1,559 research outputs found
Engineering formal systems in constructive type theory
This thesis presents a practical methodology for formalizing the meta-theory of formal systems with binders and coinductive relations in constructive type theory. While constructive type theory offers support for reasoning about formal systems built out of inductive definitions, support for syntax with binders and coinductive relations is lacking. We provide this support. We implement syntax with binders using well-scoped de Bruijn terms and parallel substitutions. We solve substitution lemmas automatically using the rewriting theory of the -calculus. We present the Autosubst library to automate our approach in the proof assistant Coq. Our approach to coinductive relations is based on an inductive tower construction, which is a type-theoretic form of transfinite induction. The tower construction allows us to reduce coinduction to induction. This leads to a symmetric treatment of induction and coinduction and allows us to give a novel construction of the companion of a monotone function on a complete lattice. We demonstrate our methods with a series of case studies. In particular, we present a proof of type preservation for CC!, a proof of weak and strong normalization for System F, a proof that systems of weakly guarded equations have unique solutions in CCS, and a compiler verification for a compiler from a non-deterministic language into a deterministic language. All technical results in the thesis are formalized in Coq.In dieser Dissertation beschreiben wir praktische Techniken um Formale Systeme mit Bindern und koinduktiven Relationen in Konstruktiver Typtheorie zu implementieren. Während Konstruktive Typtheorie bereits gute Unterstützung für Induktive Definition bietet, gibt es momentan kaum Unterstützung für syntaktische Systeme mit Bindern, oder koinduktiven Definitionen. Wir kodieren Syntax mit Bindern in Typtheorie mit einer de Bruijn Darstellung und zeigen alle Substitutionslemmas durch Termersetzung mit dem -Kalkül. Wir präsentieren die Autosubst Bibliothek, die unseren Ansatz im Beweisassistenten Coq implementiert. Für koinduktive Relationen verwenden wir eine induktive Turmkonstruktion, welche das typtheoretische Analog zur Transfiniten Induktion darstellt. Auf diese Art erhalten wir neue Beweisprinzipien für Koinduktion und eine neue Konstruktion von Pous’ “companion” einer monotonen Funktion auf einem vollständigen Verband. Wir validieren unsere Methoden an einer Reihe von Fallstudien. Alle technischen Ergebnisse in dieser Dissertation sind mit Coq formalisiert
Higher-order-in-spin interaction Hamiltonians for binary black holes from Poincar\'e invariance
The fulfillment of the space-asymptotic Poincar\'e algebra is used to derive
new higher-order-in-spin interaction Hamiltonians for binary black holes in the
Arnowitt-Deser-Misner canonical formalism almost completing the set of the
formally spin-interaction Hamiltonians involving nonlinear spin terms.
To linear order in , the expressions for the - and the
-Hamiltonians are completed. It is also shown that there are no quartic
nonlinear -Hamiltonians to linear order in .Comment: REVTeX4, 14 pages; center-of-mass-vector corrected Eq. (2.25) and
modified coefficients of the Hamiltonian Eq. (7.3) and corresponding source
terms Eqs. (7.5) and (7.6) following hereof; version to appear in Phys Rev
Spin-squared Hamiltonian of next-to-leading order gravitational interaction
The static, i.e., linear momentum independent, part of the next-to-leading
order (NLO) gravitational spin(1)-spin(1) interaction Hamiltonian within the
post-Newtonian (PN) approximation is calculated from a 3-dim. covariant ansatz
for the Hamilton constraint. All coefficients in this ansatz can be uniquely
fixed for black holes. The resulting Hamiltonian fits into the canonical
formalism of Arnowitt, Deser, and Misner (ADM) and is given in their
transverse-traceless (ADMTT) gauge. This completes the recent result for the
momentum dependent part of the NLO spin(1)-spin(1) ADM Hamiltonian for binary
black holes (BBH). Thus, all PN NLO effects up to quadratic order in spin for
BBH are now given in Hamiltonian form in the ADMTT gauge. The equations of
motion resulting from this Hamiltonian are an important step toward more
accurate calculations of templates for gravitational waves.Comment: REVTeX4, 10 pages, v2: minor improvements in the presentation, v3:
added omission in Eq. (4) and corrected coefficients in the result, Eq. (9);
version to appear in Phys. Rev.
