Preliminary study on CAD-based method of characteristics for neutron transport calculation

Our new method makes use of a CAD-based automatic modeling tool, MCAM, for geometry modeling and ray tracing of particle transport in method of characteristics (MOC). It was found that it could considerably enhance the capability of MOC to deal with more complicated models for neutron transport calculation. In our study, the diamond-difference scheme was applied to MOC to reduce the spatial discretization errors of the flat flux approximation. Based on MCAM and MOC, a new 2D MOC code was developed and integrated into the SuperMC system, which is a Super Multi-function Computational system for neutronics and radiation simulation. The numerical results demonstrated the feasibility and effectiveness of the new method for neutron transport calculation in MOC.     

Hidden Symmetries for Thermodynamics and Emergence of Relativity

Erik Verlinde recently proposed an idea about the thermodynamic origin ofgravity. Though this is a beautiful idea, which may resolve many longstanding problems in the theories of gravity, it also raises many otherproblems. In this article I will comment on some of the problems ofVerlinde's proposal with special emphasis on the thermodynamical originof the principle of relativity. It is found that there is a large group of hiddensymmetries of thermodynamics, which contains the Poincare group of thespacetime for which space is emergent. This explains the thermodynamicorigin of the principle of relativity.     

Modular forms and three-loop superstring amplitudes

We study a proposal of D'Hoker and Phong for the chiral superstring measure for genus three. A minor modification of the constraints they impose on certain Siegel modular forms leads to a unique solution. We reduce the problem of finding these modular forms, which depend on an even spin structure, to finding a modular form of weight 8 on a certain subgroup of the modular group. An explicit formula for this form, as a polynomial in the even theta constants, is given. We checked that our result is consistent with the vanishing of the cosmological constant. We also verified a conjecture of D'Hoker and Phong on modular forms in genus 3 and 4 using results of Igusa.     

The ν4 and ν2 + ν5 high resolution infrared bands of FClO3 and FClO3

The high resolution infrared spectra of monoisotopic F³⁵Cl¹⁸O₃ and F³⁷Cl¹⁸O₃ have been studied in the region of the ν₄ fundamentals, centered at 1278.3 and 1263.3 cm⁻¹, respectively. Large perturbations are observed in both bands due to a Fermi type anharmonic resonance with the ν₂ + ν₅ combination bands, centered at 1270.7 cm⁻¹ in F³⁵Cl¹⁸O₃ and 1257.3 cm⁻¹ in F³⁷Cl¹⁸O₃. In particular, they affect the kl > 0 levels of the v₄ = 1 and v₂ = v₅ = 1 states which cross at kl ? 18 in F³⁵Cl¹⁸O₃ and kl ? 3 in F³⁷Cl¹⁸O₃, due to the opposite values of and . The Δl = Δk = ±2 and Δl = 0, Δk = ±3 essential resonances are also effective in the excited states of the dyad in F³⁵Cl¹⁸O₃, while in F³⁷Cl¹⁸O₃ only the Δl = Δk = ±2 one is active. In the spectrum of F³⁵Cl¹⁸O₃ 3423 transitions have been assigned, 10% of them belonging to ν₂ + ν₅. The rovibrational parameters and the interaction constants between the v₄ = 1 and v₂ = v₅ = 1 levels have been obtained. The depertubed band origins of ν₄ and ν₂ + ν₅ are 1277.310567(165) and 1271.753733(195) cm⁻¹, respectively, and the anharmonic resonance constant is 2.804416(153) cm⁻¹. For F³⁷Cl¹⁸O₃, 3022 transitions have been assigned, 38% belonging to the ν₂ + ν₅ combination band. The depertubed band origins are 1260.856338(123) and 1259.872338(134) cm⁻¹, for ν₄and ν₂ + ν₅ and the constant is 2.9350669(405) cm⁻¹. The equilibrium geometry of perchloryl fluoride, r_e (ClO) = 139.7(3) pm, r_e (ClF) = 161.0(5) pm, and α_e (OClO) = 115.7(4) degree, has been determined using the A_e and B_e equilibrium constants of the four symmetric isotopologues of perchloryl fluoride, F^35/37Cl¹⁶O₃ and F^35/37Cl¹⁸O₃.     

A contribution to the global formulation of the higher-order Poincaré-Cartan form

The global formulation of the higher-order Poincaré-Cartan form for Lagrangian field theories in the calculus of variations is re-examined in terms of the theory of lifts of tensor fields on a manifold to its higher-order prolongated jet bundles.Partially supported by CNPq, Brazil, Proc. MA 30.1115/79.     

Euler characteristic and related measures for random geometric sets

By an elementary calculation we obtain the exact mean values of Minkowksi functionals for a standard model of percolating sets. In particular, a recurrence theorem for the mean Euler characteristic recently put forward is shown to be incorrect. Related previous mathematical work is mentioned. We also conjecture bounds for the threshold density of continuum percolation, which are associated with the Euler characteristic.     

On the performance of peeling algorithms

The peeling of a d-dimensional set of points is usually performed with successive calls to a convex hull algorithm; the optimal worst-case convex hull algorithm, known to have an O(n^˙ Log (n)) execution time, may give an O(n^˙n^˙ Log (n)) to peel all the set; an O(n^˙n) convex hull algorithm, m being the number of extremal points, is shown to peel every set with an O(n-n) time, and proved to be optimal; an implementation of this algorithm is given for planar sets and spatial sets, but the latter give only an approximate O(n^˙n) performance.