2,294 research outputs found
Negative fluctuation-dissipation ratios in the backgammon model
We analyze fluctuation-dissipation relations in the Backgammon model: a
system that displays glassy behavior at zero temperature due to the existence
of entropy barriers. We study local and global fluctuation relations for the
different observables in the model. For the case of a global perturbation we
find a unique negative fluctuation-dissipation ratio that is independent of the
observable and which diverges linearly with the waiting time. This result
suggests that a negative effective temperature can be observed in glassy
systems even in the absence of thermally activated processes.Comment: 32 pages, 10 figures. Accepted in PR
Effects of friction on cosmic strings
We study the evolution of cosmic strings taking into account the frictional
force due to the surrounding radiation. We consider small perturbations on
straight strings, oscillation of circular loops and small perturbations on
circular loops. For straight strings, friction exponentially suppresses
perturbations whose co-moving scale crosses the horizon before cosmological
time (in Planck units), where is the string tension.
Loops with size much smaller than will be approximately circular at the
time when they start the relativistic collapse. We investigate the possibility
that such loops will form black holes. We find that the number of black holes
which are formed through this process is well bellow present observational
limits, so this does not give any lower or upper bounds on . We also
consider the case of straight strings attached to walls and circular holes that
can spontaneously nucleate on metastable domain walls.Comment: 32 pages, TUTP-93-
Zero-th law in structural glasses: an example
We investigate the validity of a zeroth thermodynamic law for non-equilibrium
systems. In order to describe the thermodynamics of the glassy systems, it has
been introduced an extra parameter, the effective temperature which generalizes
the fluctuation-dissipation theorem (FDT) to off-equilibrium systems and
supposedly describes thermal fluctuations around the aging state. In particular
we analyze two coupled systems of harmonic oscillators with Monte Carlo
dynamics. We study in detail two types of dynamics: sequential dynamics, where
the coupling between the subsystems comes only from the Hamiltonian; and
parallel dynamics where there is another source of coupling: the dynamics. We
show how in the first case the effective temperatures of the two interacting
subsystems are different asymptotically due to the smallness of the thermal
conductivity in the aging regime. This explains why, in structural glasses,
different interacting degrees of freedom can stay at different effective
temperatures, and never thermalize.Comment: 10 pages. Contribution to the Proceedings of the ESF SPHINX meeting
`Glassy behaviour of kinetically constrained models' (Barcelona, March 22-25,
2001). To appear in a special issue of J. Phys. Cond. Mat
Moments in graphs
Let be a connected graph with vertex set and a {\em weight function}
that assigns a nonnegative number to each of its vertices. Then, the
{\em -moment} of at vertex is defined to be
M_G^{\rho}(u)=\sum_{v\in V} \rho(v)\dist (u,v) , where \dist(\cdot,\cdot)
stands for the distance function. Adding up all these numbers, we obtain the
{\em -moment of }: M_G^{\rho}=\sum_{u\in
V}M_G^{\rho}(u)=1/2\sum_{u,v\in V}\dist(u,v)[\rho(u)+\rho(v)]. This
parameter generalizes, or it is closely related to, some well-known graph
invariants, such as the {\em Wiener index} , when for every
, and the {\em degree distance} , obtained when
, the degree of vertex . In this paper we derive some
exact formulas for computing the -moment of a graph obtained by a general
operation called graft product, which can be seen as a generalization of the
hierarchical product, in terms of the corresponding -moments of its
factors. As a consequence, we provide a method for obtaining nonisomorphic
graphs with the same -moment for every (and hence with equal mean
distance, Wiener index, degree distance, etc.). In the case when the factors
are trees and/or cycles, techniques from linear algebra allow us to give
formulas for the degree distance of their product
Universality of Fluctuation-Dissipation Ratios: The Ferromagnetic Model
We calculate analytically the fluctuation-dissipation ratio (FDR) for Ising
ferromagnets quenched to criticality, both for the long-range model and its
short-range analogue in the limit of large dimension. Our exact solution shows
that, for both models, if the system is unmagnetized while
if the initial magnetization is non-zero. This indicates that
two different classes of critical coarsening dynamics need to be distinguished
depending on the initial conditions, each with its own nontrivial FDR. We also
analyze the dependence of the FDR on whether local and global observables are
used. These results clarify how a proper local FDR (and the corresponding
effective temperature) should be defined in long-range models in order to avoid
spurious inconsistencies and maintain the expected correspondence between local
and global results; global observables turn out to be far more robust tools for
detecting non-equilibrium FDRs.Comment: 14 pages, revtex4, published version. Changes from v1: added
discussion of refs [16,36,37], other observables and local
correlation/response in short-range mode
Second Order Perturbations of a Macroscopic String; Covariant Approach
Using a world-sheet covariant formalism, we derive the equations of motion
for second order perturbations of a generic macroscopic string, thus
generalizing previous results for first order perturbations. We give the
explicit results for the first and second order perturbations of a contracting
near-circular string; these results are relevant for the understanding of the
possible outcome when a cosmic string contracts under its own tension, as
discussed in a series of papers by Vilenkin and Garriga. In particular, second
order perturbations are necessaary for a consistent computation of the energy.
