Interfacial deflection and jetting of a paramagnetic particle-laden fluid: theory and experiment

We describe the results of experiments and mathematical analysis of the deformation of a free surface by an aggregate of magnetic particles. The system we study is differentiated from ferrofluid systems because it contains regions rich with magnetic material as well as regions of negligible magnetic content. In our experiments, the magnetic force from a spherical permanent magnet collects magnetic particles to a liquid–air interface, and deforms the free surface to form a hump. The hump is composed of magnetic and non-magnetic regions due to the particle collection. When the magnet distance falls below a threshold value, we observe the transition of the hump to a jet. The mathematical model we develop, which consists of a numerical solution and an asymptotic approximation, captures the shape of the liquid–air interface during the deformation stage and a scaling prediction for the critical magnet distance for the hump to become a jet

Instantaneous Bethe-Salpeter Equation and Its Exact Solution

We present an approach to solve a Bethe-Salpeter (BS) equation exactly without any approximation if the kernel of the BS equation exactly is instantaneous, and take positronium as an example to illustrate the general features of the solutions. As a middle stage, a set of coupled and self-consistent integration equations for a few scalar functions can be equivalently derived from the BS equation always, which are solvable accurately. For positronium, precise corrections to those of the Schr\"odinger equation in order $v$ (relative velocity) in eigenfunctions, in order $v^2$ in eigenvalues, and the possible mixing, such as that between $S$ ($P$) and $D$ ($F$) components in $J^{PC}=1^{--}$ ($J^{PC}=2^{++}$) states as well, are determined quantitatively. Moreover, we also point out that there is a problematic step in the classical derivation which was proposed first by E.E. Salpeter. Finally, we emphasize that for the effective theories (such as NRQED and NRQCD etc) we should pay great attention on the corrections indicated by the exact solutions.Comment: 4 pages, replace for shortening the manuscrip

Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two

We consider the billiard dynamics in a non-compact set of R^d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called `quenched random Lorentz tube'. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.Comment: Final version for J. Stat. Phys., 18 pages, 4 figure

An adaptive large neighborhood search heuristic for the share-a-ride problem

The Share-a-Ride Problem (SARP) aims at maximizing the profit of serving a set of passengers and parcels using a set of homogeneous vehicles. We propose an adaptive large neighborhood search (ALNS) heuristic to address the SARP. Furthermore, we study the problem of determining the time slack in a SARP schedule. Our proposed solution approach is tested on three sets of realistic instances. The performance of our heuristic is benchmarked against a mixed integer programming (MIP) solver and the Dial-a-Ride Problem (DARP) test instances. Compared to the MIP solver, our heuristic is superior in both the solution times and the quality of the obtained solutions if the CPU time is limited. We also report new best results for two out of twenty benchmark DARP instances

Dynamics of quantum Hall stripes in double-quantum-well systems

The collective modes of stripes in double layer quantum Hall systems are computed using the time-dependent Hartree-Fock approximation. It is found that, when the system possesses spontaneous interlayer coherence, there are two gapless modes, one a phonon associated with broken translational invariance, the other a pseudospin-wave associated with a broken U(1) symmetry. For large layer separations the modes disperse weakly for wavevectors perpendicular to the stripe orientation, indicating the system becomes akin to an array of weakly coupled one-dimensional XY systems. At higher wavevectors the collective modes develop a roton minimum associated with a transition out of the coherent state with further increasing layer separation. A spin wave model of the system is developed, and it is shown that the collective modes may be described as those of a system with helimagnetic ordering.Comment: 16 pages including 7 postscript figure

Towards the understanding of vertical-axis wind turbines in double-rotor configuration

Vertical-axis wind turbines (VAWTs) in double-rotor configuration, meaning two rotors in close proximity, have the ability to enhance the power performance. In this study, we work towards the understanding of vertical-axis wind turbines in double-rotor configuration. Numerical simulations are performed to gain insight in the physics behind the double-rotor concept. Furthermore, a parametric study is performed to explore the effect of the double-rotor lay-out, rotor loading, rotor spacing and wind direction on the flow characteristics and the power generation.</p

Observation of Enhanced Beaming from Photonic Crystal Waveguides

We report on the experimental observation of the beaming effect in photonic crystals enhanced via surface modes. We experimentally map the spatial field distribution of energy emitted from a subwavelength photonic crystal waveguide into free-space, rendering with crisp clarity the diffractionless beaming of energy. Our experimental data agree well with our numerical studies of the beaming enhancement in photonic crystals with modulated surfaces. Without loss of generality, we study the beaming effect in a photonic crystal scaled to microwave frequencies and demonstrate the technological capacity to deliver long-range, wavelength-scaled beaming of energy.Comment: 4 pages, 6 figure