1,006 research outputs found
Projections, Pseudo-Stopping Times and the Immersion Property
Given two filtrations , we study under which
conditions the -optional projection and the -dual
optional projection coincide for the class of -optional processes
with integrable variation. It turns out that this property is equivalent to the
immersion property for and , that is every -local martingale is a -local martingale, which, equivalently, may
be characterised using the class of -pseudo-stopping times. We also
show that every -stopping time can be decomposed into the minimum of
two barrier hitting times
On static spherically symmetric solutions of the vacuum Brans-Dicke theory
It is shown that among the four classes of the static spherically symmetric
solution of the vacuum Brans-Dicke theory of gravity only two are really
independent. Further by matching exterior and interior (due to physically
reasonable spherically symmetric matter source) scalar fields it is found that
only Brans class I solution with certain restriction on solution parameters may
represent exterior metric for a nonsingular massive object. The physical
viability of the black hole nature of the solution is investigated. It is
concluded that no physical black hole solution different from the Schwarzschild
black hole is available in the Brans-Dicke theory.Comment: 15 pages, To be published in Gen. Rel. and Grav, typos in references
correcte
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
Schramm-Loewner Equations Driven by Symmetric Stable Processes
We consider shape, size and regularity of the hulls of the chordal
Schramm-Loewner evolution driven by a symmetric alpha-stable process. We obtain
derivative estimates, show that the complements of the hulls are Hoelder
domains, prove that the hulls have Hausdorff dimension 1, and show that the
trace is right-continuous with left limits almost surely.Comment: 22 pages, 4 figure
What we don't know about time
String theory has transformed our understanding of geometry, topology and
spacetime. Thus, for this special issue of Foundations of Physics commemorating
"Forty Years of String Theory", it seems appropriate to step back and ask what
we do not understand. As I will discuss, time remains the least understood
concept in physical theory. While we have made significant progress in
understanding space, our understanding of time has not progressed much beyond
the level of a century ago when Einstein introduced the idea of space-time as a
combined entity. Thus, I will raise a series of open questions about time, and
will review some of the progress that has been made as a roadmap for the
future.Comment: 15 pages; Essay for a special issue of Foundations of Physics
commemorating "Forty years of string theory
Exponential martingales and changes of measure for counting processes
We give sufficient criteria for the Dol\'eans-Dade exponential of a
stochastic integral with respect to a counting process local martingale to be a
true martingale. The criteria are adapted particularly to the case of counting
processes and are sufficiently weak to be useful and verifiable, as we
illustrate by several examples. In particular, the criteria allow for the
construction of for example nonexplosive Hawkes processes as well as counting
processes with stochastic intensities depending on diffusion processes
Stationary State Solutions of a Bond Diluted Kinetic Ising Model: An Effective-Field Theory Analysis
We have examined the stationary state solutions of a bond diluted kinetic
Ising model under a time dependent oscillating magnetic field within the
effective-field theory (EFT) for a honeycomb lattice . Time evolution of
the system has been modeled with a formalism of master equation. The effects of
the bond dilution, as well as the frequency and amplitude of
the external field on the dynamic phase diagrams have been discussed in detail.
We have found that the system exhibits the first order phase transition with a
dynamic tricritical point (DTCP) at low temperature and high amplitude regions,
in contrast to the previously published results for the pure case \cite{Ling}.
Bond dilution process on the kinetic Ising model gives rise to a number of
interesting and unusual phenomena such as reentrant phenomena and has a
tendency to destruct the first-order transitions and the DTCP. Moreover, we
have investigated the variation of the bond percolation threshold as functions
of the amplitude and frequency of the oscillating field.Comment: 8 pages, 4 figure
Extended Birkhoff's Theorem in the f(T) Gravity
The f(T) theory, a generally modified teleparallel gravity, has been proposed
as an alternative gravity model to account for the dark energy phenomena.
Following our previous work [Xin-he Meng and Ying-bin Wang, EPJC(2011),
arXiv:1107.0629v1], we prove that the Birkhoff's theorem holds in a more
general context, specifically with the off diagonal tetrad case, in this
communication letter. Then, we discuss respectively the results of the external
vacuum and internal gravitational field in the f(T) gravity framework, as well
as the extended meaning of this theorem. We also investigate the validity of
the Birkhoff's theorem in the frame of f(T) gravity via conformal
transformation by regarding the Brans-Dicke-like scalar as effective matter,
and study the equivalence between both Einstein frame and Jordan frame.Comment: 7 pages, 1 figure, submitted to EPJ-C. arXiv admin note: substantial
text overlap with arXiv:1107.062
Rings and rigidity transitions in network glasses
Three elastic phases of covalent networks, (I) floppy, (II) isostatically
rigid and (III) stressed-rigid have now been identified in glasses at specific
degrees of cross-linking (or chemical composition) both in theory and
experiments. Here we use size-increasing cluster combinatorics and constraint
counting algorithms to study analytically possible consequences of
self-organization. In the presence of small rings that can be locally I, II or
III, we obtain two transitions instead of the previously reported single
percolative transition at the mean coordination number , one from a
floppy to an isostatic rigid phase, and a second one from an isostatic to a
stressed rigid phase. The width of the intermediate phase and the
order of the phase transitions depend on the nature of medium range order
(relative ring fractions). We compare the results to the Group IV
chalcogenides, such as Ge-Se and Si-Se, for which evidence of an intermediate
phase has been obtained, and for which estimates of ring fractions can be made
from structures of high T crystalline phases.Comment: 29 pages, revtex, 7 eps figure
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