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DOE OSTI2021

TOI 540 b: A Planet Smaller than Earth Orbiting a Nearby Rapidly Rotating Low-mass Star

We present the discovery of TOI 540 b, a hot planet slightly smaller than Earth orbiting the low-mass star 2MASS J05051443-4756154. The planet has an orbital period of P = 1.239149 days (±170 ms) and a radius of r=0.903±0.052R{sub ⊕}, and is likely terrestrial based on the observed mass–radius distribution of small exoplanets at similar insolations. The star is 14.008 pc away and we estimate its mass and radius to be M=0.159±0.014 M{sub ⊙} and R=0.1895±0.0079R{sub ⊙}, respectively. The star is distinctive in its very short rotational period of P{sub rot}=17.4264±0.0094 hr and correspondingly small Rossby number of 0.007 as well as its high X-ray-to-bolometric luminosity ratio of L{sub X}/L{sub bol}=0.0028 based on a serendipitous XMM-Newton detection during a slew operation. This is consistent with the X-ray emission being observed at a maximum value of L{sub X}/L{sub bol}≃10{sup −3} as predicted for the most rapidly rotating M dwarfs. TOI 540 b may be an alluring target to study atmospheric erosion due to the strong stellar X-ray emission. It is also among the most accessible targets for transmission and emission spectroscopy and eclipse photometry with the James Webb Space Telescope, and may permit Doppler tomography with high-resolution spectroscopy during transit. This discovery is based on precise photometric data from the Transiting Exoplanet Survey Satellite and ground-based follow-up observations by the MEarth team.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

Transition to Petschek Reconnection in Subrelativistic Pair Plasmas: Implications for Particle Acceleration

While relativistic magnetic reconnection in pair plasmas has emerged in recent years as a candidate for the origin of radiation from extreme astrophysical environments, the corresponding subrelativistic pair-plasma regime has remained less explored, leaving open the question of how relativistic physics affects reconnection. In this paper, we investigate the differences between these regimes by contrasting two-dimensional particle-in-cell simulations of reconnection in pair plasmas with relativistic magnetization (σ ≫ 1) and subrelativistic magnetization (σ < 1). By utilizing unprecedentedly large domain sizes and outflow boundary conditions, we demonstrate that lowering the magnetization results in a change in the reconnection geometry from a plasmoid chain to a Petschek geometry, where laminar exhausts bounded by slow-mode shocks emanate from a single diffusion region. We attribute this change to the reduced plasmoid production rate in the low-σ case: When the secondary tearing rate is sufficiently low, plasmoids are too few in number to prevent the system from relaxing into a stable Petschek configuration. This geometric change also affects particle energization: We show that while high-σ plasmoid chains generate power-law energy spectra, low-σ Petschek exhausts merely heat incoming plasma and yield negligible nonthermal acceleration. These results have implications for predicting the global current sheet geometry and the resulting energy spectra in a variety of systems.

Plasma astrophysics↗

DOE OSTI2020

Kinetically constrained freezing transition in a dipole-conserving system

Here, we study a stochastic lattice gas of particles in one dimension with strictly finite-range interactions that respect the fractonlike conservation laws of total charge and dipole moment. As the charge density is varied, the connectivity of the system's charge configurations under the dynamics changes qualitatively. We find two distinct phases: Near half filling the system thermalizes subdiffusively, with almost all configurations belonging to a single dynamically connected sector. As the charge density is tuned away from half filling there is a phase transition to a frozen phase, where locally active finite bubbles cannot exchange particles and the system fails to thermalize. The two phases exemplify what has recently been referred to as weak and strong Hilbert space fragmentation, respectively. We study the static and dynamic scaling properties of this weak-to-strong fragmentation phase transition in a kinetically constrained classical Markov circuit model, obtaining some conjectured exact critical exponents.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

The research into the propagation law of the shock wave of a gas explosion inside a building

