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At least 1,081 records · Page 60

The simulation of complete 11 and 12 year modulation cycles for cosmic rays in the heliosphere using a drift model with global merged interaction regions

Two-dimensional, time-dependent drift models have done exceptionally well in explaining major modulation features, especially during the A less than 0 magnetic polarity cycle of the heliospheric magnetic field when positively charge particles are drifting in along the heliospheric neutral sheet (HNS). These models were found to do well when the heliospheric 'tilt angles' alpha less than approximately 30 deg (le Roux & Potgeiter). However, they seem to do less well when alpha greater than approximately 30 deg during A less than 0 cycles seem to fail when this happens in A greater than 0 cycles. Progress was made in understanding these phases of the modulation cycle when merged interaction regions (MIRs) were incorporated in time-dependent drift models (Potgieter et al.). It was also explicitly shown that in obtaining large step decreases in cosmic rays, the MIRs had to be global, i.e., having a latitudinal extent of more than approximately 60 deg. Other classes of MIRs, such as local MIRs and co-rotating MIRs were found to be of secondary importance for establishing long-term modulation. In a previous paper we studied the effects of two consecutive, identical global MIRs, together with a changing wavy HNS, on long-term modulation (Potegieter & le Roux). This approach gave a very natural and convincing explanation for the observed step decreases in cosmic-ray modulation. Emphasis was placed in the declining and recovery phases of the 11 yr modulation cycle. In this paper, four consecutive, nonidentical global MIRs, in combination with a varying wavy HNS, were included in our time-dependent drift model in order to do simulations closer to what was observed between 1977 and 1987. By doing this we could model, for the first time, complete 11 and 22 yr cycles in the heliospheric modulation of galactic cosmic-rays, including the solar magnetic polarity reversals.

Le Roux, J. A.↗

Measurement of Microscopic Growth Rates in Float-Zone Silicon Crystals

Time dependent convective flows during crystal growth of doped semiconductors lead to fluctuations of the composition, so called dopant striations. In general, it is difficult to decide which is the main mechanism for the generation of these striations, it might be either the fluctuation of the concentration field in the melt and the extent of the solute boundary layer ahead of the solid-liquid interface or a variation of the growth velocity. Direct access to the concentration field is rather complicated to achieve, especially considering the high process temperature and the chemical activity of liquid silicon. The contribution of growth rate fluctuations to the formation of compositional fluctuations can be determined by measuring microscopic growth rates. The classical method of current pulses requires electrical feed-throughs and good electrical contacts, both are critical issues for the growth of high purity silicon crystals. Using a radiation based heating system, the heating power can be modulated very fast and effectively. We added to the normal heater power a sinusoidal off-set in the frequency range of 1 to 10 Hz, generating a narrow spaced weak rippling in the grown crystals which are superposed to the dopant striations caused by natural and by thermocapillary convection. The pulling speed was varied between 1 and 4mm/min. The microscope images of etched crystals slices have been analyzed by peak-search algorithms (measuring the spacing between each artificially induced marker) and by FFT. Performing growth experiments under a time-dependent flow regime, fluctuations of the microscopic growth velocity of Delta(v)/v(sub average) up to 50% have been measured. Damping the time-dependent convection by the use of an axial, static magnetic field of 500mT, the microscopic growth rate became constant within the resolution limit of this method. The results will be discussed using analytical methods for the calculation of microscopic growth velocity and by comparing them with measurements of temperature fluctuations in the melt during growth experiments itself.

