Weakly Enforced Boundary Conditions for the NURBS-Based Finite Cell Method

In this paper, we present a variationally consistent formulation for the weak enforcement of essential boundary conditions as an extension to the finite cell method, a fictitious domain method of higher order. The absence of boundary fitted elements in fictitious domain or immersed boundary methods significantly restricts a strong enforcement of essential boundary conditions to models where the boundary of the solution domain coincides with the embedding analysis domain. Penalty methods and Lagrange multiplier methods are adequate means to overcome this limitation but often suffer from various drawbacks with severe consequences for a stable and accurate solution of the governing system of equations. In this contribution, we follow the idea of NITSCHE [29] who developed a stable scheme for the solution of the Laplace problem taking weak boundary conditions into account. An extension to problems from linear elasticity shows an appropriate behavior with regard to numerical stability, accuracy and an adequate convergence behavior. NURBS are chosen as a high-order approximation basis to benefit from their smoothness and flexibility in the process of uniform model refinement

Ultrashort pulses and short-pulse equations in (2+1)−(2+1)-dimensions

In this paper, we derive and study two versions of the short pulse equation (SPE) in $(2+1)-$dimensions. Using Maxwell's equations as a starting point, and suitable Kramers-Kronig formulas for the permittivity and permeability of the medium, which are relevant, e.g., to left-handed metamaterials and dielectric slab waveguides, we employ a multiple scales technique to obtain the relevant models. General properties of the resulting $(2+1)$-dimensional SPEs, including fundamental conservation laws, as well as the Lagrangian and Hamiltonian structure and numerical simulations for one- and two-dimensional initial data, are presented. Ultrashort 1D breathers appear to be fairly robust, while rather general two-dimensional localized initial conditions are transformed into quasi-one-dimensional dispersing waveforms

Jet evolution from weak to strong coupling

Recent studies, using the AdS/CFT correspondence, of the radiation produced by a decaying system or by an accelerated charge in the N=4 supersymmetric Yang-Mills theory, led to a striking result: the 'supergravity backreaction', which is supposed to describe the energy density at infinitely strong coupling, yields exactly the same result as at zero coupling, that is, it shows no trace of quantum broadening. We argue that this is not a real property of the radiation at strong coupling, but an artifact of the backreaction calculation, which is unable to faithfully capture the space-time distribution of the radiation. This becomes obvious in the case of a decaying system ('virtual photon'), for which the backreaction is tantamount to computing a three-point function in the conformal gauge theory, which is independent of the coupling since protected by symmetries. Whereas this non-renormalization property is specific to the conformal N=4 SYM theory, we argue that the failure of the three-point function to provide a local measurement is in fact generic: it holds in any field theory with non-trivial interactions. To properly study a localized distribution, one should rather compute a four-point function, as standard in deep inelastic scattering. We substantiate these considerations with studies of the radiation produced by the decay of a time-like photon at both weak and strong coupling. We show that by computing four-point functions, in perturbation theory at weak coupling and, respectively, from Witten diagrams at strong coupling, one can follow the quantum evolution and thus demonstrate the broadening of the energy distribution. This broadening is slow when the coupling is weak but it proceeds as fast as possible in the limit of a strong coupling.Comment: 49 pages, 6 figure

Ballistic electronic transport in Quantum Cables

We studied theoretically ballistic electronic transport in a proposed mesoscopic structure - Quantum Cable. Our results demonstrated that Qauntum Cable is a unique structure for the study of mesoscopic transport. As a function of Fermi energy, Ballistic conductance exhibits interesting stepwise features. Besides the steps of one or two quantum conductance units ($2e^2/h$), conductance plateaus of more than two quantum conductance units can also be expected due to the accidental degeneracies (crossings) of subbands. As structure parameters is varied, conductance width displays oscillatory properties arising from the inhomogeneous variation of energy difference betweeen adjoining transverse subbands. In the weak coupling limits, conductance steps of height $2e^2/h$ becomes the first and second plateaus for the Quantum Cable of two cylinder wires with the same width.Comment: 11 pages, 5 figure

Viscoelastic model for the dynamic structure of binary systems

This paper presents the viscoelastic model for the Ashcroft-Langreth dynamic structure factors of liquid binary mixtures. We also provide expressions for the Bhatia-Thornton dynamic structure factors and, within these expressions, show how the model reproduces both the dynamic and the self-dynamic structure factors corresponding to a one-component system in the appropriate limits (pseudobinary system or zero concentration of one component). In particular we analyze the behavior of the concentration-concentration dynamic structure factor and longitudinal current, and their corresponding counterparts in the one-component limit, namely, the self dynamic structure factor and self longitudinal current. The results for several lithium alloys with different ordering tendencies are compared with computer simulations data, leading to a good qualitative agreement, and showing the natural appearance in the model of the fast sound phenomenon.Comment: 20 pages, 19 figures, submitted to PR

R-Current DIS on a Shock Wave: Beyond the Eikonal Approximation

We find the DIS structure functions at strong coupling by calculating R-current correlators on a finite-size shock wave using AdS/CFT correspondence. We improve on the existing results in the literature by going beyond the eikonal approximation for the two lowest orders in graviton exchanges. We argue that since the eikonal approximation at strong coupling resums integer powers of 1/x (with x the Bjorken-x variable), the non-eikonal corrections bringing in positive integer powers of x can not be neglected in the small-x limit, as the non-eikonal order-x correction to the (n+1)st term in the eikonal series is of the same order in x as the nth eikonal term in that series. We demonstrate that, in qualitative agreement with the earlier DIS analysis based on calculation of the expectation value of the Wilson loop in the shock wave background using AdS/CFT, after inclusion of non-eikonal corrections DIS structure functions are described by two momentum scales: Q_1^2 ~ \Lambda^2 \, A^{1/3}/x and Q_2^2 ~ \Lambda^2 \, A^{2/3}, where \Lambda is the typical transverse momentum in the shock wave and A is the atomic number if the shock wave represents a nucleus. We discuss possible physical meanings of the scales Q_1 and Q_2.Comment: 44 pages, 3 figures; v2: typos corrected, refs added, discussion extende

The Kuramoto model with distributed shear

We uncover a solvable generalization of the Kuramoto model in which shears (or nonisochronicities) and natural frequencies are distributed and statistically dependent. We show that the strength and sign of this dependence greatly alter synchronization and yield qualitatively different phase diagrams. The Ott-Antonsen ansatz allows us to obtain analytical results for a specific family of joint distributions. We also derive, using linear stability analysis, general formulae for the stability border of incoherence.Comment: 6 page

Hanbury Brown and Twiss Correlations of Anderson Localized Waves

When light waves propagate through disordered photonic lattices, they can eventually become localized due to multiple scattering effects. Here we show experimentally that while the evolution and localization of the photon density distribution is similar in the two cases of diagonal and off-diagonal disorder, the density-density correlation carries a distinct signature of the type of disorder. We show that these differences reflect a symmetry in the spectrum and eigenmodes that exists in off-diagonally disordered lattices but is absent in lattices with diagonal disorder.Comment: 4 pages, 3 figures, comments welcom