Accurate depolarization ratio measurements for all diatomic hydrogen isotopologues

The Raman depolarization ratios for individual Q₁(J”) branch lines of all diatomic hydrogen isotopologues – H₂, HD, D₂, HT, DT, and T₂ – were measured, for all rotational levels with population larger than 1/100 relative to the Boltzmann maximum at room temperature. For these measurements, the experimental setup normally used for the monitoring of the tritiated hydrogen molecules at KArlsruhe TRItium Neutrino experiment was adapted to optimally control the excitation laser power and polarization, and to precisely define the Raman light collection geometry. The measured Raman depolarization values were compared to theoretical values, which are linked to polarizability tensor quantities. For this, the ‘raw data’ were corrected taking into account distinct aspects affecting Raman depolarization data, including (1) excitation polarization impurities; (2) extended Raman excitation volumes; and (3) Raman light collection over finite solid angles. Our corrected depolarization ratios of the hydrogen isotopologues agree with the theoretical values (based on ab initio quantum calculations by R.J. LeRoy, University of Waterloo, Canada) to better than 5% for nearly all of the measured Q₁(J”) lines, with 1σ confidence level. The results demonstrate that reliable, accurate Raman depolarization ratios can be extracted from experimental measurements, which may be substantially distorted by excitation polarization impurities and by geometrical effects. Copyright © 2013 John Wiley & Sons, Ltd.     

Evaluation method for Raman depolarization measurements including geometrical effects and polarization aberrations

In this article, we address the notoriously difficult problem to quantitatively link measured Raman depolarization values to theoretical polarizability tensor quantities, since quantum calculations do not incorporate experimental parameters. For this, we introduce a numerical model to calculate, for realistic experimental configurations, effective Raman line strength functions, Φ, which find their way into depolarization ratios, ρ. The model is based on interlinked integrations over the angles in the light collection path and a finite Raman source volume along the excitation laser beam. The model deals also with the conditional aperture parameters, associated with more than one optical component in the light collection path. Finally, we also can take into account polarization aberrations introduced by the sample cell windows. The procedure was fully tested for Raman depolarization spectra of selected hydrogen isotopologues. Distinct aspects affecting Raman depolarization data were validated, namely: (1) excitation polarization impurities; (2) extended Raman excitation volumes; (3) Raman light collection over finite solid angles; and (4) polarization aberrations introduced by optics in the light collection path. The correction of the experimental measurement data for the aforementioned effects resulted in depolarization ratios for the Q₁(J " ) Raman lines of H₂ and T₂, which mostly differed by less than 5% from those obtained by quantum‐calculations. Copyright © 2013 John Wiley & Sons, Ltd.     

Joule–Thomson Effects on the Flow of Liquid Water

We present a revised form of the energy balance for the coupled thermodynamics of liquid water flowing in porous media and give examples of situations where a commonly used formulation based on transport of enthalpy leads to erroneous results. Assuming negligible contribution from kinetic energy as well as sources and sinks such as energy from radioactive decay, total energy conservation is reduced to a balance between changes in internal energy, enthalpy, conductive heat flux, and gravitational potential energy. The Joule–Thomson coefficient is defined as the change in temperature with respect to an increase in pressure at constant enthalpy. Because liquid water has a negative Joule–Thomson coefficient at low temperatures, at a constant gravitational potential water cools as it compresses and heats as it expands. If one ignores the gravitational energy, transport of enthalpy alone leads to water heating by 2 \(^\circ \) C per kilometer as it is brought up from depth. The corrected energy balance transports methalpy, which is enthalpy plus gravitational potential energy. Although the simpler form leads to small changes in the temperature profile for typical simulations, there are several instances where this effect may prove to be important. The most important impact of the erroneous form is probably in the field of geothermal energy production, where the creation of a few degrees of heat in a simulation could lead to miscalculation of power plant efficiencies.     

