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DOE OSTI2024

An Updated Simulation of the Booster Neutrino Beam

For accelerator neutrino experiments, an accurate prediction of the incoming neutrino flux is crucial for reducing uncertainties for all physics measurements. In this exciting period for the Short-Baseline Neutrino program at Fermilab, with far detector (ICARUS) already operating and the near detector (SBND) nearing operation, an updated flux model for the Booster Neutrino Beam (BNB) is presented. The BNB delivers 8 GeV protons to a beryllium target, subsequently producing neutrinos from the decay of the secondary beam of hadrons. A updated Monte-Carlo simulation of beam production in GEANT4 has been created, allowing predictions to be made for detectors with different baselines, offsets and sizes. This new simulation contains new features, such as a full neutrino ancestry to handle hadron production systematics with more precision, with a view to storing all resulting particles - including neutral mesons - from the proton-Beryllium scatter to allow the study of exotic BSM scenarios. Results are presented, with comparisons to the original flux simulated for the MiniBooNE experiment.

Paton, Josephine↗

NASA NTRS1992

Precipitation of fast ion beams from the plasma sheet boundary layer

This paper presents a model of precipitated fluxes from the PSBL and CPS. Simulation results and data from Aureol-3 spacecraft indicate the presence of velocity dispersed precipitated ion structures (VDIS) at the poleward edge of the auroral oval. These structures are associated with fast ion beams in the PSBL region of the earth's magnetotail, confirming previous experimental results. The simulations also reveal possible substructuring of the VDIS. The bulk of the PSBL population which is not precipitated is very effectively thermalized and quasi-isotropized after multiple interactions with the magnetotail current layer. After each reflection cycle some part of the distribution is precipitated and forms multiple 'echoes' of VDIS. The CPS distributions occurring as a result of scattering, convection, multiple reflections and Fermi acceleration appear isotropic in the simulation model. This paper portrays the important role of the VDIS auroral region medium for complicated and energetically significant processes occurring in different regions of the distant magnetotail.

Ashour-Abdalla, M.↗

NASA NTRS2005

Dusty-Plasma Particle Accelerator

A dusty-plasma apparatus is being investigated as means of accelerating nanometer- and micrometer-sized particles. Applications for the dusty-plasma particle accelerators fall into two classes: Simulation of a variety of rapidly moving dust particles and micrometeoroids in outer-space environments that include micrometeoroid streams, comet tails, planetary rings, and nebulae and Deposition or implantation of nanoparticles on substrates for diverse industrial purposes that could include hardening, increasing thermal insulation, altering optical properties, and/or increasing permittivities of substrate materials. Relative to prior apparatuses used for similar applications, dusty-plasma particle accelerators offer such potential advantages as smaller size, lower cost, less complexity, and increased particle flux densities. A dusty-plasma particle accelerator exploits the fact that an isolated particle immersed in plasma acquires a net electric charge that depends on the relative mobilities of electrons and ions. Typically, a particle that is immersed in a low-temperature, partially ionized gas, wherein the average kinetic energy of electrons exceeds that of ions, causes the particle to become negatively charged. The particle can then be accelerated by applying an appropriate electric field. A dusty-plasma particle accelerator (see figure) includes a plasma source such as a radio-frequency induction discharge apparatus containing (1) a shallow cup with a biasable electrode to hold the particles to be accelerated and (2) a holder for the substrate on which the particles are to impinge. Depending on the specific design, a pair of electrostatic-acceleration grids between the substrate and discharge plasma can be used to both collimate and further accelerate particles exiting the particle holder. Once exposed to the discharge plasma, the particles in the cup quickly acquire a negative charge. Application of a negative voltage pulse to the biasable electrode results in the initiation of a low-current, high-voltage cathode spot. Plasma pressure associated with the cathode spot as well as the large voltage drop at the cathode spot accelerates the charged particles toward the substrate. The ultimate kinetic energy attained by particles exiting the particle holder depends in part on the magnitude of the cathode spot sheath potential difference, which is proportional to the magnitude of the voltage pulse, and the on the electric charge on the dust. The magnitude of the voltage pulse can be controlled directly, whereas the particle s electric charge can be controlled indirectly by controlling the operating parameters of the plasma apparatus.