Dold, P.↗

Electron-Beam-Induced Molecular Plasmon Excitation and Energy Transfer in Silver Molecular Nanowires

In this work, we investigate (1) electron-beam-induced plasmon absorption spectra of Ag molecular nanowire dimers and (2) electron-beam-induced energy transfer between two nanowires. We employ linear-response time-dependent density functional theory (TDDFT) and real-time TDDFT methods to simulate the electron-beam-induced plasmonic excitations, dynamics, and corresponding electron energy loss spectrum for small models of a single molecular nanowire with four Ag atoms and for two Ag nanowires. An array of different relative orientations of nanowires and of different initial excitation conditions resulting from applying an electron beam at different positions with respect to the Ag nanowires is investigated. The results demonstrate (1) an electron beam can induce plasmonic excitations from the molecular Ag nanowire ground state to the excited states that are both optically allowed and forbidden, (2) a tunability for selective excitations that can be controlled by the position of a focused electron beam, and (3) kinetic and dynamic behaviors of time-dependent electron-beam-induced energy transfer between two Ag molecular nanowires depend on the position of the beam source and nanowire separation distance, providing insights into the spatial dependences of plasmonic couplings in nanowire arrays.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Resolving the phase of Fano resonance wave packets with photoelectron frequency-resolved optical gating

The creation of structured electronic wave packets (EWPs) energetically close to Fano resonances has been achieved with ultrafast extreme ultraviolet coherent light sources. However, direct real-time observations of EWP evolution and full reconstructions of the quantum properties of EWPs, including both amplitude and phase, are lacking. Here we introduce and demonstrate a comprehensive approach for the direct measurement and complete characterization of structured EWPs created within a prototypical Fano resonance. Because of its analogy with frequency-resolved optical gating (FROG), we named the method photoelectron FROG. The correlated EWP is initiated by a carefully engineered extreme UV pump pulse. A weak near-infrared laser field, serving as a probe pulse, samples the evolution of the EWPs in the time domain, as well as in the frequency domain. The amplitude and phase of the EWPs are obtained via a time-dependent reconstruction algorithm based on a short-time Fourier transformation. Given the excellent agreement between our experimental results and time-dependent reconstructions, we expect this method to be broadly applicable to the study of ultrafast processes, especially electronic ones, in complex systems, as well as the coherent control of such systems on their fundamental timescales.

quantum optics↗

Microscopic predictions for the production of neutron-rich nuclei in the reaction Yb 176 + Yb 176

Background: Production of neutron-rich nuclei is of vital importance to both understanding nuclear structure far from stability and to informing astrophysical models of the rapid neutron capture process (r-process). Multinucleon transfer (MNT) in heavy-ion collisions offers a possibility to produce neutron-rich nuclei far from stability. Purpose: The 176 Yb + 176 Yb reaction has been suggested as a potential candidate to explore the neutron-rich region surrounding the principal fragments. The current study has been conducted with the goal of providing guidance for future experiments wishing to study this (or similar) system. Methods: Time-dependent Hartree-Fock (TDHF) and its time-dependent random-phase approximation (TDRPA) extension are used to examine both scattering and MNT characteristics in 176 Yb + 176 Yb. TDRPA calculations are performed to compute fluctuations and correlations of the neutron and proton numbers, allowing for estimates of primary fragment production probabilities. Results: Both scattering results from TDHF and transfer results from the TDRPA are presented for different energies, orvientations, and impact parameters. In addition to fragment composition, scattering angles and total kinetic energies, as well as correlations between these observables are presented. Conclusions: 176 Yb + 176 Yb appears to be an interesting probe for the midmass neutron-rich region of the chart of nuclides. Lastly, the predictions of both TDHF and TDRPA are speculative, and will benefit from future experimental results to test the validity of this approach to studying MNT in heavy, symmetric collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Coalescence of Liquid Drops

When two liquid drops come into contact, a neck forms between them and grows rapidly. We are interested in the very early stage of the coalescence process, which can be characterized by the time dependence of the radius of the neck. The functional dependence of the size of the neck on time depends on the properties of the liquid. Experimentally, we are investigating a liquid in Stokes flow regime where the viscosity provides the principal retarding force to the surface tension. Recently, it has been predicted that the neck radius should change as t ln|t| in this regime. Theoretically, we have studied the situation when the velocity at each point on the surface is proportional to the local curvature and directed normal to the surface. This is the case that should be applicable to superfluid helium at low temperature when the mean free path of the thermal excitations are comparable to the size of liquid drops. For this system, the radius of the neck is found to be proportional to t(sup 1/3). We are able to find a simple expression for the shape of the interface in the vicinity of the neck.

