Effects of constraints in general branched molecules: A quantitative ab initio study in HCO-L-Ala-NH2

A general approach to the design of accurate classical potentials for protein folding is described. It includes the introduction of a meaningful statistical measure of the differences between approximations of the same potential energy, the definition of a set of Systematic and Approximately Separable and Modular Internal Coordinates (SASMIC), much convenient for the simulation of general branched molecules, and the imposition of constraints on the most rapidly oscillating degrees of freedom. All these tools are used to study the effects of constraints in the Conformational Equilibrium Distribution (CED) of the model dipeptide HCO-L-Ala-NH2. We use ab initio Quantum Mechanics calculations including electron correlation at the MP2 level to describe the system, and we measure the conformational dependence of the correcting terms to the naive CED based in the Potential Energy Surface (PES) without any simplifying assumption. These terms are related to mass-metric tensors determinants and also occur in the Fixman's compensating potential. We show that some of the corrections are non-negligible if one is interested in the whole Ramachandran space. On the other hand, if only the energetically lower region, containing the principal secondary structure elements, is assumed to be relevant, then, all correcting terms may be neglected up to peptides of considerable length. This is the first time, as far as we know, that the analysis of the conformational dependence of these correcting terms is performed in a relevant biomolecule with a realistic potential energy function.Comment: 8 pages, 1 figure, LaTeX, aipproc style (included

A Statistical Study of Photospheric Magnetic Field Changes During 75 Solar Flares

Abrupt and permanent changes of photospheric magnetic fields have been observed during solar flares. The changes seem to be linked to the reconfiguration of magnetic fields, but their origin is still unclear. We carried out a statistical analysis of permanent line-of-sight magnetic field ($B_{\rm LOS}$) changes during 18 X-, 37 M-, 19 C- and 1 B-class flares using data from Solar Dynamics Observatory/Helioseismic and Magnetic Imager. We investigated the properties of permanent changes, such as frequency, areas, and locations. We detected changes of $B_{\rm LOS}$ in 59/75 flares. We find that strong flares are more likely to show changes, with all flares $\ge$ M1.6 exhibiting them. For weaker flares, permanent changes are observed in 6/17 C-flares. 34.3\% of the permanent changes occurred in the penumbra and 18.9\% in the umbra. Parts of the penumbra appeared or disappeared in 23/75 flares. The area where permanent changes occur is larger for stronger flares. Strong flares also show a larger change of flux, but there is no dependence of the magnetic flux change on the heliocentric angle. The mean rate of change of flare-related magnetic field changes is 20.7 Mx cm$^{-2}$ min$^{-1}$. The number of permanent changes decays exponentially with distance from the polarity inversion line. The frequency of the strength of permanent changes decreases exponentially, and permanent changes up to 750 Mx cm$^{-2}$ were observed. We conclude that permanent magnetic field changes are a common phenomenon during flares, and future studies will clarify their relation to accelerated electrons, white light emission, and sunquakes to further investigate their origin.Comment: Piblished in Ap

Flow damping in stellarators close to quasisymmetry

Quasisymmetric stellarators are a type of optimized stellarators for which flows are undamped to lowest order in an expansion in the normalized Larmor radius. However, perfect quasisymmetry is impossible. Since large flows may be desirable as a means to reduce turbulent transport, it is important to know when a stellarator can be considered to be sufficiently close to quasisymmetry. The answer to this question depends strongly on the size of the spatial gradients of the deviation from quasisymmetry and on the collisionality regime. Recently, formal criteria for closeness to quasisymmetry have been derived in a variety of situations. In particular, the case of deviations with large gradients was solved in the $1/\nu$ regime. Denoting by $\alpha$ a parameter that gives the size of the deviation from quasisymmetry, it was proven that particle fluxes do not scale with $\alpha^{3/2}$, as typically claimed, but with $\alpha$. It was also shown that ripple wells are not necessarily the main cause of transport. This paper reviews those works and presents a new result in another collisionality regime, in which particles trapped in ripple wells are collisional and the rest are collisionless.Comment: 14 pages, 2 figures. To appear in Plasma Physics and Controlled Fusio

