Constraints on axion-like particles and non-Newtonian gravity from measuring the difference of Casimir forces

We derive constraints on the coupling constants of axion-like particles to nucleons and on the Yukawa-type corrections to Newton's gravitational law from the results of recent experiment on measuring the difference of Casimir forces between a Ni-coated sphere and Au and Ni sectors of a structured disc. Over the wide range of axion masses from 2.61\,meV to 0.9\,eV the obtained constraints on the axion-to-nucleon coupling are up to a factor of 14.6 stronger than all previously known constraints following from experiments on measuring the Casimir interaction. The constraints on non-Newtonian gravity found here are also stronger than all that following from the Casimir and Cavendish-type experiments over the interaction range from 30\,nm to $5.4\,\mu$m. They are up to a factor of 177 stronger than the constraints derived recently from measuring the difference of lateral forces. Our constraints confirm previous somewhat stronger limits obtained from the isoelectronic experiment, where the contribution of the Casimir force was nullified.Comment: 13 pages, 3 figure

Speeding up the constraint-based method in difference logic

"The final publication is available at http://link.springer.com/chapter/10.1007%2F978-3-319-40970-2_18"Over the years the constraint-based method has been successfully applied to a wide range of problems in program analysis, from invariant generation to termination and non-termination proving. Quite often the semantics of the program under study as well as the properties to be generated belong to difference logic, i.e., the fragment of linear arithmetic where atoms are inequalities of the form u v = k. However, so far constraint-based techniques have not exploited this fact: in general, Farkas’ Lemma is used to produce the constraints over template unknowns, which leads to non-linear SMT problems. Based on classical results of graph theory, in this paper we propose new encodings for generating these constraints when program semantics and templates belong to difference logic. Thanks to this approach, instead of a heavyweight non-linear arithmetic solver, a much cheaper SMT solver for difference logic or linear integer arithmetic can be employed for solving the resulting constraints. We present encouraging experimental results that show the high impact of the proposed techniques on the performance of the VeryMax verification systemPeer ReviewedPostprint (author's final draft

Constraints on Area Variables in Regge Calculus

We describe a general method of obtaining the constraints between area variables in one approach to area Regge calculus, and illustrate it with a simple example. The simplicial complex is the simplest tessellation of the 4-sphere. The number of independent constraints on the variations of the triangle areas is shown to equal the difference between the numbers of triangles and edges, and a general method of choosing independent constraints is described. The constraints chosen by using our method are shown to imply the Regge equations of motion in our example.Comment: Typographical errors correcte

An Improved Tight Closure Algorithm for Integer Octagonal Constraints

Integer octagonal constraints (a.k.a. ``Unit Two Variables Per Inequality'' or ``UTVPI integer constraints'') constitute an interesting class of constraints for the representation and solution of integer problems in the fields of constraint programming and formal analysis and verification of software and hardware systems, since they couple algorithms having polynomial complexity with a relatively good expressive power. The main algorithms required for the manipulation of such constraints are the satisfiability check and the computation of the inferential closure of a set of constraints. The latter is called `tight' closure to mark the difference with the (incomplete) closure algorithm that does not exploit the integrality of the variables. In this paper we present and fully justify an O(n^3) algorithm to compute the tight closure of a set of UTVPI integer constraints.Comment: 15 pages, 2 figure