Foster, John E.↗

NASA NTRS2002

Hubble Space Telescope Pointing Performance Due to Micro-Dynamic Disturbances from the NICMOS Cryogenic Cooler

The Vibration Admittance Test (VET) was performed to measure the emitted disturbances of the Near Infrared Camera and Multi-Object Spectrometer (NICMOS) Cryogenic Cooler (NCC) in preparation for NCC installation onboard the Hubble Space Telescope (HST) during Servicing Mission 3B (SM3B). Details of the VET ground-test are described, including facility characteristics, sensor complement and configuration, NCC suspension, and background noise measurements. Kinematic equations used to compute NCC mass center displacements and accelerations from raw measurements are presented, and dynamic equations of motion for the NCC VET system are developed and verified using modal test data. A MIMO linear frequency-domain analysis method is used to compute NCC-induced loads and HST boresight jitter from VET measurements. These results are verified by a nonlinear time-domain analysis approach using a high-fidelity structural dynamics and pointing control simulation for HST. NCC emitted acceleration levels not exceeding 35 micro-g rms were measured in the VET and analysis methods herein predict 3.1 milli-areseconds rms jitter for HST on-orbit. Because the NCC is predicted to become the predominant disturbance source for HST, VET results indicate that HST will continue to meet the 7 milli-arcsecond pointing stability mission requirement in the post-SM3B era.

Clapp, Brian R.↗

DOE OSTI2024

RADIATION DOSE SIMULATIONS FOR JEFFERSON LAB’S PERMANENT MAGNET RESILIENCY LDRD STUDY

In late 2023, Thomas Jefferson National Accelerator Facil- ity (Jefferson Lab) funded a Laboratory Directed Research and Development (LDRD) grant dedicated to investigating the impact of radiation on permanent magnet materials. This research initiative is specifically geared towards assessing materials slated for use in the CEBAF energy upgrade. The experimental approach involves strategically placing perma- nent magnet samples throughout the accelerator, exposing them to varying radiation doses. The simulation code BD- SIM is used to first validate the data and then to simulate the effects on future higher energy passes to study the degra- dation effects on the permanent magnets. In this paper we present the progress of that work.

Deitrick, K.↗

DOE OSTI2024

Accelerating transients with NekRS: GPU overlapping domain implementation and multi-rate timestepping

The simulation of nuclear transients using Computational Fluid Dynamics (CFD) presents significant computational challenges due to the inherent complexity and the wide separation in temporal scales between various flow physical phenomena. These disparities lead to high computational costs, often making the simulation of transients impractical without advanced techniques. Consequently, multiple research initiatives are being pursued by the NEAMS thermal-hydraulic area, some driven by academic institutions and some by national laboratories. Overall, they are exploring novel methods to make transient simulations more feasible and efficient. This report delves into recent advancements within the CFD code NekRS, specifically those achieved in Fiscal Year 2024 under the CONNECT effort, aimed at improving the performance and feasibility of transient simulations. The first major advancement involves the porting of NekRS to Aurora, one of the Department of Energy’s (DOE) most powerful supercomputers. Additionally, the report discusses the implementation of an overlapping domain capability within NekRS. This novel GPU-accelerated capability allows different spatial regions of the domain to be solved independently, enhancing the code’s efficiency, particularly when running large-scale simulations in complex domains. The scalability of this approach is demonstrated, highlighting its potential to transform how transients are approached in CFD simulations. Lastly, the report focuses on how this overlapping domain capability specifically accelerates transient simulations through multi-rate timestepping. By decoupling different regions and facilitating faster computations, this method offers a promising pathway to making nuclear transient simulations more computationally feasible, addressing one of the critical bottlenecks in the field. Together, these advancements represent a significant leap forward in transient simulation technology, bringing closer the possibility of handling highly complex nuclear scenarios with greater efficiency and accuracy.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS2009

