Amplitude equations for systems with long-range interactions

We derive amplitude equations for interface dynamics in pattern forming systems with long-range interactions. The basic condition for the applicability of the method developed here is that the bulk equations are linear and solvable by integral transforms. We arrive at the interface equation via long-wave asymptotics. As an example, we treat the Grinfeld instability, and we also give a result for the Saffman-Taylor instability. It turns out that the long-range interaction survives the long-wave limit and shows up in the final equation as a nonlocal and nonlinear term, a feature that to our knowledge is not shared by any other known long-wave equation. The form of this particular equation will then allow us to draw conclusions regarding the universal dynamics of systems in which nonlocal effects persist at the level of the amplitude description.Comment: LaTeX source, 12 pages, 4 figures, accepted for Physical Review

Extending the scope of microscopic solvability: Combination of the Kruskal-Segur method with Zauderer decomposition

Successful applications of the Kruskal-Segur approach to interfacial pattern formation have remained limited due to the necessity of an integral formulation of the problem. This excludes nonlinear bulk equations, rendering convection intractable. Combining the method with Zauderer's asymptotic decomposition scheme, we are able to strongly extend its scope of applicability and solve selection problems based on free boundary formulations in terms of partial differential equations alone. To demonstrate the technique, we give the first analytic solution of the problem of velocity selection for dendritic growth in a forced potential flow.Comment: Submitted to Europhys. Letters, No figures, 5 page

Influence of external flows on crystal growth: numerical investigation

We use a combined phase-field/lattice-Boltzmann scheme [D. Medvedev, K. Kassner, Phys. Rev. E {\bf 72}, 056703 (2005)] to simulate non-facetted crystal growth from an undercooled melt in external flows. Selected growth parameters are determined numerically. For growth patterns at moderate to high undercooling and relatively large anisotropy, the values of the tip radius and selection parameter plotted as a function of the Peclet number fall approximately on single curves. Hence, it may be argued that a parallel flow changes the selected tip radius and growth velocity solely by modifying (increasing) the Peclet number. This has interesting implications for the availability of current selection theories as predictors of growth characteristics under flow. At smaller anisotropy, a modification of the morphology diagram in the plane undercooling versus anisotropy is observed. The transition line from dendrites to doublons is shifted in favour of dendritic patterns, which become faster than doublons as the flow speed is increased, thus rendering the basin of attraction of dendritic structures larger. For small anisotropy and Prandtl number, we find oscillations of the tip velocity in the presence of flow. On increasing the fluid viscosity or decreasing the flow velocity, we observe a reduction in the amplitude of these oscillations.Comment: 10 pages, 7 figures, accepted for Physical Review E; size of some images had to be substantially reduced in comparison to original, resulting in low qualit

Nonequilibrium molecular dynamics simulation of rapid directional solidification

We present the results of non-equilibrium molecular dynamics simulations for the growth of a solid binary alloy from its liquid phase. The regime of high pulling velocities, $V$, for which there is a progressive transition from solute segregation to solute trapping, is considered. In the segregation regime, we recover the exponential form of the concentration profile within the liquid phase. Solute trapping is shown to settle in progressively as $V$ is increased and our results are in good agreement with the theoretical predictions of Aziz [J. Appl. Phys. {\bf 53}, 1158 (1981)]. In addition, the fluid advection velocity is shown to remain directly proportional to $V$, even at the highest velocities considered here ($V\simeq10$ms$^{-1}$).Comment: Submitted to Phys. Rev.

Stress corrosion cracking of candidate waste container materials; Final report

Six alloys have been selected as candidate container materials for the storage of high-level nuclear waste at the proposed Yucca mountain site in Nevada. These materials are Type 304L stainless steel (SS). Type 316L SS, Incoloy 825, phosphorus-deoxidized Cu, Cu-30%Ni, and Cu-7%Al. The present program has been initiated to determine whether any of these materials can survive for 300 years in the site environment without developing through-wall stress corrosion cracks. and to assess the relative resistance of these materials to stress corrosion cracking (SCC)- A series of slow-strain-rate tests (SSRTs) and fracture-mechanics crack-growth-rate (CGR) tests was performed at 93{degree}C and 1 atm of pressure in simulated J-13 well water. This water is representative, prior to the widespread availability of unsaturated-zone water, of the groundwater present at the Yucca Mountain site. Slow-strain-rate tests were conducted on 6.35-mm-diameter cylindrical specimens at strain rates of 10-{sup {minus}7} and 10{sup {minus}8} s{sup {minus}1} under crevice and noncrevice conditions. All tests were interrupted after nominal elongation strain of 1--4%. Scanning electron microscopy revealed some crack initiation in virtually all the materials, as well as weldments made from these materials. A stress- or strain-ratio cracking index ranks these materials, in order of increasing resistance to SCC, as follows: Type 304 SS < Type 316L SS < Incoloy 825 < Cu-30%Ni < Cu and Cu-7%Al. Fracture-mechanics CGR tests were conducted on 25.4-mm-thick compact tension specimens of Types 304L and 316L stainless steel (SS) and Incoloy 825. Crack-growth rates were measured under various load conditions: load ratios M of 0.5--1.0, frequencies of 10{sup {minus}3}-1 Hz, rise nines of 1--1000s, and peak stress intensities of 25--40 MPa{center_dot}m {sup l/2}

