Small Relaxation Research Articles

Efficient representations of upper limits and confidence intervals for experimental data

Upper limits and confidence intervals are a convenient way to present experimental results. With modern experiments producing more and more data, it is often necessary to reduce the volume of the results for convenient distribution. A common approach is to take a maximum over a set of upper limits, which yields an upper limit valid for the entire set. This, however, can result in significant sensitivity loss, because we discard more constraining data. In this paper, we introduce upper limits and confidence intervals that allow one to summarize results with a small relaxation of constraints. A toy example and an application to upper limits in all-sky continuous gravitational wave searches are worked out. Published by the American Physical Society 2024

Understanding vortex dynamics in CaK(Fe,Ni)4As4 and Ba(Fe,Co)2As2 single crystals under the influence of random point disorder

Abstract We report on the influence of doping on vortex dynamics in 3 MeV proton-irradiated single crystals of CaK(Fe1−x Ni x )4As4 (1144, x = 0.015, 0.025, and 0.03) and Ba(Fe1−x Co x )2As2 (x = 0.04, 0.062, 0.066 and 0.074). Non-irradiated crystals of the 1144 system display superconducting critical temperatures ranging from 31 K for x = 0.015–20.5 K, as doping increases to 0.03. On the other hand, pristine crystals of the 122 system show Tc values between 14.6 and 23.6 K, with the maximum Tc occurring at intermediate doping levels. The fluence was set at 3 × 1016 p cm−2, resulting in a decrease in the Tc by around 1.5 K for all samples and significantly affecting the vortex dynamics by reducing the flux creep relaxation compared to previously reported values for unirradiated crystals. Parameters such as vortex pinning energy U 0 and the glassy exponent μ dependencies on doping and magnetic field strength are identified. For the 1144 system, U 0 reaches values approaching 500 K for small fields in samples with Tc = 29.3 K (x = 0.015), systematically decreasing to around 200 K as Tc falls below 20 K. Furthermore, U 0 decreases as the field increases to 3 T for the same sample, varying from approximately 250 K to 100 K as Tc decreases. These changes are typically accompanied by modifications in μ, gradually increasing from values around 1 towards 1.5, corresponding to small bundle relaxation in the collective creep theory. Despite differences in the substitutional disorder and magnetic phase diagram with respect to the 1144 system, the results for 122 single crystals follow a similar tendency in which U 0 usually reduces and μ increase rise as the applied magnetic field is increased. Due to moderate U 0 in these systems (few hundreds of kelvins), the resulting decay of persistent current at liquid helium temperatures is primarily determined by a balance between U 0 and bundle size contribution. These findings provide valuable insights for potential applications of these systems, particularly in the context of intrinsic superconducting parameters and the resulting pinning landscape.

Coordinated active-reactive power optimization considering photovoltaic abandon based on second order cone programming in active distribution networks

On the basis of predecessors’ coordination optimization of active and reactive power in distribution network, For the necessity of the optimal operation in the distribution network, part of power generated from photovoltaic (PV) cannot be sold to users, and cannot enjoy subsidies. Similarly, the network loss in the power transmission will also bring a certain economic loss. This paper comprehensively considers the economic loss caused by the network loss and PV abandon of the distribution system, and establishes a model to minimize the economic loss. To solve this problem efficiently, the method of DistFlow equation and mixed integer second order cone programming (MISOCP) is used to solve the problem, in this method, the original mixed integer nonlinear programming non-convex problem is transformed into a convex problem, which makes the optimization problem easy to solve. The modified IEEE 33 and IEEE 69 distribution networks are tested by the above method. The optimized results are able to meet the target and have very small relaxation gaps, and the voltage level is also optimized. This coordinated optimization approach helps to optimize the economic operation for active distribution networks with PVs.

What is the physical origin of the gradient flow structure of variational fracture models?

