Stratified Rotating Boussinesq Equations in Geophysical Fluid Dynamics: Dynamic Bifurcation and Periodic Solutions

The main objective of this article is to study the dynamics of the stratified rotating Boussinesq equations, which are a basic model in geophysical fluid dynamics. First, for the case where the Prandtl number is greater than one, a complete stability and bifurcation analysis near the first critical Rayleigh number is carried out. Second, for the case where the Prandtl number is smaller than one, the onset of the Hopf bifurcation near the first critical Rayleigh number is established, leading to the existence of nontrivial periodic solutions. The analysis is based on a newly developed bifurcation and stability theory for nonlinear dynamical systems (both finite and infinite dimensional) by two of the authors [16]

Densely distributed and real-time scour hole monitoring using piezoelectric rod sensors

This study aims to validate a piezoelectric driven-rod scour monitoring system that can sense changes in scour depth along the entire rod at its instrumented location. The proposed sensor is a polymeric slender rod with a thin strip of polyvinylidene fluoride that runs through its midline. Extraction of the fundamental frequency allows the direct calculation of the exposed length (or scour depth) of the slender rod undergoing fluid flow excitation. First, laboratory validation in dry conditions is presented. Second, hydrodynamic testing of the sensor system in a soil-bed flume is discussed. Each rod was installed using a three-dimensional-printed footing designed for ease of installation and stabilization during testing. The sensors were installed in a layout designed to capture symmetric scour conditions around a scaled pier. In order to analyze the system out of steady-state conditions, water velocity was increased in stages during testing to induce different degrees of scour. As ambient water flow excited the portion of the exposed rods, the embedded piezoelectric element outputted a time-varying voltage signal. Different methods were then employed to extract the fundamental frequency of each rod, and the results were compared. Further testing was also performed to characterize the relationship between frequency outputs and flow velocity, which were previously thought to be independent. In general, the proposed driven-rod scour monitoring system successfully captured changing frequencies under varied flow conditions

Report on Characterization of U-10 wt.% Zr Alloy

This report summarizes the chemical and structural characterization results for a U-10 wt.% Zr alloy to be used in an ultra-high burn-up nuclear fuel concept. The as-cast alloy material was received from Texas A and M University. Characterization and an initial heat treatment of the alloy material were conducted at Lawrence Livermore National Laboratory. The as-received ingot was sectioned for X-ray analysis, metallography, SEM, TEM, and heat treatments, as shown in Figure 1

On the Micromechanisms of Anomalous Slip in BCC Metals

Dislocation substructures developed in high-purity Mo single crystals deformed under uniaxial compression at room temperature to a total strain of {approx} 0.5% with a strain rate of 1 s{sup -1} have been investigated using transmission electron microscopy (TEM) techniques in order to elucidate the underlying micromechanisms of the anomalous operation of {l_brace}0{bar 1}1{r_brace} slip systems, i.e. Schmid-law violation, in bcc metals. The crystals were oriented with the stress axis parallel to a nominal single-slip orientation of [{bar 2}920], in which the ({bar 1}01)[111] slip system is the only system having a maximum value of Schmid factor (m = 0.5). Nevertheless, the recorded stress-strain curve reveals no single-slip or easy-glide stage, and the anomalous slip occurs in both (011) and (0{bar 1}1) planes. TEM examination of the dislocation structure in the ({bar 1}01) primary slip plane reveals that in addition to the operation of the ({bar 1}01)[111] slip system, the coplanar ({bar 1}01)[1{bar 1}1] slip system that has a much smaller Schmid factor (m = 0.167) is also operative. Similarly, the (0{bar 1}1)[111] slip system (m = 0.25) is cooperative with the coplanar (0{bar 1}1)[{bar 1}11] system (m = 0.287), and the (011)[1{bar 1}1] slip system (m = 0.222) is cooperative with the coplanar (011)[11{bar 1}] system (m = 0.32). The occurrence of {l_brace}0{bar 1}1{r_brace} anomalous slip is accordingly proposed to be initiated from the cooperative dislocation multiplication and mutual trapping and blocking of 1/2[111] and 1/2[1{bar 1}1] coplanar dislocation arrays in the ({bar 1}01) plane. The resulted internal stresses render the propagation of both 1/2[111] and 1/2[1{bar 1}1] screw dislocations from the ({bar 1}01) plane onto the {l_brace}0{bar 1}1{r_brace} planes and subsequently result in the occurrence of anomalous slip

