A method for calculating invariant subspaces of symmetric hyperbolic equations

An algorithm is constructed for calculating invariant subspaces of symmetric hyperbolic systems arising in electromagnetic, acoustic, and elasticity problems. Discrete approximations are calculated for subspaces that correspond to minimal eigenvalues and smooth eigenfunctions. Difficulties related to the presence of an infinite-dimensional kernel in the differential operator are successfully handled. The efficiency of the algorithm is demonstrated using acoustics equations.     

The application of a vehicle routing model to a waste-collection problem: two case studies

In this paper we suggest a unique model for estimating the operating cost of each of three waste-collection systems. Under the traditional system, which is widely used, waste is typically collected in plastic bags and a three-man crew is needed on each vehicle. The other two systems require a one-man crew for vehicle collecting street containers. The side-loader system with fixed body automatically empties street containers into the vehicle body and empties the load at the disposal site. The side-loader system with demountable body allows the separation of the waste collection phase from transport to the disposal site, since the vehicle body can be demounted. We also present two case studies and show how the estimation of operating costs is a critical issue in decisions regarding the type of system to be used for waste collection.     

The Markov power moment problem in problems of controllability and frequency extinguishing for the wave equation on a half-axis

In this paper necessary and sufficient conditions of null-controllability and approximate null-controllability are obtained for the wave equation on a half-axis. Controls solving these problems are found explicitly. Moreover, bang-bang controls solving the approximate null-controllability problem are constructed with the aid of solutions of a frequency extinguishing problem in the restricted band (−a,a) for this equation and the Markov power moment problem.     

Non-linear Stability of Modulated Fronts¶for the Swift–Hohenberg Equation

We consider front solutions of the Swift–Hohenberg equation ∂ _t u= -(1+ ∂ _x ²)² u + ɛ² u -u ³. These are traveling waves which leave in their wake a periodic pattern in the laboratory frame. Using renormalization techniques and a decomposition into Bloch waves, we show the non-linear stability of these solutions. It turns out that this problem is closely related to the question of stability of the trivial solution for the model problem ∂ _t u(x,t) = ∂ _x ² u (x,t)+(1+tanh(x-ct))u(x,t)+u(x,t) ^p with p>3. In particular, we show that the instability of the perturbation ahead of the front is entirely compensated by a diffusive stabilization which sets in once the perturbation has hit the bulk behind the front. Received: 23 February 2001 / Accepted: 27 August 2001     

On c‐Bhaskar Rao designs with block size 4

Several new families of c‐Bhaskar Rao designs with block size 4 are constructed. The necessary conditions for the existence of a c‐BRD (υ,4,λ) are that: (1)λ_min=?λ/3 ≤ c ≤ λ and (2a) c≡λ (mod 2), if υ > 4 or (2b) c≡ λ (mod 4), if υ = 4 or (2c) c≠ λ ? 2, if υ = 5. It is proved that these conditions are necessary, and are sufficient for most pairs of c and λ; in particular, they are sufficient whenever λ?c ≠ 2 for c > 0 and whenever c ? λ_min≠ 2 for c < 0. For c < 0, the necessary conditions are sufficient for υ> 101; for the classic Bhaskar Rao designs, i.e., c = 0, we show the necessary conditions are sufficient with the possible exception of 0‐BRD (υ,4,2)'s for υ≡ 4 (mod 6). © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 361–386, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10009     

Black-hole horizon and metric singularity at the brane separating two sliding superfluids

An analogue of a black hole can be realized in the low-temperature laboratory. The horizon can be constructed for “relativistic” ripplons (surface waves) living on the brane. The brane is represented by the interface between two superfluid liquids, ³He-A and ³He-B, sliding along each other without friction. A similar experimental arrangement was recently used for the observation and investigation of the Kelvin-Helmholtz type of instability in superfluids [1]. The shear-flow instability in superfluids is characterized by two critical velocities. The lowest threshold measured in recent experiments [1] corresponds to the appearance of the ergoregion for ripplons. In the modified geometry, this will give rise to the black-hole event horizon in the effective metric experienced by ripplons. In the region behind the horizon, the brane vacuum is unstable due to interaction with the higher-dimensional world of bulk superfluids. The time of the development of instability can be made very long at low temperature. This will allow us to reach and investigate the second critical velocity—the proper Kelvin-Helmholtz instability threshold. The latter corresponds to the singularity inside the black hole, where the determinant of the effective metric becomes infinite.     

Laser induced copper electroless plating on polyimide with Q-switch Nd:YAG laser

The results of laser induced deposition of copper on polyimide substrate from copper electrolyte solution are reported. Unlike most work reported in the literatures where CW Ar⁺ lasers were used, a second harmonic (532 nm wavelength) Q-switch Nd:YAG laser was used for our experiments. The deposition process was conducted by laser-catalyzing of the polyimide surface and subsequent photothermal-accelerated reduction of copper-complex ions in an alkaline reducing environment. The characteristics of the deposited copper line were investigated in terms of laser beam scanning speed, and the number of scans. The surface morphology and chemical composition of the deposited copper were analyzed using field emission scanning electron microscope (FESEM) and energy dispersive spectrometer (EDX). The optimum processing conditions have been identified. The copper deposit was found to adhere well to the substrate.     

Temperature and junction-type dependency of Andreev reflection in MgB2

We studied the voltage and temperature dependency of the dynamic conductance of normal metal-MgB₂ junctions obtained either with the point-contact technique (with Au and Pt tips) or by making Ag-paint spots on the surface of MgB₂ samples. The fit of the conductance curves with the generalized BTK model gives evidence of pure s-wave gap symmetry. The temperature dependency of the gap, measured in Ag-paint junctions (dirty limit), follows the standard BCS curve with 2Δ/k_BT_c=3.3. In out-of-plane, high-pressure point-contacts we obtained almost ideal Andreev reflection characteristics showing a single small s-wave gap Δ=2.6±0.2 meV (clean limit).     

Reductions of interval nonlinear programming problem

A general nonlinear programming problem with interval functions is considered. Two reductions of this problem to the deterministic nonlinear programming problem are proposed, and illustrative examples are discussed.