We investigate a physical characterization of the gradient flow structure of variational fracture models for brittle materials: a Griffith-type fracture model and an irreversible fracture phase field model. We derive the Griffith-type fracture model by assuming that the fracture energy in Griffith's theory is an increasing function of the crack tip velocity. Such a velocity dependence of the fracture energy is typically observed in polymers. We also prove an energy dissipation identity of the Griffith-type fracture model, in other words, its gradient flow structure. On the other hand, the irreversible fracture phase field model is derived as a unidirectional gradient flow of a regularized total energy. We have considered the time relaxation parameter a mathematical approximation parameter, which we should choose as small as possible. In this research, however, we reveal the physical origin of the gradient flow structure of the fracture phase field model (F-PFM) and show that the small time relaxation parameter is characterized as the rate of velocity dependence of the fracture energy. It is verified by comparing the energy dissipation properties of those two models and by analysing a travelling wave solution of the irreversible F-PFM. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'.

Association of body adiposity with left ventricular concentric remodeling and diastolic dysfunction

AbstractBackgroundObesity is a significant risk factor for heart failure with preserved ejection fraction (HFpEF). In this study, we explore the relationships between body mass index (BMI) and adipose tissue compartments such as visceral adipose tissue (VAT), subcutaneous adipose tissue (SAT), and epicardial adipose tissue (EAT), with respect to left ventricular (LV) structure and function in subjects with preserved LV systolic function.MethodsBetween January and December 2020, this retrospective study included 749 participants who exhibited preserved LV systolic function and underwent transthoracic echocardiography along with abdominal computed tomography. LV structural and functional variables as well as EAT, VAT, and SAT thickness were evaluated using echocardiography and computed tomography.ResultsSAT decreased, while VAT and EAT progressively increased with age. There were significant correlations between BMI and various adipose tissues, with the strongest correlation observed with SAT (r = .491, p < .001) compared to VAT (r = .371, p < .001) or EAT (r = .135, p < .001). However, EAT demonstrated the most substantial association with decreased LV end‐diastolic dimension, LV end‐systolic dimension, and septal mitral annular velocity and increased relative wall thickness (all p < .05), while VAT and SAT did not show significant associations with LV remodeling and functional parameters after adjusting for clinical variables.ConclusionEAT is the most critical adipose tissue influencing LV geometric and functional changes, compared with VAT or SAT. Thick EAT is associated small LV chamber size, concentric remodeling, and relaxation abnormalities.

Versailles Santa Barbara-5 derived bifunctional one-dimensional electrocatalysts of hierarchical Ni3S2 nanoprism@nanosheets arrays for self-supporting and binder-free efficient supercapacitor and methanol oxidation reaction

We herein present a structure consisting of two-dimensional (2D) single-crystal Ni3S2 nanosheets designed on one-dimensional (1D) Ni3S2 nanoprism arrays (also known as Ni3S2 nanoprism@nanosheets). These arrays are directly synthesized over nickel foam, which is referred to as Ni3S2/NF. These structures can be used as binderless, self-supporting electrodes for bifunctional methanol oxidation reaction (MOR) applications and high energy density hybrid supercapacitors (HSC). Ni3S2/NF is synthesized through the two steps of hydrothermal processes. In step I, 1D hexagonal Versailles Santa Barbara-5 (VSB-5) nanorod arrays have been prepared onto the surface of NF (denoted as VSB-5/NF). The precursor for step II was 1D VSB-5 nanorod arrays, which were transformed into Ni3S2 using Na2S as a sulfur source via the Kirkendall effect. Electrochemical examination results show that as-synthesized Ni3S2/NF electrode exhibited a high specific capacitance (Cs) of 145.0 mA h g−1 at 5 A g−1, low series resistance (0.18 Ω) and charge-transfer resistance (0.05 Ω), small relaxation time constant (τ0 = 8 ms) and high frequency response at 125.8 Hz. Ni3S2/NF has a superior specific capacity of 145.0 mA h g−1 at 5 A g−1 as a SC electrode. The Ni3S2/NF//CNTs/NF HSC can be operated up to 1.6 V in a 3 M KOH electrolyte, delivering an impressive energy density of 256.35 W h kg−1 at a power density of 6400 W kg−1. The as-assembled Ni3S2/NF//CNTs/NF HSC device exhibited an impressive stability of 81 % even after undergoing 10,000 charge-discharge cycles. When compared to previously reported catalysts, Ni3S2/NF was proved to be an excellent electrocatalyst for MOR due to its ability to generate a current density of 215.0 mA cm−2 at 0.5 VSCE, while maintaining a superior and stable current density of 619.2 mA cm−2 at 0.8 VSCE.

