5,732 research outputs found
Wave and Particle Limit for Multiple Barrier Tunneling
The particle approach to one-dimensional potential scattering is applied to
non relativistic tunnelling between two, three and four identical barriers. We
demonstrate as expected that the infinite sum of particle contributions yield
the plane wave results. In particular, the existence of resonance/transparency
for twin tunnelling in the wave limit is immediately obvious. The known
resonances for three and four barriers are also derived. The transition from
the wave limit to the particle limit is exhibit numerically.Comment: 15 pages, 3 figure
Sacrificing Accuracy for Reduced Computation: Cascaded Inference Based on Softmax Confidence
We study the tradeoff between computational effort and accuracy in a cascade
of deep neural networks. During inference, early termination in the cascade is
controlled by confidence levels derived directly from the softmax outputs of
intermediate classifiers. The advantage of early termination is that
classification is performed using less computation, thus adjusting the
computational effort to the complexity of the input. Moreover, dynamic
modification of confidence thresholds allow one to trade accuracy for
computational effort without requiring retraining. Basing of early termination
on softmax classifier outputs is justified by experimentation that demonstrates
an almost linear relation between confidence levels in intermediate classifiers
and accuracy. Our experimentation with architectures based on ResNet obtained
the following results. (i) A speedup of 1.5 that sacrifices 1.4% accuracy with
respect to the CIFAR-10 test set. (ii) A speedup of 1.19 that sacrifices 0.7%
accuracy with respect to the CIFAR-100 test set. (iii) A speedup of 2.16 that
sacrifices 1.4% accuracy with respect to the SVHN test set
Crack roughness and avalanche precursors in the random fuse model
We analyze the scaling of the crack roughness and of avalanche precursors in
the two dimensional random fuse model by numerical simulations, employing large
system sizes and extensive sample averaging. We find that the crack roughness
exhibits anomalous scaling, as recently observed in experiments. The roughness
exponents (, ) and the global width distributions are found
to be universal with respect to the lattice geometry. Failure is preceded by
avalanche precursors whose distribution follows a power law up to a cutoff
size. While the characteristic avalanche size scales as , with a
universal fractal dimension , the distribution exponent differs
slightly for triangular and diamond lattices and, in both cases, it is larger
than the mean-field (fiber bundle) value
Reversible and Irreversible Spacetime Thermodynamics for General Brans-Dicke Theories
We derive the equations of motion for Palatini F(R) gravity by applying an
entropy balance law T dS= \delta Q+\delta N to the local Rindler wedge that can
be constructed at each point of spacetime. Unlike previous results for metric
F(R), there is no bulk viscosity term in the irreversible flux \delta N. Both
theories are equivalent to particular cases of Brans-Dicke scalar-tensor
gravity. We show that the thermodynamical approach can be used ab initio also
for this class of gravitational theories and it is able to provide both the
metric and scalar equations of motion. In this case, the presence of an
additional scalar degree of freedom and the requirement for it to be dynamical
naturally imply a separate contribution from the scalar field to the heat flux
\delta Q. Therefore, the gravitational flux previously associated to a bulk
viscosity term in metric F(R) turns out to be actually part of the reversible
thermodynamics. Hence we conjecture that only the shear viscosity associated
with Hartle-Hawking dissipation should be associated with irreversible
thermodynamics.Comment: 12 pages, 1 figure; v2: minor editing to clarify Section III, fixed
typos; v3: fixed typo
Statistical properties of fracture in a random spring model
Using large scale numerical simulations we analyze the statistical properties
of fracture in the two dimensional random spring model and compare it with its
scalar counterpart: the random fuse model. We first consider the process of
crack localization measuring the evolution of damage as the external load is
raised. We find that, as in the fuse model, damage is initially uniform and
localizes at peak load. Scaling laws for the damage density, fracture strength
and avalanche distributions follow with slight variations the behavior observed
in the random fuse model. We thus conclude that scalar models provide a
faithful representation of the fracture properties of disordered systems.Comment: 12 pages, 17 figures, 1 gif figur
Effect of Disorder and Notches on Crack Roughness
We analyze the effect of disorder and notches on crack roughness in two
dimensions. Our simulation results based on large system sizes and extensive
statistical sampling indicate that the crack surface exhibits a universal local
roughness of and is independent of the initial notch size
and disorder in breaking thresholds. The global roughness exponent scales as
and is also independent of material disorder. Furthermore, we
note that the statistical distribution of crack profile height fluctuations is
also independent of material disorder and is described by a Gaussian
distribution, albeit deviations are observed in the tails.Comment: 6 pages, 6 figure
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