4,268 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 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
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
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
FC-groups with finitely many automorphism orbits
Let be a group. The orbits of the natural action of on are
called "automorphism orbits" of , and the number of automorphism orbits of
is denoted by . In this paper we prove that if is an
FC-group with finitely many automorphism orbits, then the derived subgroup
is finite and admits a decomposition , where
is the torsion subgroup of and is a divisible characteristic subgroup
of . We also show that if is an infinite FC-group with , then either is soluble or , where
is an infinite abelian group with . Moreover, we describe the
structure of the infinite non-soluble FC-groups with at most eleven
automorphism orbits.Comment: Submitted to an internacional journa
On state-closed representations of restricted wreath product of groups of type G_{p,d}=C_{p}wrC^{d}
Let be the restricted wreath product where
is a cyclic group of order a prime and a free abelian group of
finite rank . We study the existence of faithful state-closed (fsc)
representations of on the -rooted -ary tree for some finite
. The group , known as the lamplighter group, admits an fsc
representation on the binary tree. We prove that for there are no
fsc representations of on the -adic tree. We characterize all fsc
representations of on the -adic tree where the first level
stabilizer of the image of contains its commutator subgroup. Furthermore,
for , we construct uniformly fsc representations of on the
-adic tree and exhibit concretely the representation of on
the -tree as a finite-state automaton group
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
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
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
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
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