Yao, Wei-Jun↗

Pulse Detonation Engine Air Induction System Analysis

A preliminary mixed-compression inlet design concept for potential pulse-detonation engine (PDE) powered supersonic aircraft was defined and analyzed. The objectives of this research were to conceptually design and integrate an inlet/PDE propulsion system into a supersonic aircraft, perform time-dependent CFD analysis of the inlet flowfield, and to estimate the installed PDE cycle performance. The study was baselined to a NASA Mach 5 Waverider study vehicle in which the baseline over/under turboramjet engines were replaced with a single flowpath PDE propulsion system. As much commonality as possible was maintained with the baseline configuration, including the engine location and forebody lines. Modifications were made to the inlet system's external ramp angles and a rotating cowl lip was incorporated to improve off-design inlet operability and performance. Engines were sized to match the baseline vehicle study's ascent trajectory thrust requirement at Mach 1.2. The majority of this study was focused on a flight Mach number of 3.0. The time-dependent Navier Stokes CFD analyses of a two-dimensional approximation of the inlet was conducted for the Mach 3.0 condition. The Lockheed Martin Tactical Aircraft Systems-developed FALCON CFD code with a two equation 'k-1' turbulence model was used. The downstream PDE was simulated by an array of four sonic nozzles in which the flow areas were rapidly varied in various opening/closing combinations. Results of the CFD study indicated that the inlet design concept operated successfully at the Mach 3.0 condition, satisfying mass capture, total pressure recovery, and operability requirements. Time-dependent analysis indicated that pressure and expansion waves from the simulated valve perturbations did not effect the inlet's operability or performance.

Pegg, R. J.↗

Improved Creep Testing Approach for Bentonite EBS

In the United States, the nuclear reactor contributes 18.7 percent of the nation’s total electricity generation and produces a significant amount of spent nuclear fuel (SNF) and high-level waste. Because SNF is being stored for longer periods than initially envisioned, the U.S. Department of Energy Office of Nuclear Energy, Office of Spent Fuel and Waste Science and Technology is assessing the technical performance of the SNF storage systems after extended durations. The concept of a sustainable geologic repository for SNF disposal relies heavily on the safety provided by multiple barriers, such as repository host rock, overlying rock formation, and human-made engineered barrier systems (EBS). One of the major components of EBS is bentonite-based buffer materials that isolate the nuclear-waste canisters from the host rock and fill the void left in the horizontally drilled boreholes. The resaturated bentonite has a swelling characteristic, which is useful for self-sealing the microcracks in the host rock and supporting the canister’s heavy weight. However, factors such as nonuniformity in the saturation, swelling pressure of bentonite, and the high temperature at the canister-bentonite interface may lead to instability of the waste canister inside the borehole. Therefore, evaluating the long-term deformation of bentonite-based material is necessary. RESPEC Company, LLC recently completed a preliminary study for the U.S. Department of Energy (DE SC0022804) that is attempting to understand the time-dependent deformation in the consolidated sand/bentonite (SB) specimens through triaxial creep experiments and improve the understanding of EBS performance under anticipated repository conditions. The project included developing a standard testing procedure for preparing the consolidated core specimen from a mixture of sand and bentonite in a 50:50 ratio by weight, fabricating a new pressure vessel in-house, modifying existing creep equipment to perform triaxial creep experiments on consolidated SB specimens, and performing six long-term triaxial creep experiments under low-deviatoric stress at two different temperature conditions, which is representative of hypothetical conditions that might be encountered in a geologic repository within a reasonable rate of success in completing creep experiments. The consolidated SB specimen was prepared using the novel specimen preparation procedure and had physical characteristics (e.g., moisture content and bulk density) reasonably comparable with the properties of bentonite-based buffer, which is proposed to be used in the EBS in the Swedish KBS-3H design and the Swiss design of SNF disposal in the horizontal drifts. The newly fabricated pressure vessel could withstand the confining pressure of up to 15 megapascals (MPa) while maintaining the test temperature of up to 90 degrees Celsius (°C) for long-term creep experiments. The preliminary results from the triaxial creep experiments suggested that the consolidated SB specimen may experience time-dependent deformation at a low-deviatoric stress state and room temperature condition. Based on the deformation recorded in the SB specimen from axial and radial linear variable differential transformers (LVDTs) and physical characteristic changes, it is apparent that the time-dependent deformation is a combination of consolidation and creep, which is influenced by the level of deviatoric stresses and temperature. The systematic creep testing of bentonite-based specimens helped develop a standard testing procedure applicable for analyzing the similar characteristics of shale or clay-like materials in different geologic conditions outside repository science, including in civil engineering and infrastructure projects, underground and open pit mining, and deep drilling.

