569 research outputs found
Approach to a rational rotation number in a piecewise isometric system
We study a parametric family of piecewise rotations of the torus, in the
limit in which the rotation number approaches the rational value 1/4. There is
a region of positive measure where the discontinuity set becomes dense in the
limit; we prove that in this region the area occupied by stable periodic orbits
remains positive. The main device is the construction of an induced map on a
domain with vanishing measure; this map is the product of two involutions, and
each involution preserves all its atoms. Dynamically, the composition of these
involutions represents linking together two sector maps; this dynamical system
features an orderly array of stable periodic orbits having a smooth parameter
dependence, plus irregular contributions which become negligible in the limit.Comment: LaTeX, 57 pages with 13 figure
The Impact of Border Carbon Adjustments under Alternative Producer Responses
Abstract and PDF report are also available on the MIT Joint Program on the Science and Policy of Global Change website (http://globalchange.mit.edu/)Border carbon adjustments (BCAs) have been proposed to address leakage and competitiveness concerns. In traditional assessments, firms regard BCAs as output taxes rather than implicit emissions taxes. Using a stylized energy-economic model, we analyze the impact of BCAs for alternative producer responses. When firms view BCAs as an implicit emissions tax, the outcome depends on whether or not firms can differentiate production across destination markets. If firms are able to produce a low-emissions variety for regions imposing BCAs, results are similar to when firms regard BCAs as an output tax. If firms produce a single variety for all markets, BCAs result in larger leakage reductions than in standard approaches. We also find that BCAs are less effective at addressing competitive concerns in scenarios that result in larger leakage reductions.This study received support from the MIT Joint Program on the Science and Policy of Global Change, which is funded by a consortium of government, industry and foundation sponsors
Comparison of Langevin and Markov channel noise models for neuronal signal generation
The stochastic opening and closing of voltage-gated ion channels produces
noise in neurons. The effect of this noise on the neuronal performance has been
modelled using either approximate or Langevin model, based on stochastic
differential equations or an exact model, based on a Markov process model of
channel gating. Yet whether the Langevin model accurately reproduces the
channel noise produced by the Markov model remains unclear. Here we present a
comparison between Langevin and Markov models of channel noise in neurons using
single compartment Hodgkin-Huxley models containing either and
, or only voltage-gated ion channels. The performance of the
Langevin and Markov models was quantified over a range of stimulus statistics,
membrane areas and channel numbers. We find that in comparison to the Markov
model, the Langevin model underestimates the noise contributed by voltage-gated
ion channels, overestimating information rates for both spiking and non-spiking
membranes. Even with increasing numbers of channels the difference between the
two models persists. This suggests that the Langevin model may not be suitable
for accurately simulating channel noise in neurons, even in simulations with
large numbers of ion channels
Thermal transport in granular metals
We study the electron thermal transport in granular metals at large tunnel
conductance between the grains, and not too low a temperature , where is the mean energy level spacing for a single grain.