Optimizing stellarators for large flows

Plasma flow is damped in stellarators because they are not intrinsically ambipolar, unlike tokamaks, in which the flux-surface averaged radial electric current vanishes for any value of the radial electric field. Only quasisymmetric stellarators are intrinsically ambipolar, but exact quasisymmetry is impossible to achieve in non-axisymmetric toroidal configurations. By calculating the violation of intrinsic ambipolarity due to deviations from quasisymmetry, one can derive criteria to assess when a stellarator can be considered quasisymmetric in practice, i.e. when the flow damping is weak enough. Let us denote by $\alpha$ a small parameter that controls the size of a perturbation to an exactly quasisymmetric magnetic field. Recently, it has been shown that if the gradient of the perturbation is sufficiently small, the flux-surface averaged radial electric current scales as $\alpha^2$ for any value of the collisionality. It was also argued that when the gradient of the perturbation is large, the quadratic scaling is replaced by a more unfavorable one. In this paper, perturbations with large gradients are rigorously treated. In particular, it is proven that for low collisionality a perturbation with large gradient yields, at best, an $O(|\alpha|)$ deviation from quasisymmetry. Heuristic estimations in the literature incorrectly predicted an $O(|\alpha|^{3/2})$ deviation.Comment: 24 pages, 2 figures. To appear in Plasma Physics and Controlled Fusio

The effect of tangential drifts on neoclassical transport in stellarators close to omnigeneity

In general, the orbit-averaged radial magnetic drift of trapped particles in stellarators is non-zero due to the three-dimensional nature of the magnetic field. Stellarators in which the orbit-averaged radial magnetic drift vanishes are called omnigeneous, and they exhibit neoclassical transport levels comparable to those of axisymmetric tokamaks. However, the effect of deviations from omnigeneity cannot be neglected in practice. For sufficiently low collision frequencies (below the values that define the $1/\nu$ regime), the components of the drifts tangential to the flux surface become relevant. This article focuses on the study of such collisionality regimes in stellarators close to omnigeneity when the gradient of the non-omnigeneous perturbation is small. First, it is proven that closeness to omnigeneity is required to preserve radial locality in the drift-kinetic equation for collisionalities below the $1/\nu$ regime. Then, it is shown that neoclassical transport is determined by two layers in phase space. One of the layers corresponds to the $\sqrt{\nu}$ regime and the other to the superbanana-plateau regime. The importance of the superbanana-plateau layer for the calculation of the tangential electric field is emphasized, as well as the relevance of the latter for neoclassical transport in the collisionality regimes considered in this paper. In particular, the tangential electric field is essential for the emergence of a new subregime of superbanana-plateau transport when the radial electric field is small. A formula for the ion energy flux that includes the $\sqrt{\nu}$ regime and the superbanana-plateau regime is given. The energy flux scales with the square of the size of the deviation from omnigeneity. Finally, it is explained why below a certain collisionality value the formulation presented in this article ceases to be valid.Comment: 36 pages. Version to be published in Plasma Physics and Controlled Fusio

Phase changes in 38 atom Lennard-Jones clusters. II: A parallel tempering study of equilibrium and dynamic properties in the molecular dynamics and microcanonical

We study the 38-atom Lennard-Jones cluster with parallel tempering Monte Carlo methods in the microcanonical and molecular dynamics ensembles. A new Monte Carlo algorithm is presented that samples rigorously the molecular dynamics ensemble for a system at constant total energy, linear and angular momenta. By combining the parallel tempering technique with molecular dynamics methods, we develop a hybrid method to overcome quasi-ergodicity and to extract both equilibrium and dynamical properties from Monte Carlo and molecular dynamics simulations. Several thermodynamic, structural and dynamical properties are investigated for LJ$_{38}$, including the caloric curve, the diffusion constant and the largest Lyapunov exponent. The importance of insuring ergodicity in molecular dynamics simulations is illustrated by comparing the results of ergodic simulations with earlier molecular dynamics simulations.Comment: Journal of Chemical Physics, accepte

Electrostatic potential variations on stellarator magnetic surfaces in low collisionality regimes

The component of the neoclassical electrostatic potential that is non-constant on the magnetic surface, that we denote by $\tilde\varphi$, can affect radial transport of highly charged impurities, and this has motivated its inclusion in some modern neoclassical codes. The number of neoclassical simulations in which $\tilde\varphi$ is calculated is still scarce, partly because they are usually demanding in terms of computational resources, especially at low collisionality. In this paper the size, the scaling with collisionality and with aspect ratio, and the structure of $\tilde\varphi$ on the magnetic surface are analytically derived in the $1/\nu$, $\sqrt{\nu}$ and superbanana-plateau regimes of stellarators close to omnigeneity; i. e. stellarators that have been optimized for neoclassical transport. It is found that the largest $\tilde\varphi$ that the neoclassical equations admit scales linearly with the inverse aspect ratio and with the size of the deviation from omnigeneity. Using a model for a perturbed omnigeneous configuration, the analytical results are verified and illustrated with calculations by the code KNOSOS. The techniques, results and numerical tools employed in this paper can be applied to neoclassical transport problems in tokamaks with broken axisymmetry.Comment: 30 pages, 12 figures, 1 table. Published versio