4,020 research outputs found
Associated Lam\'{E} Equation, Periodic Potentials and sl(2,R)
We propose a new approach based on the algebraization of the Associated
Lam\'{e} equation within sl(2,R) to
derive the corresponding periodic potentials. The band edge eigenfunctions and
energy spectra are explicitly obtained for integers m,. We also obtain
the explicit expressions of the solutions for half-integer m and integer or
half-integer .Comment: 8 pages, no figure, tex file(version 2.09
Forward Analysis and Model Checking for Trace Bounded WSTS
We investigate a subclass of well-structured transition systems (WSTS), the
bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete
deterministic ones, which we claim provide an adequate basis for the study of
forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth.
Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered
previously for the termination of forward analysis, boundedness is decidable.
Boundedness turns out to be a valuable restriction for WSTS verification, as we
show that it further allows to decide all -regular properties on the
set of infinite traces of the system
PSpectRe: A Pseudo-Spectral Code for (P)reheating
PSpectRe is a C++ program that uses Fourier-space pseudo-spectral methods to
evolve interacting scalar fields in an expanding universe. PSpectRe is
optimized for the analysis of parametric resonance in the post-inflationary
universe, and provides an alternative to finite differencing codes, such as
Defrost and LatticeEasy. PSpectRe has both second- (Velocity-Verlet) and
fourth-order (Runge-Kutta) time integrators. Given the same number of spatial
points and/or momentum modes, PSpectRe is not significantly slower than finite
differencing codes, despite the need for multiple Fourier transforms at each
timestep, and exhibits excellent energy conservation. Further, by computing the
post-resonance equation of state, we show that in some circumstances PSpectRe
obtains reliable results while using substantially fewer points than a finite
differencing code. PSpectRe is designed to be easily extended to other problems
in early-universe cosmology, including the generation of gravitational waves
during phase transitions and pre-inflationary bubble collisions. Specific
applications of this code will be pursued in future work.Comment: 22 pages; source code for PSpectRe available:
http://easther.physics.yale.edu v2 Typos fixed, minor improvements to
wording; v3 updated as per referee comment
Estimation of stratospheric input to the Arctic troposphere: 7Be and 10Be in aerosols at Alert, Canada
Concentrations of 7Be and 210Pb in 2 years of weekly high-volume aerosol samples collected at Alert, Northwest Territories, Canada, showed pronounced seasonal variations. We observed a broad winter peak in 210Pb concentration and a spring peak in 7Be. These peaks were similar in magnitude and duration to previously reported results for a number of stations in the Arctic Basin. Beryllium 10 concentrations (determined only during the first year of this study) were well correlated with those of 7Be; the atom ratio 10Be/7Be was nearly constant at 2.2 throughout the year. This relatively high value of 10Be/7Be indicates that the stratosphere must constitute an important source of both Be isotopes in the Arctic troposphere throughout the year. A simple mixing model based on the small seasonal variations of 10Be/7Be indicates an approximately twofold increase of stratospheric influence in the free troposphere in late summer. The spring maxima in concentrations of both Be isotopes at the surface apparently reflect vertical mixing in rather than stratospheric injections into the troposphere. We have merged the results of the Be-based mixing model with weekly O3 soundings to assess Arctic stratospheric impact on the surface O3 budget at Alert. The resulting estimates indicate that stratospheric inputs can account for a maximum of 10-15% of the 03 at the surface in spring and for less during the rest of the year. These estimates are most uncertain during the winter. The combination of Be isotopic measurements and O3 vertical profiles could allow quantification of the contributions of O3 from the Arctic stratosphere and lower latitude regions to the O3 budget in the Arctic troposphere. Although at present the lack of a quantitative understanding of the temporal variation of O3 lifetime in the Arctic troposphere precludes making definitive calculations, qualitative examples of the power of this approach are given
A New Algebraization of the Lame Equation
We develop a new way of writing the Lame Hamiltonian in Lie-algebraic form.