On the Micromechanisms of Shock-Induced Martensitic Transformation in Tantalum

Shock-induced twinning and martensitic transformation in tantalum, which exhibits no solid-state phase transformation under hydrostatic pressures up to 100 GPa, have been further investigated. Since the volume fraction and size of twin and phase domains are small in scale, they are considered foming by heterogeneous nucleation that is catalyzed by high density lattice dislocations. A dynamic dislocation mechanism is accordingly proposed based upon the observation of dense dislocation clustering within shock-recovered tantalum. The dense dislocation clustering can cause a significant increase of strain energy in local regions of {beta} (bcc) matrix, which renders mechanical instability and initiates the nucleation of twin and phase domains through the spontaneous reactions of dislocation dissociation within the dislocation clusters. That is, twin domains can be nucleated within the clusters through the homogeneous dissociation of 1/2<111> dislocations into 1/6<111> partial dislocations, and {omega} phase domains can be nucleated within the closters through the inhomogeneous dissociation of 1/2<111> dislocations into 1/12<111>, 1/3<111> and 1/12<111> partial dislocations

POWDER METALLURGY TiAl ALLOYS: MICROSTRUCTURES AND PROPERTIES

The microstructures and properties of powder metallurgy TiAl alloys fabricated by hot extrusion of gas-atomized powder at different elevated temperatures were investigated. Microstructure of the alloy fabricated at 1150 C consisted of a mixture of fine ({gamma} + {alpha}{sub 2}) equiaxed grains and coarse ordered B2 grains. Particles of ordered hexagonal {omega} phase were also observed in some B2 grains. The alloy containing B2 grains displayed a low-temperature superplastic behavior: a tensile elongation of 310% was measured when the alloy was tested at 800 C under a strain rate of 2 x 10{sup -5} s{sup -1}. Microstructure of the alloy fabricated at 1250 C consisted of a mixture of fine ({gamma} + {alpha}{sub 2}) equiaxed grains, coarse {alpha}{sub 2} grains, and lamellar ({gamma} + {alpha}{sub 2}) colonies. An observation of stacking faults associated with fine {gamma} lamellae in {alpha}{sub 2} grains reveals that the stacking fault of {alpha}{sub 2} phase plays an important role in the formation of lamellar ({gamma} + {alpha}{sub 2}) colonies. Unlike the alloy fabricated at 1150{sup o}, the alloy fabricated at 1250{sup o} displayed no low-temperature superplasticity, but a tensile elongation of 260% at 1000 C was measured. Microstructure of the alloy fabricated at 1400 C consisted of fully lamellar ({gamma} + {alpha}{sub 2}) colonies with the colony size ranging between 50 {micro}m and 100 {micro}m, in which the width of {gamma} lamella is in a range between 100 nm and 350 nm, and the width of {alpha}{sub 2} lamella is in a range between 10 nm and 50 nm. Creep behavior of the ultrafine lamellar alloy and the effects of alloying addition on the creep resistance of the fully lamellar alloy are also investigated

Thermodynamic curvature measures interactions

Thermodynamic fluctuation theory originated with Einstein who inverted the relation $S=k_B\ln\Omega$ to express the number of states in terms of entropy: $\Omega= \exp(S/k_B)$. The theory's Gaussian approximation is discussed in most statistical mechanics texts. I review work showing how to go beyond the Gaussian approximation by adding covariance, conservation, and consistency. This generalization leads to a fundamentally new object: the thermodynamic Riemannian curvature scalar $R$, a thermodynamic invariant. I argue that $|R|$ is related to the correlation length and suggest that the sign of $R$ corresponds to whether the interparticle interactions are effectively attractive or repulsive.Comment: 29 pages, 7 figures (added reference 27

Energy‐Distribution Function for Hot Atoms Produced by Nuclear Transformations

The energy‐distribution function for hot atoms produced by nuclear transformations is examined in terms of the fraction of the initial hot‐atom energy. Energy dependent and independent asymmetric scattering is specifically considered. For gaseous tritium generated by the 3He(n, p) process, the asymptotic solution probably can serve as a reasonable approximation of the distribution function in the energy range 2–20 eV. For hot atoms produced with an initial distribution of energies, such as 79Br(n, γ)‐produced 80Br, the asymptotic solution will be less valid than for tritium, but may still be a valid approximation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70454/2/JCPSA6-41-6-1595-1.pd

Clerodane diterpenes: sources, structures, and biological activities

The clerodane diterpenoids are a widespread class of secondary metabolites and have been found in several hundreds of plant species from various families and in organisms from other taxonomic groups