Taking into account the electron-electron interaction effects we calculate the
thermal conductivity and show that the Wiedemann-Franz law is violated for
granular metals. We find that interaction effects suppress the thermal
conductivity less than the electrical conductivity.Comment: Replaced with published versio
Ground states for a class of deterministic spin models with glassy behaviour
We consider the deterministic model with glassy behaviour, recently
introduced by Marinari, Parisi and Ritort, with \ha\ , where is the discrete sine Fourier transform. The
ground state found by these authors for odd and prime is shown to
become asymptotically dege\-ne\-ra\-te when is a product of odd primes,
and to disappear for even. This last result is based on the explicit
construction of a set of eigenvectors for , obtained through its formal
identity with the imaginary part of the propagator of the quantized unit
symplectic matrix over the -torus.Comment: 15 pages, plain LaTe
Consequences of converting graded to action potentials upon neural information coding and energy efficiency
Information is encoded in neural circuits using both graded and action potentials, converting between them within single neurons and successive processing layers. This conversion is accompanied by information loss and a drop in energy efficiency. We investigate the biophysical causes of this loss of information and efficiency by comparing spiking neuron models, containing stochastic voltage-gated Na+ and K+ channels, with generator potential and graded potential models lacking voltage-gated Na+ channels. We identify three causes of information loss in the generator potential that are the by-product of action potential generation: (1) the voltage-gated Na+ channels necessary for action potential generation increase intrinsic noise and (2) introduce non-linearities, and (3) the finite duration of the action potential creates a ‘footprint’ in the generator potential that obscures incoming signals. These three processes reduce information rates by ~50% in generator potentials, to ~3 times that of spike trains. Both generator potentials and graded potentials consume almost an order of magnitude less energy per second than spike trains. Because of the lower information rates of generator potentials they are substantially less energy efficient than graded potentials. However, both are an order of magnitude more efficient than spike trains due to the higher energy costs and low information content of spikes, emphasizing that there is a two-fold cost of converting analogue to digital; information loss and cost inflation
Factorizations and Physical Representations
A Hilbert space in M dimensions is shown explicitly to accommodate
representations that reflect the prime numbers decomposition of M.
Representations that exhibit the factorization of M into two relatively prime
numbers: the kq representation (J. Zak, Phys. Today, {\bf 23} (2), 51 (1970)),
and related representations termed representations (together with
their conjugates) are analysed, as well as a representation that exhibits the
complete factorization of M. In this latter representation each quantum number
varies in a subspace that is associated with one of the prime numbers that make
up M
Social physique anxiety and physical activity in early adolescent girls : the influence of maturation and physical activity motives
This study considered the influence of maturation on social physique anxiety (SPA), the relationship between SPA and current and future physical activity (PA) levels and the influence of motives for physical activity on this relationship in early adolescent girls (n=162; mean age=11.80±0.33 years). Participants completed the Pubertal Development Scale, the modified Social Physique Anxiety Scale and the Motives for Physical Activity Scale at baseline and the Physical Activity Questionnaire for Older Children at baseline and 6 months later. The girls became less active across the 6 months and girls in the early stages of maturation had significantly lower SPA than the girls in the middle and late stages of maturation. SPA was not related to current or future physical activity in the sample as a whole. Cluster analysis identified four groups with different motive profiles and the High Appearance and Fitness group demonstrated a moderate negative relationship between SPA and PA at phase 1, whereas the other groups did not. These findings indicate that SPA may increase with maturation and the relationship between SPA and PA is dependent on reasons for being active. For girls who are motivated to be active primarily by body-related reasons SPA is likely to lead to lower levels of PA
Superconducting fluctuations and the Nernst effect: A diagrammatic approach
We calculate the contribution of superconducting fluctuations above the
critical temperature to the transverse thermoelectric response
, the quantity central to the analysis of the Nernst effect. The
calculation is carried out within the microscopic picture of BCS, and to linear
order in magnetic field. We find that as , the dominant contribution
to arises from the Aslamazov-Larkin diagrams, and is equal to the
result previously obtained from a stochastic time-dependent Ginzburg-Landau
equation [Ussishkin, Sondhi, and Huse, arXiv:cond-mat/0204484]. We present an
argument which establishes this correspondence for the heat current. Other
microscopic contributions, which generalize the Maki-Thompson and density of
states terms for the conductivity, are less divergent as .Comment: 11 pages, 5 figure
Plasmon oscillations in ellipsoid nanoparticles: beyond dipole approximation
The plasmon oscillations of a metallic triaxial ellipsoid nanoparticle have
been studied within the framework of the quasistatic approximation. A general
method has been proposed for finding the analytical expressions describing the
potential and frequencies of the plasmon oscillations of an arbitrary
multipolarity order. The analytical expressions have been derived for an
electric potential and plasmon oscillation frequencies of the first 24 modes.
Other higher orders plasmon modes are investigated numerically.Comment: 33 pages, 12 figure
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