Based on the dissipation rate conservation equations of turbulent kinetic energy in the k‐ ε turbulence model, a complicated three‐dimensional finite element model of a kitchen filled with gas mixture is developed by using the open source field operation and manipulation (OpenFOAM). Two representative kitchens were used to investigate the propagation law of the shock wave of a gas explosion inside a building by considering the key characteristics of the blast shock wave. The influence of some crucial parameters, such as initial conditions and kitchen parameters, on the properties of the blast shock wave is investigated. The basic steps to predict the peak pressure of the blast shock wave are given in consideration of the initial condition and the kitchen whilst the injury effect of the blast shock wave on the humans and animals is evaluated. The research results indicate that the pressure time history and the peak pressure space distribution are greatly influenced by the kitchen design layout. The coupled interaction between the initial temperature and gas volume concentration, especially at the upper and lower explosion limits of the gas, significantly affects the peak pressure. The peak pressure varies significantly with the opening and the buffer; however, it has little relation with the width, length, and height of the kitchen. The proposed method can accurately and effectively predict the peak pressure of the blast shock wave inside buildings. In terms of the peak pressure space distribution of the explosion shock wave, the peak pressure is much higher than the threshold of the killing pressure, which is unsafe for the humans and animals in the building.

Lin, Shu-Chao↗

DOE OSTI2019

A Robust and Efficient Deep Learning Method for Dynamical Mass Measurements of Galaxy Clusters

We demonstrate the ability of convolutional neural networks (CNNs) to mitigate systematics in the virial scaling relation and produce dynamical mass estimates of galaxy clusters with remarkably low bias and scatter. We present two models, CNN 1D and CNN 2D , which leverage this deep learning tool to infer cluster masses from distributions of member galaxy dynamics. Our first model, CNN 1D , infers cluster mass directly from the distribution of member galaxy line-of-sight velocities. Our second model, CNN 2D , extends the input space ofCNN 1D to learn on the joint distribution of galaxy line-of-sight velocities and projected radial distances. We train each model as a regression over cluster mass using a labeled catalog of realistic mock cluster observations generated from the MultiDark simulation and UniverseMachine catalog. We then evaluate the performance of each model on an independent set of mock observations selected from the same simulated catalog. The CNN models produce cluster mass predictions with lognormal residuals of scatter as low as 0.132 dex, greater than a factor of 2 improvement over the classical M–σ power-law estimator. Furthermore, the CNN model reduces prediction scatter relative to similar machinelearning approaches by up to 17% while executing in drastically shorter training and evaluation times (by a factor of 30) and producing considerably more robust mass predictions (improving prediction stability under variations in galaxy sampling rate by 30%).

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Plasma production and composition from hypervelocity impacts on solar cell cover glass

Satellites are subjected to detrimental effects from the space environment, including impacts by orbital debris and meteoroids that can cause mechanical or electrical damage. While mechanical damage is well studied, electrical effects resulting from hypervelocity impact (HVI) remain poorly understood. In HVIs, where the projectile speed exceeds the speed of sound in the target material, the impact energy ionizes the material near the surface, creating a plasma that can cause radio frequency emission. This emission is the main source of electrical anomalies in satellites, but the mechanism behind its creation is still unknown. Ground-based experiments have been used to characterize HVI plasma, including the empirical power law relations that describe the impact charge produced as a function of impactor mass and speed. Quantifying these power law relations gives us a better understanding of the species formed in the impact which can eventually lead to plasma evolution models and help us first, understand the mechanism behind radio frequency emission and second, ways to prevent its damage to the satellites. In this paper, we interpret the results of the HVI experiments on solar cell coverglass targets and identify the potential chemical or molecular reactions that form the impact ion species. This is done by looking simultaneously at multiple data sets for different species within the same impact configuration, and using a new technique for quantifying the power law relations for each emitted species. We use time of flight analysis (TOF) to detect the charged particle compositions and determine their initial speeds. The results suggest that the charge production power law is species specific, with different formation mechanisms involved in a single HVI event, some of which are associated with dissociation and some with ionization of a molecule. Furthermore, our results also show that electrons have different power laws that depend on the spacecraft surface charge. TOF measurements of ions from impact events on solar cell cover glass shows the presence of SiO + and SiO – 2 as the dominant species present in plasmas on positively and negatively charged targets, respectively, as well as the formation of FeO + .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Chandra Discovery of a Candidate Hyperluminous X-Ray Source in MCG+11-11-032

