Search NASA⌕ Search

SEARCH · Search NASA

Results for “PERTURBATION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Plasma response to rotating resonant magnetic perturbations with a locked mode in the J-TEXT tokamak

Disruption affected by locked modes (LMs) is one of the most critical issues to be solved for tokamak fusion reactors. This paper aimed to understand the plasma response to external rotating resonant magnetic perturbations (RMPs), which are applied at a few kilohertz for controlling the pre-existing LMs. In the J-TEXT tokamak, the plasma response to a rotating RMP showed a feature of travelling wave, if no tearing mode (TM) existed. With a LM, the application of a rotating RMP led to unique features of plasma responses, which could be roughly described by the formula δb θ (θ, t)=2Asin(mθ–mθ O )cos(2πf RRMP t), where δb θ , A, m, θ O and f RRMP are the perturbed poloidal magnetic field, the amplitude, the poloidal mode number, the poloidal location of the TM's O-point and the frequency of the rotating RMP. These features are analogous to that of a standing wave in the TM rest frame, with the nodes locating at the O-/X- points. The perturbations of electron temperature, T e , due to plasma responses were zero or minimal inside the magnetic island or outside the magnetic island but at the same poloidal positions as the O-/X- points. Both δb θ and the T e perturbations increased linearly with the rotating RMP. A phenomenological model is presented that the rotating RMP drives the phase oscillation of the TM by applying a periodical electromagnetic torque. Then the phase oscillation of TM, combined with the poloidal gradient of the plasma parameters, induces the plasma response measured experimentally. The nonlinear numerical modelling confirmed the forced phase oscillation of the TM, and qualitatively verified the amplitude and phase dependences among the plasma response, the phase oscillation of the TM and the rotating RMP, which have been predicted by the model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Controlling the size of non-axisymmetric magnetic footprints using resonant magnetic perturbations

The structure of the non-axisymmetric heat load distribution at the divertor plates is determined not only by the toroidal but also from the poloidal spectrum of non-axisymmetric field perturbations. Whether they are intrinsic, like error fields, or they are applied through 3D coils, the non-axisymmetric fields produce complex 3D edge magnetic topologies (footprints) that alter the properties of the heat and particle flux distributions on the divertor target plates. In this manuscript, a study of the impact of applied 3D field poloidal spectrum on the footprint size and structure is done for the DIII-D tokamak using the resistive MHD code M3D-C1 coupled with the field line tracing code TRIP3D. To resolve the impact of the poloidal spectrum of the magnetic perturbation, the relative phase of the two rows of in-vessel 3D coils used to produce both a n = 2 and a n = 3 perturbation is varied, where n is the toroidal harmonic of the magnetic perturbation. This shows that the largest footprint is predicted when the relative phase of the two rows is close to zero, which is also where the resonant coupling with the plasma is maximized. These results suggest that it will be challenging to decouple the footprint size from the requisite resonant coupling for RMP–ELM control. The correlation between the measured heat load and particle flux distributions at the outer divertor plates in DIII-D and the magnetic measurements is in good agreement with the predicted dependence of the magnetic footprint size on the amplitude of the resonant component of the plasma response.

3D fields↗
DOE OSTI2023

Resonant mode effects on rotation braking induced by n = 1 resonant magnetic perturbations in the EAST tokamak

Abstract The spectrum effects on toroidal rotation braking, induced by n = 1 resonant magnetic perturbations (RMPs) in the discharges with q 95 = 4.1 and q 95 = 5.1 , are studied in the EAST tokamak. Here n is the toroidal mode number, RMP spectrum is varied by scanning δ ϕ U L , the phase difference between the upper and lower rows of RMP coils. The toroidal rotation changes periodically with the periodic δ ϕ U L scanning and such an effect is stronger in the discharge with lower q 95 = 4.1 . The spectrum dependence of the neoclassical toroidal viscosity (NTV) torque, modeled by NTVTOK based on the magnetic perturbation obtained from MARS-F calculation, agrees well with that of the experimentally observed braking torques in both discharges. The modeled NTV torque is stronger in the discharge with lower q 95 , which also agrees with the observations. The comparisons between the spectrum dependence of the NTV and magnetic perturbations show that the resonant mode of magnetic perturbations near the plasma edge mainly contribute the NTV torque. These agreements between modeling and experiments highlight the capability of NTV theory in explaining the experimental observation in the EAST tokamak.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Active control of Alfvén eigenmodes by external magnetic perturbations with different spatial spectra

