Application of standard and refined heat balance integral methods to one-dimensional Stefan problems

The work in this paper concerns the study of conventional and refined heat balance integral methods for a number of phase change problems. These include standard test problems, both with one and two phase changes, which have exact solutions to enable us to test the accuracy of the approximate solutions. We also consider situations where no analytical solution is available and compare these to numerical solutions. It is popular to use a quadratic profile as an approximation of the temperature, but we show that a cubic profile, seldom considered in the literature, is far more accurate in most circumstances. In addition, the refined integral method can give greater improvement still and we develop a variation on this method which turns out to be optimal in some cases. We assess which integral method is better for various problems, showing that it is largely dependent on the specified boundary conditions.

A one-dimensional Keller-Segel equation with a drift issued from the boundary

We investigate in this note the dynamics of a one-dimensional Keller-Segel type model on the half-line. On the contrary to the classical configuration, the chemical production term is located on the boundary. We prove, under suitable assumptions, the following dichotomy which is reminiscent of the two-dimensional Keller-Segel system. Solutions are global if the mass is below the critical mass, they blow-up in finite time above the critical mass, and they converge to some equilibrium at the critical mass. Entropy techniques are presented which aim at providing quantitative convergence results for the subcritical case. This note is completed with a brief introduction to a more realistic model (still one-dimensional).

One-dimensional solidification of supercooled melts

In this paper a one-phase supercooled Stefan problem, with a nonlinear relation between the phase change temperature and front velocity, is analysed. The model with the standard linear approximation, valid for small supercooling, is first examined asymptotically. The nonlinear case is more difficult to analyse and only two simple asymptotic results are found. Then, we apply an accurate heat balance integral method to make further progress. Finally, we compare the results found against numerical solutions. The results show that for large supercooling the linear model may be highly inaccurate and even qualitatively incorrect. Similarly as the Stefan number β → 1&sup&+&/sup& the classic Neumann solution which exists down to β =1 is far from the linear and nonlinear supercooled solutions and can significantly overpredict the solidification rate.

Effects of convection on the removal of the multiplicity of stable states in one-dimensional vertical models

Here I develop a model of a radiative-convective atmosphere with both radiative and convective schemes highly simplified. The atmospheric absorption of radiation at selective wavelengths makes use of constant mass absorption coefficients in finite width spectral bands. The convective regime is introduced by using a prescribed lapse rate in the troposphere. The main novelty of the radiative-convective model developed here is that it is solved without using any angular approximation for the radiation field. The solution obtained in the purely radiation mode (i. e. with convection ignored) leads to multiple equilibria of stable states, being very similar to some results recently found in simple models of planetary atmospheres. However, the introduction of convective processes removes the multiple equilibria of stable states. This shows the importance of taking convective processes into account even for qualitative analyses of planetary atmosphere

Effective one-dimensional square well for two-dimensional quantum wires

The symmetrical two-dimensional quantum wire with two straight leads joined to an arbitrarily shaped interior cavity is studied with emphasis on the single-mode approximation. It is found that for both transmission and bound-state problems the solution is equivalent to that for an energy-dependent one-dimensional square well. Quantum wires with a circular bend, and with single and double right-angle bends, are examined as examples. We also indicate a possible way to detect bound states in a double bend based on the experimental setup of Wu et al.

MADAP, a flexible clustering tool for the interpretation of one-dimensional genome annotation data.

A recurring task in the analysis of mass genome annotation data from high-throughput technologies is the identification of peaks or clusters in a noisy signal profile. Examples of such applications are the definition of promoters on the basis of transcription start site profiles, the mapping of transcription factor binding sites based on ChIP-chip data and the identification of quantitative trait loci (QTL) from whole genome SNP profiles. Input to such an analysis is a set of genome coordinates associated with counts or intensities. The output consists of a discrete number of peaks with respective volumes, extensions and center positions. We have developed for this purpose a flexible one-dimensional clustering tool, called MADAP, which we make available as a web server and as standalone program. A set of parameters enables the user to customize the procedure to a specific problem. The web server, which returns results in textual and graphical form, is useful for small to medium-scale applications, as well as for evaluation and parameter tuning in view of large-scale applications, requiring a local installation. The program written in C++ can be freely downloaded from ftp://ftp.epd.unil.ch/pub/software/unix/madap. The MADAP web server can be accessed at http://www.isrec.isb-sib.ch/madap/.

