Flavour democracy calls for the fourth generation

It is argued with the help of an illustrative model, that the inter species hierarchy among the fermion masses and the quark mixing angles can be accommodated naturally in the standard model with (approximate) flavor democracy provided there are three exactly massless neutrinos and four families of sequential quark-leptons with all members of the fourth family having roughly equal masses. The special problem of light neutrino masses (if any) and possible solutions are also discussed.     

Measurement: It ain't over till it's over

Elby (1993) has raised certain problems that appear to be devastating for modal interpretations of quantum mechanics, but do not arise for Bohm's pilot wave theory. Here I show that the features Elby identifies as objectionable in my version of the modal interpretation have their counterpart in Bohm's theory. To the extent that Bohm's theory works as a no collapse solution to the measurement problem - and I think it does - so does my modal interpretation.     

Numerical simulation of inductive method for determining spatial distribution of critical current density

The inductive method for measuring the critical current density j_C in a high-temperature superconducting (HTS) thin film has been investigated numerically. In order to simulate the method, a non-axisymmetric numerical code has been developed for analyzing the time evolution of the shielding current density. In the code, the governing equation of the shielding current density is spatially discretized with the finite element method and the resulting first-order ordinary differential system is solved by using the 5th-order Runge–Kutta method with an adaptive step-size control algorithm. By using the code, the threshold current I_T is evaluated for various positions of a coil. The results of computations show that, near a film edge, the accuracy of the estimating formula for j_C is remarkably degraded. Moreover, even the proportional relationship between j_C and I_T will be lost there. Hence, the critical current density near a film edge cannot be estimated by using the inductive method.     

线性互补问题基于模同步块多重分裂方法的收敛性

通过利用不动点迭代来研究线性互补问题,根据基模同步多重分裂迭代方法将其线性互补问题的系数矩阵是点的形式推广到块H+的形式,并且分析了当系数矩阵是块矩阵时线性互补问题解的收敛情况。     

Adiabatic Hyperspherical Approach to the Problems of Muon Catalyzed Fusion

The adiabatic hyperspherical approach (AHSA) is applied for the numerical investigation of the scattering processes and resonances in Coulomb three-body mesic atomic systems. The results of the calculations of elastic and inelastic cross sections in low-energy collisions aμ + b (a, b = p, d, t), energies, lifetimes and local characteristics of resonant states of mesic molecular ions ⁿ Heaμ⁺ (n = 3, 4) are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

A perturbed martingale approach to global optimization

A new global stochastic search, guided mainly through derivative-free directional information computable from the sample statistical moments of the design variables within a Monte Carlo setup, is proposed. The search is aided by imparting to the directional update term additional layers of random perturbations referred to as ‘coalescence’ and ‘scrambling’. A selection step, constituting yet another avenue for random perturbation, completes the global search. The direction-driven nature of the search is manifest in the local extremization and coalescence components, which are posed as martingale problems that yield gain-like update terms upon discretization. As anticipated and numerically demonstrated, to a limited extent, against the problem of parameter recovery given the chaotic response histories of a couple of nonlinear oscillators, the proposed method appears to offer a more rational, more accurate and faster alternative to most available evolutionary schemes, prominently the particle swarm optimization.     

Optimal time advancing dispersion relation preserving schemes

In this paper we examine the constrained optimization of explicit Runge–Kutta (RK) schemes coupled with central spatial discretization schemes to solve the one-dimensional convection equation. The constraints are defined with respect to the correct error propagation equation which goes beyond the traditional von Neumann analysis   developed in Sengupta et al. [T.K. Sengupta, A. Dipankar, P. Sagaut, Error dynamics: beyond von Neumann analysis, J. Comput. Phys. 226 (2007) 1211–1218]. The efficiency of these optimal schemes is demonstrated for the one-dimensional convection problem and also by solving the Navier–Stokes equations for a two-dimensional lid-driven cavity (LDC) problem. For the LDC problem, results for Re=1000$\mathit{Re}=1000$ are compared with results using spectral methods in Botella and Peyret [O. Botella, R. Peyret, Benchmark spectral results on the lid-driven cavity flow, Comput. Fluids 27 (1998) 421–433] to calibrate the method in solving the steady state problem. We also report the results of the same flow at Re=10,000$\mathit{Re}=10\text{,}000$ and compare them with some recent results to establish the correctness and accuracy of the scheme for solving unsteady flow problems. Finally, we also compare our results for a wave-packet propagation problem with another method developed for computational aeroacoustics.     

Principles of instrumentation and signal processing method of PLDA

It is shown in this paper that in geometrical space two polarization planes of thelinearly polarized light waves scattered by particles in measuring ellipsoid constitute anangle of π/2. while in sequence of time the signals sent out by two symmetricphotodetectors in PLDA ard separated by a phase angle π.This property of PLDAenables the improvement of SNR.The similarity between power spectrum of photoelectrical current of PLDA andprobability density function P_d(u_c)of investigated flow velocity has been provedtheoretically and checked by agreement of obtained results with classical theory andgenerally accepted experiments.     

The traveling salesman problem in graphs with some excluded minors

Given a graph and a length function defined on its edge-set, the Traveling Salesman Problem can be described as the problem of finding a family of edges (an edge may be chosen several times) which forms a spanning Eulerian subgraph of minimum length. In this paper we characterize those graphs for which the convex hull of all solutions is given by the nonnegativity constraints and the classical cut constraints. This characterization is given in terms of excluded minors. A constructive characterization is also given which uses a small number of basic graphs.