Alfvén eigenmodes have been suppressed and excited in tokamak plasmas by (just) modifying the poloidal spectra of externally applied static magnetic perturbations. This effect is observed experimentally when toroidal spectra of n = 2, n = 4 as well as a mixed spectrum of n = 2 and n = 4 is applied. Under the n = 2 magnetic perturbations, the modes are excited or suppressed by modifying the coil phasing between the upper and the lower set of coils. Regardless of the absolute rotation, an even parity for the n = 4 perturbation is observed to reduce the amplitude of the Alfvénic instabilities, while an odd parity amplifies it. To combine the stabilizing (and destabilizing) effect of n = 2 and n = 4, a mixed spectrum is applied, finding similar reduction (and amplification) trends. However, the impact on the mode amplitude is more subtle, due to the reduced coil current required for a mixed spectrum. The signal level on the fast-ion loss detector is sensitive to the applied poloidal spectrum, which is consistent with Hamiltonian full-orbit modelling of an edge resonant transport layer activated by the 3D perturbative fields. An internal redistribution of the fast-ion population is induced, modifying the phase-space gradients driving the Alfvénic instabilities, and ultimately determining their existence. The calculated edge resonant layers for both n = 2 and n = 4 toroidal spectra are consistent with the observed suppressed and excited phases. Moreover, hybrid kinetic-magnetohydrodynamic (MHD) simulations reveal that this edge resonant transport layer overlaps in phase-space with the population responsible for the fast-ion drive. The results presented here may help to control fast-ion driven Alfvénic instabilities in future burning plasmas with a significant fusion born alpha particle population.

Alfvén waves↗
DOE OSTI2021

Star formation in CALIFA survey perturbed galaxies – II. Star-formation histories and oxygen abundances

ABSTRACT Galaxy evolution is generally affected by tidal interactions. First, in this series, we reported several effects that suggest that tidal interactions contribute to the regulation of star formation (SF). To confirm this, we now compare stellar mass assembly histories and SF look-back time annular profiles between CALIFA survey tidally and non-tidally perturbed galaxies. We pair their respective star-forming regions at the closest stellar mass surface densities to reduce the influence of stellar mass. The assembly histories and annular profiles show statistically significant differences so that higher star-formation rates characterize regions in tidally perturbed galaxies. These regions underwent a more intense (re)activation of SF in the last 1 Gyr. Varying shapes of the annular profiles also reflect fluctuations between suppression and (re)activation of SF. Since gas-phase abundances used to be lower in more actively than in less actively star-forming galaxies, we further explore the plausible presence of metal-poor gas inflows able to dilute such abundances. The resolved relations of oxygen (O) abundance with stellar mass density and with total gas fraction show slightly lower O abundances for regions in tidally perturbed galaxies. The single distributions of O abundances statistically validate this. Moreover, from a metallicity model based on stellar feedback, the mass rate differentials (inflows−outflows) show statistically valid higher values for regions in tidally perturbed galaxies. These differentials, and the metal fractions from the population synthesis, suggest dominant gas inflows in these galaxies. This dominance and the differences in SF through time confirm the previously reported effects of tidal interactions on SF.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

The nature and energetics of AGN-driven perturbations in the hot gas in the Perseus Cluster

In this paper, cores of relaxed galaxy clusters are often disturbed by AGN. Their Chandra observations revealed a wealth of structures induced by shocks, subsonic gas motions, bubbles of relativistic plasma, etc. In this paper, we determine the nature and energy content of gas fluctuations in the Perseus core by probing statistical properties of emissivity fluctuations imprinted in the soft- and hard-band X-ray images. About 80 per cent of the total variance of perturbations on ~8–70 kpc scales in the core have an isobaric nature, i.e. are consistent with subsonic displacements of the gas in pressure equilibrium with the ambient medium. The observed variance translates to the ratio of energy in perturbations to thermal energy of ~13 per cent. In the region dominated by weak ‘ripples’, about half of the total variance is associated with isobaric perturbations on scales of a few tens of kpc. If these isobaric perturbations are induced by buoyantly rising bubbles, then these results suggest that most of the AGN-injected energy should first go into bubbles rather than into shocks. Using simulations of a shock propagating through the Perseus atmosphere, we found that models reproducing the observed features of a central shock have more than 50 per cent of the AGN-injected energy associated with the bubble enthalpy and only about 20 per cent is carried away with the shock. Such energy partition is consistent with the AGN-feedback model, mediated by bubbles of relativistic plasma, and supports the importance of turbulence in the cooling–heating balance.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Canalization of Phenotypes—When the Transcriptome is Constantly but Weakly Perturbed

