9,029 research outputs found
Nonlinear dynamic intertwining of rods with self-contact
Twisted marine cables on the sea floor can form highly contorted
three-dimensional loops that resemble tangles. Such tangles or hockles are
topologically equivalent to the plectomenes that form in supercoiled DNA
molecules. The dynamic evolution of these intertwined loops is studied herein
using a computational rod model that explicitly accounts for dynamic
self-contact. Numerical solutions are presented for an illustrative example of
a long rod subjected to increasing twist at one end. The solutions reveal the
dynamic evolution of the rod from an initially straight state, through a
buckled state in the approximate form of a helix, through the dynamic collapse
of this helix into a near-planar loop with one site of self-contact, and the
subsequent intertwining of this loop with multiple sites of self-contact. This
evolution is controlled by the dynamic conversion of torsional strain energy to
bending strain energy or, alternatively by the dynamic conversion of twist (Tw)
to writhe (Wr).
KEY WORDS Rod Dynamics, Self-contact, Intertwining, DNA Supercoiling, Cable
HocklingComment: 35 pages, 9 figures, submitted to Proceedings of the Royal Society A:
Mathematical, Physical and Engineering Science
Spin-1 effective Hamiltonian with three degenerate orbitals: An application to the case of V_2O_3
Motivated by recent neutron and x-ray observations in V_2O_3, we derive the
effective Hamiltonian in the strong coupling limit of an Hubbard model with
three degenerate t_{2g} states containing two electrons coupled to spin S = 1,
and use it to re-examine the low-temperature ground-state properties of this
compound. An axial trigonal distortion of the cubic states is also taken into
account. Since there are no assumptions about the symmetry properties of the
hopping integrals involved, the resulting spin-orbital Hamiltonian can be
generally applied to any crystallographic configuration of the transition metal
ion giving rise to degenerate t_{2g} orbitals. Specializing to the case of
V_2O_3 we consider the antiferromagnetic insulating phase. We find two
variational regimes, depending on the relative size of the correlation energy
of the vertical pairs and the in-plane interaction energy. The former favors
the formation of stable molecules throughout the crystal, while the latter
tends to break this correlated state. We determine in both cases the minimizing
orbital solutions for various spin configurations, and draw the corresponding
phase diagrams. We find that none of the symmetry-breaking stable phases with
the real spin structure presents an orbital ordering compatible with the
magnetic space group indicated by very recent observations of non-reciprocal
x-ray gyrotropy in V_2O_3. We do however find a compatible solution with very
small excitation energy in two distinct regions of the phase space, which might
turn into the true ground state of V_2O_3 due to the favorable coupling with
the lattice. We illustrate merits and drawbacks of the various solutions and
discuss them in relation to the present experimental evidence.Comment: 36 pages, 19 figure
Black Holes in Higher-Derivative Gravity
Extensions of Einstein gravity with higher-order derivative terms arise in
string theory and other effective theories, as well as being of interest in
their own right. In this paper we study static black-hole solutions in the
example of Einstein gravity with additional quadratic curvature terms. A
Lichnerowicz-type theorem simplifies the analysis by establishing that they
must have vanishing Ricci scalar curvature. By numerical methods we then
demonstrate the existence of further black-hole solutions over and above the
Schwarzschild solution. We discuss some of their thermodynamic properties, and
show that they obey the first law of thermodynamics.Comment: Typos corrected, discussion added, figure changed. 4 pages, 6 figure
Lichnerowicz Modes and Black Hole Families in Ricci Quadratic Gravity
A new branch of black hole solutions occurs along with the standard
Schwarzschild branch in -dimensional extensions of general relativity
including terms quadratic in the Ricci tensor. The standard and new branches
cross at a point determined by a static negative-eigenvalue eigenfunction of
the Lichnerowicz operator, analogous to the Gross-Perry-Yaffe eigenfunction for
the Schwarzschild solution in standard dimensional general relativity.
