3,678 research outputs found
Anticipated backward stochastic differential equations
In this paper we discuss new types of differential equations which we call
anticipated backward stochastic differential equations (anticipated BSDEs). In
these equations the generator includes not only the values of solutions of the
present but also the future. We show that these anticipated BSDEs have unique
solutions, a comparison theorem for their solutions, and a duality between them
and stochastic differential delay equations.Comment: Published in at http://dx.doi.org/10.1214/08-AOP423 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Ising-like transitions in the O() loop model on the square lattice
We explore the phase diagram of the O() loop model on the square lattice
in the plane, where is the weight of a lattice edge covered by a
loop. These results are based on transfer-matrix calculations and finite-size
scaling. We express the correlation length associated with the staggered loop
density in the transfer-matrix eigenvalues. The finite-size data for this
correlation length, combined with the scaling formula, reveal the location of
critical lines in the diagram. For we find Ising-like phase transitions
associated with the onset of a checkerboard-like ordering of the elementary
loops, i.e., the smallest possible loops, with the size of an elementary face,
which cover precisely one half of the faces of the square lattice at the
maximum loop density. In this respect, the ordered state resembles that of the
hard-square lattice gas with nearest-neighbor exclusion, and the finiteness of
represents a softening of its particle-particle potentials. We also
determine critical points in the range . It is found that the
topology of the phase diagram depends on the set of allowed vertices of the
loop model. Depending on the choice of this set, the transition may
continue into the dense phase of the loop model, or continue as a
line of O() multicritical points
Special transitions in an O() loop model with an Ising-like constraint
We investigate the O() nonintersecting loop model on the square lattice
under the constraint that the loops consist of ninety-degree bends only. The
model is governed by the loop weight , a weight for each vertex of the
lattice visited once by a loop, and a weight for each vertex visited twice
by a loop. We explore the phase diagram for some values of . For
, the diagram has the same topology as the generic O() phase diagram
with , with a first-order line when starts to dominate, and an
O()-like transition when starts to dominate. Both lines meet in an
exactly solved higher critical point. For , the O()-like transition
line appears to be absent. Thus, for , the phase diagram displays
a line of phase transitions for . The line ends at in an
infinite-order transition. We determine the conformal anomaly and the critical
exponents along this line. These results agree accurately with a recent
proposal for the universal classification of this type of model, at least in
most of the range . We also determine the exponent describing
crossover to the generic O() universality class, by introducing topological
defects associated with the introduction of `straight' vertices violating the
ninety-degree-bend rule. These results are obtained by means of transfer-matrix
calculations and finite-size scaling.Comment: 19 pages, 11 figure
A molecular dynamics simulation of DNA damage induction by ionizing radiation
We present a multi-scale simulation of early stage of DNA damages by the
indirect action of hydroxyl (OH) free radicals generated by electrons
and protons. The computational method comprises of interfacing the Geant4-DNA
Monte Carlo with the ReaxFF molecular dynamics software. A clustering method
was employed to map the coordinates of OH-radicals extracted from the
ionization track-structures onto nano-meter simulation voxels filled with DNA
and water molecules. The molecular dynamics simulation provides the time
evolution and chemical reactions in individual simulation voxels as well as the
energy-landscape accounted for the DNA-OH chemical reaction that is
essential for the first principle enumeration of hydrogen abstractions,
chemical bond breaks, and DNA-lesions induced by collection of ions in clusters
less than the critical dimension which is approximately 2-3 \AA. We show that
the formation of broken bonds leads to DNA base and backbone damages that
collectively propagate to DNA single and double strand breaks. For illustration
of the methodology, we focused on particles with initial energy of 1 MeV. Our
studies reveal a qualitative difference in DNA damage induced by low energy
electrons and protons. Electrons mainly generate small pockets of
OH-radicals, randomly dispersed in the cell volume. In contrast,
protons generate larger clusters along a straight-line parallel to the
direction of the particle. The ratio of the total DNA double strand breaks
induced by a single proton and electron track is determined to be 4
in the linear scaling limit. The tool developed in this work can be used in the
future to investigate the relative biological effectiveness of light and heavy
ions that are used in radiotherapy.Comment: 7 pages, 7 figures, accepted for publication in Physics in Medicine
and Biolog
Photon-assisted Landau-Zener transition: Role of coherent superposition states
We investigate a Landau-Zener (LZ) transition process modeled by a quantum
two-level system (TLS) coupled to a photon mode when the bias energy is varied
linearly in time. The initial state of the photon field is assumed to be a
superposition of coherent states, leading to a more intricate LZ transition.
Applying the rotating-wave approximation (RWA), analytical results are obtained
revealing the enhancement of the LZ probability by increasing the average
photon number. We also consider the creation of entanglement and the change of
photon statistics during the LZ process. Without the RWA, we find some
qualitative differences of the LZ dynamics from the RWA results, e.g., the
average photon number no longer monotonically enhances the LZ probability. The
ramifications and implications of these results are explored.Comment: 9 pages, 7 figure
Investigation of jet quenching and elliptic flow within a pQCD-based partonic transport model
The partonic transport model BAMPS (a Boltzmann approach to multiparton
scatterings) is employed to investigate different aspects of heavy ion
collisions within a common framework based on perturbative QCD. This report
focuses on the joint investigation of the collective behavior of the created
medium and the energy loss of high-pT gluons traversing this medium. To this
end the elliptic flow and the nuclear modification factor of gluons in heavy
ion collisions at 200 AGeV are simulated with BAMPS. The mechanism for the
energy loss of high energy gluons within BAMPS is studied in detail. For this,
purely elastic interactions are compared to radiative processes, gg -> ggg,
that are implemented based on the matrix element by Gunion and Bertsch. The
latter are found to be the dominant source of energy loss within the framework
employed in this work.Comment: To appear in the proceedings of the 26th Winter Workshop on Nuclear
Dynamics (2010)
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