Formation of Quantum Shock Waves by Merging and Splitting Bose-Einstein Condensates

The processes of merging and splitting dilute-gas Bose-Einstein condensates are studied in the nonadiabatic, high-density regime. Rich dynamics are found. Depending on the experimental parameters, uniform soliton trains containing more than ten solitons or the formation of a high-density bulge as well as quantum (or dispersive) shock waves are observed experimentally within merged BECs. Our numerical simulations indicate the formation of many vortex rings. In the case of splitting a BEC, the transition from sound-wave formation to dispersive shock-wave formation is studied by use of increasingly stronger splitting barriers. These experiments realize prototypical dispersive shock situations.Comment: 10 pages, 8 figure

Determinants and impact of suboptimal asthma control in Europe : The INTERNATIONAL CROSS-SECTIONAL AND LONGITUDINAL ASSESSMENT ON ASTHMA CONTROL (LIAISON) study

Acknowledgements We are grateful to THERAmetrics for the study management, data collection and analysis. The authors would like to thank the following investigators for their contribution (>30 patients enrolled): F. Fohler, A.G. Haider, J. Hesse-Tonsa, J. Messner, W. Pohl (Austria); G. Joos, J.L. Halloy, R. Peche, H. Simonis, P. Van den Brande (Belgium); B. Bugnas, J.M. Chavaillon, P. Debove, S. Dury, L. Mathieu, O. Lagrange, A. Prudhomme, S. Verdier (France); A. Benedix, O. Kestermann, A. Deimling, G. Eckhardt, M. Gernhold, V. Grimm-Sachs, M. Hoefer, G. Hoheisel, C. Stolpe, C. Schilder, M. John, J. Uerscheln, K.H. Zeisler (Germany); A. Chaniotou, P. Demertzis, V. Filaditaki-Loverdou, A. Gaga, E. Georgatou-Papageorgiou, S. Michailidis, G. Pavkalou, M. Toumpis (Greece); K. Csicsari, K. Hajdu, M. Póczi, M. Kukuly, T. Kecskes, C. Hangonyi, J. Schlezak, E. Takács, M. Szabo,G. Szabó, C. Szabo (Hungary); G.W. Canonica, W. Castellani, A. Cirillo, M.P. Foschino Barbaro, M. Gjomarkaj, G. Guerra, G. Idotta, D. Legnani, M. Lo Schiavo, R. Maselli, F. Mazza, S. Nutini, P. Paggiaro, A. Pietra, O. Resta, S. Salis, N.A. Scichilone, M.C. Zappa, A. Zedda (Italy); M. Goosens, R. Heller, K. Mansour, C. Meek, J. van den Berg (The Netherlands); A. Antczak, M. Faber, D. Madra-Rogacka, G. Mincewicz, M. Michnar, D. Olejniczak, G. Pulka, Z. Sankowski, K. Kowal, I. Krupa-Borek, B. Kubicka Kozik, K. Kuczynska, P. Kuna, A. Kwasniewski, M. Wozniak (Poland); F. Casas Maldonado, C. Cisneros, J. de Miguel Díez, L.M. Entrenas Costa, B. Garcìa-Cosio, M.V. Gonzales, L. Lores, M. Luengo, C. Martinez, C. Melero, I. Mir, X. Munoz, A. Pacheco, V. Plaza, J. Serra, J. Serrano, J.G. Soto Campos (Spain); T. Bekci, R. Demir, N. Dursunoglu, D. Ediger, A. Ekici, O. Goksel, H. Gunen, I.K. Oguzulgen, Z.F. Ozseker, (Turkey); L. Barnes, T. Hall, S. Montgomerie, J. Purohit, J. Ryan (United Kingdom). The authors would also like to thank P. Galletti (THERAMetrics S.p.A., Sesto San Giovanni, Italy) and K. Stockmeyer (THERAMetrics GmbH, Essen, Germany) for providing editorial assistance in the preparation of this manuscript.Peer reviewedPublisher PD

Defect Modes and Homogenization of Periodic Schr\"odinger Operators

We consider the discrete eigenvalues of the operator H_\eps=-\Delta+V(\x)+\eps^2Q(\eps\x), where V(\x) is periodic and Q(\y) is localized on $\R^d,\ \ d\ge1$. For \eps>0 and sufficiently small, discrete eigenvalues may bifurcate (emerge) from spectral band edges of the periodic Schr\"odinger operator, H_0 = -\Delta_\x+V(\x), into spectral gaps. The nature of the bifurcation depends on the homogenized Schr\"odinger operator L_{A,Q}=-\nabla_\y\cdot A \nabla_\y +\ Q(\y). Here, $A$ denotes the inverse effective mass matrix, associated with the spectral band edge, which is the site of the bifurcation.Comment: 26 pages, 3 figures, to appear SIAM J. Math. Ana

Dispersive and diffusive-dispersive shock waves for nonconvex conservation laws

We consider two physically and mathematically distinct regularization mechanisms of scalar hyperbolic conservation laws. When the flux is convex, the combination of diffusion and dispersion are known to give rise to monotonic and oscillatory traveling waves that approximate shock waves. The zero-diffusion limits of these traveling waves are dynamically expanding dispersive shock waves (DSWs). A richer set of wave solutions can be found when the flux is non-convex. This review compares the structure of solutions of Riemann problems for a conservation law with non-convex, cubic flux regularized by two different mechanisms: 1) dispersion in the modified Korteweg--de Vries (mKdV) equation; and 2) a combination of diffusion and dispersion in the mKdV-Burgers equation. In the first case, the possible dynamics involve two qualitatively different types of DSWs, rarefaction waves (RWs) and kinks (monotonic fronts). In the second case, in addition to RWs, there are traveling wave solutions approximating both classical (Lax) and non-classical (undercompressive) shock waves. Despite the singular nature of the zero-diffusion limit and rather differing analytical approaches employed in the descriptions of dispersive and diffusive-dispersive regularization, the resulting comparison of the two cases reveals a number of striking parallels. In contrast to the case of convex flux, the mKdVB to mKdV mapping is not one-to-one. The mKdV kink solution is identified as an undercompressive DSW. Other prominent features, such as shock-rarefactions, also find their purely dispersive counterparts involving special contact DSWs, which exhibit features analogous to contact discontinuities. This review describes an important link between two major areas of applied mathematics, hyperbolic conservation laws and nonlinear dispersive waves.Comment: Revision from v2; 57 pages, 19 figure

Interactions of large amplitude solitary waves in viscous fluid conduits

The free interface separating an exterior, viscous fluid from an intrusive conduit of buoyant, less viscous fluid is known to support strongly nonlinear solitary waves due to a balance between viscosity-induced dispersion and buoyancy-induced nonlinearity. The overtaking, pairwise interaction of weakly nonlinear solitary waves has been classified theoretically for the Korteweg-de Vries equation and experimentally in the context of shallow water waves, but a theoretical and experimental classification of strongly nonlinear solitary wave interactions is lacking. The interactions of large amplitude solitary waves in viscous fluid conduits, a model physical system for the study of one-dimensional, truly dissipationless, dispersive nonlinear waves, are classified. Using a combined numerical and experimental approach, three classes of nonlinear interaction behavior are identified: purely bimodal, purely unimodal, and a mixed type. The magnitude of the dispersive radiation due to solitary wave interactions is quantified numerically and observed to be beyond the sensitivity of our experiments, suggesting that conduit solitary waves behave as "physical solitons." Experimental data are shown to be in excellent agreement with numerical simulations of the reduced model. Experimental movies are available with the online version of the paper.Comment: 13 pages, 4 figure