This static eigenfunction has two r\^oles: both as a perturbation away from
Schwarzschild along the new black-hole branch and also as a threshold unstable
mode lying at the edge of a domain of Gregory-Laflamme-type instability of the
Schwarzschild solution for small-radius black holes. A thermodynamic analogy
with the Gubser and Mitra conjecture on the relation between quantum
thermodynamic and classical dynamical instabilities leads to a suggestion that
there may be a switch of stability properties between the old and new
black-hole branches for small black holes with radii below the branch crossing
point.Comment: 33 pages, 8 figure
Spherically Symmetric Solutions in Higher-Derivative Gravity
Extensions of Einstein gravity with quadratic curvature terms in the action
arise in most effective theories of quantised gravity, including string theory.
This article explores the set of static, spherically symmetric and
asymptotically flat solutions of this class of theories. An important element
in the analysis is the careful treatment of a Lichnerowicz-type `no-hair'
theorem. From a Frobenius analysis of the asymptotic small-radius behaviour,
the solution space is found to split into three asymptotic families, one of
which contains the classic Schwarzschild solution. These three families are
carefully analysed to determine the corresponding numbers of free parameters in
each. One solution family is capable of arising from coupling to a
distributional shell of matter near the origin; this family can then match on
to an asymptotically flat solution at spatial infinity without encountering a
horizon. Another family, with horizons, contains the Schwarzschild solution but
includes also non-Schwarzschild black holes. The third family of solutions
obtained from the Frobenius analysis is nonsingular and corresponds to `vacuum'
solutions. In addition to the three families identified from near-origin
behaviour, there are solutions that may be identified as `wormholes', which can
match symmetrically on to another sheet of spacetime at finite radius.Comment: 57 pages, 6 figures; version appearing in journal; minor corrections
and clarifications to v
Assessing the Effectiveness of a Computer Simulation in Introductory Undergraduate Environments
We present studies documenting the effectiveness of using a computer simulation, specifically the Circuit Construction Kit (CCK) developed as part of the Physics Education Technology Project (PhET) [1, 2], in two environments: an interactive college lecture and an inquiry-based laboratory. In the first study conducted in lecture, we compared students viewing CCK to viewing a traditional demonstration during Peer Instruction [3]. Students viewing CCK had a 47% larger relative gain (11% absolute gain) on measures of conceptual understanding compared to traditional demonstrations. These results led us to study the impact of the simulation's explicit representation for visualizing current flow in a laboratory environment, where we removed this feature for a subset of students. Students using CCK with or without the explicit visualization of current performed similarly to each other on common exam questions. Although the majority of students in both groups favored the use of CCK over real circuit equipment, the students who used CCK without the explicit current model favored the simulation more than the other grou
Magnetic excitations in vanadium spinels
We study magnetic excitations in vanadium spinel oxides AVO (A=Zn,
Mg, Cd) using two models: first one is a superexchange model for vanadium S=1
spins, second one includes in addition spin-orbit coupling, and crystal
anisotropy. We show that the experimentally observed magnetic ordering can be
obtained in both models, however the orbital ordering is different with and
without spin-orbit coupling and crystal anisotropy. We demonstrate that this
difference strongly affects the spin-wave excitation spectrum above the
magnetically ordered state, and argue that the neutron measurement of such
dispersion is a way to distinguish between the two possible orbital orderings
in AVO.Comment: accepted in Phys. Rev.
A New Instrument For Measuring Student Beliefs About Physics and Learning Physics: The Colorado Learning Attitudes About Science Survey
The Colorado Learning Attitudes about Science Survey (CLASS) is a new instrument designed to measure student beliefs about physics and about learning physics. This instrument extends previous work by probing additional aspects of student beliefs and by using wording suitable for students in a wide variety of physics courses. The CLASS has been validated using interviews, reliability studies, and extensive statistical analyses of responses from over 5000 students. In addition, a new methodology for determining useful and statistically robust categories of student beliefs has been developed. This paper serves as the foundation for an extensive study of how student beliefs impact and are impacted by their educational experiences. For example, this survey measures: that most teaching practices cause substantial drops in student scores; that a student's likelihood of becoming a physics major correlates with their 'Personal Interest' score; and that, for a majority of student populations, women's scores in some categories, including 'Personal Interest' and 'Real World Connections', are significantly different than men's scores
- …