Evidence for a singularity in ideal magnetohydrodynamics: implications for fast reconnection

Numerical evidence for a finite-time singularity in ideal 3D magnetohydrodynamics (MHD) is presented. The simulations start from two interlocking magnetic flux rings with no initial velocity. The magnetic curvature force causes the flux rings to shrink until they come into contact. This produces a current sheet between them. In the ideal compressible calculations, the evidence for a singularity in a finite time $t_c$ is that the peak current density behaves like $|J|_\infty \sim 1/(t_c-t)$ for a range of sound speeds (or plasma betas). For the incompressible calculations consistency with the compressible calculations is noted and evidence is presented that there is convergence to a self-similar state. In the resistive reconnection calculations the magnetic helicity is nearly conserved and energy is dissipated.Comment: 4 pages, 4 figure

Asymptotically stable particle-in-cell methods for the Vlasov-Poisson system with a strong external magnetic field

International audienceThis paper deals with the numerical resolution of the Vlasov-Poissonsystem with a strong external magnetic field by Particle-In-Cell(PIC) methods. In this regime, classical PIC methods are subject tostability constraints on the time and space steps related to the smallLarmor radius and plasma frequency. Here, we propose anasymptotic-preserving PIC scheme which is not subjected to theselimitations. Our approach is based on first and higher order semi-implicit numericalschemes already validated on dissipative systems. Additionally, when the magnitude of the external magneticfield becomes large, this method provides a consistent PICdiscretization of the guiding-center equation, that is, incompressibleEuler equation in vorticity form. We propose several numerical experiments which provide a solid validation of the method and its underlying concepts

Probability-Changing Cluster Algorithm: Study of Three-Dimensional Ising Model and Percolation Problem

We present a detailed description of the idea and procedure for the newly proposed Monte Carlo algorithm of tuning the critical point automatically, which is called the probability-changing cluster (PCC) algorithm [Y. Tomita and Y. Okabe, Phys. Rev. Lett. {\bf 86} (2001) 572]. Using the PCC algorithm, we investigate the three-dimensional Ising model and the bond percolation problem. We employ a refined finite-size scaling analysis to make estimates of critical point and exponents. With much less efforts, we obtain the results which are consistent with the previous calculations. We argue several directions for the application of the PCC algorithm.Comment: 6 pages including 8 eps figures, to appear in J. Phys. Soc. Jp

Controlling magnetic order and quantum disorder in molecule-based magnets.

We investigate the structural and magnetic properties of two molecule-based magnets synthesized from the same starting components. Their different structural motifs promote contrasting exchange pathways and consequently lead to markedly different magnetic ground states. Through examination of their structural and magnetic properties we show that [Cu(pyz)(H 2 O)(gly) 2 ](ClO 4 ) 2 may be considered a quasi-one-dimensional quantum Heisenberg antiferromagnet whereas the related compound [Cu(pyz)(gly)](ClO 4 ) , which is formed from dimers of antiferromagnetically interacting Cu 2+ spins, remains disordered down to at least 0.03 K in zero field but shows a field-temperature phase diagram reminiscent of that seen in materials showing a Bose-Einstein condensation of magnons

Nonexistence of self-similar singularities for the 3D incompressible Euler equations

We prove that there exists no self-similar finite time blowing up solution to the 3D incompressible Euler equations. By similar method we also show nonexistence of self-similar blowing up solutions to the divergence-free transport equation in $\Bbb R^n$. This result has direct applications to the density dependent Euler equations, the Boussinesq system, and the quasi-geostrophic equations, for which we also show nonexistence of self-similar blowing up solutions.Comment: This version refines the previous one by relaxing the condition of compact support for the vorticit

Controlling magnetic order and quantum disorder in molecule-based magnets

We investigate the structural and magnetic properties of two molecule-based magnets synthesized from the same starting components. Their different structural motifs promote contrasting exchange pathways and consequently lead to markedly different magnetic ground states. Through examination of their structural and magnetic properties we show that [Cu(pyz)(H2O)(gly)2](ClO4)2 may be considered a quasi-one-dimensional quantum Heisenberg antiferromagnet whereas the related compound [Cu(pyz)(gly)](ClO4), which is formed from dimers of antiferromagnetically interacting Cu2+ spins, remains disordered down to at least 0.03 K in zero field but shows a field-temperature phase diagram reminiscent of that seen in materials showing a Bose-Einstein condensation of magnons

Random-cluster multi-histogram sampling for the q-state Potts model

Using the random-cluster representation of the $q$-state Potts models we consider the pooling of data from cluster-update Monte Carlo simulations for different thermal couplings $K$ and number of states per spin $q$. Proper combination of histograms allows for the evaluation of thermal averages in a broad range of $K$ and $q$ values, including non-integer values of $q$. Due to restrictions in the sampling process proper normalization of the combined histogram data is non-trivial. We discuss the different possibilities and analyze their respective ranges of applicability.Comment: 12 pages, 9 figures, RevTeX

Blow up criterion for compressible nematic liquid crystal flows in dimension three

In this paper, we consider the short time strong solution to a simplified hydrodynamic flow modeling the compressible, nematic liquid crystal materials in dimension three. We establish a criterion for possible breakdown of such solutions at finite time in terms of the temporal integral of both the maximum norm of the deformation tensor of velocity gradient and the square of maximum norm of gradient of liquid crystal director field.Comment: 22 page