A Note on Quantum Entropy

Incremental information, as measured by the quantum entropy, is increasing when two ensembles are united. This result was proved by Lieb and Ruskai, and it is the foundation for the proof of strong subadditivity of quantum entropy. We present a truly elementary proof of this fact in the context of the broader family of matrix entropies introduced by Chen and Tropp.     

Assessment technique for evaluating military vehicular impacts to vegetation in the Mojave desert

A new plant-damage assessment technique was developed. The technique consists of linear transects the width of a military vehicle’s tracks located in existing tracks in the soil (usually during a prior training rotation period of 30 days or since the last rain or wind storm). Measurements of vegetation within the tracks are used to determine the area of plant parts impacted. The percent of the plant parts damaged and the percent expected to recover are estimated. The technique documents prior-damage classes based on estimates of damage that plants have apparently experienced previously (as assessed from field indicators of damage such as plant shape and height). The technique was used to evaluate different vehicle types (rubber-tire wheels vs. metal tracks) in six areas at the NTC with different soils and training intensity levels. The technique provides tabular data that can be sorted and queried to show a variety of trends related to military vehicular impacts. It also is suitable for assessing other non-military off-road traffic impacts. The study reports: (1) differences in plant sensitivity to different vehicle track types, (2) plant cover and density by species and training area after prolonged impact, (3) the degree to which rubber tire wheels have less impact than metal tracks, and (4) mean percent survival was inversely proportional to the degree of prior damage received by the vegetation (i.e., plants previously impacted have lower survival than plants not previously impacted).     

Study of fracture permeability using Lattice Gas Automata

We study the problem of flow permeability of fracture joints using Lattice-Gas Automata simulations. We model the fracture as a rough channel bounded by a self-affine surface. Changing the surface roughness exponent, rough walls having different microstructures are obtained. Different relative roughnesses — defined as the height of the largest surface asperity divided by the mean aperture — are obtained pulling apart the two surfaces that constitute the rough walls of the channel. We calculate the macroscopic variables volume flow rate and pressure difference using microscopic balances. In the low Reynolds number regime the pressure difference and the flow rate are linearly related (the behavior is described by Darcy's law). In this regime, we study the effect of geometry on the permeability. We have found that permeability is independent of the surface roughness exponentH and it is fully determined in terms of the relative roughness and mean aperture of the fracture joint. For larger Reynolds numbers a transition to a regime in which pressure difference and flow rate are not longer linearly related is observed. This transition is observed in a domain of Reynolds numbers for which the behavior in a smooth channel remains linear. We discuss this transition.     

Modeling the microstructural evolution of metallic polycrystalline materials under localization conditions

In general, the shear localization process involves initiation and growth. Initiation is expected to be a stochastic process in material space where anisotropy in the elastic-plastic behavior of single crystals and inter-crystalline interactions serve to form natural perturbations to the material's local stability. A hat-shaped sample geometry was used to study shear localization growth. It is an axi-symmetric sample with an upper “hat” portion and a lower “brim” portion with the shear zone located between the hat and brim. The shear zone length was 870-890 μm with deformation imposed through a Split-Hopkinson Pressure Bar system at maximum top-to-bottom velocity in the range of 8-25 m/s. The deformation behavior of tantalum tophat samples is modeled through direct polycrystal simulations. An embedded Voronoï-tessellated two-dimensional microstructure is used to represent the material within the shear zone of the sample. A thermo-mechanically coupled elasto-viscoplastic single crystal model is presented and used to represent the response of the grains within the aggregate shear zone. In the shoulder regions away from the shear zone where strain levels remain on the order of 0.05, the material is represented by an isotropic J₂ flow theory based upon the elasto-viscoplastic Mechanical Threshold Stress (MTS) model for flow strength. The top surface stress versus displacement results were compared to those of the experiments and over-all the simulated stress magnitude is over-predicted. It is believed that the reason for this is that the simulations are two-dimensional. A region within the numerical shear zone was isolated for statistical examination. The vonMises stress state within this isolated shear zone region suggests an approximate normal distribution with a factor of two difference between the minimum and maximum points in the distribution. The equivalent plastic strain distribution within this same region has values ranging between 0.4 and 1.5 and is not symmetric. Other material state distributions are also given. The crystallographic texture within this isolated shear zone is also compared to the experimental texture and found to match reasonably well considering the simulations are two-dimensional.     

Dynamics of two delay coupled van der Pol oscillators

In this paper, the dynamics of a system of two van der Pol oscillators with delayed position and velocity coupling is studied by the method of averaging together with truncation of Taylor expansions. According to the slow-flow equations, the dynamics of 1:1 internal resonance is more complex than that of non-1:1 internal resonance. For 1:1 internal resonance, the stability and the number of periodic solutions vary with different time delay for given coupling coefficients. The condition necessary for saddle-node and Hopf bifurcations for symmetric modes, namely in-phase and out-of-phase modes, are determined. The numerical results, obtained from direct integration of the original equation, are found to be in good agreement with analytical predictions.     

Efficient laser operation of diode-pumped Pr3+,Mg2+:SrAl12O19

We report on diode-pumped laser operation of Pr³⁺,Mg²⁺:SrAl₁₂O₁₉ at lasing wavelengths of λ _L = 724.4 nm, λ _L = 643.5 nm, and λ _L = 622.8 nm. Furthermore, the laser threshold could be reached in the green spectral range. By pumping the crystal longitudinally from each side with two polarization beam combined InGaN laser diodes, a total pump power of ≈4 W was available. In the deep red spectral range, a maximum output power of 564 mW was achieved with a maximum slope efficiency of 50 % with respect to the absorbed pump power. The maximum possible internal losses were estimated to ≈1 %. Beam quality factors M ² were in the range of 1.2–1.5.     

Implicit Euler and Lie splitting discretizations of nonlinear parabolic equations with delay

A convergence analysis is presented for the implicit Euler and Lie splitting schemes when applied to nonlinear parabolic equations with delay. More precisely, we consider a vector field which is the sum of an unbounded dissipative operator and a delay term, where both point delays and distributed delays fit into the framework. Such equations are frequently encountered, e.g. in population dynamics. The main theoretical result is that both schemes converge with an order (of at least) \(q=1/2\) , without any artificial regularity assumptions. We discuss implementation details for the methods, and the convergence results are verified by numerical experiments demonstrating both the correct order, as well as the efficiency gain of Lie splitting as compared to the implicit Euler scheme.