Abstract Recent studies have increasingly pointed to microRNAs (miRNAs) as the agent of gene regulatory network (GRN) stabilization as well as developmental canalization against constant but small environmental perturbations. To analyze mild perturbations, we construct a Dicer-1 knockdown line (dcr-1 KD) in Drosophila that modestly reduces all miRNAs by, on average, ∼20%. The defining characteristic of stabilizers is that, when their capacity is compromised, GRNs do not change their short-term behaviors. Indeed, even with such broad reductions across all miRNAs, the changes in the transcriptome are very modest during development in stable environment. By comparison, broad knockdowns of other regulatory genes (esp. transcription factors) by the same method should lead to drastic changes in the GRNs. The consequence of destabilization may thus be in long-term development as postulated by the theory of canalization. Flies with modest miRNA reductions may gradually deviate from the developmental norm, resulting in late-stage failures such as shortened longevity. In the optimal culture condition, the survival to adulthood is indeed normal in the dcr-1 KD line but, importantly, adult longevity is reduced by ∼90%. When flies are stressed by high temperature, dcr-1 KD induces lethality earlier in late pupation and, as the perturbations are shifted earlier, the affected stages are shifted correspondingly. Hence, in late stages of development with deviations piling up, GRN would be increasingly in need of stabilization. In conclusion, miRNAs appear to be a solution to weak but constant environmental perturbations.

Lu, Guang-An↗
DOE OSTI2025

Probing topological phases in a perturbed Kane-Mele model via RKKY interaction: Application to monolayer jacutingaite Pt 2 ⁢HgSe 3

Quantum spin Hall insulators (QSHIs) leverage strong spin-orbit coupling (SOC) for efficient spin manipulation, making them promising for spintronics. Here, in this study, we investigate the noncollinear Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities in a perturbed Kane-Mele model with strong SOC, relevant to monolayer jacutingaite Pt 2 ⁢HgSe 3 as a prominent QSHI. Following the previous studies that mainly focused on the model and its general applications, we provide a systematic examination of the effects of various perturbations and strong spin-orbit hybridizations, which drive phase transitions that have not been extensively explored before. By incorporating these perturbations into the model and accurately accounting for spin-orbit hybridizations through spin-space Green's functions and the RKKY interactions, we uncover distinct, relative (rather than absolute) signatures of different phase transitions. These phase transitions are induced by both static and dynamic perturbations on the magnetic impurities. Notably, we identify additional phases emerging from the interplay with the magnetic substrate. All these influence the switching between ferromagnetic and antiferromagnetic, as well as clockwise and counterclockwise magnetic interactions. Our results provide a practical way to track topological phases through magnetic properties, offering new insights into phase control and spin manipulation in QSHIs.

Kane-Mele model↗
DOE OSTI2022

Perturbative approaches in relativistic kinetic theory and the emergence of first-order hydrodynamics

Hydrodynamics can be formulated in terms of a perturbative series in derivatives of the temperature, chemical potential, and flow velocity around an equilibrium state. Different formulations for this series have been proposed over the years, which consequently led to the development of various hydrodynamic theories. In this work, we discuss the relativistic generalizations of the perturbative expansions put forward by Chapman and Enskog, and Hilbert, using general matching conditions in kinetic theory. This allows us to describe, in a comprehensive way, how different out-of-equilibrium definitions for the hydrodynamic fields affect the development of the hydrodynamic perturbative series. We provide a perturbative method for systematically deriving the hydrodynamic formulation recently proposed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK) from relativistic kinetic theory. The various transport coefficients that appear in BDNK (at first-order) are explicitly computed using a new formulation of the relaxation time approximation for the Boltzmann equation. Assuming Bjorken flow, we also determine the hydrodynamic attractors of BDNK theory and compare the overall hydrodynamic evolution obtained using this formulation with that generated by the Israel-Stewart equations of motion and also kinetic theory.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Perturbative quantum evolution of the gravitational state and dressing in general backgrounds

