142 research outputs found
The frustration-based approach of supercooled liquids and the glass transition: a review and critical assessment
One of the most spectacular phenomena in physics in terms of dynamical range
is the glass transition and the associated slowing down of flow and relaxation
with decreasing temperature. That it occurs in many different liquids seems to
call for a "universal" theory. In this article, we review one such theoretical
approach which is based on the concept of "frustration". Frustration in this
context describes an incompatibility between extension of the locally preferred
order in a liquid and tiling of the whole space. We provide a critical
assessment of what has been achieved within this approach and we discuss the
relation with other theories of the glass transition.Comment: 48 pages, 13 figures, submitted to J. Phys : Cond. Matte
Symmetry breaking of dipole orientations on Caspar-Klug lattices
Anisotropic dipole-dipole interaction often plays a key role in biological,
soft, and complex matter. For it to induce non-trivial order in the system,
there must be additional repulsive interactions or external potentials involved
that partially or completely fix the positions of the dipoles. These positions
can often be represented as an underlying lattice on which dipole interaction
induces orientational ordering of the particles. On lattices in the Euclidean
plane, dipoles have been found to assume different ground state configurations
depending on the lattice type, with a global ordering in the form of a
macrovortex being observed in many cases. A similar macrovortex configuration
of dipoles has recently been shown to be the sole ground state for dipoles
positioned on spherical lattices based on solutions of the Thomson problem. At
the same time, no symmetric configurations have been observed, even though the
positional order of Thomson lattices exhibits a high degree of symmetry. Here,
we show that a different choice of spherical lattices based on Caspar-Klug
construction leads to ground states of dipoles with various degrees of
symmetry, including the icosahedral symmetry of the underlying lattice. We
analyze the stability of the highly symmetric metastable states, their symmetry
breaking into subsymmetries of the icosahedral symmetry group, and present a
phase diagram of symmetries with respect to lattice parameters. The observed
relationship between positional order and dipole-induced symmetry breaking
hints at ways of fine-tuning the structure of spherical assemblies and their
design.Comment: 9 pages, 7 figure
Review of Rotational Symmetry Breaking in Baby Skyrme Models
We discuss one of the most interesting phenomena exhibited by baby skyrmions
-- breaking of rotational symmetry. The topics we will deal with here include
the appearance of rotational symmetry breaking in the static solutions of baby
Skyrme models, both in flat as well as in curved spaces, the zero-temperature
crystalline structure of baby skyrmions, and finally, the appearance of
spontaneous breaking of rotational symmetry in rotating baby skyrmions.Comment: 35 pages, 16 figures. A version of this manuscript with
higher-resolution figures is available at
http://www.tau.ac.il/~itayhe/SkReview/SkReview.ra
Symetric Monopoles
We discuss Bogomolny monopoles of arbitrary charge invariant
under various symmetry groups. The analysis is largely in terms of the spectral
curves, the rational maps, and the Nahm equations associated with monopoles. We
consider monopoles invariant under inversion in a plane, monopoles with cyclic
symmetry, and monopoles having the symmetry of a regular solid. We introduce
the notion of a strongly centred monopole and show that the space of such
monopoles is a geodesic submanifold of the monopole moduli space.
By solving Nahm's equations we prove the existence of a tetrahedrally
symmetric monopole of charge and an octahedrally symmetric monopole of
charge , and determine their spectral curves. Using the geodesic
approximation to analyse the scattering of monopoles with cyclic symmetry, we
discover a novel type of non-planar -monopole scattering process
Rotated Versions of the Jablonowski SteadyâState and Baroclinic Wave Test Cases: A Dynamical Core Intercomparison
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95316/1/jame31.pd
The ICON-1.2 hydrostatic atmospheric dynamical core on triangular grids â Part 1: Formulation and performance of the baseline version
Abstract. As part of a broader effort to develop next-generation models for numerical weather prediction and climate applications, a hydrostatic atmospheric dynamical core is developed as an intermediate step to evaluate a finite-difference discretization of the primitive equations on spherical icosahedral grids. Based on the need for mass-conserving discretizations for multi-resolution modelling as well as scalability and efficiency on massively parallel computing architectures, the dynamical core is built on triangular C-grids using relatively small discretization stencils. This paper presents the formulation and performance of the baseline version of the new dynamical core, focusing on properties of the numerical solutions in the setting of globally uniform resolution. Theoretical analysis reveals that the discrete divergence operator defined on a single triangular cell using the Gauss theorem is only first-order accurate, and introduces grid-scale noise to the discrete model. The noise can be suppressed by fourth-order hyper-diffusion of the horizontal wind field using a time-step and grid-size-dependent diffusion coefficient, at the expense of stronger damping than in the reference spectral model. A series of idealized tests of different complexity are performed. In the deterministic baroclinic wave test, solutions from the new dynamical core show the expected sensitivity to horizontal resolution, and converge to the reference solution at R2B6 (35 km grid spacing). In a dry climate test, the dynamical core correctly reproduces key features of the meridional heat and momentum transport by baroclinic eddies. In the aqua-planet simulations at 140 km resolution, the new model is able to reproduce the same equatorial wave propagation characteristics as in the reference spectral model, including the sensitivity of such characteristics to the meridional sea surface temperature profile. These results suggest that the triangular-C discretization provides a reasonable basis for further development. The main issues that need to be addressed are the grid-scale noise from the divergence operator which requires strong damping, and a phase error of the baroclinic wave at medium and low resolutions
Conservative Space and Time Regularizations for the ICON Model
In this article, we consider two modified (regularized) versions of the shallow water equations which are of potential interest for the construction of global oceanic and atmospheric models. The first modified system is the
Lagrangian averaged shallow water system, which involves the use of a regularized advection velocity and which has been recently proposed as a turbulence parametrization for ocean models in order to avoid an excessive damping of the computed solution. The second modified system is the pressure regularized shallow water system, which provides an alternative to traditional semi-implicit time integration schemes and which results in larger freedom in the design of the time integrator and in a better treatment of nearly geostrophic flows. The two modified systems are both nondissipative, in that they do not result in an increase of the overall dissipation of the flow. We first show how the numerical discretization of the two regularized equation sets can be constructed in a natural way within the finite difference formulation adopted for the
ICON general circulation model currently under developed at the Max Planck Institute for Meteorology and at the German
Weather Service. The resulting scheme is then validated on a set of idealized tests in both planar and spherical geometry, and the effects of the considered regularizations on the computed solution are analyzed concerning: stability properties and maximum allowable time steps, similarities and differences in the behavior of the solutions, discrete conservation of flow invariants such as total energy and enstrophy. Our analysis should be considered as a first step toward the use of the regularization ideas in the simulation of more complex and more realistic flows
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