84 research outputs found
Technical Notes on Classical Electromagnetism, with exercises
The present technical notes offer a brief summary of the essential points of
electromagnetism at the undergraduate physics level. Some problems are
presented at the end of each section; those with solutions are marked with an
asterisk.Comment: 34 page
An Inhomogeneous Space-Time Patching Model Based on a Nonlocal and Nonlinear Schrodinger Equation
We consider an integrable, nonlocal and nonlinear, Schr\"odinger equation
(NNSE) as a model for building space-time patchings in inhomogeneous loop
quantum cosmology (LQC). We briefly review exact solutions of the NNSE,
specially those obtained through "geometric equivalence" methods. Furthemore,
we argue that the integrability of the NNSE could be linked to consistency
conditions derived from LQC, under the assumption that the patchwork dynamics
behaves as an integrable many-body system.Comment: 29 pages, 2 figures, accepted for publication in Foundations of
Physic
An Approach to Loop Quantum Cosmology Through Integrable Discrete Heisenberg Spin Chains
The quantum evolution equation of Loop Quantum Cosmology (LQC) -- the quantum
Hamiltonian constraint -- is a difference equation. We relate the LQC
constraint equation in vacuum Bianchi I separable (locally rotationally
symmetric) models with an integrable differential-difference nonlinear
Schr\"odinger type equation, which in turn is known to be associated with
integrable, discrete Heisenberg spin chain models in condensed matter physics.
We illustrate the similarity between both systems with a simple constraint in
the linear regime.Comment: 6 pages, accepted for publication in Foundations of Physics; minor
changes in accordance with referee's suggestio
A Note on Norton's Dome
"Norton's Dome" is an example of a Newtonian system that violates the
Lipschitz condition at a single point, leading to non-unique solutions
(indeterminism). Here we reformulate this problem into a "weak" form (in the
sense of distributions). In our description the indeterminism manifests through
the problematic interpretation of initial conditions, since distributions (as
linear functionals on the space of test functions) do not have values at
individual points.Comment: 11 pages, no figures, added a new reference, typos corrected;
comments welcom
Energy Ranking Preservation in a N-Body Cosmological Simulation
In this paper we present a study of the cosmic flow from the point of view of
how clusterings at different dynamical regimes in an expanding universe evolve
according to a `coarse-grained' partitioning of their ranked energy
distribution. By analysing a Lambda-CDM cosmological simulation from the Virgo
Project, we find that cosmic flows evolve in an orderly sense, when tracked
from their coarse-grained energy cells, even when nonlinearities are already
developed. We show that it is possible to characterize scaling laws for the
Pairwise Velocity Distribution in terms of the energy cells, generally valid at
the linear and nonlinear clustering regimes.Comment: 8 pages, 3 figures, accepted for publication in the MNRA
A Self-Consistent Extrapolation Method for the Complex Permittivity and Permeability Based on Finite Frequency Data
We describe a method of extrapolation based on a "truncated" Kramers-Kronig
relation for the complex permittivity () and permeability ()
parameters of a material, based on finite frequency data. Considering a few
assumptions, such as the behavior of the loss tangent and the overall nature of
corrections, the method is robust within a small relative error, if the assumed
hypotheses hold at the extrapolated frequency range.Comment: 27 pages, 19 figures, accepted for publication in the Journal of
Computational Interdisciplinary Sciences (JCIS); this version matches the
accepted versio
Dependence of microwave absorption properties on ferrite volume fraction in MnZn ferrite/rubber radar absorbing materials
We report the analysis of measurements of the complex magnetic permeability
() and dielectric permittivity () spectra of a rubber radar
absorbing material (RAM) with various MnZn ferrite volume fractions. The
transmission/reflection measurements were carried out in a vector network
analyzer. Optimum conditions for the maximum microwave absorption were
determined by substituting the complex permeability and permittivity in the
impedance matching equation. Both the MnZn ferrite content and the RAM
thickness effects on the microwave absorption properties, in the frequency
range of 2 to 18 GHz, were evaluated. The results show that the complex
permeability and permittivity spectra of the RAM increase directly with the
ferrite volume fraction. Reflection loss calculations by the impedance matching
degree (reflection coefficient) show the dependence of this parameter on both
thickness and composition of RAM.Comment: 9 pages, 6 figures; accepted for the Journal of Magnetism and
Magnetic Material
Counts-in-Cells of subhaloes in the IllustrisTNG simulations: the role of baryonic physics
We present an analysis of the Counts-in-Cells (CiC) statistics of subhaloes
in the publicly available IllustrisTNG cosmological simulations (TNG100-1,
TNG100-3 and TNG300-3), considering their full and dark-only versions, in
redshifts ranging from to , and different cell sizes. We evaluated
two CiC models: the gravitational quasi-equilibrium distribution (GQED) and the
negative binomial distribution (NBD), both presenting good fits, with small
detectable differences in the presence of baryons. Scaling and time
dependencies of the best-fit parameters showed similar trends compared with the
literature. We derived a matter density-in-cells probability distribution
function (PDF), associated with the GQED, which was compared to the PDF given
in Uhlemann et al. (2016), for the IllustrisTNG 100-3-Dark run at . Our
results indicate that the simplest gravithermodynamical assumptions of the GQED
model hold in the presence of baryonic dissipation. Interestingly, the smoothed
(density-in-cells) version of the GQED is also adequate for describing the dark
matter one-point statistics of subhaloes and converges, to subpercentage levels
(for an interval of parameters), to the Uhlemann et al. PDF in the high density
range.Comment: Revised version, 17 pages, 9 figures, with clarifications and new
results concerning the PDFs of density-in-cells statistic
The two-component virial theorem and the acceleration-discrepancy relation
We revisit the "two-component virial theorem" (2VT) in the light of recent
theoretical and observational results related to the "dark matter"(DM) problem.
This modification of the virial theorem offers a physically meaningful
framework to investigate possible dynamical couplings between the baryonic and
DM components of extragalactic systems. In particular, we examine the
predictions of the 2VT with respect to the "acceleration-discrepancy relation"
(ADR). Considering the combined data (composed of systems supported by rotation
and by velocity dispersion), we find that: (i) the overall behavior of the 2VT
is consistent with the ADR; and (ii) the 2VT predicts a nearly constant
behavior in the lower acceleration regime, as suggested in recent data on dwarf
spheroidals. We also briefly comment on possible differentiations between the
2VT and some modified gravity theories.Comment: 8 pages, 4 figures, appendices. Submitted to MNRAS. A substantially
shortened and clarified version in order to address the referee's repor
Non-linear (loop) quantum cosmology
Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete
patches, whose interacting many-body equations can be mapped to a non-linear
minisuperspace equation by methods analogous to Bose-Einstein condensation.
Complicated gravitational dynamics can therefore be described by
more-manageable equations for finitely many degrees of freedom, for which
powerful solution procedures are available, including effective equations. The
specific form of non-linear and non-local equations suggests new questions for
mathematical and computational investigations, and general properties of
non-linear wave equations lead to several new options for physical effects and
tests of the consistency of loop quantum gravity. In particular, our quantum
cosmological methods show how sizeable quantum corrections in a low-curvature
universe can arise from tiny local contributions adding up coherently in large
regions.Comment: 20 page
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