Validation of Finite Element Crash Test Dummy Models for Predicting Orion Crew Member Injuries During a Simulated Vehicle Landing

A series of crash tests were conducted with dummies during simulated Orion crew module landings at the Wright-Patterson Air Force Base. These tests consisted of several crew configurations with and without astronaut suits. Some test results were collected and are presented. In addition, finite element models of the tests were developed and are presented. The finite element models were validated using the experimental data, and the test responses were compared with the computed results. Occupant crash data, such as forces, moments, and accelerations, were collected from the simulations and compared with injury criteria to assess occupant survivability and injury. Some of the injury criteria published in the literature is summarized for completeness. These criteria were used to determine potential injury during crew impact events.

Tabiei, Al↗

NASA NTRS2014

A Monte Carlo Approach to Modeling the Breakup of the Space Launch System EM-1 Core Stage with an Integrated Blast and Fragment Catalogue

The Liquid Propellant Fragment Overpressure Acceleration Model (L-FOAM) is a tool developed by Bangham Engineering Incorporated (BEi) that produces a representative debris cloud from an exploding liquid-propellant launch vehicle. Here it is applied to the Core Stage (CS) of the National Aeronautics and Space Administration (NASA) Space Launch System (SLS launch vehicle). A combination of Probability Density Functions (PDF) based on empirical data from rocket accidents and applicable tests, as well as SLS specific geometry are combined in a MATLAB script to create unique fragment catalogues each time L-FOAM is run-tailored for a Monte Carlo approach for risk analysis. By accelerating the debris catalogue with the BEi blast model for liquid hydrogen / liquid oxygen explosions, the result is a fully integrated code that models the destruction of the CS at a given point in its trajectory and generates hundreds of individual fragment catalogues with initial imparted velocities. The BEi blast model provides the blast size (radius) and strength (overpressure) as probabilities based on empirical data and anchored with analytical work. The coupling of the L-FOAM catalogue with the BEi blast model is validated with a simulation of the Project PYRO S-IV destruct test. When running a Monte Carlo simulation, L-FOAM can accelerate all catalogues with the same blast (mean blast, 2 σ blast, etc.), or vary the blast size and strength based on their respective probabilities. L-FOAM then propagates these fragments until impact with the earth. Results from L-FOAM include a description of each fragment (dimensions, weight, ballistic coefficient, type and initial location on the rocket), imparted velocity from the blast, and impact data depending on user desired application. LFOAM application is for both near-field (fragment impact to escaping crew capsule) and far-field (fragment ground impact footprint) safety considerations. The user is thus able to use statistics from a Monte Carlo set of L-FOAM catalogues to quantify risk for a multitude of potential CS destruct scenarios. Examples include the effect of warning time on the survivability of an escaping crew capsule or the maximum fragment velocities generated by the ignition of leaking propellants in internal cavities.

Richardson, Erin↗

NASA NTRS1984

Road load simulator tests of the Gould phase 1 functional model silicon controlled rectifier ac motor controller for electric vehicles

The test results for a functional model ac motor controller for electric vehicles and a three-phase induction motor which were dynamically tested on the Lewis Research Center road load simulator are presented. Results show that the controller has the capability to meet the SAE-J227a D cycle test schedule and to accelerate a 1576-kg (3456-lb) simulated vehicle to a cruise speed of 88.5 km/hr (55 mph). Combined motor controller efficiency is 72 percent and the power inverter efficiency alone is 89 percent for the cruise region of the D cycle. Steady state test results for motoring, regeneration, and thermal data obtained by operating the simulator as a conventional dynamometer are in agreement with the contractor's previously reported data. The regeneration test results indicate that a reduction in energy requirements for urban driving cycles is attainable with regenerative braking. Test results and data in this report serve as a data base for further development of ac motor controllers and propulsion systems for electric vehicles. The controller uses state-of-the-art silicon controlled rectifier (SCR) power semiconductors and microprocessor-based logic and control circuitry. The controller was developed by Gould Laboratories under a Lewis contract for the Department of Energy's Electric and Hybrid Vehicle program.

