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

Dynamic Phase Transition, Universality, and Finite-size Scaling in the Two-dimensional Kinetic Ising Model in an Oscillating Field

We study the two-dimensional kinetic Ising model below its equilibrium critical temperature, subject to a square-wave oscillating external field. We focus on the multi-droplet regime where the metastable phase decays through nucleation and growth of many droplets of the stable phase. At a critical frequency, the system undergoes a genuine non-equilibrium phase transition, in which the symmetry-broken phase corresponds to an asymmetric stationary limit cycle for the time-dependent magnetization. We investigate the universal aspects of this dynamic phase transition at various temperatures and field amplitudes via large-scale Monte Carlo simulations, employing finite-size scaling techniques adopted from equilibrium critical phenomena. The critical exponents, the fixed-point value of the fourth-order cumulant, and the critical order-parameter distribution all are consistent with the universality class of the two-dimensional equilibrium Ising model. We also study the cross-over from the multi-droplet to the strong-field regime, where the transition disappears

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

Vorticity alignment results for the three-dimensional Euler and Navier-Stokes equations

We address the problem in Navier-Stokes isotropic turbulence of why the vorticity accumulates on thin sets such as quasi-one-dimensional tubes and quasi-two-dimensional sheets. Taking our motivation from the work of Ashurst, Kerstein, Kerr and Gibson, who observed that the vorticity vector {\boldmath\omega} aligns with the intermediate eigenvector of the strain matrix $S$, we study this problem in the context of both the three-dimensional Euler and Navier-Stokes equations using the variables \alpha = \hat{{\boldmath\xi}}\cdot S\hat{{\boldmath\xi}} and {\boldmath\chi} = \hat{{\boldmath\xi}}\times S\hat{{\boldmath\xi}} where \hat{{\boldmath\xi}} = {\boldmath\omega}/\omega. This introduces the dynamic angle $\phi (x,t) = \arctan(\frac{\chi}{\alpha})$, which lies between {\boldmath\omega} and S{\boldmath\omega}. For the Euler equations a closed set of differential equations for $\alpha$ and {\boldmath\chi} is derived in terms of the Hessian matrix of the pressure $P = \{p_{,ij}\}$. For the Navier-Stokes equations, the Burgers vortex and shear layer solutions turn out to be the Lagrangian fixed point solutions of the equivalent (\alpha,{\boldmath\chi}) equations with a corresponding angle $\phi = 0$. Under certain assumptions for more general flows it is shown that there is an attracting fixed point of the (\alpha,\bchi) equations which corresponds to positive vortex stretching and for which the cosine of the corresponding angle is close to unity. This indicates that near alignment is an attracting state of the system and is consistent with the formation of Burgers-like structures.Comment: To appear in Nonlinearity Nov. 199

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

Fermions and Disorder in Ising and Related Models in Two Dimensions

The aspects of phase transitions in the two-dimensional Ising models modified by quenched and annealed site disorder are discussed in the framework of fermionic approach based on the reformulation of the problem in terms of integrals with anticommuting Grassmann variables.Comment: 11 pages, 1 table, no figures. The discussion is merely based on a talk given at the International Bogoliubov Conference on Problems of Theoretical and Mathematical Physics, MIRAS--JINR, Moscow--Dubna, Russia, August 21--27, 200

The derivation of the formyl-group oxygen of chlorophyll b in higher plants from molecular oxygen.

The mechanism of formation of the formyl group of chlorophyll b has long been obscure but, in this paper, the origin of the 7-formyl-group oxygen of chlorophyll b in higher plants was determined by greening etiolated maize leaves, excised from dark-grown plants, by illumination under white light in the presence of either H218O or 18O2 and examining the newly synthesized chlorophylls by mass spectroscopy. To minimize the possible loss of 18O label from the 7-formyl substituent by reversible formation of chlorophyll b-71-gem-diol (hydrate) with unlabelled water in the cell, the formyl group was reduced to a hydroxymethyl group during extraction with methanol containing NaBH4: chlorophyll a remained unchanged during this rapid reductive extraction process. Mass spectra of chlorophyll a and [7-hydroxymethyl]-chlorophyll b extracted from leaves greened in the presence of either H218O or 18O2 revealed that 18O was incorporated only from molecular oxygen but into both chlorophylls: the mass spectra were consistent with molecular oxygen providing an oxygen atom not only for incorporation into the 7-formyl group of chlorophyll b but also for the well-documented incorporation into the 131-oxo group of both chlorophylls a and b [see Walker, C. J., Mansfield, K. E., Smith, K. M. & Castelfranco, P. A. (1989) Biochem. J. 257, 599–602]. The incorporation of isotope led to as much as 77% enrichment of the 131-oxo group of chlorophyll a: assuming identical incorporation into the 131 oxygen of chlorophyll b, then enrichment of the 7-formyl oxygen was as much as 93%. Isotope dilution by re-incorporation of photosynthetically produced oxygen from unlabelled water was negligible as shown by a greening experiment in the presence of 3-(3,4-dichlorophenyl)-1,1-dimethylurea. The high enrichment using 18O2, and the absence of labelling by H218O, unequivocally demonstrates that molecular oxygen is the sole precursor of the 7-formyl oxygen of chlorophyll b in higher plants and strongly suggests a single pathway for the formation of the chlorophyll b formyl group involving the participation of an oxygenase-type enzyme

Surface critical exponents at a uniaxial Lifshitz point

Using Monte Carlo techniques, the surface critical behaviour of three-dimensional semi-infinite ANNNI models with different surface orientations with respect to the axis of competing interactions is investigated. Special attention is thereby paid to the surface criticality at the bulk uniaxial Lifshitz point encountered in this model. The presented Monte Carlo results show that the mean-field description of semi-infinite ANNNI models is qualitatively correct. Lifshitz point surface critical exponents at the ordinary transition are found to depend on the surface orientation. At the special transition point, however, no clear dependency of the critical exponents on the surface orientation is revealed. The values of the surface critical exponents presented in this study are the first estimates available beyond mean-field theory.Comment: 10 pages, 7 figures include

The geometry of nonlinear least squares with applications to sloppy models and optimization

Parameter estimation by nonlinear least squares minimization is a common problem with an elegant geometric interpretation: the possible parameter values of a model induce a manifold in the space of data predictions. The minimization problem is then to find the point on the manifold closest to the data. We show that the model manifolds of a large class of models, known as sloppy models, have many universal features; they are characterized by a geometric series of widths, extrinsic curvatures, and parameter-effects curvatures. A number of common difficulties in optimizing least squares problems are due to this common structure. First, algorithms tend to run into the boundaries of the model manifold, causing parameters to diverge or become unphysical. We introduce the model graph as an extension of the model manifold to remedy this problem. We argue that appropriate priors can remove the boundaries and improve convergence rates. We show that typical fits will have many evaporated parameters. Second, bare model parameters are usually ill-suited to describing model behavior; cost contours in parameter space tend to form hierarchies of plateaus and canyons. Geometrically, we understand this inconvenient parametrization as an extremely skewed coordinate basis and show that it induces a large parameter-effects curvature on the manifold. Using coordinates based on geodesic motion, these narrow canyons are transformed in many cases into a single quadratic, isotropic basin. We interpret the modified Gauss-Newton and Levenberg-Marquardt fitting algorithms as an Euler approximation to geodesic motion in these natural coordinates on the model manifold and the model graph respectively. By adding a geodesic acceleration adjustment to these algorithms, we alleviate the difficulties from parameter-effects curvature, improving both efficiency and success rates at finding good fits.Comment: 40 pages, 29 Figure