This yields, in a natural way, an explicit formula for both the Lame
polynomials and the classical non-meromorphic Lame functions in terms of
Chebyshev polynomials and of a certain family of weakly orthogonal polynomialsComment: Latex2e with AMS-LaTeX and cite packages; 32 page
Automatic Verification of Erlang-Style Concurrency
This paper presents an approach to verify safety properties of Erlang-style,
higher-order concurrent programs automatically. Inspired by Core Erlang, we
introduce Lambda-Actor, a prototypical functional language with
pattern-matching algebraic data types, augmented with process creation and
asynchronous message-passing primitives. We formalise an abstract model of
Lambda-Actor programs called Actor Communicating System (ACS) which has a
natural interpretation as a vector addition system, for which some verification
problems are decidable. We give a parametric abstract interpretation framework
for Lambda-Actor and use it to build a polytime computable, flow-based,
abstract semantics of Lambda-Actor programs, which we then use to bootstrap the
ACS construction, thus deriving a more accurate abstract model of the input
program. We have constructed Soter, a tool implementation of the verification
method, thereby obtaining the first fully-automatic, infinite-state model
checker for a core fragment of Erlang. We find that in practice our abstraction
technique is accurate enough to verify an interesting range of safety
properties. Though the ACS coverability problem is Expspace-complete, Soter can
analyse these verification problems surprisingly efficiently.Comment: 12 pages plus appendix, 4 figures, 1 table. The tool is available at
http://mjolnir.cs.ox.ac.uk/soter
New spin Calogero-Sutherland models related to B_N-type Dunkl operators
We construct several new families of exactly and quasi-exactly solvable
BC_N-type Calogero-Sutherland models with internal degrees of freedom. Our
approach is based on the introduction of two new families of Dunkl operators of
B_N type which, together with the original B_N-type Dunkl operators, are shown
to preserve certain polynomial subspaces of finite dimension. We prove that a
wide class of quadratic combinations involving these three sets of Dunkl
operators always yields a spin Calogero-Sutherland model, which is
(quasi-)exactly solvable by construction. We show that all the spin
Calogero-Sutherland models obtainable within this framework can be expressed in
a unified way in terms of a Weierstrass P function with suitable half-periods.
This provides a natural spin counterpart of the well-known general formula for
a scalar completely integrable potential of BC_N type due to Olshanetsky and
Perelomov. As an illustration of our method, we exactly compute several energy
levels and their corresponding wavefunctions of an elliptic quasi-exactly
solvable potential for two and three particles of spin 1/2.Comment: 18 pages, typeset in LaTeX 2e using revtex 4.0b5 and the amslatex
package Minor changes in content, one reference adde
The complexity of coverability in ν-Petri nets
We show that the coverability problem in ν-Petri nets is complete for ‘double Ackermann’ time, thus closing an open complexity gap between an Ackermann lower bound and a hyper-Ackermann upper bound. The coverability problem captures the verification of safety properties in this nominal extension of Petri nets with name management and fresh name creation. Our completeness result establishes ν-Petri nets as a model of intermediate power among the formalisms of nets enriched with data, and relies on new algorithmic insights brought by the use of well-quasi-order ideals
On algebraic classification of quasi-exactly solvable matrix models
We suggest a generalization of the Lie algebraic approach for constructing
quasi-exactly solvable one-dimensional Schroedinger equations which is due to
Shifman and Turbiner in order to include into consideration matrix models. This
generalization is based on representations of Lie algebras by first-order
matrix differential operators. We have classified inequivalent representations
of the Lie algebras of the dimension up to three by first-order matrix
differential operators in one variable. Next we describe invariant
finite-dimensional subspaces of the representation spaces of the one-,
two-dimensional Lie algebras and of the algebra sl(2,R). These results enable
constructing multi-parameter families of first- and second-order quasi-exactly
solvable models. In particular, we have obtained two classes of quasi-exactly
solvable matrix Schroedinger equations.Comment: LaTeX-file, 16 pages, submitted to J.Phys.A: Math.Ge
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