58 GEOSCIENCES↗

Parallel-in-Time Multigrid Methods for Hyperbolic Problems, with a Focus on the Shallow Water Equations

The coming massive parallelism of exascale computing presents a pressing challenge for the many DOE simulations of time-dependent partial differential equations, which typically use traditional sequential time stepping methods. Since this traditional approach is inherently serial, it presents a sequential bottleneck when moving to exascale computing, because future performance gains will come through greater concurrency, not faster clock speeds. Thus, the goal of this work is to research parallelism in time, i.e., methods that compute multiple time values simultaneously, not sequentially. The focus will be on hyperbolic problems of programmatic interest to DOE, with the goal of enabling scalable simulations of time-dependent hyperbolic problems on future architectures. The difficulty lies in the fact that hyperbolic problems are well-known to be difficult for parallel-in-time methods, with the most common parallel-in-time method, Parareal, diverging in many cases. Here, the chosen methodology for scalably solving these hyperbolic space-time equations is multigrid-reductionin-time (MGRIT), because multigrid (when it works) is a powerful, optimal, and scalable solver for discretized PDEs. To further research in this area, this project will explore a model hyperbolic problem (the shallow water equations) in the context of recent advances (e.g., by Wingate and Haut) in constructing improved coarse time-grid time-propagators by using the slow asymptotic structure of the equations. In particular, we will investigate if such coarse time-propagators offer significant advantages in an MGRIT setting, and explore any broader insights gained into parallel-in-time for hyperbolic problems.

97 MATHEMATICS AND COMPUTING↗

Magnetic properties of the 110K superconducting phase in Pb-doped Bi-Sr-Ca-Cu-O thin films

The relaxation of the remnant moment induced in a nearly single phase high T(sub c) thin film of Pd-doped Bi-Sr-Ca-Cu-O was investigated. Measurements reveal that the relaxation obeys a logarithmic time dependence for observation times up to 2000 seconds. The temperature dependence of the initial magnetization of the film and its decay rate are obtained. The initial magnetization monotonically decreases. However, the decay rate normalized by initial magnetization has a peak at approximately 14 K for an applied field of 500 gauss. The peak shifts to lower temperature for a stronger magnetic field. These data are compared with existing data on other high T(sub c) superconducting materials.

Tanaka, Atsushi↗

Parallel Multigrid in Time and Space for Extreme-Scale Computational Science: Chaotic and Hyperbolic Problems