Gourash, F.↗

NASA NTRS1961

A Three-Axis Fixed-Simulator Investigation of the Effects on Control Precision of Various Ways of Utilizing Rate Signals

A three-axis vehicle control study has been made by use of a fixed simulator and analog computing equipment, to evaluate the effects of various ways of utilizing rate information. A side-arm controller providing proportional acceleration control was used with a simulated vehicle having no inherent stability or damping. Vehicle rate signals were used to provide control feedback or system damping and were used in the instrument display either separate from or summed with displacement signals. Near optimum performance of both transitions in roll and control of system disturbance was obtained by using a combination of system damping and summed displacement signals and rate signals.

McKee, John W.↗

DOE OSTI2026

Studying AC-LGAD strip sensors from laser and testbeam measurements

Here, this paper presents the setup assembled to characterize and measure the spatial and timing resolutions of AC-coupled Low Gain Avalanche Diodes (AC-LGADs), using a 1060 nm laser source to deposit initial charges with a defined calibration methodology. The results were compared to those obtained with a 120 GeV proton beam. Despite the differences in the charge deposition mechanism between the laser and proton beam, the spatial and temporal resolutions were found to be compatible between the two sources after calibration. With 4D tracking detectors expected to play a vital role in upcoming collider experiments, we foresee this work as a way to evaluate the performance of semiconductor sensors that can augment testbeam measurements and accelerate R&D efforts. Additionally, simulation studies using Silvaco TCAD and Weightfield2 were carried out to understand the various contributing factors to the total time resolution in AC-LGAD sensors, measured using the laser source.

FOS: Physical sciences↗

DOE OSTI2024

2019 Budget Request for the DOE Computational Science Graduate Fellowship (CSGF) Grant

The Department of Energy Computational Science Graduate Fellowship (DOE CSGF) is necessary to meet the continual challenging national workforce needs that arise as computational science and engineering problems continue to grow in scope and complexity. Computational science and engineering (CSE) is a multidisciplinary approach that uses scientific computing to solve practical problems methods and to supply technical tools across the scientific discovery spectrum. In particular, the DOE CSGF emphasizes high-performance computing (HPC) that enables CSE that advances science and engineering in directions important to the DOE and the economy in general. Over the past half-century, HPC has been an essential tool for DOE’s success. During this period, important missions, such as nuclear stockpile stewardship, have turned to HPC as an essential technology. Entire science disciplines, such as biology and cosmology, have been transformed through the augmentation of scientific observation via HPC. At government laboratories and in industry, DOE CSGF alumni are helping push traditional HPC boundaries while contributing to discoveries in high-energy physics, renewable energy, fusion-reactor design, additive manufacturing, nanomaterials for next-generation batteries and transistors, and turbine and advanced nuclear reactor modeling. In addition, HPC is used to address national health needs that will eventually point to cures both by helping cancer researchers manage and analyze huge troves of data, by simulating biological mechanisms, and by accelerating drug development — including continuing to rise to the challenge of pandemic-related research. A 2023 report from the ASCAC Subcommittee on American Competitiveness and Innovation to the ASCR office, “Can the United States Maintain Its Leadership in High-Performance Computing?” says of the Program, “The CSGF program provides a barometer for disciplines that will be of interest to future DOE computing.” An explosion in scientific and technological data has driven the need for increasingly sophisticated HPC to transform those data into scientific understanding. With access to more and more data and the proliferation of HPC, Machine Learning and Artificial Intelligence are experiencing a renaissance, complementing the now well-established use of computational simulation. Indeed, in its September 2020 subcommittee report on “AI/ML, Data Intensive Science and High-Performance Computing”, the DOE Advanced Scientific Computing Advisory Committee (ASCAC) explicitly called for a fellowship program to train computational and data scientists to tackle exascale and data-intensive computing challenges. This collaboration of empirical and theory-based modeling will increasingly inform federal policymakers whose decisions affect American society and future generations, and it requires highly skilled and intellectually agile computational scientists who can support the fast-moving DOE National Laboratory research environment. In fact, the DOE CSGF program has explicitly and consistently addressed this need.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1988