Fenchel decomposition for stochastic mixed-integer programming

This paper introduces a new cutting plane method for two-stage stochastic mixed-integer programming (SMIP) called Fenchel decomposition (FD). FD uses a class of valid inequalities termed, FD cuts, which are derived based on Fenchel cutting planes from integer programming. First, we derive FD cuts based on both the first and second-stage variables, and devise an FD algorithm for SMIP and establish finite convergence for binary first-stage. Second, we derive FD cuts based on the second-stage variables only and use an idea from disjunctive programming to lift the cuts to the higher dimension space including the first-stage variables. We then devise an alternative algorithm (FD-L algorithm) based on the lifted FD cuts. Finally, we report on computational results based on several test instances from the literature involving the special structure of knapsack problems with nonnegative left-hand side coefficients. The results are promising and show that both algorithms can outperform a standard direct solver and a disjunctive decomposition algorithm on large-scale instances. Furthermore, the FD-L algorithm provides better performance than the FD algorithm in general. Since Fenchel cuts can be computationally expensive in general and are best suited for problems with special structure, both algorithms exploit the special structure of the test instances by reducing the size of the cut generation problems based on the number of nonzero components in the non-integer solution that needs to be cut off.     

Character correspondences and nilpotent fully-ramified sections

The focus of this paper is a well-known lemma: A continuous group homomorphism between profinite groups which has dense image must be an open surjection. Its importance lies in the common occurrence of infinite inversely directed systems of finite groups. A limit, in the category of groups, is rarely useful. Instead, experience reveals that an inverse limit in the topologized sense completely characterizes the system. Principles like the above lemma empower this model.

The author needs “good” inverse limits for a broad clas of categories. We develop an idea from the 1960s: Given a categoryn C, expand it with purely formal projective limits.

Although definition of such a category is elementary, the approach has difficulties. In the past, crucial manipulations refused generalization. Our thesis is that, by tightening hypotheses, the method creates a category valuable to analysis. In this paper, we

1. review and modify the categorical formulation,

2. prove a structure theory for pullbacks and inversely directed systems, and

3. generalize the indicated lemma.     

Semi-algebraic functions have small subdifferentials

We prove that the subdifferential of any semi-algebraic extended-real-valued function on $\mathbf{R}^n$ has $n$ -dimensional graph. We discuss consequences for generic semi-algebraic optimization problems.     

Density of rational curves on K3 surfaces

Using the dynamics of self rational maps of elliptic $K3$ surfaces together with deformation theory, we prove that the union of rational curves is dense on a very general $K3$ surface and that the union of elliptic curves is dense in the 1st jet space of a very general $K3$ surface, both in the strong topology.     

Mathematical modelling of tongue deformation during swallow in patients with head and neck cancer

ABSTRACT

Cancer localized to the tongue is often characterized by increased stiffness in the affected region. This stiffness affects swallow in a manner that is difficult to quantify in patients. A biomechanical model was developed to simulate the spatio-temporal deformation of the tongue during the pharyngeal phase of swallow in patients with cancer of the tongue base. The model involves finite element analysis (FEA) of a three-dimensional (3D) model of the tongue reconstructed from magnetic resonance images (MRI). The tongue tissue is assumed to be hyper-elastic. In order to examine the effects of tissue change (increased stiffness) due to the presence of cancer localized to the tongue base, various sections of the 3D geometry are modified to exhibit different elastic properties. Three cases are considered, representing the normal tongue, a tongue with early-stage cancer, and tongue with late-stage cancer. Early- and late-stage cancers are differentiated by the degree of stiffness within the base of tongue tissue. Analysis of the model suggests that healthy tongue has a maximum deformation of 9.38 mm, whereas tongues having mild cancer and severe cancer have a maximum deformation of 8.65 and 6.17 mm, respectively. Biomechanical modelling is a useful tool to explain and estimate swallowing abnormalities associated with tongue cancer and post-treatment characteristics.     

Terahertz surfoluminescence

The cleaving of a solid to form two new surfaces may result in the emission of light. Conventional mechanoluminescence involves the transfer of charge between the two surfaces. We now demonstrate that the ultra-fast separation of charge within a newly-formed surface will lead to the emission of electromagnetic radiation. In contrast to the visible light previously observed and modeled, the intra-surface radiation contains terahertz frequencies. This new mechanism – named here surfoluminescence – introduces a new class of terahertz-frequency emitters. It also may in part explain the recent observation of terahertz emission from peeling adhesive tape.