755 research outputs found
A Dynamic Programming Approach to Adaptive Fractionation
We conduct a theoretical study of various solution methods for the adaptive
fractionation problem. The two messages of this paper are: (i) dynamic
programming (DP) is a useful framework for adaptive radiation therapy,
particularly adaptive fractionation, because it allows us to assess how close
to optimal different methods are, and (ii) heuristic methods proposed in this
paper are near-optimal, and therefore, can be used to evaluate the best
possible benefit of using an adaptive fraction size.
The essence of adaptive fractionation is to increase the fraction size when
the tumor and organ-at-risk (OAR) are far apart (a "favorable" anatomy) and to
decrease the fraction size when they are close together. Given that a fixed
prescribed dose must be delivered to the tumor over the course of the
treatment, such an approach results in a lower cumulative dose to the OAR when
compared to that resulting from standard fractionation. We first establish a
benchmark by using the DP algorithm to solve the problem exactly. In this case,
we characterize the structure of an optimal policy, which provides guidance for
our choice of heuristics. We develop two intuitive, numerically near-optimal
heuristic policies, which could be used for more complex, high-dimensional
problems. Furthermore, one of the heuristics requires only a statistic of the
motion probability distribution, making it a reasonable method for use in a
realistic setting. Numerically, we find that the amount of decrease in dose to
the OAR can vary significantly (5 - 85%) depending on the amount of motion in
the anatomy, the number of fractions, and the range of fraction sizes allowed.
In general, the decrease in dose to the OAR is more pronounced when: (i) we
have a high probability of large tumor-OAR distances, (ii) we use many
fractions (as in a hyper-fractionated setting), and (iii) we allow large daily
fraction size deviations.Comment: 17 pages, 4 figures, 1 tabl
Flory-Huggins theory for athermal mixtures of hard spheres and larger flexible polymers
A simple analytic theory for mixtures of hard spheres and larger polymers
with excluded volume interactions is developed. The mixture is shown to exhibit
extensive immiscibility. For large polymers with strong excluded volume
interactions, the density of monomers at the critical point for demixing
decreases as one over the square root of the length of the polymer, while the
density of spheres tends to a constant. This is very different to the behaviour
of mixtures of hard spheres and ideal polymers, these mixtures although even
less miscible than those with polymers with excluded volume interactions, have
a much higher polymer density at the critical point of demixing. The theory
applies to the complete range of mixtures of spheres with flexible polymers,
from those with strong excluded volume interactions to ideal polymers.Comment: 9 pages, 4 figure
Muon-Spin Rotation Spectra in the Mixed Phase of High-T_c Superconductors : Thermal Fluctuations and Disorder Effects
We study muon-spin rotation (muSR) spectra in the mixed phase of highly
anisotropic layered superconductors, specifically Bi_2+xSr_2-xCaCu_2O_8+delta
(BSCCO), by modeling the fluid and solid phases of pancake vortices using
liquid-state and density functional methods. The role of thermal fluctuations
in causing motional narrowing of muSR lineshapes is quantified in terms of a
first-principles theory of the flux-lattice melting transition. The effects of
random point pinning are investigated using a replica treatment of liquid state
correlations and a replicated density functional theory. Our results indicate
that motional narrowing in the pure system, although substantial, cannot
account for the remarkably small linewidths obtained experimentally at
relatively high fields and low temperatures. We find that satisfactory
agreement with the muSR data for BSCCO in this regime can be obtained through
the ansatz that this ``phase'' is characterized by frozen short-range
positional correlations reflecting the structure of the liquid just above the
melting transition. This proposal is consistent with recent suggestions of a
``pinned liquid'' or ``glassy'' state of pancake vortices in the presence of
pinning disorder. Our results for the high-temperature liquid phase indicate
that measurable linewidths may be obtained in this phase as a consequence of
density inhomogeneities induced by the pinning disorder. The results presented
here comprise a unified, first-principles theoretical treatment of muSR spectra
in highly anisotropic layered superconductors in terms of a controlled set of
approximations.Comment: 50 pages Latex file, including 10 postscript figure
Inhomogeneous isospin distribution in the reactions of 28Si + 112Sn and 124Sn at 30 and 50 MeV/nucleon
We have created quasiprojectiles of varying isospin via peripheral reactions
of 28Si + 112Sn and 124Sn at 30 and 50 MeV/nucleon. The quasiprojectiles have
been reconstructed from completely isotopically identified fragments. The
difference in N/Z of the reconstructed quasiprojectiles allows the
investigation of the disassembly as a function of the isospin of the
fragmenting system. The isobaric yield ratio 3H/3He depends strongly on N/Z
ratio of quasiprojectiles. The dependences of mean fragment multiplicity and
mean N/Z ratio of the fragments on N/Z ratio of the quasiprojectile are
different for light charged particles and intermediate mass fragments.
