Complete list of Darboux Integrable Chains of the form t1x=tx+d(t,t1)t_{1x}=t_x+d(t,t_1)

We study differential-difference equation of the form $$\frac{d}{dx}t(n+1,x)=f(t(n,x),t(n+1,x),\frac{d}{dx}t(n,x))$$ with unknown $t(n,x)$ depending on continuous and discrete variables $x$ and $n$. Equation of such kind is called Darboux integrable, if there exist two functions $F$ and $I$ of a finite number of arguments $x$, $\{t(n\pm k,x)\}_{k=-\infty}^\infty$, ${\frac{d^k}{dx^k}t(n,x)}_{k=1}^\infty$, such that $D_xF=0$ and $DI=I$, where $D_x$ is the operator of total differentiation with respect to $x$, and $D$ is the shift operator: $Dp(n)=p(n+1)$. Reformulation of Darboux integrability in terms of finiteness of two characteristic Lie algebras gives an effective tool for classification of integrable equations. The complete list of Darboux integrable equations is given in the case when the function $f$ is of the special form $f(u,v,w)=w+g(u,v)$

Testing Hawking particle creation by black holes through correlation measurements

Hawking's prediction of thermal radiation by black holes has been shown by Unruh to be expected also in condensed matter systems. We show here that in a black hole-like configuration realised in a BEC this particle creation does indeed take place and can be unambiguously identified via a characteristic pattern in the density-density correlations. This opens the concrete possibility of the experimental verification of this effect.Comment: 13 pages, 2 figures. Honorable mention in the 2010 GRF Essay Competitio

Hierarchy of Conservation Laws of Diffusion--Convection Equations

We introduce notions of equivalence of conservation laws with respect to Lie symmetry groups for fixed systems of differential equations and with respect to equivalence groups or sets of admissible transformations for classes of such systems. We also revise the notion of linear dependence of conservation laws and define the notion of local dependence of potentials. To construct conservation laws, we develop and apply the most direct method which is effective to use in the case of two independent variables. Admitting possibility of dependence of conserved vectors on a number of potentials, we generalize the iteration procedure proposed by Bluman and Doran-Wu for finding nonlocal (potential) conservation laws. As an example, we completely classify potential conservation laws (including arbitrary order local ones) of diffusion--convection equations with respect to the equivalence group and construct an exhaustive list of locally inequivalent potential systems corresponding to these equations.Comment: 24 page

Using Ground Transportation for Aviation System Disruption Alleviation

An investigation was made into whether passenger delays and airline costs due to disruptive events affecting European airports could be reduced by a coordinated strategy of using alternative flights and ground transportation to help stranded passengers reach their final destination using airport collaborative decision-making concepts. Optimizing for airline cost for hypothetical disruptive events suggests that, for airport closures of up to 10 h, airlines could benefit from up to a 20% reduction in passenger delay-related costs. The mean passenger delay could be reduced by up to 70%, mainly via a reduction in very long delays

Crossover from commensurate to incommensurate antiferromagnetism in stoichiometric NaFeAs revealed by single-crystal 23Na,75As-NMR experiments

We report results of 23Na and 75As nuclear magnetic resonance (NMR) experiments on a self-flux grown high-quality single crystal of stoichiometric NaFeAs. The NMR spectra revealed a tetragonal to twinned-orthorhombic structural phase transition at T_O = 57 K and an antiferromagnetic (AF) transition at T_AF = 45 K. The divergent behavior of nuclear relaxation rate near T_AF shows significant anisotropy, indicating that the critical slowing down of stripe-type AF fluctuations are strongly anisotropic in spin space. The NMR spectra at low enough temperatures consist of sharp peaks showing a commensurate stripe AF order with a small moment \sim 0.3 muB. However, the spectra just below T_AF exhibits highly asymmetric broadening pointing to an incommensurate modulation. The commensurate-incommensurate crossover in NaFeAs shows a certain similarity to the behavior of SrFe2As2 under high pressure.Comment: 5 pages, 5 figures, revised version to appear in J. Phys. Soc. Jp

A Physicist's Proof of the Lagrange-Good Multivariable Inversion Formula

We provide yet another proof of the classical Lagrange-Good multivariable inversion formula using techniques of quantum field theory.Comment: 9 pages, 3 diagram

Darboux transformations for a 6-point scheme

We introduce (binary) Darboux transformation for general differential equation of the second order in two independent variables. We present a discrete version of the transformation for a 6-point difference scheme. The scheme is appropriate to solving a hyperbolic type initial-boundary value problem. We discuss several reductions and specifications of the transformations as well as construction of other Darboux covariant schemes by means of existing ones. In particular we introduce a 10-point scheme which can be regarded as the discretization of self-adjoint hyperbolic equation

Modus D3.1 Modal choice analysis and expert assessment

Modus Deliverable 3.1 has the objective to identify and assess (future) drivers that influence passenger demand and supply of mobility, and how these affect passenger modal choice. A comprehensive literature review is provided and identifies a set of high-level and detailed drivers of supply and demand. This analysis is complemented by an expert survey, to gain initial high-level insights regarding the potential importance of various factors, and by a multimodality workshop, to identify additional factors and acquire a first insight into potential enablers and barriers of future mobility solutions. Combining all the identified drivers reveals that most drivers are of a social, economic or technological nature. A large number of social drivers are demand drivers concerned with the passenger aspects of mobility. On the other hand, a large number of economic drivers belong to the supply drivers concerned with various cost-related factors or with transport operations, the market structure and available infrastructure

Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability into the light of Kolmogorov and Nekhoroshev theories

We investigate the long-time stability of the Sun-Jupiter-Saturn-Uranus system by considering a planar secular model, that can be regarded as a major refinement of the approach first introduced by Lagrange. Indeed, concerning the planetary orbital revolutions, we improve the classical circular approximation by replacing it with a solution that is invariant up to order two in the masses; therefore, we investigate the stability of the secular system for rather small values of the eccentricities. First, we explicitly construct a Kolmogorov normal form, so as to find an invariant KAM torus which approximates very well the secular orbits. Finally, we adapt the approach that is at basis of the analytic part of the Nekhoroshev's theorem, so as to show that there is a neighborhood of that torus for which the estimated stability time is larger than the lifetime of the Solar System. The size of such a neighborhood, compared with the uncertainties of the astronomical observations, is about ten times smaller.Comment: 31 pages, 2 figures. arXiv admin note: text overlap with arXiv:1010.260

Future multimodal mobility scenarios within Europe

The European transport system faces multiple pressing challenges, including the need for significant emissions reduction in the sector and the provision of a seamless, multimodal journey to travellers. In order to address these challenges, a thorough understanding and assessment of different development pathways are required. This paper elaborates on four different scenarios developed within the scope of the Modus project. Based on these as well as additional insights from experts of the air and rail sector, initial implications for emissions reduction potential, travel times, or technological options are discussed