Acceleration ground test program to verify GAS payload No. 559 structure/support avionics and experiment structural integrity

Acceleration ground tests were conducted on the Get Away Special (GAS) payload 559 to verify the structural integrity of the structure/support avionics and two of the planned three flight experiments. The ITA (Integrated Test Area) Standardized Experiment Module (ISEM) structure was modified to accommodate the experiments for payload 559. The ISEM avionics consisted of a heavy duty sliver zinc power supply, three orthogonal-mounted low range microgravity accelerometers, a tri-axis high range accelerometer, a solid state recorder/programmer sequencer, and pressure and temperature sensors. The tests were conducted using the Gravitational Plant Physiology Laboratory Centrifuge of the University City Science Center in Philadelphia, PA. The launch-powered flight steady state acceleration profile of the shuttle was simulated from lift-off through jettison of the External Tank (3.0 g's). Additional tests were conducted at twice the nominal powered flight acceleration levels (6 g's) and an over-test condition of four times the powered flight loads to 12.6 g's. The present test program has demonstrated the value of conducting ground tests to verify GAS payload experiment integrity and operation before flying on the shuttle.

Cassanto, John M.↗

DOE OSTI2025

2020 Budget Request for the DOE Computational Science Graduate Fellowship (CSGF) Grant

The Department of Energy Computational Science Graduate Fellowship (DOE CSGF) is essential for addressing the increasingly complex national workforce demands stemming from the growth of computational science and engineering challenges. Computational science and engineering (CSE) takes a multidisciplinary approach that utilizes scientific computing to tackle practical problems and provide technical tools across the spectrum of scientific discovery. The DOE CSGF specifically highlights high-performance computing (HPC) as a critical enabling technology in CSE, driving advancements in science and engineering that are vital to both the DOE and the broader economy. Over the past half-century, HPC has been an essential tool for DOE’s success. During this period, important missions, such as nuclear stockpile stewardship, have turned to HPC as an essential technology. Entire science disciplines have been transformed through the augmentation of scientific observation via HPC. At government laboratories, academic institutions, and in industry, DOE CSGF alumni are helping push traditional HPC boundaries while contributing to discoveries in high-energy physics, quantum information systems, fusion-reactor design, machine learning, additive manufacturing, nano materials for next-generation batteries and transistors, and advanced nuclear reactor modeling. In addition, HPC is used to address national health needs that will eventually point to cures both by helping cancer researchers manage and analyze huge troves of data, by simulating biological mechanisms, and by accelerating drug development. A 2023 report from the ASCAC Subcommittee on American Competitiveness and Innovation to the ASCR office, “Can the United States Maintain Its Leadership in High-Performance Computing?” says of the Program, “The CSGF program provides a barometer for disciplines that will be of interest to future DOE computing. Computational biology, machine learning, and quantum computing are among the subjects that began to swell in the ranks of CSGF applicants before the labs were hiring as high a percentage of employees in these categories.” The explosion of scientific and technological data has heightened the demand for advanced high-performance computing (HPC) to transform these data into meaningful scientific insights. As access to vast amounts of data increases, the fields of Machine Learning and Artificial Intelligence are experiencing a resurgence, enhancing the established practices of computational modeling and simulation. In its September 2020 subcommittee report on "AI/ML, Data Intensive Science, and High-Performance Computing," the DOE Advanced Scientific Computing Advisory Committee (ASCAC) specifically called for a fellowship program to train computational and data scientists to address exascale and data-intensive computing challenges. This integration of empirical and theoretical modeling will increasingly guide federal policymakers in making decisions that impact American society and future generations. It demands a workforce of highly skilled and intellectually agile computational scientists capable of navigating the rapid advancements in scientific computing within the DOE National Laboratory research environment. The DOE CSGF program has consistently addressed this critical need.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Kinetic Monte Carlo Framework for Coupled Degradation and Dehydration of Anion Exchange Membranes