Observation of a different N/Z ratio of light charged particles and
intermediate mass fragments is consistent with an inhomogeneous distribution of
isospin in the fragmenting system.Comment: 5 pages, 4 Postscript figures, RevTe
Strongly coupled quantum criticality with a Fermi surface in two dimensions: fractionalization of spin and charge collective modes
We describe two dimensional models with a metallic Fermi surface which
display quantum phase transitions controlled by strongly interacting critical
field theories below their upper critical dimension. The primary examples
involve transitions with a topological order parameter associated with
dislocations in collinear spin density wave ("stripe") correlations: the
gapping of the order parameter fluctuations leads to a fractionalization of
spin and charge collective modes, and this transition has been proposed as a
candidate for the cuprates near optimal doping. The coupling between the order
parameter and long-wavelength volume and shape deformations of the Fermi
surface is analyzed by the renormalization group, and a runaway flow to a
non-perturbative regime is found in most cases. A phenomenological scaling
analysis of simple observable properties of possible second order quantum
critical points is presented, with results quite similar to those near quantum
spin glass transitions and to phenomenological forms proposed by Schroeder et
al. (cond-mat/0011002).Comment: 16 pages, 4 figures; (v2) additional clarifying remark
Phase fluctuations, dissipation and superfluid stiffness in d-wave superconductors
We study the effect of dissipation on quantum phase fluctuations in d-wave
superconductors. Dissipation, arising from a nonzero low frequency optical
conductivity which has been measured in experiments below , has two
effects: (1) a reduction of zero point phase fluctuations, and (2) a reduction
of the temperature at which one crosses over to classical thermal fluctuations.
For parameter values relevant to the cuprates, we show that the crossover
temperature is still too large for classical phase fluctuations to play a
significant role at low temperature. Quasiparticles are thus crucial in
determining the linear temperature dependence of the in-plane superfluid
stiffness. Thermal phase fluctuations become important at higher temperatures
and play a role near .Comment: Presentation improved, new references added (10 latex pages, 3 eps
figures). submitted to PR
Inertial Mass of a Vortex in Cuprate Superconductors
We present here a calculation of the inertial mass of a moving vortex in
cuprate superconductors. This is a poorly known basic quantity of obvious
interest in vortex dynamics. The motion of a vortex causes a dipolar density
distortion and an associated electric field which is screened. The energy cost
of the density distortion as well as the related screened electric field
contribute to the vortex mass, which is small because of efficient screening.
As a preliminary, we present a discussion and calculation of the vortex mass
using a microscopically derivable phase-only action functional for the far
region which shows that the contribution from the far region is negligible, and
that most of it arises from the (small) core region of the vortex. A
calculation based on a phenomenological Ginzburg-Landau functional is performed
in the core region. Unfortunately such a calculation is unreliable, the reasons
for it are discussed. A credible calculation of the vortex mass thus requires a
fully microscopic, non-coarse grained theory. This is developed, and results
are presented for a s-wave BCS like gap, with parameters appropriate to the
cuprates. The mass, about 0.5 per layer, for magnetic field along the
axis, arises from deformation of quasiparticle states bound in the core, and
screening effects mentioned above. We discuss earlier results, possible
extensions to d-wave symmetry, and observability of effects dependent on the
inertial mass.Comment: 27 pages, Latex, 3 figures available on request, to appear in
Physical Review
Phase Diagram Of A Hard-sphere System In A Quenched Random Potential: A Numerical Study
We report numerical results for the phase diagram in the density-disorder
plane of a hard sphere system in the presence of quenched, random, pinning
disorder. Local minima of a discretized version of the Ramakrishnan-Yussouff
free energy functional are located numerically and their relative stability is
studied as a function of the density and the strength of disorder. Regions in
the phase diagram corresponding to liquid, glassy and nearly crystalline states
are mapped out, and the nature of the transitions is determined. The liquid to
glass transition changes from first to second order as the strength of the
disorder is increased. For weak disorder, the system undergoes a first order
crystallization transition as the density is increased. Beyond a critical value
of the disorder strength, this transition is replaced by a continuous glass
transition. Our numerical results are compared with those of analytical work on
the same system. Implications of our results for the field-temperature phase
diagram of type-II superconductors are discussed.Comment: 14 pages, 10 postscript figures (included), submitted to Phys. Rev.
Elastic moduli, dislocation core energy and melting of hard disks in two dimensions
Elastic moduli and dislocation core energy of the triangular solid of hard
disks of diameter are obtained in the limit of vanishing dislocation-
antidislocation pair density, from Monte Carlo simulations which incorporates a
constraint, namely that all moves altering the local connectivity away from
that of the ideal triangular lattice are rejected. In this limit, we show that
the solid is stable against all other fluctuations at least upto densities as
low as . Our system does not show any phase transition so
diverging correlation lengths leading to finite size effects and slow
relaxations do not exist. The dislocation pair formation probability is
estimated from the fraction of moves rejected due to the constraint which
yields, in turn, the core energy E_c and the (bare) dislocation fugacity y.
Using these quantities, we check the relative validity of first order and
Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) melting scenarios and obtain
numerical estimates of the typical expected transition densities and pressures.
We conclude that a KTHNY transition from the solid to a hexatic phase preempts
the solid to liquid first order transition in this system albeit by a very
small margin, easily masked by crossover effects in unconstrained
``brute-force'' simulations with small number of particles.Comment: 17 pages, 8 figure
Quantum Smoluchowski equation: Escape from a metastable state
We develop a quantum Smoluchowski equation in terms of a true probability
distribution function to describe quantum Brownian motion in configuration
space in large friction limit at arbitrary temperature and derive the rate of
barrier crossing and tunneling within an unified scheme. The present treatment
is independent of path integral formalism and is based on canonical
quantization procedure.Comment: 10 pages, To appear in the Proceedings of Statphys - Kolkata I
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