We present a multiwavelength analysis of MCG+11-11-032, a nearby active galactic nucleus (AGN), with a unique classification as being both a binary and a dual AGN candidate. With new Chandra observations, we aim to resolve any dual AGN system via imaging data and search for signs of a binary AGN via analysis of the X-ray spectrum. Analyzing the Chandra spectrum, we find no evidence of the previously suggested double-peaked Fe Kα lines; the spectrum is instead best fit by an absorbed power law with a single Fe Kα line, as well as an additional line centered at ≈7.5 keV. The Chandra observation reveals faint, soft, and extended X-ray emission, possibly linked to low-level nuclear outflows. Further analysis shows evidence for a compact hard source—MCG+11-11-032 X2—located 3.″3 from the primary AGN. Modeling MCG+11-11-032 X2 as a compact source, we find that it is relatively luminous (L2–10 keV=1.5−0.5+0.9×1041erg s$^{−1}$), and the location is coincident with a compact and off-nuclear source resolved in Hubble Space Telescope infrared (F105W) and optical (F621M, F547M) bands. Pairing our X-ray results with a 144 MHz radio detection at the host galaxy location, we observe X-ray and radio properties similar to those of ESO 243-49 HLX-1, suggesting that MCG+11-11-032 X2 may be a hyperluminous X-ray source. This detection with Chandra highlights the importance of a high-resolution X-ray imager as well as how previous binary AGN candidates detected with large-aperture instruments can benefit from high-resolution follow-up. Future spatially resolved optical spectra, and deeper X-ray observations, can better constrain the origin of MCG+11-11-032 X2.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Conservation laws and effective hadronization models

Hadronization models based on local string-breaking dynamics are typically Markovian by construction, yet the physical ensemble of final states is shaped by global constraints that couple the entire fragmentation trajectory. Recasting hadronization as a conditioned stochastic diffusion process provides a precise mathematical resolution to this tension. In particular, this language reveals explicitly that constraints stemming from conservation laws induce non-Markovian correlations between otherwise independent fragmentation steps, and that these correlations can be absorbed exactly into a renormalization of the local dynamics through a Doob $h$-transform. We develop this formalism for a $q\bar{q}$ string in the chiral limit, where the longitudinal-transverse factorization of the Lund kernel becomes exact, enabling systematic power counting and clean ultraviolet (UV)/infrared (IR) separation. The dynamics organize naturally into a tower of effective theories distinguished by the remaining string mass, spanning a UV fixed point with scale-invariant transport coefficients, an intermediate regime where transverse phase space induces controlled running, and an IR boundary layer where non-local effects enter at leading order. The tower exhibits genuine Wilsonian structure, including $β$-functions, anomalous dimensions, and systematic matching conditions. The resulting framework achieves a clean factorization of universal microscopic fragmentation dynamics from infrared constraint effects, and opens new directions for both the theoretical analysis and practical simulation of hadronization.