Argonne National Laboratory Reports

The uniaxial stress-strain behavior of Zircaloy-2 and -4, Zircaloy-oxygen alloys with a uniform oxygen distribution, and composite specimens with a ZrO2/alpha/beta layer structure was investigated over the range of experimental conditions: temperature 25-1400 degrees C; strain rate ; oxygen content 0.11 - 4.4 wt %; grain size 5-50 micrometers; texture longitudinal, transverse, and diagonal orientations; and microstructural state, which consists of the equiaxed alpha phase and various transformed beta acicular structures. The work-hardening and strain-rate sensitivity parameters were determined from the experimental results, and the tensile properties were correlated with oxygen concentration, oxygen distribution in the material, and microstructure. Dynamic strain-aging phenomena were observed in Zircaloy at 200, 400, and 700 degrees C, and super-plastic deformation occurred at 850 and 1000 degrees C. An increase in the oxygen concentration in homogeneous Zircaloy-oxygen alloys increased the ultimate tensile strength and decreased the total strain, particularly below approximately 900/sup 0/C. In composite specimens with the ZrO2/alpha/beta structure, the total oxygen content had little effect on the ultimate tensile strength below approximately 1000 degrees C, but the strength increased with oxygen content at higher temperatures. Information on the effects of grain size, oxygen content, texture, and strain rate on the stress-strain behavior suggests that the dominant mechanism of super-plastic deformation in Zircaloy near approximately 850/sup 0/C is grain-boundary sliding at the alpha-beta interface with accommodation by diffusional creep, dislocation slip, and grain-boundary migration. Good correlation was obtained between ductility and values of the strain-rate sensitivity parameter

Test plan for high-burnup fuel cladding behavior under loss-of- coolant accident conditions

Excessive oxidation, hydriding, and extensive irradiation damage occur in high-burnup fuel cladding, and as result, mechanical properties of high-burnup fuels are degraded significantly. This may influence the current fuel cladding failure limits for loss-of- coolant-accident (LOCA) situations, which are based on fuel cladding behavior for zero burnup. To avoid cladding fragmentation and fuel dispersal during a LOCA, 10 CFR 50.46 requires that peak cladding temperature shall not exceed 1204 degrees C (2200 degrees F) and that total oxidation of the fuel cladding nowhere exceeds 0.17 times total cladding thickness before oxidation. Because of the concern, a new experimental program to investigate high-burnup fuel cladding behavior under LOCA situations has been initiated under the sponsorship of the U.S. Nuclear Regulatory Commission. A hot-cell test plan to investigate single-rod behavior under simulated LOCA conditions is described in this paper. In the meantime, industry fuel design and operating conditions are expected to undergo further changes as more advanced cladding materials are developed. Under these circumstances, mechanical properties of high-burnup fuel cladding require further investigation so that results from studies on LOCA, reactivity- initiated-accident (RIA), operational transient, and power-ramping situations, can be extrapolated to modified or advanced cladding materials and altered irradiation conditions without repeating major integral experiments in test reactors. To provide the applicable data base and mechanistic understanding, tests will be conducted to determine dynamic and static fracture toughness and tensile properties. Background and rationale for selecting the specific mechanical properties tests are also described

Evidence for a Second Order Phase Transition in Glasses at Very Low Temperatures -- A Macroscopic Quantum State of Tunneling Systems

Dielectric measurements at very low temperature indicate that in a glass with the eutectic composition BaO-Al$_2$O$_3$-SiO$_2$ a phase transition occurs at 5.84 mK. Below that temperature small magnetic fields of the order of 10 $\mu$T cause noticeable changes of the dielectric constant although the glass is insensitive to fields up to 20 T above 10 mK. The experimental findings may be interpreted as the signature of the formation of a new phase in which many tunneling systems perform a coherent motion resulting in a macroscopic wave function.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

Quantum phase transition of Ising-coupled Kondo impurities

We investigate a model of two Kondo impurities coupled via an Ising interaction. Exploiting the mapping to a generalized single-impurity Anderson model, we establish that the model has a singlet and a (pseudospin) doublet phase separated by a Kosterlitz-Thouless quantum phase transition. Based on a strong-coupling analysis and renormalization group arguments, we show that at this transition the conductance G through the system either displays a zero-bias anomaly, G ~ |V|^{-2(\sqrt{2}-1)}, or takes a universal value, G = e^2/(\pi\hbar) cos^2[\pi/(2\sqrt{2})], depending on the experimental setup. Close to the Toulouse point of the individual Kondo impurities, the strong-coupling analysis allows to obtain the location of the phase boundary analytically. For general model parameters, we determine the phase diagram and investigate the thermodynamics using numerical renormalization group calculations. In the singlet phase close to the quantum phase transtion, the entropy is quenched in two steps: first the two Ising-coupled spins form a magnetic mini-domain which is, in a second step, screened by a Kondoesque collective resonance in an effective solitonic Fermi sea. In addition, we present a flow equation analysis which provides a different mapping of the two-impurity model to a generalized single-impurity Anderson model in terms of fully renormalized couplings, which is applicable for the whole range of model parameters.Comment: 24 pages, 12 figs; (v2) minor changes, flow equation section extende

Correlated Persistent Tunneling Currents in Glasses

Low temperature properties of glasses are derived within a generalized tunneling model, considering the motion of charged particles on a closed path in a double-well potential. The presence of a magnetic induction field B violates the time reversal invariance due to the Aharonov-Bohm phase, and leads to flux periodic energy levels. At low temperature, this effect is shown to be strongly enhanced by dipole-dipole and elastic interactions between tunneling systems and becomes measurable. Thus, the recently observed strong sensitivity of the electric permittivity to weak magnetic fields can be explained. In addition, superimposed oscillations as a function of the magnetic field are predicted.Comment: 4 page