87 research outputs found
Order-by-disorder in classical oscillator systems
We consider classical nonlinear oscillators on hexagonal lattices. When the
coupling between the elements is repulsive, we observe coexisting states, each
one with its own basin of attraction. These states differ by their degree of
synchronization and by patterns of phase-locked motion. When disorder is
introduced into the system by additive or multiplicative Gaussian noise, we
observe a non-monotonic dependence of the degree of order in the system as a
function of the noise intensity: intervals of noise intensity with low
synchronization between the oscillators alternate with intervals where more
oscillators are synchronized. In the latter case, noise induces a higher degree
of order in the sense of a larger number of nearly coinciding phases. This
order-by-disorder effect is reminiscent to the analogous phenomenon known from
spin systems. Surprisingly, this non-monotonic evolution of the degree of order
is found not only for a single interval of intermediate noise strength, but
repeatedly as a function of increasing noise intensity. We observe noise-driven
migration of oscillator phases in a rough potential landscape.Comment: 12 pages, 13 figures; comments are welcom
Pair-factorized steady states on arbitrary graphs
Stochastic mass transport models are usually described by specifying hopping
rates of particles between sites of a given lattice, and the goal is to predict
the existence and properties of the steady state. Here we ask the reverse
question: given a stationary state that factorizes over links (pairs of sites)
of an arbitrary connected graph, what are possible hopping rates that converge
to this state? We define a class of hopping functions which lead to the same
steady state and guarantee current conservation but may differ by the induced
current strength. For the special case of anisotropic hopping in two dimensions
we discuss some aspects of the phase structure. We also show how this case can
be traced back to an effective zero-range process in one dimension which is
solvable for a large class of hopping functions.Comment: IOP style, 9 pages, 1 figur
Critical Phenomena with Linked Cluster Expansions in a Finite Volume
Linked cluster expansions are generalized from an infinite to a finite
volume. They are performed to 20th order in the expansion parameter to approach
the critical region from the symmetric phase. A new criterion is proposed to
distinguish 1st from 2nd order transitions within a finite size scaling
analysis. The criterion applies also to other methods for investigating the
phase structure such as Monte Carlo simulations. Our computational tools are
illustrated at the example of scalar O(N) models with four and six-point
couplings for and in three dimensions. It is shown how to localize
the tricritical line in these models. We indicate some further applications of
our methods to the electroweak transition as well as to models for
superconductivity.Comment: 36 pages, latex2e, 7 eps figures included, uuencoded, gzipped and
tarred tex file hdth9607.te
Islanding the power grid on the transmission level: less connections for more security
Islanding is known as a management procedure of the power system that is implemented at the distribution level to preserve sensible loads from outages and to guarantee the continuity in electricity supply, when a high amount of distributed generation occurs. In this paper we study islanding on the level of the transmission grid and shall show that it is a suitable measure to enhance energy security and grid resilience. We consider the German and Italian transmission grids. We remove links either randomly to mimic random failure events, or according to a topological characteristic, their so-called betweenness centrality, to mimic an intentional attack and test whether the resulting fragments are self-sustainable. We test this option via the tool of optimized DC power flow equations. When transmission lines are removed according to their betweenness centrality, the resulting islands have a higher chance of being dynamically self-sustainable than for a random removal. Less connections may even increase the grid’s stability. These facts should be taken into account in the design of future power grids
Islanding the power grid on the transmission level: Less connections for more security
Islanding is known as a management procedure of the power system that is implemented at the distribution level to preserve sensible loads from outages and to guarantee the continuity in electricity supply, when a high amount of distributed generation occurs. In this paper we study islanding on the level of the transmission grid and shall show that it is a suitable measure to enhance energy security and grid resilience. We consider the German and Italian transmission grids. We remove links either randomly to mimic random failure events, or according to a topological characteristic, their so-called betweenness centrality, to mimic an intentional attack and test whether the resulting fragments are self-sustainable. We test this option via the tool of optimized DC power flow equations. When transmission lines are removed according to their betweenness centrality, the resulting islands have a higher chance of being dynamically self-sustainable than for a random removal. Less connections may even increase the grid's stability. These facts should be taken into account in the design of future power grids
