4,615 research outputs found
Locally preferred structure in simple atomic liquids
We propose a method to determine the locally preferred structure of model
liquids. This latter is obtained numerically as the global minimum of the
effective energy surface of clusters formed by small numbers of particles
embedded in a liquid-like environment. The effective energy is the sum of the
intra-cluster interaction potential and of an external field that describes the
influence of the embedding bulk liquid at a mean-field level. Doing so we
minimize the surface effects present in isolated clusters without introducing
the full blown geometrical frustration present in bulk condensed phases. We
find that the locally preferred structure of the Lennard-Jones liquid is an
icosahedron, and that the liquid-like environment only slightly reduces the
relative stability of the icosahedral cluster. The influence of the boundary
conditions on the nature of the ground-state configuration of Lennard-Jones
clusters is also discussed.Comment: RevTeX 4, 17 pages, 6 eps figure
Asymmetric isolated skyrmions in polar magnets with easy-plane anisotropy
We introduce a new class of isolated magnetic skyrmions emerging within
tilted ferromagnetic phases of polar magnets with easy-plane anisotropy. The
asymmetric magnetic structure of these skyrmions is associated with an
intricate pattern of the energy density, which exhibits positive and negative
asymptotics with respect to the surrounding state with a ferromagnetic moment
tilted away from the polar axis. Correspondingly, the skyrmion-skyrmion
interaction has an anisotropic character and can be either attractive or
repulsive depending on the relative orientation of the skyrmion pair. We
investigate the stability of these novel asymmetric skyrmions against the
elliptical cone state and follow their transformation into axisymmetric
skyrmions, when the tilted ferromagnetic moment of the host phase is reduced.
Our theory gives clear directions for experimental studies of isolated
asymmetric skyrmions and their clusters embedded in tilted ferromagnetic
phases
On the Plateau-Douglas problem for the Willmore energy of surfaces with planar boundary curves
For a smooth closed embedded planar curve , we consider the
minimization problem of the Willmore energy among immersed surfaces of a given
genus having the curve as boundary, without any
prescription on the conormal. By general lower bound estimates, in case
is a circle we prove that such problem is equivalent if restricted to
embedded surfaces, we prove that do not exist minimizers, and the infimum
equals , where is the energy of
the closed minimizing surface of genus . We also prove that the
same result also holds if is a straight line for the suitable
analogously defined minimization problem on asymptotically flat surfaces.\\
Then we study the case in which is compact, and the
competitors are restricted to a suitable class of varifolds
including embedded surfaces. We prove that under suitable assumptions
minimizers exists in this class of generalized surfaces
Coarse-graining microscopic strains in a harmonic, two-dimensional solid and its implications for elasticity: non-local susceptibilities and non-affine noise
In soft matter systems the local displacement field can be accessed directly
by video microscopy enabling one to compute local strain fields and hence the
elastic moduli using a coarse-graining procedure. We study this process for a
simple triangular lattice of particles connected by harmonic springs in
two-dimensions. Coarse-graining local strains obtained from particle
configurations in a Monte Carlo simulation generates non-trivial, non-local
strain correlations (susceptibilities), which may be understood within a
generalized, Landau type elastic Hamiltonian containing up to quartic terms in
strain gradients (K. Franzrahe et al., Phys. Rev. E 78, 026106 (2008)). In
order to demonstrate the versatility of the analysis of these correlations and
to make our calculations directly relevant for experiments on colloidal solids,
we systematically study various parameters such as the choice of statistical
ensemble, presence of external pressure and boundary conditions. We show that
special care needs to be taken for an accurate application of our results to
actual experiments, where the analyzed area is embedded within a larger system,
to which it is mechanically coupled. Apart from the smooth, affine strain
fields, the coarse-graining procedure also gives rise to a noise field made up
of non-affine displacements. Several properties of this noise field may be
rationalized for the harmonic solid using a simple "cell model" calculation.
Furthermore the scaling behavior of the probability distribution of the noise
field is studied and a master curve is obtained.Comment: 16 pages, 12 figure
Easy plane baby skyrmions
The baby Skyrme model is studied with a novel choice of potential, . This "easy plane" potential vanishes at the equator of the target
two-sphere. Hence, in contrast to previously studied cases, the boundary value
of the field breaks the residual SO(2) internal symmetry of the model.
Consequently, even the unit charge skyrmion has only discrete symmetry and
consists of a bound state of two half lumps. A model of long-range
inter-skyrmion forces is developed wherein a unit skyrmion is pictured as a
single scalar dipole inducing a massless scalar field tangential to the vacuum
manifold. This model has the interesting feature that the two-skyrmion
interaction energy depends only on the average orientation of the dipoles
relative to the line joining them. Its qualitative predictions are confirmed by
numerical simulations. Global energy minimizers of charges B=1,...,14,18,32 are
found numerically. Up to charge B=6, the minimizers have 2B half lumps
positioned at the vertices of a regular 2B-gon. For charges B >= 7, rectangular
or distorted rectangular arrays of 2B half lumps are preferred, as close to
square as possible.Comment: v3: replaced with journal version, one new reference, one deleted
reference; 8 pages, 5 figures v2: fixed some typos and clarified the
relationship with condensed matter systems 8 pages, 5 figure
Minimum energy configurations of the 2-dimensional HP-model of proteins by self-organizing networks
We use self-organizing maps (SOM) as an efficient tool to find the minimum energy configurations of the 2-dimensional HP-models of proteins. The usage of the SOM for the protein folding problem is similar to that for the Traveling Salesman Problem. The lattice nodes represent the cities whereas the neurons in the network represent the amino acids moving towards the closest cities, subject to the HH interactions. The valid path that maximizes the HH contacts corresponds to the minimum energy configuration of the protein. We report promising results for the cases when the protein completely fills a lattice and discuss the current problems and possible extensions. In all the test sequences up to 36 amino acids, the algorithm was able to find the global minimum and its degeneracies
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