1,653 research outputs found
A CDCL-style calculus for solving non-linear constraints
In this paper we propose a novel approach for checking satisfiability of
non-linear constraints over the reals, called ksmt. The procedure is based on
conflict resolution in CDCL style calculus, using a composition of symbolical
and numerical methods. To deal with the non-linear components in case of
conflicts we use numerically constructed restricted linearisations. This
approach covers a large number of computable non-linear real functions such as
polynomials, rational or trigonometrical functions and beyond. A prototypical
implementation has been evaluated on several non-linear SMT-LIB examples and
the results have been compared with state-of-the-art SMT solvers.Comment: 17 pages, 3 figures; accepted at FroCoS 2019; software available at
<http://informatik.uni-trier.de/~brausse/ksmt/
Alternative Fourier Expansions for Inverse Square Law Forces
Few-body problems involving Coulomb or gravitational interactions between
pairs of particles, whether in classical or quantum physics, are generally
handled through a standard multipole expansion of the two-body potentials. We
discuss an alternative based on a compact, cylindrical Green's function
expansion that should have wide applicability throughout physics. Two-electron
"direct" and "exchange" integrals in many-electron quantum systems are
evaluated to illustrate the procedure which is more compact than the standard
one using Wigner coefficients and Slater integrals.Comment: 10 pages, latex/Revtex4, 1 figure
Special Algorithm for Stability Analysis of Multistable Biological Regulatory Systems
We consider the problem of counting (stable) equilibriums of an important
family of algebraic differential equations modeling multistable biological
regulatory systems. The problem can be solved, in principle, using real
quantifier elimination algorithms, in particular real root classification
algorithms. However, it is well known that they can handle only very small
cases due to the enormous computing time requirements. In this paper, we
present a special algorithm which is much more efficient than the general
methods. Its efficiency comes from the exploitation of certain interesting
structures of the family of differential equations.Comment: 24 pages, 5 algorithms, 10 figure
Spherical Vesicles Distorted by a Grafted Latex Bead: An Exact Solution
We present an exact solution to the problem of the global shape description
of a spherical vesicle distorted by a grafted latex bead. This solution is
derived by treating the nonlinearity in bending elasticity through the
(topological) Bogomol'nyi decomposition technique and elastic compatibility. We
recover the ``hat-model'' approximation in the limit of a small latex bead and
find that the region antipodal to the grafted latex bead flattens. We also
derive the appropriate shape equation using the variational principle and
relevant constraints.Comment: 12 pages, 2 figures, LaTeX2e+REVTeX+AmSLaTe
Relativistic MHD and black hole excision: Formulation and initial tests
A new algorithm for solving the general relativistic MHD equations is
described in this paper. We design our scheme to incorporate black hole
excision with smooth boundaries, and to simplify solving the combined Einstein
and MHD equations with AMR. The fluid equations are solved using a finite
difference Convex ENO method. Excision is implemented using overlapping grids.
Elliptic and hyperbolic divergence cleaning techniques allow for maximum
flexibility in choosing coordinate systems, and we compare both methods for a
standard problem. Numerical results of standard test problems are presented in
two-dimensional flat space using excision, overlapping grids, and elliptic and
hyperbolic divergence cleaning.Comment: 22 pages, 8 figure
A Survey of Satisfiability Modulo Theory
Satisfiability modulo theory (SMT) consists in testing the satisfiability of
first-order formulas over linear integer or real arithmetic, or other theories.
In this survey, we explain the combination of propositional satisfiability and
decision procedures for conjunctions known as DPLL(T), and the alternative
"natural domain" approaches. We also cover quantifiers, Craig interpolants,
polynomial arithmetic, and how SMT solvers are used in automated software
analysis.Comment: Computer Algebra in Scientific Computing, Sep 2016, Bucharest,
Romania. 201
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