The O(2) model in polar coordinates at nonzero temperature
We study the restoration of spontaneously broken symmetry at nonzero
temperature in the framework of the O(2) model using polar coordinates. We
apply the CJT formalism to calculate the masses and the condensate in the
double-bubble approximation, both with and without a term that explicitly
breaks the O(2) symmetry. We find that, in the case with explicitly broken
symmetry, the mass of the angular degree of freedom becomes tachyonic above a
temperature of about 300 MeV. Taking the term that explicitly breaks the
symmetry to be infinitesimally small, we find that the Goldstone theorem is
respected below the critical temperature. However, this limit cannot be
performed for temperatures above the phase transition. We find that, no matter
whether we break the symmetry explicitly or not, there is no region of
temperature in which the radial and the angular degree of freedom become
degenerate in mass. These results hold also when the mass of the radial mode is
sent to infinity.Comment: 23 pages, 10 figure
Influence of the U(1)_A Anomaly on the QCD Phase Transition
The SU(3)_{r} \times SU(3)_{\ell} linear sigma model is used to study the
chiral symmetry restoring phase transition of QCD at nonzero temperature. The
line of second order phase transitions separating the first order and smooth
crossover regions is located in the plane of the strange and nonstrange quark
masses. It is found that if the U(1)_{A} symmetry is explicitly broken by the
U(1)_{A} anomaly then there is a smooth crossover to the chirally symmetric
phase for physical values of the quark masses. If the U(1)_{A} anomaly is
absent, then there is a phase transition provided that the \sigma meson mass is
at least 600 MeV. In both cases, the region of first order phase transitions in
the quark mass plane is enlarged as the mass of the \sigma meson is increased.Comment: 5 pages, 3 figures, Revtex, discussion extended and references added.
To appear in PR
Dynamics of Phase Transitions by Hysteresis Methods I
In studies of the QCD deconfining phase transition or crossover by means of
heavy ion experiments, one ought to be concerned about non-equilibrium effects
due to heating and cooling of the system. Motivated by this, we look at
hysteresis methods to study the dynamics of phase transitions. Our systems are
temperature driven through the phase transition using updating procedures in
the Glauber universality class. Hysteresis calculations are presented for a
number of observables, including the (internal) energy, properties of
Fortuin-Kasteleyn clusters and structure functions. We test the methods for 2d
Potts models, which provide a rich collection of phase transitions with a
number of rigorously known properties. Comparing with equilibrium
configurations we find a scenario where the dynamics of the transition leads to
a spinodal decomposition which dominates the statistical properties of the
configurations. One may expect an enhancement of low energy gluon production
due to spinodal decomposition of the Polyakov loops, if such a scenario is
realized by nature.Comment: 12 pages, revised after referee report, to appear in Phys. Rev.
Center Dominance in SU(2) Gauge-Higgs Theory
We study the SU(2) gauge-Higgs system in D=4 dimensions, and analyze the
influence of the fundamental-representation Higgs field on the vortex content
of the gauge field. It is shown that center projected Polyakov lines, at low
temperature, are finite in the infinite volume limit, which means that the
center vortex distribution is consistent with color screening. In addition we
confirm and further investigate the presence of a "Kertesz-line" in the
strong-coupling region of the phase diagram, which we relate to the percolation
properties of center vortices. It is shown that this Kertesz-line separates the
gauge-Higgs phase diagram into two regions: a confinement-like region, in which
center vortices percolate, and a Higgs region, in which they do not. The free
energy of the gauge-Higgs system, however, is analytic across the Kertesz line.Comment: 7 pages, 10 figure
Tuning the shape of the condensate in spontaneous symmetry breaking
We investigate what determines the shape of a particle condensate in
situations when it emerges as a result of spontaneous breaking of translational
symmetry. We consider a model with particles hopping between sites of a
one-dimensional grid and interacting if they are at the same or at neighboring
nodes. We predict the envelope of the condensate and the scaling of its width
with the system size for various interaction potentials and show how to tune
the shape from a delta-peak to a rectangular or a parabolic-like form.Comment: 4 pages, 2 figures, major revision, the title has been change
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