Peter Y. P. Chen

A computational study of transient plane front solidification of alloys in a Bridgman apparatus under microgravity conditions

A mathematical model of heat, momentum and solute transfer during directional solidification of binary alloys in a Bridgman furnace has been developed. A fixed grid single domain approach (enthalpy method) is used. The effects of coupling with the phase diagram (a concentration-dependent melting temperature) and of thermal and solutal convection on segregation of solute, shape and position of the solid/liquid interface are investigated. A vorticity–stream function formulation is used for calculation of the velocity fields. The results presented include calculations at 1 and 10 μg, both neglecting and including the dependence of melting temperature on concentration.

Experiences with an electronic whiteboard teaching laboratory and tablet PC based lecture presentations [DSP courses]

This paper presents our experience in constructing an electronic whiteboard-based computer laboratory for teaching digital signal processing (DSP) courses in Australian undergraduate and postgraduate programs. Student interaction with the electronic whiteboard-based tutorial class environment is also reported. Away from the laboratory, DSP lectures were presented using a tablet PC as a digital whiteboard. This supported high quality handwriting annotation of lecture slides, and overcame the limited flexibility present in the existing PowerPoint mode of lecture delivery. For selected self-paced tutorial questions, solutions were provided in electronic format comprising the lecturers handwritten explanation on a blank slide, input using the tablet PC, combined with audio commentary. An evaluation of student opinions towards this multi-mode delivery of DSP education was illuminating, and the overall experience with these technological aids was that signal processing could be effectively and naturally taught with high student attention span.

A computational study of binary alloy solidification in the MEPHISTO experiment

Abstract A computational model is presented for the study of the solidification of a binary alloy. The enthalpy method has been modified and incorporated into both an in-house code SOLCON (Heat Transfer 98, 1998, p. 241) and the commercial CFD code CFX (CFX 4.2: Solver, 1997). The model has been used to simulate experiments on solidification of a bismuth–tin alloy which were performed during the 1997 flight of the MEPHISTO-4 experiment on the US Space Shuttle Columbia. The effects of thermal and solutal convection in the microgravity environment and of concentration-dependent melting temperature on the phase change processes are included. Comparisons of numerical solutions with actual microprobe results obtained from the MEPHISTO experiments are presented.

A model of a dual-core matter-wave soliton laser

We propose a system which can generate a periodic array of solitary-wave pulses from a finite reservoir of coherent Bose–Einstein condensate (BEC). The system is built as a set of two parallel quasi-one-dimensional traps (the reservoir proper and a pulse-generating cavity), which are linearly coupled by the tunnelling of atoms. The scattering length is tuned to be negative and small in the absolute value in the cavity, and still smaller but positive in the reservoir. Additionally, a parabolic potential profile is created around the centre of the cavity. Both edges of the reservoir and one edge of the cavity are impenetrable. Solitons are released through the other cavitys edge, which is semi-transparent. Two different regimes of the intrinsic operation of the laser are identified: circulations of a narrow wavefunction pulse in the cavity, and oscillations of a broad standing pulse. The latter regime is stable, readily providing for the generation of an array containing up to 10 000 permanent-shape pulses. The circulation regime provides for no more than 40 cycles, and then it transforms into the oscillation mode. The dependence of the dynamical regime on parameters of the system is investigated in detail.

Single- and multi-peak solitons in two-component models of metamaterials and photonic crystals

Abstract We report results of the study of solitons in a system of two nonlinear-Schrodinger (NLS) equations coupled by the XPM interaction, which models the co-propagation of two waves in metamaterials (MMs). The same model applies to photonic crystals (PCs), as well as to ordinary optical fibers, close to the zero-dispersion point. A peculiarity of the system is a small positive or negative value of the relative group-velocity dispersion (GVD) coefficient in one equation, assuming that the dispersion is anomalous in the other. In contrast to earlier studied systems of nonlinearly coupled NLS equations with equal GVD coefficients, which generate only simple single-peak solitons, the present model gives rise to families of solitons with complex shapes, which feature extended oscillatory tails and/or a double-peak structure at the center. Regions of existence are identified for single- and double-peak bimodal solitons, demonstrating a broad bistability in the system. Behind the existence border, they degenerate into single-component solutions. Direct simulations demonstrate stability of the solitons in the entire existence regions. Effects of the group-velocity mismatch (GVM) and optical loss are considered too. It is demonstrated that the solitons can be stabilized against the GVM by means of the respective “management” scheme. Under the action of the loss, complex shapes of the solitons degenerate into simple ones, but periodic compensation of the loss supports the complexity.