Some asymptotic profiles for the viscous Moore-Gibson-Thompson equation in the Lq framework

This manuscript studies some qualitative properties of solutions to the Cauchy problem for the viscous Moore-Gibson-Thompson (MGT) equation. For one thing, by applying the WKB analysis and diagonalization procedure, we derive some Lp−Lq decay estimates and the large time asymptotic profile for a suitable energy term, which provides a new way to treat higher order MGT-type coupled systems. For another, we obtain the global (in time) singular limits in the Lq framework and the higher order asymptotic profile with respect to small thermal relaxation via the multi-scale analysis and the Fourier analysis. Especially, provided the incompatible initial condition between the viscous MGT equation and the strongly damped wave equation, the formation of initial layer is rigorously justified.

Instability of Jeffrey Fluid Throughflow in a Porous Layer Induced by Heat Source and Soret Effect

Abstract In this study, we investigated the instability of thermosolutal convection of Jeffrey fluid in a porous layer with internal heating and the Soret effect. The layer is bounded by two fixed permeable parallel plates which are assumed to be isothermal and isosolutal. An existing initial flow in the vertical direction is passing the layer at a constant speed. The flow fields are adequately presented by PDEs and transformed into dimensionless forms. A small perturbation to the basic flow profiles with linear stability analysis results the problem in an eigenvalue problem. The Runge-Kutta method is used to derive the numerical value of the critical thermal Rayleigh number. The convective instability for asymptotic cases for Le = 1 and Pe = 0 are also examined as special cases. The analysis reveals that for a non-positive Soret parameter, the flow is stable for all Lewis numbers and independent of the heat source. But with a positive Soret parameter in the absence of a heat source, the fluid flow is stable for Le = 3 while the influence of a heat source destabilizes the flow for Le > 2. In high and low shear flows with increasing solutal gradient, the solutal Rayleigh number shows a highly destabilizing nature for all Le. Moreover, smaller relaxation and higher retardation time are the most unstable characteristics of the heat source system. In convective longitudinal rolls, the uni-cellular streamline patterns tend to become bi-cellular by the influence of positive Soret parameters and energy sources.

Nonlinear acoustic equations of fractional higher order at the singular limit

When high-frequency sound waves travel through media with anomalous diffusion, such as biological tissues, their motion can be described by nonlinear acoustic equations of fractional higher order. In this work, we relate them to the classical second-order acoustic equations and, in this sense, justify them as their approximations for small relaxation times. To this end, we perform a singular limit analysis and determine their behavior as the relaxation time tends to zero. We show that, depending on the nonlinearities and assumptions on the data, these models can be seen as approximations of the Westervelt, Blackstock, or Kuznetsov wave equations in nonlinear acoustics. We furthermore establish the convergence rates and thus determine the error one makes when exchanging local and nonlocal models. The analysis rests upon the uniform bounds for the solutions of the acoustic equations with fractional higher-order derivatives, obtained through a testing procedure tailored to the coercivity property of the involved (weakly) singular memory kernel.

