940 research outputs found
Reasoning about transfinite sequences
We introduce a family of temporal logics to specify the behavior of systems
with Zeno behaviors. We extend linear-time temporal logic LTL to authorize
models admitting Zeno sequences of actions and quantitative temporal operators
indexed by ordinals replace the standard next-time and until future-time
operators. Our aim is to control such systems by designing controllers that
safely work on -sequences but interact synchronously with the system in
order to restrict their behaviors. We show that the satisfiability problem for
the logics working on -sequences is EXPSPACE-complete when the
integers are represented in binary, and PSPACE-complete with a unary
representation. To do so, we substantially extend standard results about LTL by
introducing a new class of succinct ordinal automata that can encode the
interaction between the different quantitative temporal operators.Comment: 38 page
Play Pedagogy, STEM, and Inquiry: Using Mousetrap Cars to Bridge Metacognition
Educators are eager to embrace the complexities of 21st century instruction, which presents challenges for integrating science, technology, engineering, and mathematics (STEM) into K-12 instructional practices. Although there are a variety of methodologies for STEM, focusing on play pedagogy and inquiry will facilitate student engagement in metacognitive skills that are necessary components of STEM constructs. Metacognition activates critical thinking skills such as collaborative planning for problem solving, analyzing, self-regulation, and evaluating. Additionally, student motivation is maximized when student led learning results in authentic student products. When educators are provided with support that guides methods for implementation, they will be more successful in the classroom. This completed practice project will present the audience with components for a STEM model that includes context, purposes, methods, evidence, analysis, scholarly discussions, and recommendations. The audience will directly experience the thrill of engaging in collaboration to plan, design, and build mousetrap cars within the context of a STEM lesson
The puzzle of 90 degree reorientation in the vortex lattice of borocarbide superconductors
We explain 90 degree reorientation in the vortex lattice of borocarbide
superconductors on the basis of a phenomenological extension of the nonlocal
London model that takes full account of the symmetry of the system. We propose
microscopic mechanisms that could generate the correction terms and point out
the important role of the superconducting gap anisotropy.Comment: 4 pages, 2 eps figure
Interplay of Anisotropy and Disorder in the Doping-Dependent Melting and Glass Transitions of Vortices in BiSrCaCuO
We study the oxygen doping dependence of the equilibrium first-order melting
and second-order glass transitions of vortices in
BiSrCaCuO. Doping affects both anisotropy and
disorder. Anisotropy scaling is shown to collapse the melting lines only where
thermal fluctuations are dominant. Yet, in the region where disorder breaks
that scaling, the glass lines are still collapsed. A quantitative fit to
melting and replica symmetry breaking lines of a 2D Ginzburg-Landau model
further reveals that disorder amplitude weakens with doping, but to a lesser
degree than thermal fluctuations, enhancing the relative role of disorder.Comment: 4 pages, 4 figure
Equilibrium First-Order Melting and Second-Order Glass Transitions of the Vortex Matter in BiSrCaCuO
The thermodynamic phase diagram of BiSrCaCuO was mapped
by measuring local \emph{equilibrium} magnetization in presence of
vortex `shaking'. Two equally sharp first-order magnetization steps are
revealed in a single temperature sweep, manifesting a liquid-solid-liquid
sequence. In addition, a second-order glass transition line is revealed by a
sharp break in the equilibrium slope. The first- and second-order lines
intersect at intermediate temperatures, suggesting the existence of four
phases: Bragg glass and vortex crystal at low fields, glass and liquid at
higher fields.Comment: 5 pages, 4 figures. To be published in Phys. Rev. Let
Nature of 45 degree vortex lattice reorientation in tetragonal superconductors
The transformation of the vortex lattice in a tetragonal superconductor which
consists of its 45 degree reorientation relative to the crystal axes is studied
using the nonlocal London model. It is shown that the reorientation occurs as
two successive second order (continuous) phase transitions. The transition
magnetic fields are calculated for a range of parameters relevant for
borocarbide superconductors in which the reorientation has been observed
The Dynamical Behaviors in (2+1)-Dimensional Gross-Neveu Model with a Thirring Interaction
We analyze (2+1)-dimensional Gross-Neveu model with a Thirring interaction,
where a vector-vector type four-fermi interaction is on equal terms with a
scalar-scalar type one. The Dyson-Schwinger equation for fermion self-energy
function is constructed up to next-to-leading order in 1/N expansion. We
determine the critical surface which is the boundary between a broken phase and
an unbroken one in () space. It is observed that the
critical behavior is mainly controlled by Gross-Neveu coupling and
the region of the broken phase is separated into two parts by the line
. The mass function is strongly
dependent upon the flavor number N for , while weakly for
, the critical flavor number
increases as Thirring coupling decreases. By driving the CJT
effective potential, we show that the broken phase is energetically preferred
to the symmetric one. We discuss the gauge dependence of the mass function and
the ultra-violet property of the composite operators.Comment: 19 pages, LaTex, 6 ps figure files(uuencoded in seperate file
Dynamical Symmetry Breaking in Models with the Yukawa Interaction
We discuss models with a massless fermion and a self-interacting massive
scalar field with the Yukawa interaction. The chiral condensate and the fermion
mass are calculated analytically. It is shown that the models have a phase
transition as a function of the squared mass of the scalar field.Comment: 7 pages, no figures, in Eqs. (7) and (11) one coefficient was change
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