10,047 research outputs found
Absence of First-order Transition and Tri-critical Point in the Dynamic Phase Diagram of a Spatially Extended Bistable System in an Oscillating Field
It has been well established that spatially extended, bistable systems that
are driven by an oscillating field exhibit a nonequilibrium dynamic phase
transition (DPT). The DPT occurs when the field frequency is on the order of
the inverse of an intrinsic lifetime associated with the transitions between
the two stable states in a static field of the same magnitude as the amplitude
of the oscillating field. The DPT is continuous and belongs to the same
universality class as the equilibrium phase transition of the Ising model in
zero field [G. Korniss et al., Phys. Rev. E 63, 016120 (2001); H. Fujisaka et
al., Phys. Rev. E 63, 036109 (2001)]. However, it has previously been claimed
that the DPT becomes discontinuous at temperatures below a tricritical point
[M. Acharyya, Phys. Rev. E 59, 218 (1999)]. This claim was based on
observations in dynamic Monte Carlo simulations of a multipeaked probability
density for the dynamic order parameter and negative values of the fourth-order
cumulant ratio. Both phenomena can be characteristic of discontinuous phase
transitions. Here we use classical nucleation theory for the decay of
metastable phases, together with data from large-scale dynamic Monte Carlo
simulations of a two-dimensional kinetic Ising ferromagnet, to show that these
observations in this case are merely finite-size effects. For sufficiently
small systems and low temperatures, the continuous DPT is replaced, not by a
discontinuous phase transition, but by a crossover to stochastic resonance. In
the infinite-system limit the stochastic-resonance regime vanishes, and the
continuous DPT should persist for all nonzero temperatures
Phase-coherent detection of an optical dipole force by Doppler velocimetry
We report phase-coherent Doppler detection of optical dipole forces using
large ion crystals in a Penning trap. The technique is based on laser Doppler
velocimetry using a cycling transition in Be near 313 nm and the
center-of-mass (COM) ion motional mode. The optical dipole force is tuned to
excite the COM mode, and measurements of photon arrival times synchronized with
the excitation potential show oscillations with a period commensurate with the
COM motional frequency. Experimental results compare well with a quantitative
model for a driven harmonic oscillator. This technique permits characterization
of motional modes in ion crystals; the measurement of both frequency and phase
information relative to the driving force is a key enabling capability --
comparable to lockin detection -- providing access to a parameter that is
typically not available in time-averaged measurements. This additional
information facilitates discrimination of nearly degenerate motional modes.Comment: Related manuscripts at http://www.physics.usyd.edu.au/~mbiercuk
The Past, Present, and Future of Multidimensional Scaling
Multidimensional scaling (MDS) has established itself as a standard tool for statisticians and applied researchers. Its success is due to its simple and easily interpretable representation of potentially complex structural data. These data are typically embedded into a 2-dimensional map, where the objects of interest (items, attributes, stimuli, respondents, etc.) correspond to points such that those that are near to each other are empirically similar, and those that are far apart are different. In this paper, we pay tribute to several important developers of MDS and give a subjective overview of milestones in MDS developments. We also discuss the present situation of MDS and give a brief outlook on its future
More on Multidimensional Scaling and Unfolding in R: smacof Version 2
The smacof package offers a comprehensive implementation of multidimensional scaling (MDS) techniques in R. Since its first publication (De Leeuw and Mair 2009b) the functionality of the package has been enhanced, and several additional methods, features and utilities were added. Major updates include a complete re-implementation of multidimensional unfolding allowing for monotone dissimilarity transformations, including row-conditional, circular, and external unfolding. Additionally, the constrained MDS implementation was extended in terms of optimal scaling of the external variables. Further package additions include various tools and functions for goodness-of-fit assessment, unidimensional scaling, gravity MDS, asymmetric MDS, Procrustes, and MDS biplots. All these new package functionalities are illustrated using a variety of real-life applications
Dynamics of an Alfven surface in core collapse supernovae
We investigate the dynamics of an Alfven surface (where the Alfven speed
equals the advection velocity) in the context of core collapse supernovae
during the phase of accretion on the proto-neutron star. Such a surface should
exist even for weak magnetic fields because the advection velocity decreases to
zero at the center of the collapsing core. In this decelerated flow, Alfven
waves created by the standing accretion shock instability (SASI) or convection
accumulate and amplify while approaching the Alfven surface. We study this
amplification using one dimensional MHD simulations with explicit physical
dissipation. In the linear regime, the amplification continues until the Alfven
wavelength becomes as small as the dissipative scale. A pressure feedback that
increases the pressure in the upstream flow is created via a non linear
coupling. We derive analytic formulae for the maximum amplification and the non
linear coupling and check them with numerical simulations to a very good
accuracy. We also characterize the non linear saturation of this amplification
when compression effects become important, leading to either a change of the
velocity gradient, or a steepening of the Alfven wave. Applying these results
to core collapse supernovae shows that the amplification can be fast enough to
affect the dynamics, if the magnetic field is strong enough for the Alfven
surface to lie in the region of strong velocity gradient just above the
neutrinosphere. This requires the presence of a strong magnetic field in the
progenitor star, which would correspond to the formation of a magnetar under
the assumption of magnetic flux conservation. An extrapolation of our analytic
formula (taking into account the nonlinear saturation) suggests that the Alfven
wave could reach an amplitude of B ~ 10^15 G, and that the pressure feedback
could significantly contribute to the pressure below the shock.Comment: 18 pages, 14 figures, accepted for publication in ApJ. Added a
discussion of the energy budget in subsection 7.
Memory Effects and Scaling Laws in Slowly Driven Systems
This article deals with dynamical systems depending on a slowly varying
parameter. We present several physical examples illustrating memory effects,
such as metastability and hysteresis, which frequently appear in these systems.
A mathematical theory is outlined, which allows to show existence of hysteresis
cycles, and determine related scaling laws.Comment: 28 pages (AMS-LaTeX), 18 PS figure
Quantum phase-slips in Josephson junction rings
We study quantum phase-slip (QPS) processes in a superconducting ring
containing N Josephson junctions and threaded by an external static magnetic
flux. In a such system, a QPS consists of a quantum tunneling event connecting
two distinct classical states of the phases with different persistent currents
[K. A. Matveev et al., Phys. Rev. Lett. 89, 096802 (2002)]. When the Josephson
coupling energy EJ of the junctions is larger than the charging energy EC =
e2/2C where C is the junction capacitance, the quantum amplitude for the QPS
process is exponentially small in the ratio EJ/EC. At given magnetic flux each
QPS can be described as the tunneling of the phase difference of a single
junction of almost 2pi, accompanied by a small harmonic displacement of the
phase difference of the other N-1 junctions. As a consequence the total QPS
amplitude nu is a global property of the ring. Here we study the dependence of
nu on the ring size N taking into account the effect of a finite capacitance C0
to ground which leads to the appearance of low-frequency dispersive modes.
Josephson and charging effects compete and lead to a nonmonotonic dependence of
the ring critical current on N. For N=infty, the system converges either
towards a superconducting or an insulating state, depending on the ratio
between the charging energy E0 = e2/2C0 and the Josephson coupling energy EJ.Comment: (19 pages, 12 figures) The final version deviated from the original
version. One of the author was removed from the lis
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