The effect of FDI regulatory barriers: evidence from OECD countries

ABSTRACT This study aims to analyse the impact of the OECD FDI Regulatory Restrictiveness Index on actual FDI (Foreign Direct Investment) flows into the 38 OECD member countries. Using PPML (Poisson Pseudo Maximum Likelihood), GLS (Generalized Least Squares method), and Heckman’s sample selection estimator, this paper undertakes to identify the impact of FDI Regulatory Restrictiveness Index on FDI inflows to all OECD member countries from 129 partner countries from 2006 to 2021. It finds that the overall level of restrictions, screening and approval measures, and other operational restrictions all have a statistically significant negative sign, except for equity restrictions (ER). This suggests that the higher the level of restrictions on FDI, the less direct investment flows into OECD countries. In other words, liberalizing or reforming FDI restrictions can lead to an increase in inward FDI. Moreover, results show that the impact of even small regulatory relaxations is not negligible. While previous studies have mainly analysed the determinants of FDI inflows based on theories from the investor (supplier) perspective, this study differs in that it provides a reference analysis of FDI policies and laws from the host country’s (demander) perspective, in which areas and to what extent they need to be liberalized.

Narrowband emission from fully-bridged triphenylamine derivatives: insights into effects of structure modification and pressure.

Triphenylamine derivatives with narrowband emission have attracted growing attention in purely organic thermally-activated fluorescence (TADF) materials owing to their enhanced color purity and flexible molecular design strategy. Combined time-dependent density functional theory (TD-DFT) and ONIOM (QM/MM) calculations indicate that the excellent planarity of the experimentally developed DQAO could result in gradually decreased intermolecular interactions in the aggregated state at ambient pressure and upon compression, which is unfavorable for suppressing structural relaxation and achieving narrowband emission in its non-doped practical application. Therefore, three structure-modified derivatives, DQAO-Cb, DQAO-Ph, and DQAO-PhCb, were theoretically designed by introducing the spherical o-carborane and dangling phenyl units positioned para to the N atom of the DQAO to provide additional geometrical distortion and steric hindrance. The explorations on the reported DQAO, OQAO, and SQAO found that small structural relaxations, suppressed low-frequency vibrations, and noticeable short-range charge-transfer (SR-CT) natures of DQAO and OQAO are responsible for their much narrower emission spectral full-width at half-maxima (FWHMs) compared to that of SQAO. Introducing the o-carborane unit directly at the para position of the N atom could result in additional scissoring and stretching vibrations of the corresponding DQAO-Cb while the presence of the phenyl unit in DQAO-Ph is beneficial for suppressing the high-frequency vibrations of the pristine DQAO. More importantly, the bridged phenyl unit incorporated in DQAO-PhCb is of particular importance to inhibit the undesired low-frequency scissoring and high-frequency stretching vibrations of the o-carborane unit, which is crucial to reduce the reorganization energy of DQAO-PhCb and achieve narrowband emission. Also, the phenyl unit in DQAO-Ph and DQAO-PhCb helps to shorten charge transfer distances and improve ISC and RISC processes. Since the o-carborane unit is an adopted building block to achieve piezochromic behaviors, the theoretically structure-modified DQAO-PhCb is expected to exhibit narrowband emission, TADF, and piezochromic features all together. Our findings will hopefully provide ideas for designing triphenylamine-based TADF emitters with narrowband emission and piezochromic behaviors.

From BGK-alignment model to the pressured Euler-alignment system with singular communication weights

This paper is devoted to a rigorous derivation of the isentropic Euler-alignment system with singular communication weights ϕα(x)=|x|−α for some α>0. We consider a kinetic BGK-alignment model consisting of a kinetic BGK-type equation with a singular Cucker-Smale alignment force. By taking into account a small relaxation parameter, which corresponds to the asymptotic regime of a strong effect from the BGK operator, we quantitatively derive the isentropic Euler-alignment system with pressure p(ρ)=ργ, γ=1+2d from that kinetic equation.