Menzo, Tony [Alabama U.; Fermilab] (ORCID:00000002↗

DOE OSTI2021

On the Symmetry of Blast Waves

This paper presents a brief historical review of G. I. Taylor’s solution of the point blast wave problem which was applied to the Trinity test of the first atomic bomb. Lie group symmetry techniques (also referred to throughout this paper as geometric techniques) are used to derive Taylor’s famous two-fifths law that relates the position of a blast wave to the time after the explosion and the total energy released. The theory of exterior differential systems is combined with the method of characteristics to demonstrate that the solution of the blast wave problem is directly related to the basic relationships that exist between the symmetry (or geometry) and the physics of wave propagation through the equations of motion. The point blast wave model is cast in terms of two exterior differential systems, and both systems are shown to be integrable with local solutions for the velocity, pressure, and density along curves in space and time behind the blast wave. This work is dedicated to the memory of Professor Roy Axford, who introduced many of his students to the topic of symmetry analysis of differential equations.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2022

Shock Formation and Vorticity Creation for 3d Euler

Abstract We analyze the shock formation process for the 3D nonisentropic Euler equations with the ideal gas law, in which sound waves interact with entropy waves to produce vorticity. Building on our theory for isentropic flows in [3, 4], we give a constructive proof of shock formation from smooth initial data. Specifically, we prove that there exist smooth solutions to the nonisentropic Euler equations which form a generic stable shock with explicitly computable blowup time, location, and direction. This is achieved by establishing the asymptotic stability of a generic shock profile in modulated self‐similar variables, controlling the interaction of wave families via: (i) pointwise bounds along Lagrangian trajectories, (ii) geometric vorticity structure, and (iii) high‐order energy estimates in Sobolev spaces. © 2022 Wiley Periodicals LLC.

Mathematics↗

DOE OSTI2025

Magnetohydrodynamic simulations preliminarily predict the habitability and radio emission of TRAPPIST-1e

TRAPPIST-1e, an Earth-sized exoplanet in the habitable zone of the nearby M dwarf TRAPPIST-1, may experience magnetospheric responses that vary with stellar space weather, which could potentially influence both its habitability and radio emissions. Our objective is to investigate how different Earth-like magnetospheric configurations of TRAPPIST-1e – specifically variations in dipolar magnetic field strength and axial tilt – respond to diverse stellar space weather conditions, including events analogous to coronal mass ejections (CMEs), and to assess their implications for potential habitability and expected radio emissions. We conducted 3D magnetohydrodynamic simulations of the TRAPPIST-1e system using the PLUTO code in spherical coordinates. The planetary magnetic field was modelled as dipolar, with equatorial strengths from Earth-like to several times stronger. The dipole axis spans a representative range of axial tilts. We investigate four stellar wind environments, from sub-Alfvénic flow to CME-like disturbances. Planetary shielding was quantified based on the magnetopause standoff distance, and radio powers were estimated via empirical scaling laws. Our simulations show that both shielding and radio power depend strongly on the magnetic configuration. Stronger fields increase protection, while larger tilts reduce it. Radio power increases with both field strength and tilt across all wind regimes. An Earth-like magnetic field can provide effective shielding even under intense CMEs, whereas high tilts require stronger fields. Predicted radio powers reach ~10 20 erg s −1 during CMEs, making bursts from close-in, magnetised planets more detectable. However, for TRAPPIST-1e, the maximum cyclotron frequency lies below the Earth’s ionospheric cutoff (~10 MHz), making ground-based detection currently infeasible.

Sun: magnetic fields↗

DOE OSTI2022

Solar Energetic Particle Acceleration at a Spherical Shock with the Shock Normal Angle $θ$ $B_n$ Evolving in Space and Time

We present a 2D kinematic model to study the acceleration of solar energetic particles (SEPs) at a shock driven by a coronal mass ejection. The shock is assumed to be spherical about an origin that is offset from the center of the Sun. This leads to a spatial and temporal evolution of the angle between the magnetic field and the shock-normal direction (θ Bn ) as it propagates through the Parker spiral magnetic field from the lower corona to 1 au. We find that the high-energy SEP intensity varies significantly along the shock front due to the evolution of θ Bn . Generally, the west flank of the shock preferentially accelerates particles to high energies compared to the east flank and shock nose. This can be understood in terms of the rate of acceleration, which is higher at the west flank. Double power-law energy spectra are reproduced in our model as a consequence of the local acceleration and transport effects. These results will help us to better understand the evolution of SEP acceleration and provide new insights into large SEP events observed by multiple spacecraft, especially those close to the Sun, such as Parker Solar Probe and Solar Orbiter.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