Phase transition at finite temperature in one dimension: Adsorbate ordering in Ba/Si(111)3x2
We demonstrate that the Ba-induced Si(111)3x2 reconstruction is a physical
realization of a one-dimensional antiferromagnetic Ising model with long-range
Coulomb interactions. Monte Carlo simulations performed on a corresponding
Coulomb-gas model, which we construct based on density-functional calculations,
reveal an adsorbate-ordering phase transition at finite temperature. We show
numerically that this unusual one-dimensional phase transition should be
detectable by low-energy electron diffraction.Comment: 11 pages + 4 figures. Surf. Sci. Lett. (in press
Higher-order-in-spin interaction Hamiltonians for binary black holes from source terms of Kerr geometry in approximate ADM coordinates
The Kerr metric outside the ergosphere is transformed into ADM coordinates up
to the orders and , respectively in radial coordinate and
reduced angular momentum variable , starting from the Kerr solution in
quasi-isotropic as well as harmonic coordinates. The distributional source
terms for the approximate solution are calculated. To leading order in linear
momenta, higher-order-in-spin interaction Hamiltonians for black-hole binaries
are derived.Comment: REVTeX4, 20 pages, typos corrected in Eq. (124) and (130
Reduced Hamiltonian for next-to-leading order Spin-Squared Dynamics of General Compact Binaries
Within the post Newtonian framework the fully reduced Hamiltonian (i.e., with
eliminated spin supplementary condition) for the next-to-leading order
spin-squared dynamics of general compact binaries is presented. The Hamiltonian
is applicable to the spin dynamics of all kinds of binaries with
self-gravitating components like black holes and/or neutron stars taking into
account spin-induced quadrupolar deformation effects in second post-Newtonian
order perturbation theory of Einstein's field equations. The corresponding
equations of motion for spin, position and momentum variables are given in
terms of canonical Poisson brackets. Comparison with a nonreduced potential
calculated within the Effective Field Theory approach is made.Comment: 11 pages, minor changes to match published version at CQ
Interplay of the forces governing steroid hormone micropollutant adsorption in vertically-aligned carbon nanotube membrane nanopores
Vertically-aligned carbon nanotube (VaCNT) membranes allow water to conduct rapidly at low pressures and open up the possibility for water purification and desalination, although the ultralow viscous stress in hydrophobic and low-tortuosity nanopores prevents surface interactions with contaminants. In this experimental investigation, steroid hormone micropollutant adsorption by VaCNT membranes is quantified and explained via the interplay of the hydrodynamic drag and friction forces acting on the hormone, and the adhesive and repulsive forces between the hormone and the inner carbon nanotube wall. It is concluded that a drag force above 2.2 × 10 pN overcomes the friction force resulting in insignificant adsorption, whereas lowering the drag force from 2.2 × 10 to 4.3 × 10 pN increases the adsorbed mass of hormones from zero to 0.4 ng cm. At a low drag force of 1.6 × 10 pN, the adsorbed mass of four hormones is correlated with the hormone−wall adhesive (van der Waals) force. These findings explain micropollutant adsorption in nanopores via the forces acting on the micropollutant along and perpendicular to the flow, which can be exploited for selectivity
Elimination of the spin supplementary condition in the effective field theory approach to the post-Newtonian approximation
The present paper addresses open questions regarding the handling of the spin
supplementary condition within the effective field theory approach to the
post-Newtonian approximation. In particular it is shown how the covariant spin
supplementary condition can be eliminated at the level of the potential (which
is subtle in various respects) and how the dynamics can be cast into a fully
reduced Hamiltonian form. Two different methods are used and compared, one
based on the well-known Dirac bracket and the other based on an action
principle. It is discussed how the latter approach can be used to improve the
Feynman rules by formulating them in terms of reduced canonical spin variables.Comment: 42 pages, document changed to match published version, in press; Ann.
Phys. (N. Y.) (2012
Eta bound states in nuclei: a probe of flavour-singlet dynamics
We argue that eta bound states in nuclei are sensitive to the singlet
component in the eta. The bigger the singlet component, the more attraction and
the greater the binding. Thus, measurements of eta bound states will yield new
information about axial U(1) dynamics and glue in mesons. Eta - etaprime mixing
plays an important role in understanding the value of the eta-nucleon
scattering length.Comment: 8 pages, version to appear in PL
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