Refined Schemes for Computing the Dynamics of Elastoviscoplastic Media

For a stable numerical solution of the system of equations governing an elastoviscoplastic continuous medium model, a second-order explicit-implicit scheme is proposed. An explicit approximation is used for the equations of motion, and an implicit approximation, for the constitutive relations containing a small relaxation time parameter in the denominator of the nonlinear free terms. A second-order implicit approximation for isotropic and anisotropic elastoviscoplastic models is constructed to match the orders of approximation of the explicit elastic and implicit adjustment steps. Refined formulas for correcting the stress deviators after the elastic step are derived for various viscosity function representations. The resulting solutions of the second-order implicit approximation for the stress deviators of the elastoviscoplastic equations admit passage to the limit as the relaxation time tends to zero. The correcting formulas obtained via this passage to the limit can be treated as regularizers of the numerical solutions to the elastoplastic systems.

Anomalously small magnetic relaxation rate of Ca10(Pt3As8)(Fe2−x Pt x As2)5 superconductor

Large critical current density and low magnetic relaxation are the main challenges for practical applications of high-temperature superconductors (HTSs). Magnetic relaxation refers to the decay of superconducting current density caused by thermal activation and/or quantum fluctuations. This process involves the motion of vortices, particularly vortex creep, which leads to energy dissipation. HTSs typically exhibit strong superconducting fluctuations and magnetic relaxation due to their short coherence length and large anisotropy. These characteristics are usually manifested by the large Ginzburg number Gi and high magnetic relaxation rate S. The correlation between the relaxation rate S and Gi is informative to understand the interplay between vortex dynamics and relevant parameters. Recently, Eley et al (2017 Nat. Mater. 16 409) proposed that almost all the HTSs follow a universal lower limit S∼ Gi 1/2(T/T c), providing new clues to design HTSs with small relaxation rate and evaluate their application potential. Here, we systematically studied the vortex dynamics in the Ca10(Pt3As8)(Fe2−x Pt x As2)5 superconductor with a large Gi∼ 0.16. Strikingly, this material exhibits a small relaxation rate (S ∼0.02 at T c/4 under 1 T), approaching the proposed lower limit of S∼ Gi 1/2(T/T c). We propose that such a small value of S in Ca10(Pt3As8)(Fe2−x Pt x As2)5 may originate from its unique structure with metallic skutterudite blocking layers. Our results suggest a promising new avenue for the search and design of HTSs with low magnetic relaxation.

R2T: Instance-optimal Truncation for Differentially Private Query Evaluation with Foreign Keys

Answering SPJA queries under differential privacy (DP), including graph pattern counting under node-DP as an important special case, has received considerable attention in recent years. The dual challenge of foreign-key constraints and self-joins is particularly tricky to deal with, and no existing DP mechanisms can correctly handle both. For the special case of graph pattern counting under node-DP, the existing mechanisms are correct (i.e., satisfy DP), but they do not offer nontrivial utility guarantees or are very complicated and costly. In this paper, we propose the first DP mechanism for answering arbitrary SPJA queries in a database with foreign-key constraints. Meanwhile, it achieves a fairly strong notion of optimality, which can be considered as a small and natural relaxation of instance optimality. Finally, our mechanism is simple enough that it can be easily implemented on top of any RDBMS and an LP solver. Experimental results show that it offers order-of-magnitude improvements in terms of utility over existing techniques, even those specifically designed for graph pattern counting.

Amino Acid Mediated Highly Ordered Carbon Dots as Phase Directing Agent for Synthesizing α-Ni(OH)2Decorated with Nitrogen Doped CD as an Electrode for an Efficient Symmetric Supercapacitor