A spatially-resolved model of neutron-irradiated tungsten coupling stochastic cluster dynamics and finite deformation plasticity

Structural materials used in nuclear reactors face severe degradation in mechanical properties, such as hardening and embrittlement. At the microscopic scale, this occurs due to creation and accumulation of irradiation-induced defects and their interaction with system dislocations. Although techniques exist which can model evolution of irradiation defects, for instance kinetic transport theory-based models, their interaction with mechanical deformation of the bulk material has not been investigated extensively. In this work, we demonstrate a novel spatially-resolved multiscale coupling between microscopic irradiation defect evolution, modeled using Stochastic Cluster Dynamics (SCD) and macroscopic mechanical deformation modeled using a finite-deformation plasticity model. SCD is used to determine the statistically averaged defect cluster spacing, dependent on operating conditions such as irradiation dose and temperature. This acts as an initial condition that governs the critical resolved shear stress of dislocation glide in the macroscopic plasticity model. This framework is used to predict mechanical behavior in post-mortem test of irradiated Tungsten samples, which has found its importance as structural material used in nuclear reactors. The results obtained using the coupled approach are in good agreement with experimental data of uniaxial tension tests. The model is able to capture the effect of temperature and irradiation dose on the material hardening. Two methods are proposed to estimate hardness – using Tabor's Law relating uniaxial yield stress to hardness and from flat-punch simulations. The results are in reasonable agreement with hardness data from micro-indentation experiments of irradiated Tungsten samples. Finally, the model is also able to reveal microstructural details such as spatial variation in defect density and local stress.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

A Bayesian analysis of classical shadows

Abstract The method of classical shadows proposed by Huang, Kueng, and Preskill heralds remarkable opportunities for quantum estimation with limited measurements. Yet its relationship to established quantum tomographic approaches, particularly those based on likelihood models, remains unclear. In this article, we investigate classical shadows through the lens of Bayesian mean estimation (BME). In direct tests on numerical data, BME is found to attain significantly lower error on average, but classical shadows prove remarkably more accurate in specific situations—such as high-fidelity ground truth states—which are improbable in a fully uniform Hilbert space. We then introduce an observable-oriented pseudo-likelihood that successfully emulates the dimension-independence and state-specific optimality of classical shadows, but within a Bayesian framework that ensures only physical states. Our research reveals how classical shadows effect important departures from conventional thinking in quantum state estimation, as well as the utility of Bayesian methods for uncovering and formalizing statistical assumptions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Photometric Objects Around Cosmic Webs (PAC) Delineated in a Spectroscopic Survey. IV. High-precision Constraints on the Evolution of the Stellar–Halo Mass Relation at Redshift z < 0.7

Taking advantage of the Photometric objects Around Cosmic webs method developed in Paper I, we measure the excess surface density $\overline{n}$ 2 w p of the photometric objects around spectroscopic objects down to stellar masses 10 8.0 M ⊙ , 10 9.2 M ⊙ , and 10 9.8 M ⊙ in the redshift ranges of z s < 0.2, 0.2 < z s < 0.4, and 0.5 < z s < 0.7, respectively, using data from the DESI Legacy Imaging Surveys and spectroscopic samples from the Sloan Digital Sky Survey (i.e., the Main, LOWZ, and CMASS samples). We model the measured in an N-body simulation, using the abundance matching method, and we constrain the stellar–halo mass relations (SHMRs) in the three redshift ranges to percent levels. With the accurate modeling, we demonstrate that the stellar mass scatter for a given halo mass is nearly a constant, and that the empirical form of Behroozi et al. describes the SHMR better than the double-power-law form at low mass. Our SHMR accurately captures the downsizing of massive galaxies from z s = 0.7, while it also indicates that small galaxies are still growing faster than their host halos. The galaxy stellar mass functions (GSMFs) from our modeling are in perfect agreement with the model-independent measurements in Paper III, although the current work extends the GSMFs to a much smaller stellar mass. Based on the GSMFs and the SHMRs, we derive the stellar mass completeness and halo occupation distributions for the LOWZ and CMASS samples, which are useful for correctly interpreting their cosmological measurements, such as galaxy–galaxy lensing and redshift space distortion.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Polymer Macrocycles: A novel topology to control dynamics of rubbery materials (Final Report)