The coming massive parallelism of exascale computing presents a pressing challenge for the many DOE simulations of time-dependent partial differential equations (PDEs), which typically use traditional sequential time stepping methods. Since this traditional approach is inherently serial, it presents a sequential bottleneck when moving to exascale computing, because future performance gains will come through greater concurrency, not faster clock speeds. Thus, the goal of this work is to research parallelism in time, i.e., methods that compute multiple time values simultaneously, not sequentially. The focus will be on hyperbolic and chaotic problems of interest to DOE, with the goal of enabling scalable simulations of time-dependent hyperbolic and chaotic problems on future architectures. The chosen methodology for solving these problems parallel-in-time is multigrid, because multigrid (when it works) is a powerful, optimal, and scalable solver for discretized PDEs. Multigrid is already commonly used in many DOE simulations for scalably and optimally solving space-only PDE problems. The areas of hyperbolic and chaotic problems are chosen because of their relevance to problems of programmatic interest to DOE. However, these problems are also well-known to be difficult for parallelin-time methods, with the most common method, parareal, diverging in many cases. The current stateof-the-art for parallel-in-time at LLNL is the multigrid reduction in time (MGRIT) XBraid package, which also struggles for such problems, while still showing some improvement over parareal. In summary, new methods are needed for an efficient parallel-in-time scheme for hyperbolic and chaotic problems, and this work shall research promising new multigrid methods in this area. In particular, we take inspiration from the Least Squares Shadowing (LSS by Wang) approach for solving chaotic problems. Here, an optimization approach is able to find “well-conditioned” shadow trajectories/solutions to the original “ill-conditioned” chaotic problem. Thus, the new multigrid methods researched here also arise in an optimization context.

97 MATHEMATICS AND COMPUTING↗

Multigrid Reduction in Time for Chaotic and Hyperbolic Problems (Final Report)

The coming massive parallelism of exascale computing presents a pressing challenge for the many DOE simulations of time-dependent partial differential equations (PDEs), which typically use traditional sequential time stepping methods. Since this traditional approach is inherently serial, it presents a sequential bottleneck when moving to exascale computing, because future performance gains will come through greater concurrency, not faster clock speeds. Thus, the goal of this work is to research parallelism in time, i.e., methods that compute multiple time values simultaneously, not sequentially. The focus will be on hyperbolic and chaotic problems of interest to DOE, with the goal of enabling scalable simulations of time-dependent hyperbolic and chaotic problems on future architectures. The chosen methodology for solving these problems parallel-in-time is multigrid, because multigrid (when it works) is a powerful, optimal, and scalable solver for discretized PDEs. Multigrid is already commonly used in many DOE simulations for scalably and optimally solving space-only PDE problems. The areas of hyperbolic and chaotic problems are chosen because of their relevance to problems of programmatic interest to DOE. However, these problems are also well-known to be difficult for parallelin-time methods, with the most common method, parareal, diverging in many cases. The current state-of-the-art for parallel-in-time at LLNL is the multigrid reduction in time (MGRIT) XBraid package, which also struggles for such problems, while still showing some improvement over parareal. In summary, new methods are needed for an efficient parallel-in-time scheme for hyperbolic and chaotic problems, and this work shall research promising new multigrid methods in this area. In particular, this work shall continue researching the directions from the current collaboration with Dr. Falgout, which are laid out in the work Toward Parallel in Time for Chaotic Dynamical Systems and showed the first known results of a parallel-in-time speedup for a chaotic problem. This work outlines two key improvements to XBraid for chaotic problems, the so-called “theta” and “delta-correction” methods. Here, these two improvements will be implemented in a high-performance but general way in XBraid and explored for more complicated problems. We will additionally research, as time allows, improvements to these techniques, as well as multigrid relaxation techniques based on Least Squares Shadowing (LSS by Wang) and a nonintrusive block tridiagonal solver based on MGRIT, called TriMGRIT.