The synthesis of the α-phase of layered Ni(OH)2 is desirable owing to its efficient charge storage applications. The hydrothermal route of synthesis usually leads to formation of mixed of α- and β-phases of Ni(OH)2. We present here a novel hydrothermal approach for synthesizing predominantly the α-phase of Ni(OH)2 using a nitrogen doped crystalline carbon dot ([N-CD]BA) as a phase directing agent. The reaction medium comprising [N-CD]BA led to the formation of a microflower-like structure denoted as Ni(OH)2/[N-CD]BA with more petal density than in pristine α/β mixed phases of Ni(OH)2. The structure, composition, texture, and morphology of the as-synthesized batches of Ni(OH)2/[N-CD]BA and pristine Ni(OH)2 are thoroughly characterized. The electrochemical studies recorded by cyclic voltammetry and galvanostatic charging–discharging measurements demonstrated a battery-type supercapacitor. The batch of Ni(OH)2 prepared with 12.5 vol % [N-CD]BA, denoted as Ni(OH)2/12.5%[N-CD]BA, exhibited an optimum specific capacity of 482 C g–1 recorded at 1.0 A g–1, which is 4.5 times higher than that of pristine Ni(OH)2. The enhanced charge storage and transport mechanism are explained from electrochemical impedance spectroscopy (EIS). The high power density is reflected from a small relaxation time (0.4 s), and the charging–discharging efficiency is also improved for α-Ni(OH)2/12.5%[N-CD]BA. The application of the materials as supercapacitors has been demonstrated by fabricating a symmetric supercapacitor (SSC) device, i.e., Ni(OH)2/[N-CD]BA//Ni(OH)2/[N-CD]BA, using 2 M KOH as the electrolyte. The SSC exhibited a maximum energy density of 24 Wh kg–1 and a power density of 1.5 kW kg–1. The real-time application of the symmetric supercapacitor device has been demonstrated by successfully illuminating red LED lamps and powering a motor driven 1.6 mW fan.

Small polaron hopping transport mechanism, dielectric relaxation and electrical conduction in NiAl2O4 electro-ceramic spinel oxide

In this study, the frequency and temperature dependent dielectric relaxation and electrical conduction mechanisms in NiAl2O4 spinel oxide ceramic have been explored in a frequency range of over a measured temperature from 163–283 K. The polycrystalline NiAl2O4 was synthesized via solid state reaction route and sintered at 1000 °C. The room temperature x-ray powder diffraction pattern confirmed the formation of NiAl2O4 spinel phase with Fd3m space group. The surface morphology of the sample was investigated by scanning electron microscopy and chemical properties by Fourier transform infrared spectroscopic analysis. Complex impedance studies revealed the presence of relaxation time distribution and charge carriers were found to be thermally activated. The Nyquist plots exhibited depressed semicircles and their fitting by an equivalent circuit model with configuration (RGCG)(RGBCGB) resolved the contributions of grains and grain-boundaries to the electrical transport properties of the material. Electrical conductivity analysis followed the Jonscher’s power law behavior and the frequency exponent suggested small polaron hopping as the governing transport mechanism in NiAl2O4 spinel oxide. Non-Debye type nature of dielectric relaxation was confirmed by the complex modulus analysis whereas dielectric constant and tangent loss analysis verified that the hopping mechanism was thermally activated.

(099) Dual Effect of a Serotonin and Dopamine Reuptake Inhibitor (IP2018), and the Search for a Depressive Rat Model with Erectile Dysfunction

