Strip-like Geometries Research Articles

Control of the Stefan problem in a periodic box

In this paper, we consider the one-phase Stefan problem with surface tension, set in a two-dimensional strip-like geometry, with periodic boundary conditions respect to the horizontal direction [Formula: see text]. We prove that the system is locally null-controllable in any positive time, by means of a control supported within an arbitrary open and non-empty subset. We proceed by a linear test and duality, but quickly find that the linearized system is not symmetric and the adjoint has a dynamic coupling between the two states through the (fixed) boundary. Hence, motivated by a Fourier decomposition with respect to [Formula: see text], we consider a family of one-dimensional systems and prove observability results which are uniform with respect to the Fourier frequency parameter. The latter results are also novel, as we compute the full spectrum of the underlying operator for the nonzero Fourier modes. The zeroth mode system, on the other hand, is seen as a controllability problem for the linear heat equation with a finite-dimensional constraint. The complete observability of the adjoint is derived by using a Lebeau–Robbiano strategy, and the local controllability of the nonlinear system is then shown by combining an adaptation of the source term method introduced in [Y. Liu, T. Takahashi and M. Tucsnak, Single input controllability of a simplified fluid–structure interaction model, ESAIM Control Optim. Calc. Var. 19 (2013) 20–42] and a Banach fixed-point argument. Numerical experiments motivate several challenging open problems, foraying even beyond the specific setting we deal with herein.

The corrosion of aluminium alloy and release of intermetallic particles in nuclear reactor emergency core coolant: Implications for clogging of sump strainers

Abstract Clogging of sump strainers that filter the recirculation water in containment after a loss-of-coolant accident (LOCA) seriously impedes the continued cooling of nuclear reactor cores. In experiments examining the corrosion of aluminium alloy 6061, a common material in containment equipment, in borated solutions simulating the water chemistry of sump water after a LOCA, we found that Fe-bearing intermetallic particles, which were initially buried in the Al matrix, were progressively exposed as corrosion continued. Their cathodic nature vis-a-vis the Al matrix provoked continuous trenching around them until they were finally released into the test solution. Such particles released from Al alloy components in a reactor containment after a LOCA will be transported to the sump entrance with the recirculation flow and trapped by the debris bed that typically forms on the strainer surface, potentially aggravating strainer clogging. These Fe-bearing intermetallic particles, many of which had a rod or thin strip-like geometry, were identified to be mainly the cubic phase αc-Al(Fe,Mn)Si with an average size of about 2.15 μm; 11.5 g of particles with a volume of about 3.2 cm3 would be released with the dissolution of every 1 kg 6061 aluminium alloy.

Round Conductor With Low AC Loss Made From High-Temperature Superconducting Tapes

The second generation of high-temperature superconductor tape exhibits rapidly progressing electric transport capacity. However, its use as a conductor in magnet technology is somewhat held up by the strip-like geometry. Possible solution is the helical layout of parallel tapes on a flexible round former (recently called the Coated Conductor on Round Core or CORC). We present the study of AC properties of single-layer CORC conductors made from tapes with non-magnetic substrate. When subjected to AC magnetic field, single-layer CORC conductors exhibit negligible coupling currents because the tapes are fully transposed. On top of this the hysteresis loss can be reduced by the tape striation. Numerical simulations of magnetization loss for CORC conductors are in good agreement with experimental data. Prediction of AC loss in a coil made from CORC is compared to that calculated for a classical double pancake one made from the same amount of tape. Result indicate that the CORC-made coil produces lower losses at AC current amplitudes approaching the critical current.

Order-disorder transition and flow noise for vortices in amorphous films

In order to examine the universality of edge contamination (EC) and an order-disorder transition (ODT) for vortex matter reported in NbSe2 single crystals, we measure voltage noise spectra SV (f) induced by current-driven vortices for amorphous MoxGe1-x films with Corbino-disk and striplike geometries. Field dependences of the critical current Ic and SV (f) are nearly independent of contact geometries, indicating that the EC effects are not important on static or dynamic vortex properties in our films. This result is in contrast to what has been reported in NbSe2 crystals. The difference may be attributed to different sample thickness. At 4.1 K, SV at low frequency f exhibits a sharp peak just below the peak field Bp of Ic, suggesting the existence of ODT and metastable vortex states at around Bp. At 5.5 K near the superconducting transition Tc(=6.2 K), however, clear evidence for ODT is not visible.