97 MATHEMATICS AND COMPUTING↗

Multigrid Reduction in Time for Chaotic and Hyperbolic Problems (Final Report)

The coming massive parallelism of exascale computing presents a pressing challenge for the many DOE simulations of time-dependent partial differential equations (PDEs), which typically use traditional sequential time stepping methods. Since this traditional approach is inherently serial, it presents a sequential bottleneck when moving to exascale computing, because future performance gains will come through greater concurrency, not faster clock speeds. Thus, the goal of this work is to research parallelism in time, i.e., methods that compute multiple time values simultaneously, not sequentially. The focus will be on hyperbolic and chaotic problems of interest to DOE, with the goal of enabling scalable simulations of time-dependent hyperbolic and chaotic problems on future architectures. The chosen methodology for solving these problems parallel-in-time is multigrid, because multigrid (when it works) is a powerful, optimal, and scalable solver for discretized PDEs. Multigrid is already commonly used in many DOE simulations for scalably and optimally solving space-only PDE problems. The areas of hyperbolic and chaotic problems are chosen because of their relevance to problems of programmatic interest to DOE. However, these problems are also well-known to be difficult for parallel-in-time methods, with the most common method, parareal, diverging in many cases. The current state of-the-art for parallel-in-time at LLNL is the multigrid reduction in time (MGRIT) XBraid package, which also struggles for such problems, while still showing some improvement over parareal. In summary, new methods are needed for an efficient parallel-in-time scheme for hyperbolic and chaotic problems, and this work shall research promising new multigrid methods in this area. In particular, this work shall continue researching the directions from the current collaboration with Dr. Falgout, which are laid out in the work Toward Parallel in Time for Chaotic Dynamical Systems and showed the first known results of a parallel-in-time speedup for a chaotic problem. This work outlines two key improvements to XBraid for chaotic problems, the so-called “theta” and “delta-correction” methods. Here, these two improvements will be further researched and improved (including with a new relaxation method inspired by on Least Squares Shadowing (LSS)) and explored for more complicated problems.

97 MATHEMATICS AND COMPUTING↗

Impact melting early in lunar history

The total amount of impact melt produced during early lunar history is examined in light of theoretically and experimentally determined relations between crater diameter (D) and impact melt volume. The time dependence of the melt production is given by the time dependent impact rate as derived from cratering statistics for two different crater-size classes. Results show that small scale cratering (D less than or equal to 30 km) leads to melt volumes which fit selected observations specifying the amount of impact melt contained in the lunar regolith and in craters with diameters less than 10 km. Larger craters (D greater than 30 km) are capable of forming the abundant impact melt breccias found on the lunar surface. The group of large craters (D greater than 30 km) produces nearly 10 times as much impact melt as all the smaller craters, and thus, the large impacts dominate the modification of the lunar surface. A contradiction between the distribution of radiometric rock ages and a model of exponentially decreasing cratering rate going back to 4.5 b.y. is reflected in uncertainty in the distribution of impact melt as a function of time on the moon.

Lange, M. A.↗

Photoluminescence of Cis-Polyacetylene Semiconductor Material

Photoluminescence (PL) is one of the key experimental characterizations of optoelectronic materials, including conjugated polymers (CPs). In this study, a simplified model of an undoped cis-polyacetylene (cis-PA) oligomer was selected and used to explain the mechanism of photoluminescence (PL) of the CPs. Using a combination of the ab initio electronic structure and a time-dependent density matrix methodology, the photo-induced time-dependent excited state dynamics were computed. We explored the phonon-induced relaxation of the photoexcited state for a single oligomer of cis-PA. Here, the dissipative Redfield equation of the motion was used to compute the dissipative excited state dynamics of electronic degrees of freedom. This equation used the nonadiabatic couplings as parameters. The computed excited state dynamics showed that the relaxation rate of the electron is faster than the relaxation rate of the hole. The dissipative excited-state dynamics were combined with radiative recombination channels to predict the PL spectrum. The simulated results showed that the absorption and emission spectra both have a similar transition. The main result is that the computed PL spectrum demonstrates two mechanisms of light emission originating from (i) the inter-band transitions, corresponding to the same range of transition energies as the absorption spectrum and (ii) intra-band transitions not available in the absorption spectra. However, the dissipative Redfield equation of the motion was used to compute the electronic degrees of freedom of the nonadiabatic couplings, which helped to process the time propagation of the excited dynamic state. This excited dynamic state shows that the relaxation rate of the electron is faster than the relaxation rate of the hole, which can be used for improving organic semiconductor materials for photovoltaic and LED applications.