Kinetic Monte Carlo (kMC) simulations, augmented with temporal-acceleration schemes, can efficiently handle stiff reaction-transport networks when fast processes rapidly relax to quasi-equilibrium on a fixed lattice. However, in glassy anion-exchange membranes (AEM), rare and irreversible chemical degradation events continuously reshape the nanoscale morphology, and the associated hydration and transport degrees of freedom remain far from a well-defined local equilibrium. This combination of evolving state space and nonequilibrated fast dynamics lies outside the scope of existing kMC acceleration frameworks. Here, to address this challenge, we introduce an auxiliary-particle kinetic Monte Carlo (AP-kMC) scheme. In AP-kMC, short-lived mobile particles spawned at degradation sites execute hop, water-elimination, and decay moves, enforcing rapid local relaxation of the hydration structure while preserving the stochastic rules of kMC. Parameterized with molecular-dynamics morphologies and experimental solution degradation kinetics, AP-kMC reproduces the evolution of ion-exchange capacity, water uptake, and conductivity, and reveals a feedback loop in which poorly hydrated sites degrade first and each degradation event induces further local dehydration. The resulting thinning and fragmentation of water channels cause loss of hydrophilic percolation and abrupt conductivity collapse well before complete charge loss. AP-kMC thus reframes AEM durability as a coupled degradation–drying–percolation problem and provides a transferable strategy to simulate reactive, out-of-equilibrium polymer electrolytes where local solvation controls reactivity.

organic↗

DOE OSTI2026

Adsorption Hysteresis Under Control: Tuning Host–Guest Interactions via a Genetic Algorithm

Mesoporous adsorbent materials offer a large volumetric capacity; however, cyclic adsorption/desorption processes in these systems often suffer from hysteresis and may require a significant pressure swing to access this capacity. To mitigate hysteresis, a proposed strategy is to include nucleation sites on the walls of the mesoporous material to facilitate droplet and bubble formation, lowering the free energy barriers to the respective phase transitions. It is unclear, however, what combination of adsorbate− adsorbent interactions and spatial patterning would be beneficial for a given application, considering that improvements to some sorption properties may come at the expense of other attributes. To understand these interconnected observables, we examine two model systems, planar-slit and cylindrical pores with tunable interaction sites, using GPU-accelerated transition matrix Monte Carlo simulations. The simulations provide a free energy map of the pressure−adsorption space in a matter of minutes, which we use to track adsorption isotherm characteristics as a function of adsorbent properties. We then leverage the rapid acquisition of simulation data to construct a genetic algorithm to iteratively modify interaction sites of the slit-pore wall to minimize the hysteresis of this system without sacrificing uptake. We find that the adsorption branch of the isotherm is easily modulated via the average host−guest interaction strength, but desorption is only adjustable if there is a suitable bubble nucleation site. Within the context of a slit-pore system, we identify relative interaction strengths and patch sizes required to gain control over both branches of the hysteresis loop.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Accelerating Thermochemical Equilibrium Calculations for Nuclear Reactor Applications