Recent Developments in Turbomachinery Modeling for Improved Balancing and Vibration Response Analysis

Present day turbogenerator installations are statically indeterminate rotor-bearing-foundation systems utilizing nonlinear hydrodynamic bearings. For optimal balancing and diagnostic purposes it is important to be able to correctly predict the system vibration behavior over the operating speed range. Essential aspects of this involve identifying the unbalance state, identifying appropriate dynamic foundation parameters, and identifying the system configuration state (relative location of the support bearings). This paper shows that, provided the system response is periodic at some speeds over the operating range and appropriate rotor and bearing housing motion measurements are made, it is possible, in principle, to satisfactorily achieve the above identifications without relying on the Reynolds equation for evaluating bearing forces. Preliminary results indicate that the identifications achieved promise to be superior to identification approaches that use the Reynolds equation.

Stable circulation modes in a dual-core matter-wave soliton laser

We consider a model of a matter-wave laser generating a periodic array of solitary-wave pulses. The system, a general version of which was recently proposed by us (2005 J. Phys. B: At. Mol. Opt. Phys. 38 4221), is composed of two parallel tunnel-coupled cigar-shaped traps (a reservoir and a lasing cavity), solitons being released through a valve at one edge of the cavity. We report a stable lasing mode accounted for by circulations of a narrow soliton in the cavity, which generates an array of strong pulses (with 103–104 atoms in each, the arrays duty cycle being 30%) when the soliton periodically hits the valve.

Stability of temporal solitons in uniform and managed quadratic nonlinear media with opposite group-velocity dispersions at fundamental and second harmonics

Abstract The problem of the stability of solitons in second-harmonic-generating media with normal group-velocity dispersion (GVD) in the second-harmonic (SH) field, which is generic to available χ (2) materials, is revisited. Using an iterative numerical scheme to construct stationary soliton solutions, and direct simulations to test their stability, we identify a full soliton-stability range in the space of the system’s parameters, including the coefficient of the group-velocity-mismatch (GVM). The soliton stability is limited by an abrupt onset of growth of tails in the SH component, the relevant stability region being defined as that in which the energy loss to the tail generation is negligible under experimentally relevant conditions. We demonstrate that the stability domain can be readily expanded with the help of two “management” techniques (spatially periodic compensation of destabilizing effects) – the dispersion management (DM) and GVM management. In comparison with their counterparts in optical fibers, DM solitons in the χ (2) medium feature very weak intrinsic oscillations.

Interactions of solitons with complex defects in Bragg gratings

We examine collisions of moving solitons in a fiber Bragg grating with a triplet composed of two closely set repulsive defects of the grating and an attractive one inserted between them. A doublet (dipole), consisting of attractive and repulsive defects with a small distance between them, is considered too. Systematic simulations demonstrate that the triplet provides for superior results, as concerns the capture of a free pulse and creation of a standing optical soliton, in comparison with recently studied traps formed by single and paired defects, as well as the doublet: 2/3 of the energy of the incident soliton can be captured when its velocity attains half the light speed in the fiber (the case most relevant to the experiment), and the captured soliton quickly relaxes to a stationary state. A subsequent collision between another free soliton and the pinned one is examined too, demonstrating that the impinging soliton always bounces back, while the pinned one either remains in the same state, or is kicked out forward, depending on the collision velocity and phase shift between the solitons.

Original article: Lanczos-Chebyshev pseudospectral methods for wave-propagation problems

The pseudospectral approach is a well-established method for studies of the wave propagation in various settings. In this paper, we report that the implementation of the pseudospectral approach can be simplified if power-series expansions are used. There is also an added advantage of an improved computational efficiency. We demonstrate how this approach can be implemented for two-dimensional (2D) models that may include material inhomogeneities. Physically relevant examples, taken from optics, are presented to show that, using collocations at Chebyshev points, the power-series approximation may give very accurate 2D soliton solutions of the nonlinear Schrodinger (NLS) equation. To find highly accurate numerical periodic solutions in models including periodic modulations of material parameters, a real-time evolution method (RTEM) is used. A variant of RTEM is applied to a system involving the copropagation of two pulses with different carrier frequencies, that cannot be easily solved by other existing methods.