Equivalence of Local and Separable Realizations of the Discontinuity-Inducing Contact Interaction and Its Perturbative Renormalizability

We prove that the separable and local approximations of the discontinuity-inducing zero-range interaction in one-dimensional quantum mechanics are equivalent. We further show that the interaction allows the perturbative treatment through the coupling renormalization. Keywords: one-dimensional system, generalized contact interaction, renormalization, perturbative expansion. PACS Nos: 3.65.-w, 11.10.Gh, 31.15.MdComment: ReVTeX 7pgs, doubl column, no figure, See also the website http://www.mech.kochi-tech.ac.jp/cheon

Bayesian Nash Equilibria and Bell Inequalities

Games with incomplete information are formulated in a multi-sector probability matrix formalism that can cope with quantum as well as classical strategies. An analysis of classical and quantum strategy in a multi-sector extension of the game of Battle of Sexes clarifies the two distinct roles of nonlocal strategies, and establish the direct link between the true quantum gain of game's payoff and the breaking of Bell inequalities.Comment: 6 pages, LaTeX JPSJ 2 column format, changes in sections 1, 3 and 4, added reference

Improvement of Fire Hydrant Design to Enhance Water Main Flushing

AbstractFlushing is a good practice to avoid problems related to sediment, bio-film growth, and corrosion. Artificial sediment was removed from fire hydrant with pilot scale water distribution main. The sediment removal in fire hydrant and main was carefully compared with different flow rate with velocity ranged from 0.3 to 3.0 m/s and the depth of fire hydrant from 0.5 m to 1.3m. The drain capability of fire hydrant decreased as the flow rate increased. Sediment with higher density was hard to remove from water main. The length effect of upward fire hydrant was relatively minor. Downward drain showed better efficiency for both sand and actual sediment

A general approximation of quantum graph vertex couplings by scaled Schroedinger operators on thin branched manifolds

We demonstrate that any self-adjoint coupling in a quantum graph vertex can be approximated by a family of magnetic Schroedinger operators on a tubular network built over the graph. If such a manifold has a boundary, Neumann conditions are imposed at it. The procedure involves a local change of graph topology in the vicinity of the vertex; the approximation scheme constructed on the graph is subsequently `lifted' to the manifold. For the corresponding operator a norm-resolvent convergence is proved, with the natural identification map, as the tube diameters tend to zero.Comment: 19 pages, one figure; introduction amended and some references added, to appear in CM

Eigenvalue and eigenspace anholonomies in hierarchical systems

An adiabatic cycle of parameters in a quantum system can yield the quantum anholonomies, nontrivial evolution not just in phase of the states, but also in eigenvalues and eigenstates. Such exotic anholonomies imply that an adiabatic cycle rearranges eigenstates even without spectral degeneracy. We show that an arbitrarily large quantum circuit generated by recursive extension can also exhibit the eigenvalue and eigenspace anholonomies.Comment: 5 pages, 3 figure

Level spacing distribution of pseudointegrable billiard

In this paper, we examine the level spacing distribution $P(S)$ of the rectangular billiard with a single point-like scatterer, which is known as pseudointegrable. It is shown that the observed $P(S)$ is a new type, which is quite different from the previous conclusion. Even in the strong coupling limit, the Poisson-like behavior rather than Wigner-like is seen for $S>1$, although the level repulsion still remains in the small $S$ region. The difference from the previous works is analyzed in detail.Comment: 11 pages, REVTeX file, 3 PostScript Figure

Comments on F-maximization and R-symmetry in 3D SCFTs

We report preliminary results on the recently proposed F-maximization principle in 3D SCFTs. We compute numerically in the large-N limit the free energy on the three-sphere of an N=2 Chern-Simons-Matter theory with a single adjoint chiral superfield which is known to exhibit a pattern of accidental symmetries associated to chiral superfields that hit the unitarity bound and become free. We observe that the F-maximization principle produces a U(1) R-symmetry consistent with previously obtained bounds but inconsistent with a postulated Seiberg-like duality. Potential modifications of the principle associated to the decoupling fields do not appear to be sufficient to account for the observed violations.Comment: 17 pages, 3 figures; v2 a reference has been added, a missing factor of 2 has been corrected in eq (3.3) and the numerical results have been accordingly updated. The new results do not show any obvious signs of violation of previously obtained bounds. A potential disagreement with a postulated Seiberg-like duality is note

Breakdown pressure and fracture surface morphology of hydraulic fracturing in shale with H2O, CO2 and N2

Slick-water fracturing is the most routine form of well stimulation in shales; however N2, LPG and CO2 have all been used as “exotic” stimulants in various hydrocarbon reservoirs. We explore the use of these gases as stimulants on Green River shale to compare the form and behavior of fractures in shale driven by different gas compositions and states and indexed by breakdown pressure and the resulting morphology of the fracture networks. Fracturing is completed on cylindrical samples containing a single blind axial borehole under simple triaxial conditions with confining pressure ranging from 10 to 25 MPa and axial stress ranging from 0 to 35 MPa (σ1 > σ2 = σ3). Results show that: (1) under the same stress conditions, CO2 returns the highest breakdown pressure, followed by N2, and with H2O exhibiting the lowest breakdown pressure; (2) CO2 fracturing, compared to other fracturing fluids, creates nominally the most complex fracturing patterns as well as the roughest fracture surface and with the greatest apparent local damage followed by H2O and then N2; (3) under conditions of constant injection rate, the CO2 pressure build-up record exhibits condensation between ~5 and 7 MPa and transits from gas to liquid through a mixed-phase region rather than directly to liquid as for H2O and N2 which do not; (4) there is a positive correlation between minimum principal stress and breakdown pressure for failure both by transverse fracturing (σ3axial) and by longitudinal fracturing (σ3radial) for each fracturing fluid with CO2 having the highest correlation coefficient/slope and lowest for H2O. We explain these results in terms of a mechanistic understanding of breakdown, and through correlations with the specific properties of the stimulating fluids

Fermion-Boson Duality of One-dimensional Quantum Particles with Generalized Contact Interaction

For a system of spinless one-dimensional fermions, the non-vanishing short-range limit of two-body interaction is shown to induce the wave-function discontinuity. We prove the equivalence of this fermionic system and the bosonic particle system with two-body $\delta$-function interaction with the reversed role of strong and weak couplings. KEYWORDS: one-dimensional system, $\epsilon$-interaction, solvable many-body problem, exact bosonizationComment: 4 pages ReVTeX 4 epsf figures included, new Ref