36 MATERIALS SCIENCE↗

Temporal and Spatial Evolution of Non-Elastic Strain Accumulation in Stanstead Granite During Brittle Creep

Understanding the long-term behavior of brittle rocks requires fundamental consideration of time-dependent strain evolution and brittle creep processes. Previous studies have evaluated sub-critical crack growth during time-dependent deformation and damage evolution in brittle rocks; however, there is an incomplete knowledge of how damage evolves spatially and temporally within the body of intact rocks, where distributed regions of damage interact and coalesce during creep. This paper presents laboratory research focusing on evaluating brittle creep damage processes in Stanstead granite (SG) using 2-dimensional digital image correlation (2D-DIC). In the laboratory, the prismatic SG specimens were loaded beyond an estimated Crack Damage stress threshold (CD) level and then maintained a constant stress to initiate the creep process. DIC was used to characterize full-field spatiotemporal strain evolution, which was then interpreted in the context of local regions of “damage”, determined according to a strain-based criterion. Here, a method was proposed for identifying “existing” and “new” damage regions over specified intervals during the test, followed by spatial clustering of these regions to assess their spatiotemporal evolution. The clustering analysis results demonstrated the extension of existing damage regions was the main damage process during brittle creep, which is consistent with existing models of sub-critical crack growth. In addition, temporal analysis of tensile and shear strains on a point-by-point basis revealed both new damage formation and the strain concentration within existing damaged regions significantly contribute to overall specimen strain during primary creep. In contrast, during secondary creep, increases in specimen deformation are influenced by the accumulation of strains within already damaged regions.

58 GEOSCIENCES↗

Alluvial fan morphology: A self-similar free boundary problem description

In this work, we examine approximate geometrically self-similar solutions to a parabolic free boundary value problem applied to alluvial fan surface morphology and growth. Alluvial fans are fan- or cone-shaped sedimentary deposits caused by the rapid deposition of sediment from a canyon discharging onto a flatter plain. Longitudinal, topographic profiles of fans can be readily described by a seemingly time independent dimensionless profile (DeChant et al., 1999). However, because an alluvial fan can be expected to grow over time, it is clear that this “steady” profile is certainly time dependent and can be described using a space-time self-similar solution. In an experimental and theory-based study, Guerit et al. (2014) developed a self-similar (or as they describe it a self-affine) linear solution based upon an approximate first order small parameter expansion solution for a 1-d homogeneous nonlinear diffusion equation. Direct substitution of this result into a linear diffusion equation suggests that this first order expression may not fully satisfy the associated governing equation. In contrast, we develop a more complete solution based upon a modeled approximation for the axi-symmetric formulation such that the associated temporal behavior is consistent with a 1/3 time power-law as described by Reitz and Jerolmack (2014). The resulting expression is an exact solution to a linear heat equation. Furthermore, we emphasize that a small parameter is not inherent to the resulting profile result and is not included in our model development. Though developed using rather different approaches, the formal solution developed here is in good agreement with the simple polynomial described by DeChant et al. (1999) suggesting that this self-similar solution is a suitable time dependent representation of alluvial fan longitudinal profile form and improves on earlier work.

58 GEOSCIENCES↗

Quantal diffusion description of isotope production via the multinucleon transfer mechanism in 48 Ca+ 238 U collisions

As an extension of previous work, we calculate the production cross section of heavy neutron-rich isotopes by employing the quantal diffusion description to 48 Ca+ 238 U collisions. The quantal diffusion is deduced from stochastic mean-field approach, and transport properties are determined in terms of time-dependent single-particle wave functions of the time-dependent Hartree-Fock theory. As a result, the approach allows for prediction of production cross sections without any adjustable parameters. Furthermore, the secondary cross sections by particle emission are calculated with the help of the statistical gemini++ code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