Generator Design Considering Mover Action to Improve Energy Conversion Efficiency in a Free-Piston Engine Generator

In a free-piston engine generator (FPEG), the power of the engine can be directly regenerated by linear generators without a crank. The mover motion of this system is interrelated with engine and power generation efficiencies due to the direct connection between the mover of the generator and the piston of the engine. The generator should be designed to improve the overall energy conversion efficiency. The dimensions and mass of the mover limit its operating stroke and drive frequency. Herein, we propose a method for designing linear generators and constructing FPEG systems, considering the mover operation to improve engine efficiency. We evaluated the effect of mover operation on the engine and generation efficiencies using thermal and electromagnetic field analysis software. The proposed design method improves the overall energy conversion efficiency compared with a generator that considers only the maximization of generation efficiency. Setting the mover operation for higher engine efficiency and designing a linear generator to realize the operation can effectively improve the energy conversion efficiency of FPEGs.

Young–Capelli bitableaux, Capelli immanants in U(gl(n)) and the Okounkov quantum immanants

The set of standard Capelli bitableaux and the set of standard Young–Capelli bitableaux are bases of [Formula: see text], whose action on the Gordan–Capelli basis of polynomial algebra [Formula: see text] have remarkable properties (see, e.g. [A. Brini, A. Palareti and A. Teolis, Gordan–Capelli series in superalgebras, Proc. Natl. Acad. Sci. USA 85 (1988) 1330–1333; A. Brini and A. Teolis, Young–Capelli symmetrizers in superalgebras, Proc. Natl. Acad. Sci. USA 86 (1989) 775–778; A. Brini and A. Teolis, Capelli bitableaux and [Formula: see text]-forms of general linear Lie superalgebras, Proc. Natl. Acad. Sci. USA 87 (1990) 56–60; A. Brini and A. Teolis, Capelli’s theory, Koszul maps, and superalgebras, Proc. Natl. Acad. Sci. USA 90 (1993) 10245–10249.]). We introduce a new class of elements of [Formula: see text], called the Capelli immanants, that can be efficiently computed and provide a system of linear generators of [Formula: see text]. The Okounkov quantum immanants [A. Okounkov, Quantum immanants and higher Capelli identities, Transform Groups 1 (1996) 99–126; A. Okounkov, Young basis, Wick formula, and higher Capelli identities, Int. Math. Res. Not. 1996(17) (1996) 817–839.] — quantum immanants, for short — are proved to be simple linear combinations of diagonal Capelli immanants, with explicit coefficients. Quantum immanants can also be expressed as sums of double Young–Capelli bitableaux. Since double Young–Capelli bitableaux uniquely expands into linear combinations of standard Young–Capelli bitableaux, this leads to canonical presentations of quantum immanants, and, furthermore, it does not involve the computation of the irreducible characters of symmetric groups.