This paper sets up a perturbative treatment of the evolving quantum state of a gravitational system, in a Schrödinger-like picture, working about a general background. This connects gauge symmetry, the constraints, gravitational dressing, and evolution. Starting with a general time slicing, we give a simple derivation of the relation between the constraints, the Hamiltonian, and its well-known boundary term. Among different approaches to quantization with constraints, we focus on a “gauge-invariant canonical quantization,” which is developed perturbatively in the gravitational coupling. The leading-order solution of the constraints (including the Wheeler-DeWitt equation) for perturbations about the background is given in terms of an explicit construction of gravitational dressings built using certain generalized Green’s functions; different such dressings corresponding to adding propagating gravitational waves to a particular solution of the constraints. Dressed operators commute with the constraints, expressing their gauge invariance, and have an algebraic structure differing significantly from the undressed operators of the underlying field theory. These operators can act on the vacuum to create dressed states, and evolution of general such states is then generated by the boundary Hamiltonian, and alternately may be characterized using other relational observables. This provides a concrete approach to studying perturbative time evolution, including the leading gravitational backreaction, of quantum states of black holes with flat or anti–de-Sitter asymptotics, for example on horizon-crossing slices. This description of evolution in turn provides a starting point for investigating possibly important corrections to quantum evolution, that go beyond quantized general relativity. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Generalized perturbations in neutrino mixing

We derive here expressions for the neutrino mixing parameters that result from complex perturbations on (1) the Majorana neutrino mass matrix (in the basis of charged lepton mass eigenstates) and on (2) the charged lepton mass matrix, for arbitrary initial (unperturbed) mixing matrices. In the first case, we find that the phases of the elements of the perturbation matrix, and the initial values of the Dirac and Majorana phases, strongly impact the leading order corrections to the neutrino mixing parameters and phases. For experimentally compatible scenarios wherein the initial neutrino mass matrix has μ-τ symmetry, we discovef that the Dirac phase can take any value under small perturbations. Similarly, in the second case, perturbations to the charged lepton mass matrix can generate large corrections to the mixing angles and phases of the PMNS matrix. As an demonstration of our generalized procedure, we apply it to a situation in which nonstandard scalar and nonstandard vector interactions simultaneously affect neutrino oscillations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Three-dimensional simulations of reshocked inclined Richtmyer-Meshkov instability: Effects of initial perturbations

The effect of initial perturbations on the evolution of the inclined Richtmyer-Meshkov turbulent mixing layer before and after reshock initiated by a shock wave with Mach number 1.55 is investigated through three-dimensional (3D) simulations using the flash code. The 3D simulations aim to reproduce both predominantly single-mode and multimode interfaces between light and heavy gases (N 2 -CO 2 , Atwood number, A≈0.22; amplitude to wavelength ratio of 0.088) which were created in an inclined shock tube facility to analyze the effects of initial conditions on mixing development in the entire flow field. The two-dimensional center slices of 3D simulations are compared with the experimental results to validate the computational code. Mixing width, mixed mass, mixed-mass thickness, and circulation in addition to concentration fields are shown to be in good agreement with the experimental data. The three-dimensional density and vorticity fields are first presented to qualitatively describe the flow behavior before and after reshock. Several measured density/velocity-related quantities indicate that the growth of the mixing material is strongly dependent on initial conditions. Before reshock and at early times after reshock, flow is clearly maintaining the memory of initial perturbations. However, at late time after reshock, although the large wavelength feature still dominates the flow motion, and the morphology of the two different interfaces indicates several differences, by breakdown of large-scale coherent structures to much finer scales, the memory of small scales of the multimode initial perturbation is not as clear as pre-reshock. Regarding three-dimensionality of the flow, before reshock in the multimode case, the baroclinic vorticity production, circulation, turbulent kinetic energy, and turbulent mass flux suggest that the small-scale roll-up features along the large inclined wavelength quickly evolves in all three dimensions. The coherent vortex tubes break down to smaller wormlike vortex structures, and turbulent fluctuations in the out-of-plane dimension are comparable to the spanwise direction. After reshock, this three-dimensionality of mixing growth was observed in the flow for both initial conditions. The results of this work represent a significant extension of previous computational studies performed on this specific topic. A different code with a different numerical method is validated through comparison with the experimental data. The initial perturbations are directly measured from the experimental results. Moreover, the entire three-dimensional experimental shock tube domain is simulated, and more quantities are investigated to understand the mixing mechanism and instability evolution in all three dimensions.