Vortex states in the peak effect regime of [formula omitted] films probed by noise

We present measurements of voltage noise spectra generated by current driven vortices taken at different fields B including the peak-effect regime for a thick a - Mo x Ge 1 - x film with Corbino-disk and strip-like contact geometries. The field dependences of the critical current, I c ( B ) , for both contact geometries are nearly identical to each other, indicating that the edge effects are not important. For the strip-like geometry voltage noise (at low frequency) takes large values around the peak field B p of I c ( B ) and a spectral shape changes drastically just above B p , suggesting that some structural transformation of vortex solid may take place around B p .

Theory of optical dispersive shock waves in photorefractive media

The theory of optical dispersive shocks generated in the propagation of light beams through photorefractive media is developed. A full one-dimensional analytical theory based on the Whitham modulation approach is given for the simplest case of a sharp steplike initial discontinuity in a beam with one-dimensional striplike geometry. This approach is confirmed by numerical simulations, which are extended also to beams with cylindrical symmetry. The theory explains recent experiments where such dispersive shock waves have been observed.

Spatial bistability and excitability in the chlorite-tetrathionate reaction in cylindrical and conical geometries.

Spatial bistability and excitability in the chlorite-tetrathionate reaction, performed in gels fed by diffusion from one boundary, have been extensively studied, both experimentally and numerically, in a flat annular striplike geometry. We first complement these numerical results. Afterwards, we extend the calculations to the cylindrical and conical geometries. In the cylinder, we compute the limits of bistability and of excitability which are important for experiments in chemomechanics but cannot be directly measured. The results of the simulations in the conical geometry agree with previous experiments on the corresponding setup. We show that the characteristics of the traveling waves which spontaneously arise in the latter geometry provide a simple and direct experimental access to these limits.

Diffusion and electromigration on disordered surfaces

We consider random q-state Potts models for $3\le q \le 8$ on the square lattice where the ferromagnetic couplings take two values $J_1>J_2$ with equal probabilities. For any q the model exhibits a continuous phase transition both in the bulk and at the boundary. Using Monte Carlo techniques the surface and the bulk magnetizations are studied close to the critical temperature and the critical exponents $\beta_1$ and $\beta$ are determined. In the strip-like geometry the critical magnetization profile is investigated with free-fixed spin boundary condition and the characteristic scaling dimension, $\beta_1/\nu$, is calculated from conformal field theory. The critical exponents and scaling dimensions are found monotonously increasing with q. Anomalous dimensions of the relevant scaling fields are estimated and the multifractal behaviour at criticality is also analyzed.

Finite-size effects and operator product expansions in a CFT for d>2

The large momentum expansion for the inverse propagator of the auxiliary field λ( x) in the conformally invariant O( N) vector model is calculated to leading order in 1/ N, in a strip-like geometry with one finite dimension of length L for 2< d<4. Its leading terms are identified as contributions from λ( x) itself and the energy momentum tensor, in agreement with a previous calculation based on conformal operator product expansions. It is found that a non-trivial cancellation takes place by virtue of the gap equation. The leading coefficient of the energy momentum tensor contribution is shown to be related to the free energy density.

The microdot gas avalanche chamber: an investigation of new geometries

The gains of the microstrip and microgap gas avalanche chambers are limited to below gains of 5 × 10 3 by geometrical and gas properties. In order to increase the maximum gain to greater than 2 × 10 4 a new detector geometry, the microdot, is proposed that can be produced at a standard silicon MOS microfabrication facility at similar cost to present microstrip gas detectors. In addition to charged particle tracking, the new geometry is also well suited to imaging applications. The operating characteristics of the new device have been investigated using a numerical simulation and a comparison with conventional strip geometries is presented. These results show that the microdot geometry reaches higher gas gains than the strip-like geometries, for the same set of electrode potentials, with a reduced cathode electric field enhancing operational stability.