Abstract Introduction In patients with major depressive disorder, up to 68% present with comorbid sexual dysfunction, which resolves in only 5% to 30% of patients treated with antidepressants. Several groups of antidepressants negatively affect sexual function. Objective The present study investigated whether a newly developed amine transport inhibitor, IP2018, improves depression and erectile function in the same dose range. Methods The dose-dependent effect of IP2018 in two different mouse models for depression, the mouse forced swim test (mFST) and mouse tail suspension test (mTST), is reported. In male Wistar, Sprague Dawley and the depressive rats (Flinders Sensitive Line (FSL) and Flinders Resistant Line (FRL)), increases in intracavernosal pressure (ICP) and mean arterial pressure (MAP) were measured, and the ratio ICP/MAP was used as a measure of erectile function. We investigated whether IP2018 induces changes in ICP or flow and whether IP2018 facilitates suboptimal increases in ICP induced by cavernosal nerve electrical stimulation. The late IP2018 procedure was performed in the rest of the rats to evaluate their erectile function. Results We found that infusion of IP2018 dose-dependently improved mFST and was more potent than citalopram. At the same time, higher doses of IP2018 were required to obtain effect in the mTST model, and IP2018 was equipotent to citalopram. Infusion of low doses of IP2018 dose-dependently increased the number and the duration of spontaneous erections. At the highest dose of IP2018, the increases in the number and duration of spontaneous erections were similar to the effect of the lowest dose, and the increases in flow were 5 times higher. IP2018 (1-30 μM) caused small relaxations in isolated corpus cavernosum strips. FSL and FRL rats showed a diminished ICP/MAP compared to Sprague Dawley control rats. Conclusions IP2018 is more potent or has a similar effect to the well-known antidepressant drug citalopram in mouse models for depression. The potent effect of IP2018 on erectile function in anaesthetized rats suggests that IP2018 in the same dose range has positive effects on both depression and erectile function. FSL/FRL rats appear to allow the study of drug effects on both depression and sexual function in one animal model. Disclosure Yes, this is sponsored by industry/sponsor: Initiator Pharma A/S Clarification Industry funding only - investigator initiated and executed study Any of the authors act as a consultant, employee or shareholder of an industry for: Initiator Pharma A/S

Stabilization of a Non-linear Fractional Problem by a Non-Integer Frictional Damping and a Viscoelastic Term

In this paper, we consider a fractional equation of order between one and two which may be looked at as an interpolation between the heat and wave equations. The problem is non-linear as it involves a power-type non-linearity. We investigate the possibilities of stabilizing the system by a lower-order fractional term and/or a memory term involving the Laplacian. We prove a global Mittag–Leffler stability result in case a fractional frictional damping is active and a local Mittag–Leffler stability result when the material is viscoelastic in case of small relaxation functions. Unlike the integer-order problems, additional serious difficulties arise in the present case. These difficulties are highlighted clearly in the introduction. They are mainly due to the memory dependence of the fractional derivatives which is the cause of the invalidity of the product rule in particular. We utilize several properties in fractional calculus. Moreover, we introduce new Lyapunov-type functionals in the context of the multiplier technique.

Small crater relaxation and ice abundance at high northern latitudes on Mars

The cold, northern high-latitudes around the Phoenix landing site feature a population of small and very shallow craters known as palimpsest craters or boulder halos that could give insight into the subsurface ice content of the region. Notably there is also a split in the population by the size of craters that feature blocky ejecta: the smallest crater sizes that are <200–350 m in diameter typically do not feature blocky ejecta, while craters larger than this size range do. This has been interpreted as there being a less consolidated layer of mainly ice that sits over a more consolidated layer containing more silicate material from which the larger craters are able to excavate the blocky ejecta. This work focuses on determining whether these 200 m - 1 km shallow craters could be indicative of topographic relaxation due to substantial ice in the subsurface, with goals to determine the subsurface structure and most importantly the amount of ice present through its abundance and depth extent. We use finite element modeling of axisymmetric simple craters, employing the most recent characterizations of solid-state creep for water ice, silicate-rich ice, and CO2 ice, to determine the timescales and magnitudes of relaxation accommodated by an icy single or multiple material layered subsurface to determine the environment's properties. Our models include a 35 m thick layer of pure ice (water, or water and CO2) over a mobile substrate of particulate rich water ice of variable thicknesses able to accommodate relaxation for larger crater sizes up to 1 km in diameter. Our findings demonstrate that relaxation is able to account for significant flattening of crater topography, though for smaller craters the relaxation is incomplete, leaving about half the depth. The accommodated relaxation of our modeled subsurface does imply associated increases in ice abundances of 4 to 10 times greater than is currently estimated for the region, dependent on the extent of the mobile layer.