42 ENGINEERING↗
DOE OSTI2022

Perturbative Quantum Monte Carlo Method for Nuclear Physics

While first order perturbation theory is routinely used in quantum Monte Carlo (QMC) calculations, higher-order terms present significant numerical challenges. We present a new approach for computing perturbative corrections in projection QMC calculations. Here we demonstrate the method by computing nuclear ground state energies up to second order for a realistic chiral interaction. We calculate the binding energies of several light nuclei up to 16 O by expanding the Hamiltonian around the Wigner SU(4) limit and find good agreement with data. In contrast to the natural ordering of the perturbative series, we find remarkably large second-order energy corrections. This occurs because the perturbing interactions break the symmetries of the unperturbed Hamiltonian. Our method is free from the sign problem and can be applied to QMC calculations for many-body systems in nuclear physics, condensed matter physics, ultracold atoms, and quantum chemistry.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

SU-E-T-609: Perturbation Effects of Pedicle Screws On Radiotherapy Dose Distributions

Purpose: Radiation therapy in conjunction with surgical implant fixation is a common combined treatment in case of bone metastases. However, metal implants generally used in orthopedic implants perturb radiation dose distributions. Carbon-Fiber Reinforced (CFR) PEEK material has been recently introduced for production of intramedullary screws and plates. Gold powder can be added to the CFR-PEEK material in order to enhance visibility of the screws during intraoperative imaging procedures. In this work, we investigated the perturbation effects of the pedicle screws made of CFR-PEEK, CFR-PEEK with added gold powder (CFR-PEEK-AU) and Titanium (Ti) on radiotherapy dose distributions. Methods: Monte Carlo (MC) simulations were performed using the EGSnrc code package for 6MV beams with 10×10 fields at SSD=100cm. By means of MC simulations, dose distributions around titanium, CFR- PEEK and CFR-PEEK-AU screws (manufactured by Carbo-Fix Orthopedics LTD, Israel) placed in a water phantom were calculated. The screw axis was either parallel or perpendicular to the beam axis. Dose perturbation (relative to dose in homogeneous water phantom) was assessed. Results: Maximum overdose due to backscatter was 10% for the Ti screws, 5% for the CFR-PEEK-AU screws and effectively zero for the CFR-PEEK screws. Maximum underdose due to attenuation was 25% for the Ti screws, 15% for the CFR-PEEK-AU screws and 5% for the CFR-PEEK screws. Conclusion: Titanium screws introduce the largest distortion on the radiation dose distribution. The gold powder added to the CFR-PEEK material improves visibility at the cost of increased dose perturbation. CFR-PEEK screws caused minimal alteration on the dose distribution. This can decrease possible over and underdose of adjacent tissue and thus favorably influence treatment efficiency. The use of such implants has potential clinical advantage in the treatment of neoplastic bone disease.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2020

Logarithmic enhancements in conformal perturbation theory and their real time interpretation

We study various corrections of correlation functions to leading order in conformal perturbation theory, both on the cylinder and on the plane. Many problems on the cylinder are mathematically equivalent to those in the plane if we give the perturbations a position dependent scaling profile. The integrals to be done are then similar to those in the study of correlation functions with one additional insertion at the center of the profile. We will be primarily interested in the divergence structure of these corrections when computed in dimensional regularization. In particular, we show that the logarithmic divergences (enhancements) that show up in the plane under these circumstances can be understood in terms of resonant behavior in time dependent perturbation theory, for a transition between states that is induced by an oscillatory perturbation on the cylinder.