We have successfully made synthetic polymer rings that are larger than previously reported having entanglement numbers as high as Z w ≈300 if the rings entangled as do linear chains. The synthesis was carried out using reversible radical recombination polymerization (R3P) of dithiols which produces a polymer with a very small persistence length. The reported results show surprising dilute solution behaviors due to the fact that polymeric rings expand more than their linear counterparts for polymer chains having a large number of persistence lengths, as developed in this study. The results strongly argue for a systematic investigation of the dilute solution properties of rings having different persistence lengths in different quality solvents, where the theta-condition should lead to results that are independent of the persistence length. For the rheological investigations related to chain entanglements, the polyDODT rings could be diluted so that the rheological data covered from less than one entanglement spacing relative to the linear counterpart to a value of Z w =300. Importantly, because we were able to dilute extremely high entanglement number polyDODT rings to a similar entanglement number as those reported for polystyrene rings that were highly purified using LCCC, we demonstrated that the dynamics of the polyDODT rings virtually overlaps with the dynamics of the polystyrene rings which is very strong evidence that these high molecular weight polyDODT rings are of high purity. Our results demonstrate that the onset of entanglement in rings, as evidenced by the appearance of a rubbery plateau G N 0 and by the onset of a strong power-law dependence of the viscosity on molecular weight (η~M w 5.8 ) or entanglement number (η~Z w 5.8 ), occurs at much higher molecular weights or polymer concentrations than is the case for linear chains. These results should serve as a benchmark for future investigations of the behavior of entangled, circular macromolecules.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2023

Polymer Macrocycles: A novel topology to control dynamics of rubbery materials

We have successfully made synthetic polymer rings that are larger than previously reported having entanglement numbers as high as $Z_w$≈300 if the rings entangled as do linear chains. The synthesis was carried out using reversible radical recombination polymerization (R3P) of dithiols which produces a polymer with a very small persistence length. The reported results show surprising dilute solution behaviors due to the fact that polymeric rings expand more than their linear counterparts for polymer chains having a large number of persistence lengths, as developed in this study. The results strongly argue for a systematic investigation of the dilute solution properties of rings having different persistence lengths in different quality solvents, where the theta-condition should lead to results that are independent of the persistence length. For the rheological investigations related to chain entanglements, the polyDODT rings could be diluted so that the rheological data covered from less than one entanglement spacing relative to the linear counterpart to a value of $Z_w$=300. Importantly, because we were able to dilute extremely high entanglement number polyDODT rings to a similar entanglement number as those reported for polystyrene rings that were highly purified using LCCC, we demonstrated that the dynamics of the polyDODT rings virtually overlaps with the dynamics of the polystyrene rings which is very strong evidence that these high molecular weight polyDODT rings are of high purity. Our results demonstrate that the onset of entanglement in rings, as evidenced by the appearance of a rubbery plateau $G_N^0$ and by the onset of a strong power-law dependence of the viscosity on molecular weight (η~$M_w^{5.8}$) or entanglement number (η~$Z_w^{5.8}$), occurs at much higher molecular weights or polymer concentrations than is the case for linear chains. These results should serve as a benchmark for future investigations of the behavior of entangled, circular macromolecules.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2021

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↗