Semiclassical coupled wave theory and its application to TE waves in one dimensional crystals

A semiclassical coupled-wave theory is developed for TE waves in one-dimensional periodic structures. The theory is used to calculate the bandwidths and reflection/transmission characteristics of such structures, as functions of the incident wave frequency. The results are in good agreement with exact numerical simulations for an arbitrary angle of incidence and for any achievable refractive index contrast on a period of the structure.

Internal and external fluctuations around nonequilibrium steady states in one-dimensional heat-conduction problems

Thermal fluctuations around inhomogeneous nonequilibrium steady states of one-dimensional rigid heat conductors are analyzed in the framework of generalized fluctuating hydrodynamics. The effect of an external source of noise is also considered. External fluctuations come from temperature and position fluctuations of the source. Contributions of each kind of noise to the temperature correlation function are computed and compared through the study of its asymptotic behavior.

Magnetic relaxation of a one-dimensional model for small particle systems with dipolar interactions: Monte Carlo simulation

Atribution as a function of the time are analyzed and this study leads to a deeper knowledge of the microscopic processes involved in the magnetic relaxation

Quasi-two-dimensional electrodeposition under forced fluid flow

Experimental quasi-two-dimensional Zn electrodeposits are grown under forced convection conditions. Large-scale effects, with preferential growth towards the impinging flow, together with small-scale roughness suppression effects are evidenced and separately analyzed by using two different radial cell configurations. Interpretations are given in terms of primary concepts concerning current and concentration distributions.

Dispersion of passive particles by a quasi-two-dimensional turbulent flow

Using the experimental data of Paret and Tabeling [Phys. Rev. Lett. 79, 4162 (1997)] we consider in detail the dispersion of particle pairs by a two-dimensional turbulent flow and its relation to the kinematic properties of the velocity field. We show that the mean square separation of a pair of particles is governed by rather rare, extreme events and that the majority of initially close pairs are not dispersed by the flow. Another manifestation of the same effect is the fact that the dispersion of an initially dense cluster is not the result of homogeneously spreading the particles within the whole system. Instead it proceeds through a splitting into smaller but also dense clusters. The statistical nature of this effect is discussed.

Further insights on dynamic morphological transitions in quasi-two-dimensional electrodeposition

Dynamic morphological transitions in thin-layer electrodeposits obtained from copper sulphate solutions have been studied. The chemical composition of the electrodeposits indicates that they appear as a consequence of the competition between copper and cuprous oxide formation. In addition, the Ohmic control of the process is verified at initial stages of the deposit growth. At higher deposit developments, gravity-induced convection currents play a role in the control of the whole process and affect the position of these transitions.

Influence of an inert electrolyte on the morphology of quasi-two-dimensional electrodeposits

The influence of an inert electrolyte (sodium sulfate) on quasi-two-dimensional copper electrodeposition from a nondeaerated aqueous copper sulfate solution has been analyzed. The different morphologies for a fixed concentration of CuSO4 have been classified in a diagram in terms of the applied potential and the inert electrolyte concentration. The main conclusion is the extension of the well-known Ohmic model for the homogeneous growth regime for copper sulfate solutions with small amounts of sodium sulfate. Moreover, we have observed the formation of fingerlike deposits at large applied potential and inert electrolyte concentration values, before hydrogen evolution becomes the main electrode reaction.

Ab Initio study of magnetic interactions in the KCuF3 and K2CuF4 low-dimensional Systems

The ab initio cluster model approach has been used to study the electronic structure and magnetic coupling of KCuF3 and K2CuF4 in their various ordered polytype crystal forms. Due to a cooperative Jahn-Teller distortion these systems exhibit strong anisotropies. In particular, the magnetic properties strongly differ from those of isomorphic compounds. Hence, KCuF3 is a quasi-one-dimensional (1D) nearest neighbor Heisenberg antiferromagnet whereas K2CuF4 is the only ferromagnet among the K2MF4 series of compounds (M=Mn, Fe, Co, Ni, and Cu) behaving all as quasi-2D nearest neighbor Heisenberg systems. Different ab initio techniques are used to explore the magnetic coupling in these systems. All methods, including unrestricted Hartree-Fock, are able to explain the magnetic ordering. However, quantitative agreement with experiment is reached only when using a state-of-the-art configuration interaction approach. Finally, an analysis of the dependence of the magnetic coupling constant with respect to distortion parameters is presented.