48,548 research outputs found
Special curves and postcritically-finite polynomials
We study the postcritically-finite (PCF) maps in the moduli space of complex
polynomials . For a certain class of rational curves in
, we characterize the condition that contains infinitely
many PCF maps. In particular, we show that if is parameterized by
polynomials, then there are infinitely many PCF maps in if and only if
there is exactly one active critical point along , up to symmetries; we
provide the critical orbit relation satisfied by any pair of active critical
points. For the curves in the space of cubic
polynomials, introduced by Milnor (1992), we show that
contains infinitely many PCF maps if and only if
. The proofs involve a combination of number-theoretic methods
(specifically, arithmetic equidistribution) and complex-analytic techniques
(specifically, univalent function theory). We provide a conjecture about
Zariski density of PCF maps in subvarieties of the space of rational maps, in
analogy with the Andr\'e-Oort Conjecture from arithmetic geometry.Comment: Final version, appeared in Forum of Math. P
First Lattice Study of Ghost Propagators in SU(2) and SU(3) Gauge Theories
We present a numerical study of the ghost propagators in Landau gauge for
SU(2) and SU(3) gauge theories at =2.7 and =6.0, respectively.
Analyzing different lattice sizes up to , we find small finite size
effects. Down to the smallest available momenta, we observe no evidence for
dipole behaviour of the ghost propagators.Comment: 7 pages, uuencoded compressed latex file, 2 figures include
Eye muscle proprioception is represented bilaterally in the sensorimotor cortex
The cortical representation of eye position is still uncertain. In the monkey a proprioceptive representation of the extraocular muscles (EOM) of an eye were recently found within the contralateral central sulcus. In humans, we have previously shown a change in the perceived position of the right eye after a virtual lesion with rTMS over the left somatosensory area. However, it is possible that the proprioceptive representation of the EOM extends to other brain sites, which were not examined in these previous studies. The aim of this fMRI study was to sample the whole brain to identify the proprioceptive representation for the left and the right eye separately. Data were acquired while passive eye movement was used to stimulate EOM proprioceptors in the absence of a motor command. We also controlled for the tactile stimulation of the eyelid by removing from the analysis voxels activated by eyelid touch alone. For either eye, the brain area commonly activated
by passive and active eye movement was located bilaterally in the somatosensory area extending into the motor and premotor cytoarchitectonic areas. We suggest this is where EOM proprioception is processed. The bilateral representation for either eye contrasts with the contralateral representation of hand proprioception. We suggest that the proprioceptive representation of the two eyes next to each other in either somatosensory cortex and extending into the premotor cortex reflects the integrative nature of the eye position sense, which combines proprioceptive information across the two eyes with the efference copy of the oculomotor comman
Solving exponential diophantine equations using lattice basis reduction algorithms
Let S be the set of all positive integers with prime divisors from a fixed finite set of primes. Algorithms are given for solving the diophantine inequality 0< x â y < yÎŽ in x, y S for fixed ÎŽ (0, 1), and for the diophantine equation x + Y = z in x, y, z S. The method is based on multi-dimensional diophantine approximation, in the real and p-adic case, respectively. The main computational tool is the L3-Basis Reduction Algorithm. Elaborate examples are presented
Effective String Theory of Vortices and Regge Trajectories
Starting from a field theory containing classical vortex solutions, we obtain
an effective string theory of these vortices as a path integral over the two
transverse degrees of freedom of the string. We carry out a semiclassical
expansion of this effective theory, and use it to obtain corrections to Regge
trajectories due to string fluctuations.Comment: 27 pages, revtex, 3 figures, corrected an error with the cutoff in
appendix E (was previously D), added more discussion of Fig. 3, moved some
material in section 9 to a new appendi
Understanding Confinement From Deconfinement
We use effective magnetic SU(N) pure gauge theory with cutoff M and fixed
gauge coupling g_m to calculate non-perturbative magnetic properties of the
deconfined phase of SU(N) Yang-Mills theory. We obtain the response to an
external closed loop of electric current by reinterpreting and regulating the
calculation of the one loop effective potential in Yang-Mills theory. This
effective potential gives rise to a color magnetic charge density, the
counterpart in the deconfined phase of color magnetic currents introduced in
effective dual superconductor theories of the confined phase via magnetically
charged Higgs fields. The resulting spatial Wilson loop has area law behavior.
Using values of M and g_m determined in the confined phase, we find SU(3)
spatial string tensions compatible with lattice simulations in the temperature
interval 1.5T_c < T < 2.5T_c. Use of the effective theory to analyze
experiments on heavy ion collisions will provide applications and further tests
of these ideas.Comment: 18 pages, 5 figures, v2: fixed archive title (only
Kinetic cross coupling between non-conserved and conserved fields in phase field models
We present a phase field model for isothermal transformations of two
component alloys that includes Onsager kinetic cross coupling between the
non-conserved phase field and the conserved concentration field. We also
provide the reduction of the phase field model to the corresponding macroscopic
description of the free boundary problem. The reduction is given in a general
form. Additionally we use an explicit example of a phase field model and check
that the reduced macroscopic description, in the range of its applicability, is
in excellent agreement with direct phase field simulations. The relevance of
the newly introduced terms to solute trapping is also discussed
The Rebound Effect: Some Questions Answered
Greenhouse gas (and other pollutant) emissions from energy use are now taken to be a problem both internationally and for individual national and regional governments. A number of mechanisms are being employed to reduce energy consumption demand as part of climate and energy policies internationally. A central policy focus is increased efficiency in the use of energy. However, the straightforward link between increased energy efficiency and reduced energy consumption has been questioned. This is due to the notion of the ârebound effectâ. Rebound occurs when improvements in energy efficiency actually stimulate the direct and indirect demand for energy in production and/or consumption. It is triggered by the fact that an increase in the efficiency in the use of energy acts to reduce the implicit price of energy, or the price of effective energy services for each physical unit of energy used. Thus, it is an economic phenomenon. The rebound effect implies that measures taken to reduce energy use might lead to increases in carbon emissions, or at least not offset them to the extent anticipated. It is possible to distiguish between direct rebound effects in energy consumption in the activity where energy efficiency has increased, indirect rebound effects from income and substitutuion effects and economy-wide rebound effects (impacts on macro-level energy use). This paper attempts to provide a non-technical overview of work on the latter, carried out under an ESRC-funded project investigating the source and magnitude of econom-wide rebound effects from increased energy efficiency in the UK.General equilibrium, energy efficiency, rebound effects, disinvestment.
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