We also quantize the perturbations and derive the mass-formula up to second
order in perturbations for an observer using world-sheet time . The high
frequency modes give the standard Minkowski result while, interestingly enough,
the Hamiltonian turns out to be non-diagonal in oscillators for low-frequency
modes. Using an alternative definition of the vacuum, it is possible to
diagonalize the Hamiltonian, and the standard string mass-spectrum appears for
all frequencies. We finally discuss how our results are also relevant for the
problems concerning string-spreading near a black hole horizon, as originally
discussed by Susskind.Comment: New discussion about the quantum mass-spectrum in chapter
Fast and adaptive fractal tree-based path planning for programmable bevel tip steerable needles
© 2016 IEEE. Steerable needles are a promising technology for minimally invasive surgery, as they can provide access to difficult to reach locations while avoiding delicate anatomical regions. However, due to the unpredictable tissue deformation associated with needle insertion and the complexity of many surgical scenarios, a real-time path planning algorithm with high update frequency would be advantageous. Real-time path planning for nonholonomic systems is commonly used in a broad variety of fields, ranging from aerospace to submarine navigation. In this letter, we propose to take advantage of the architecture of graphics processing units (GPUs) to apply fractal theory and thus parallelize real-time path planning computation. This novel approach, termed adaptive fractal trees (AFT), allows for the creation of a database of paths covering the entire domain, which are dense, invariant, procedurally produced, adaptable in size, and present a recursive structure. The generated cache of paths can in turn be analyzed in parallel to determine the most suitable path in a fraction of a second. The ability to cope with nonholonomic constraints, as well as constraints in the space of states of any complexity or number, is intrinsic to the AFT approach, rendering it highly versatile. Three-dimensional (3-D) simulations applied to needle steering in neurosurgery show that our approach can successfully compute paths in real-time, enabling complex brain navigation
Solutions to the cosmological constant problems
We critically review several recent approaches to solving the two
cosmological constant problems. The "old" problem is the discrepancy between
the observed value of and the large values suggested by particle
physics models. The second problem is the "time coincidence" between the epoch
of galaxy formation and the epoch of -domination t_\L. It is
conceivable that the "old" problem can be resolved by fundamental physics
alone, but we argue that in order to explain the "time coincidence" we must
account for anthropic selection effects. Our main focus here is on the
discrete- models in which can change through nucleation of
branes. We consider the cosmology of this type of models in the context of
inflation and discuss the observational constraints on the model parameters.
The issue of multiple brane nucleation raised by Feng {\it et. al.} is
discussed in some detail. We also review continuous-\L models in which the
role of the cosmological constant is played by a slowly varying potential of a
scalar field. We find that both continuous and discrete models can in principle
solve both cosmological constant problems, although the required values of the
parameters do not appear very natural. M-theory-motivated brane models, in
which the brane tension is determined by the brane coupling to the four-form
field, do not seem to be viable, except perhaps in a very tight corner of the
parameter space. Finally, we point out that the time coincidence can also be
explained in models where is fixed, but the primordial density
contrast is treated as a random variable.Comment: 30 pages, 3 figures, two notes adde
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