Physics↗
DOE OSTI2021

A Verification of Flux Sensitivity Estimates Using the MCNP Tally Perturbation Tool

Nuclear data is commonly used in applications such as nuclear nonproliferation, safeguards, and criticality safety. More specifically, nuclear data is used in predictive simulation codes like the Monte-Carlo N-Particle (MCNP ® ) transport code, Serpent, and similar radiation transport codes. The improvement of nuclear data enables more precise and accurate simulations, which result in higher fidelity designs and reduced operational/procedural costs. Therefore, the improvement of nuclear data is of paramount importance across the nuclear community. Nuclear data is improved and validated through integral benchmark experiments. The design of benchmark experiments is an extensive process; therefore, these experiments are often optimized on multiple characteristics, including sensitivity to the nuclear data, during the design process. Sensitivity is a measure of how much a quantity changes due to changes in independent variables such as experimental configuration. An experimental design that has a larger sensitivity to the nuclear data of interest will have a larger impact on the accuracy and precision of the validated data. Past integral benchmark experiments have primarily used the effective multiplication factor ($k_{eff}$) as the predominant measured quantity; however, experiments designed with other quantities in mind would be able to optimize on validating different areas of the nuclear data. A primary goal of the EUCLID project is to design, constrain, and reduce compensating errors in experiments focused on quantities other than $k_{eff}$ to better validate nuclear data across the board. Currently, there is a capability in MCNP to easily calculate the sensitivity of $k_{eff}$ to specific nuclear data of numerous reactions types and isotopes (KSEN card); however, the sensitivity of other quantities must be estimated in more strenuous manners. For example, the perturbation feature (PERT card) of MCNP can be used to estimate first-order sensitivities of some response in fixed source simulations. A recent announcement revealed that the first- and second-order perturbation features in previous releases of MCNP contained a bug. It was identified that particles were being scored into the wrong energy bin. The bug is in the most recent public release (MCNP6.2); however, a patch has been added to the most up to date version (MCNP6.2.2) that has not been released publicly. A direct comparison of the PERT card results for an F4 (neutron flux averaged over a cell) tally before and after the patch are shown in figure 1. All simulations used in the sensitivity estimates in this report were performed with MCNP6.2.2. This work verifies the patched MCNP perturbation tool by comparing first order sensitivities made using the PERT card to estimates made using manual perturbation of the compact ENDF (ACE) files.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Historical Contingency in Microbial Resilience to Hydrologic Perturbations

Development of reliable biogeochemical models requires a mechanistic consideration of microbial interactions with hydrology. Microbial response to and its recovery after hydrologic perturbations (i.e., resilience) is a critical component to understand in this regard, but generally difficult to predict because the impacts of future events can be dependent on the history of perturbations (i.e., historical contingency). Fundamental issues underlying this phenomenon include how microbial resilience to hydrologic perturbations is influenced by historical contingency and how their relationships vary depending on the characteristics of microbial functions. To answer these questions, we considered a simple microbial community composed of two species that redundantly consume a common substrate but specialize in producing distinct products and developed a continuous flow reactor model where the two species grow with trade-offs along the flow rate. Simulations of this model revealed that (1) the history of hydrologic perturbations can lead to the shifts in microbial populations, which consequently affect the community's functional dynamics, and (2) while historical contingency in resilience was consistently predicted for all microbial functions, it was more pronounced for specialized functions, compared to the redundant function. As a signature of historical contingency, our model also predicted the emergence of hysteresis in the transitions across conditions, a critical aspect that can affect transient formation of intermediate compounds in biogeochemistry. This work presents microbial growth traits and their functional redundancy or specialization as fundamental factors that control historical contingencies in resilience.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

A Canonical Transformation to Eliminate Resonant Perturbations. I

We study dynamical systems that admit action-angle variables at leading order, which are subject to nearly resonant perturbations. If the frequencies characterizing the unperturbed system are not in resonance, the long-term dynamical evolution may be integrated by orbit-averaging over the high-frequency angles, thereby evolving the orbit-averaged effect of the perturbations. It is well known that such integrators may be constructed via a canonical transformation, which eliminates the high-frequency variables from the orbit-averaged quantities. An example of this algorithm in celestial mechanics is the von Zeipel transformation. However, if the perturbations are inside or close to a resonance, i.e., the frequencies of the unperturbed system are commensurate; these canonical transformations are subject to divergences. We introduce a canonical transformation that eliminates the high-frequency phase variables in the Hamiltonian without encountering divergences. This leads to a well-behaved symplectic integrator. We demonstrate the algorithm through two examples: a resonantly perturbed harmonic oscillator and the gravitational three-body problem in mean motion resonance.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