Resonant Raman scattering from screened longitudinal optical phonons in EuTe

Forbidden resonant Raman scattering from screened longitudinal optical, LO, phonons has been observed in the back-reflection geometry from n-type EuTe at 2°K. The Raman shift increased with increasing excitation frequency but was always between the LO and TO phonon frequencies. This effect is explained in terms of a varying ‘effective’ carrier concentration as a function of laser penetration depth through the surface depletion layer in the situation of large phonon wave vector. Conduction band and lattice parameters have been calculated from infrared Reststrahlen and plasma edge measurements.     

Light quarks and instantons

Instantons and anti-instantons can profoundly influence the structure of a non-Abelian gauge theory involving N flavors of massless quarks. Interactions of the quarks with these pseudoparticles can spontaneously generate a quark mass, break the theory's SU(N) × SU(N) chiral symmetry and bind quark-antiquark pairs to form N² ? 1 Goldstone bosons. If the spontaneously generated quark mass is small, multipseudoparticle configurations can be treated in a dilute gas approximation.     

Study of a carbon dioxide ring laser gyroscope

We have experimentally investigated a basic ring laser gyroscope (RLG) with carbon dioxide gain, and studied the prospects of developing a practical CO₂ RLG. Rotation sensing was demonstrated on a number of transitions in the 9.4 m and 10.4 m vibration-rotation bands. Gyro response is discussed with regard to lock-in, bias, homogeneous broadening effects, and high power operation. We show that such a system may offer important advantages over standard helium-neon RLGs, including reduced quantum limit and backscattering. The prospects and possible approaches for developing a practical high power CO₂ RLG are discussed, and a method of eliminating cross-saturation at high pressure is proposed and analyzed.     

A column generation approach for the rail crew re-scheduling problem

When tracks are out of service for maintenance during a certain period, trains cannot be operated on those tracks. This leads to a modified timetable, and results in infeasible rolling stock and crew schedules. Therefore, these schedules need to be repaired. The topic of this paper is the re-scheduling of crew.     

The conjugate-pairing rule for non-Hamiltonian systems

In systems that satisfy the Conjugate Pairing Rule (CPR), the spectrum of Lyapunov exponents is symmetric. The sum of each conjugate pair of exponents is identical. Since in dissipative systems the sum of all the exponents is the entropy production divided by Boltzmann's constant, the calculation of transport coefficients from the Lyapunov exponents is greatly simplified in systems that satisfy CPR. Sufficient conditions for CPR are well known: the underlying adiabatic dynamics should be symplectic. However, the necessary conditions for CPR are not known. In this paper we report on the results of computer simulations which shed light on the necessary conditions for the CPR to hold. We provide, for the first time, convincing evidence that the standard molecular dynamics algorithm for calculating shear viscosity violates the CPR, even in the thermodynamic limit. In spite of this it appears that the sum of the maximal exponents is equal to the entropy production per degree of freedom. Thus it appears that the shear viscosity can still be calculated using the standard viscosity algorithm by summing the maximal pair of exponents.(c) 1998 American Institute of Physics.     

An SR1/BFGS SQP algorithm for nonconvex nonlinear programs with block-diagonal Hessian matrix

We present a quasi-Newton sequential quadratic programming (SQP) algorithm for nonlinear programs in which the Hessian of the Lagrangian function is block-diagonal. Problems with this characteristic frequently arise in the context of optimal control; for example, when a direct multiple shooting parametrization is used. In this article, we describe an implementation of a filter line-search SQP method that computes search directions using an active-set quadratic programming (QP) solver. To take advantage of the block-diagonal structure of the Hessian matrix, each block is approximated separately by quasi-Newton updates. For nonconvex instances, that arise, for example, in optimum experimental design control problems, these blocks are often found to be indefinite. In that case, the block-BFGS quasi-Newton update can lead to poor convergence. The novel aspect in this work is the use of SR1 updates in place of BFGS approximations whenever possible. The resulting indefinite QPs necessitate an inertia control mechanism within the sparse Schur-complement factorization that is carried out by the active-set QP solver. This permits an adaptive selection of the Hessian approximation that guarantees sufficient progress towards a stationary point of the problem. Numerical results demonstrate that the proposed approach reduces the number of SQP iterations and CPU time required for the solution of a set of optimal control problems.     

Spectral approximation for drainage of an Elastico‐viscous liquid and error analysis

A Fourier‐Galerkin spectral method is proposed and used to analyze a system of quasilinear partial differential equations governing the drainage of liquids of the Oldroyd four‐constant type. It is shown that, Fourier‐Galerkin approximations are convergent with spectral accuracy. An efficient and accurate algorithm based on the Fourier‐Galerkin approximations to the system of quasilinear partial differential equations are developed and implemented. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 492–505, 2012     

A Practical Solution to a Cargo Loading Problem at Bethlehem Steel

The optimum assignment of structural steel shapes to rail cars is an important logistical problem in the steel industry. In this paper, we discuss an application at Bethlehem Steel that not only involves weight and dimensional constraints, but also customer unloading constraints. The formulation is a generalized bin packing problem which is solved by modifying and extending the first fit decreasing algorithm. The solution algorithm, SOLID (for Structural Optimal Loading IDentification), has been used extensively for one of Bethlehem's high tonnage customers providing very good practical (implementable) results that achieve the desired goals. Bethlehem has enhanced this approach for use with other customers.     

Off-equilibrium photon production during the chiral phase transition

In the early stage of ultrarelativistic heavy-ion collisions chiral symmetry is restored temporarily. During this so-called chiral phase transition, the quark masses change from their constituent to their bare values. This mass shift leads to the spontaneous non-perturbative creation of quark–antiquark pairs, which effectively contributes to the formation of the quark–gluon plasma. We investigate the photon production induced by this creation process. We provide an approach that eliminates possible unphysical contributions from the vacuum polarization and renders the resulting photon spectra integrable in the ultraviolet domain. The off-equilibrium photon numbers are of quadratic order in the perturbative coupling constants while a thermal production is only of quartic order. Quantitatively, we find, however, that for the most physical mass-shift scenarios and for photon momenta larger than 1 GeV the off-equilibrium processes contribute less photons than the thermal processes.     

On non-measurability of in its second dual

We show that with the weak topology is not an intersection of Borel sets in its Cech-Stone extension (and hence in any compactification). Assuming (CH), this implies that has no continuous injection onto a Borel set in a compact space, or onto a Lindelöf space. Under (CH), this answers a question of Arhangel'ski.