Thermochemical properties play a key role in modeling and simulation of several key phenomena in nuclear reactors. There has been an increasing interest in incorporating CALPHAD-based formulations in multiphysics simulations including for Molten Salt Reactors where knowledge of phase evolution of the salt and the chemical potentials of various elements are of utmost importance in source term analyses and redox control. However, the size of such simulations is often limited by the high computational cost of full thermodynamic equilibrium calculations. This work discusses the current efforts aimed at accelerating thermochemical equilibrium calculations for multiphysics simulations performed using the open-source finite element / finite volume code Multiphysics Object Oriented Simulation Environment (MOOSE) [1]. While several methods have been proposed for accelerating phase equilibrium calculations [2], most focus on relatively small systems and often rely on a- priori knowledge of the state-space of the system. Nuclear materials, however, are often multi-component systems owing to the evolution of composition under irradiation and an approach based on a-priori mapping of phase diagram is often not enough. This work is aimed at demonstrating an on-the-fly surrogate modeling framework that uses active learning to reduce the number of full equilibrium calculations that must be performed. By combining with efficient coupling approaches, the surrogate framework helps in reducing the computational cost of thermodynamic equilibrium informed multiphysics simulations of nuclear materials. The performance is benchmarked against full coupling with the thermochemistry library Thermochimica [3]. This work uses a machine learning based approach for constructing surrogate models to predict the stable phases in a multicomponent system. The surrogates were constructed using neural networks and Gaussian process classification. In this work, we compare the relative performance of the two methods. We also demonstrate the use of caching previous calculations by interpolating the values from nearest neighbors. References [1] Lindsay, A.D., et al. "2.0 – MOOSE: Enabling massively parallel multiphysics simulation", SoftwareX, 20 (2022): 101202. [2] Roos, W.A. and Zietsman J.H. "Accelerating complex chemical equilibrium calculations – A Review", Calphad, 77 (2022): 102380. [3] Piro, M.H.A., et al. "The thermochemistry library Thermochimica", Computational Materials Science, 67 (2013): 266-272.

36 MATERIALS SCIENCE↗

DOE OSTI2025

On a Critical Acceleration Scale of Dark Matter in ΛCDM and Dynamical Dark Energy

Abstract Universal acceleration a 0 emerges in various empirical laws, yet its fundamental nature remains unclear. Using Illustris and Virgo N -body simulations, we focus on the velocity and acceleration fluctuations in collisionless dark matter involving long-range gravity. For comparison, in the kinetic theory of gases, molecules undergo random elastic collisions involving short-range interactions, where only velocity fluctuations are relevant. Hierarchical structure formation proceeds through the merging of smaller halos to form larger halos, which facilitates a continuous energy cascade from small to large halos at a constant rate ε u ≈ −10 −7 m 2 s −3 . Velocity fluctuations involve a critical velocity u c ∝ (1 + z ) −3/4 . Acceleration fluctuations involve a critical acceleration a c ∝ (1 + z ) 3/4 . Two critical quantities are related by the rate of energy cascade ε u ≈ − a c u c /[2(3 π ) 2 ], where factor 3 π is from the angle of incidence during merging. With critical velocity u c on the order of 300 km s −1 at z = 0, the critical acceleration is determined to be a c 0 ≡ a c ( z = 0) ≈ 10 −10 m s −2 , suggesting a c might explain the universal acceleration a 0 ≈ 10 −10 m s −2 in the empirical Tully–Fisher relation or modified Newtonian dynamics. The redshift evolution a c ∝ (1 + z ) 3/4 is in good agreement with Magneticum and EAGLE simulations and in reasonable agreement with limited observations. This suggests a larger a 0 at a higher redshift such that galaxies of fixed mass rotate faster at a higher redshift. Note that for dark energy (DE) density ρ DE 0 ≈ a c 0 2 / G = 1 0 − 10 J m −3 , we postulate an entropic origin of the DE from acceleration fluctuations of dark matter, analogous to the gas pressure from velocity fluctuations. This leads to a dynamical DE coupled to the structure evolution involving a relatively constant DE density followed by a slow weakening phase, suggesting possible deviations from the standard ΛCDM paradigm.

N-body simulations↗