Effect of birefringence on light scattering from oriented systems

The effect of birefringence on the intensity of polarized scattered light from an oriented polymer film is analyzed on the basis of a model in which the scattering element is imbedded in a homogeneous birefringent matrix. The scattering intensity is shown to depend upon the polarizer and analyzer angles, the scattering angles, the sample birefringence and thickness, and the scattering coefficients for the four polarization combinations. Computer calculations for reasonable values of these parameters indicate that these corrections can be quite appreciable.     

Resonance raman and infrared spectra of ClO3 radicals in electron irradiated NaClO3

Resonance Raman and infrared absorption spectra of ClO₃ radicals have been observed from measurements of crystalline NaClO₃ irradiated at 77 K with 1.5 MeV electrons. The ClO₃ radicals occupy two sets of nonequivalent sites; radicals at one site are observed from resonance scattering using 6328 Å excitation while those at the other site are observed from resonance scattering with 5145 Å excitation. The red sensitive radicals decompose at 77 K with a half-life of ≈29 min while the green sensitive radicals are more stable at this temperature.     

Vibrational spectrum, ab initio calculations, conformational equilibria and torsional modes of 1,3-dichloropropane

Ab initio calculations are reported for three of four possible conformers of 1,3-dichloropropane. The fourth conformer, with Cs symmetry, has a predicted enthalpy difference of more than 1500 cm(-1) from the most stable conformer from each calculation regardless of the basis set used, so there is little chance of observing it. Thus, there is no evidence in the infrared or Raman spectrum of the presence of a fourth conformer. The order of stability given by the ab initio calculations is C2(GG)>C1(AG)>C2v(AA)>Cs(GG'), where A indicates the anti form for one of the CH2Cl groups and G indicates the gauche conformation for the other CH2Cl group relative to the plane of the carbon atoms. Almost every band observed can be confidently assigned to one or another of the conformers. Many observed bands proved to be of a composite nature, with several nearly coincident vibrations of different conformers contributing to the band contour. Nonetheless, a complete assignment of fundamentals is possible for the most stable C2 conformer, and 5 of the fundamentals of the C2v conformer and 13 those of the C1 conformer can be confidently assigned.     

Stochastic clearing systems

A stochastic clearing system is characterized by a non-decreasing stochastic input process $\text{{Y(t), t ≧ 0}}$, where Y(t) is the cumulative quantity entering the system in [0, t], and an output mechanism that intermittently and instantaneously clears the system, that is, removes all the quantity currently present. Examples may be found in the theory of queues, inventories, and other stochastic service and storage systems. In this paper we derive an explicit expression for the stationary (in some cases, limiting) distribution of the quantity in the system, under the assumption that the clearing instants are regeneration points and, in particular, first entrance times into sets of the form {y: y>q}. The expression is in terms of the sojourn measure W associated with $\text{{Y(t), t ≧ 0}: W{A} =}\text{E}${time spent in A by Y(t), 0 ≤ t < ∞}. The results are applied to compound input processes and processes with stationary independent increments. In particular, we show that, contrary to a wide-spread belief, the uniform stationary distribution characteristic of deterministic models does not usually carry over to genuinely stochastic models.     

Resonance raman scattering from metastable O2 molecules in γ-irradiated NaClO3

Resonance Raman scattering has been observed from metastable O₂ molecules produced in single crystals of NaClO₃ by γ-irradiation at 300 K. Evidence that the observed bands are due to O₂ is provided by the Raman spectrum of irradiated ¹⁸O enriched NaClO₃ in which bands due to ¹⁶O₂, ¹⁶O ¹⁸O, and ¹⁸O₂ were identified. The Raman band at 1544 cm^?1 ascribed to metastable O₂ disappears on bleaching with intense 4880 Å radiation enabling the identification of a weaker band at 1557 cm^?1 that is assigned to the stable form of O₂.     

Raman and infrared spectra, conformational stability, ab initio calculations and assignment of fundamentals for 1-bromo-3-fluoropropane

The infrared and Raman spectrum of 1-bromo-3-fluoropropane is reported in the gas, liquid, amorphous solid and annealed polycrystalline states. Only one of the five possible conformers is stable in the crystal, designated the C conformer. The disordered phases show the presence of several other conformers of higher energy, due entirely to conformers designated B and D. Ab initio calculations were performed as rhf/4-31g*/MIDI-4*, rhf/6-31g* and mp2/6-31g* (both frozen core and full electron correlation) for all five conformers. The scaled harmonic force field obtained using the mp2 = full/6-31g* level of the theory is reported for the most stable conformer together with an assignment of fundamentals and potential energy distributions for local symmetry coordinates. Selected computational results are reported for all conformers together with scaled and unscaled wavenumbers and infrared and Raman intensities. The temperature dependent Raman spectrum is reported from room temperature to -100 degrees C. Only three of the five possible conformers can be identified in this spectrum, and there is no evidence of the other two. The energy differences between conformers in the liquid phase were found experimentally to be 132+/-27, 232+/-46 and 106+/-30 cm(-1), respectively between the D and C, B and C and D and B conformers. These differences are substantially less than the differences calculated ab initio at the highest level of the theory used, suggesting that energy differences were decreased by large dipole-dipole interactions present in the liquid but not in the gas.     

Sample-path conservation laws,with applications to scheduling queues and fluid systems

The achievable-region approach, based on strong conservation laws, has most often been applied to stochastic scheduling and other control problems in the context of performance measures that are steady-state expected quantities. For some problems, however, strong conservation laws hold for performance measures at every time point on every sample path. We exploit this property to study optimal control for certain scheduling problems on a sample-path basis. Examples include preemptive scheduling to minimize a weighted sum of work in the system in each class, nonpreemptive scheduling to minimize a weighted sum of the number of customers in each class (when all classes have the same service-time distribution), and scheduling the processing of fluid in a multiclass fluid system operating in a random environment. The last problem is solved by considering the related Skorohod problem and its minimal solution. This revised version was published online in June 2006 with corrections to the Cover Date.     

Characterization of large molecular weight ester‐functionalized norbornene and hydroxylated norbornane carboxylic acid polymers prepared by ring‐opening metathesis polymerization

5‐Norbornene‐2‐ethyl ester (mixture of endo and exo) is polymerized via ring‐opening metathesis polymerization, yielding polymers with molecular weights ranging from 50,000 to 5,000,000 g/mol. The polymers are hydroxylated and saponified without alteration of the molecular weight. The polymers are analyzed by NMR, gel permeation chromatography, differential scanning calorimetry, and thermogravimetric analysis. Films are cast from the polymers at several molecular weights and their rheological properties are investigated. The results showed greater solid‐like character with increasing molecular weight for all polymers analyzed. Cell viability studies showed that the films possessed minimal cytotoxicity. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

On the optimality of a full-service policy for a queueing system with discounted costs

We provide weak sufficient conditions for a full-service policy to be optimal in a queueing control problem in which the service rate is a dynamic decision variable. In our model there are service costs and holding costs and the objective is to minimize the expected total discounted cost over an infinite horizon. We begin with a semi-Markov decision model for a single-server queue with exponentially distributed inter-arrival and service times. Then we present a general model with weak probabilistic assumptions and demonstrate that the full-service policy minimizes both finite-horizon and infinite-horizon total discounted cost on each sample path.