermediate in systematic position between known basal and derived dromaeosaurids. The discovery of Linheraptor exquisitus is thus important for understanding the evolution of some salient features seen in the derived dromaeosaurids

Absence of dissipationless transport in clean 2D superconductors

Dissipationless charge transport is one of the defining properties of superconductors (SC). The interplay between dimensionality and disorder in determining the onset of dissipation in SCs remains an open theoretical and experimental problem. In this work, we present measurements of the dissipation phase diagrams of SCs in the two dimensional (2D) limit, layer by layer, down to a monolayer in the presence of temperature (T), magnetic field (B), and current (I) in 2H-NbSe2. Our results show that the phase-diagram strongly depends on the SC thickness even in the 2D limit. At four layers we can define a finite region in the I-B phase diagram where dissipationless transport exists at T=0. At even smaller thicknesses, this region shrinks in area. In a monolayer, we find that the region of dissipationless transport shrinks towards a single point, defined by T=B=I=0. In applied field, we show that time-dependent-Ginzburg-Landau (TDGL) simulations that describe dissipation by vortex motion, qualitatively reproduce our experimental I-B phase diagram. Last, we show that by using non-local transport and TDGL calculations that we can engineer charge flow and create phase boundaries between dissipative and dissipationless transport regions in a single sample, demonstrating control over non-equilibrium states of matter.Comment: Manuscript, figures and supplemental informatio