Coarsening dynamics in one dimension: The phase diffusion equation and its numerical implementation

Many nonlinear partial differential equations (PDEs) display a coarsening dynamics, i.e., an emerging pattern whose typical length scale $L$ increases with time. The so-called coarsening exponent $n$ characterizes the time dependence of the scale of the pattern, $L(t)\approx t^n$, and coarsening dynamics can be described by a diffusion equation for the phase of the pattern. By means of a multiscale analysis we are able to find the analytical expression of such diffusion equations. Here, we propose a recipe to implement numerically the determination of $D(\lambda)$, the phase diffusion coefficient, as a function of the wavelength $\lambda$ of the base steady state $u_0(x)$. $D$ carries all information about coarsening dynamics and, through the relation $|D(L)| \simeq L^2 /t$, it allows us to determine the coarsening exponent. The main conceptual message is that the coarsening exponent is determined without solving a time-dependent equation, but only by inspecting the periodic steady-state solutions. This provides a much faster strategy than a forward time-dependent calculation. We discuss our method for several different PDEs, both conserved and not conserved

Measure the Measure: the Impact of Differences in Pesticide MRLs on Chilean Fruit Exports to the EU

This paper advances the measurement of nontariff measures (NTMs) by discussing a framework for how to compare regulations. We argue that relative differences in SPS regulations trigger the impact on trade flows between trading partner countries and specifically look at maximum residue levels (MRLs) for pesticides in a case study on Chilean fruit exports to the EU. In order to capture the relative differences and stringency in tolerance levels of trading partners, a simple indicator is constructed and applied in an econometric analysis. In comparison to existing indices of regulatory heterogeneity, the depth of information generated by our indicator severely compromises its coverage. Further development of our heterogeneity index will need to aim at including elements of process standards and conformity assessment procedures

Role of the target orientation angle and orbital angular momentum in the evaporation residue production

The influence of the orientation angles of the target nucleus symmetry axis relative to the beam direction on the production of the evaporation residues is investigated for the $^{48}$Ca+$^{154}$Sm reaction as a function of the beam energy. At low energies ($E_{\rm c.m.}<$137 MeV), the yield of evaporation residues is observed only for collisions with small orientation angles ($\alpha_T<45^0$). At large energies (about $E_{\rm c.m.}=$140--180 MeV) all the orientation angles $\alpha_T$ can contribute to the evaporation residue cross section $\sigma_{ER}$ in the 10--100 mb range, and at $E_{c.m.}>$180 MeV $\sigma_{ER}$ ranges around 0.1--10 mb because the fission barrier for a compound nucleus decreases by increasing its excitation energy and angular momentum.Comment: 20 pages, 10 figures, submitted to JPS

Evolution of the decay mechanisms in central collisions of XeXe + SnSn from E/AE/A = 8 to 29 MeVMeV

Collisions of Xe+Sn at beam energies of $E/A$ = 8 to 29 $MeV$ and leading to fusion-like heavy residues are studied using the $4\pi$ INDRA multidetector. The fusion cross section was measured and shows a maximum at $E/A$ = 18-20 $MeV$. A decomposition into four exit-channels consisting of the number of heavy fragments produced in central collisions has been made. Their relative yields are measured as a function of the incident beam energy. The energy spectra of light charged particles (LCP) in coincidence with the fragments of each exit-channel have been analyzed. They reveal that a composite system is formed, it is highly excited and first decays by emitting light particles and then may breakup into 2- or many- fragments or survives as an evaporative residue. A quantitative estimation of this primary emission is given and compared to the secondary decay of the fragments. These analyses indicate that most of the evaporative LCP precede not only fission but also breakup into several fragments.Comment: Invited Talk given at the 11th International Conference on Nucleus-Nucleus Collisions (NN2012), San Antonio, Texas, USA, May 27-June 1, 2012. To appear in the NN2012 Proceedings in Journal of Physics: Conference Series (JPCS