Self-consistent Feedback Research Articles

Second-order phase transitions and divergent linear response in dynamical mean-field theory

Second-order phase transitions appear as a divergence in one of the linear response functions. For a system of correlated electrons, the relevant divergent response can and does involve many-particle observables, most famously the double occupancy. Generally, evaluating the linear response function of many-particle observables requires a many-particle generalization of the Bethe-Salpeter equation. However, here I show that the divergence of linear response functions in dynamical mean-field theory is governed by a -particle Bethe-Salpeter equation, even for many-particle observables. The reason for this is that the divergence at the second-order phase transition is produced by the self-consistent feedback of the dynamical mean field. Published by the American Physical Society 2024

Therapist verification of patient self-concepts as a responsive precondition for early alliance development and subsequent introject change

Objective Social psychological research has indicated that people strive for self-consistent feedback and interactions, even if negative, to preserve the epistemic security of knowing themselves. Without such self-verification, any interpersonal exchange may become frustrated, anxiety-riddled, and at risk for deterioration. Thus, it may be important for therapists to meet patients’ self-verification needs as a responsive precondition for early alliance establishment and development. We tested this hypothesis with patients receiving cognitive behavioral therapy for generalized anxiety disorder—a condition that may render one’s self-verification needs especially strong. We also tested the hypothesis that better early alliance quality would relate to subsequent adaptive changes in and posttreatment level of patients’ self-concepts. Method Eighty-four patients rated their self-concepts at baseline and across treatment and follow-up, their postsession recollection of their therapist’s interpersonal behavior toward them during session 2, and their experience of alliance quality rated after sessions 3–6. Results As predicted, the more therapists verified at session 2 a patient’s baseline self-concepts (which trended toward disaffiliative and overcontrolling, on average), the more positively that patient perceived their next-session alliance. Moreover, better session 3 alliance related to more adaptive affiliative and autonomy-granting self-concepts at posttreatment. Conclusion Results are discussed within a therapist responsiveness framework.

Temperature–chemistry coupling in the evolution of gas giant atmospheres driven by stellar flares

ABSTRACT The effect of enhanced UV irradiation associated with stellar flares on the atmospheric composition and temperature of gas giant exoplanets was investigated. This was done using a 1D radiative-convective-chemical model with self-consistent feedback between the temperature and the non-equilibrium chemistry. It was found that flare-driven changes to chemical composition and temperature give rise to prolonged trends in evolution across a broad range of pressure levels and species. Allowing feedback between chemistry and temperature plays an important role in establishing the quiescent structure of these atmospheres, and determines their evolution due to flares. It was found that cooler planets are more susceptible to flares than warmer ones, seeing larger changes in composition and temperature, and that temperature–chemistry feedback modifies their evolution. Long-term exposure to flares changes the transmission spectra of gas giant atmospheres; these changes differed when the temperature structure was allowed to evolve self-consistently with the chemistry. Changes in spectral features due to the effects of flares on these atmospheres can be associated with changes in composition. The effects of flares on the atmospheres of sufficiently cool planets will impact observations made with JWST. It is necessary to use self-consistent models of temperature and chemistry in order to accurately capture the effects of flares on features in the transmission spectra of cooler gas giants, but this depends heavily on the radiation environment of the planet.

Parametric instability in warped astrophysical discs: growth, saturation, and feedback

ABSTRACT Attempts to understand the dynamics of warped astrophysical discs have garnered significant attention, largely motivated by the growing catalogue of observed distorted systems. Previous studies have shown that the evolution of the warp is crucially regulated by the internal flow fields established by the undulating geometry. These are typically modelled as laminar horizontal, shearing flows which oscillate back and forth at approximately the orbital frequency. However this shearing motion is known to be susceptible to a hydrodynamic, parametric instability of inertial waves which might modify the warped dynamics. Whilst the linear growth phase is well understood, the subsequent non-linear saturation combined with the self-consistent feedback onto the warp has not been studied. In this work, we implement a novel numerical setup using the recent ring model framework of Fairbairn and Ogilvie, within the Lagrangian code gizmo. We formally identify several locally growing modes in the simulation, as predicted by a three-mode coupling analysis of the instability, and find decent agreement with the theoretical growth rates. We understand the saturation mechanism as a wave breaking process which suppresses the growth of shorter wavelength parametric couplings first, whilst allowing the longest mode to dominate the final quasi-steady, wave-like turbulence. The Reynolds stresses, transporting energy from the warp to the small scales, can be effectively modelled using a time-dependent, anisotropic viscous alpha model which closely captures the amplitude and phase evolution of the warp. Consequently, this model might help inform future global studies which are commonplace but typically do not resolve the parametric instability.

The signature of large-scale turbulence driving on the structure of the interstellar medium

ABSTRACT The mechanisms that maintain turbulence in the interstellar medium (ISM) are still not identified. This work investigates how we can distinguish between two fundamental driving mechanisms: the accumulated effect of stellar feedback versus the energy injection from galactic scales. We perform a series of numerical simulations describing a stratified star-forming ISM subject to self-consistent stellar feedback. Large-scale external turbulent driving, of various intensities, is added to mimic galactic driving mechanisms. We analyse the resulting column density maps with a technique called Multi-scale non-Gaussian segmentation, which separates the coherent structures and the Gaussian background. This effectively discriminates between the various simulations and is a promising method to understand the ISM structure. In particular, the power spectrum of the coherent structures flattens above 60 pc when turbulence is driven only by stellar feedback. When large-scale driving is applied, the turn-over shifts to larger scales. A systematic comparison with the Large Magellanic Cloud (LMC) is then performed. Only 1 out of 25 regions has a coherent power spectrum that is consistent with the feedback-only simulation. A detailed study of the turn-over scale leads us to conclude that regular stellar feedback is not enough to explain the observed ISM structure on scales larger than 60 pc. Extreme feedback in the form of supergiant shells likely plays an important role but cannot explain all the regions of the LMC. If we assume ISM structure is generated by turbulence, another large-scale driving mechanism is needed to explain the entirety of the observations.

Nature of Phase Transitions (Role of the Self-Consistent Feedback in the Evolution of Material Structures)

Nature of Phase Transitions (Role of the Self-Consistent Feedback in the Evolution of Material Structures)

The Environmental Dependence of the XCO Conversion Factor

Abstract is the most widely used observational tracer of molecular gas. The observable luminosity is translated to mass via a conversion factor, , which is a source of uncertainty and bias. Despite variations in , the empirically determined solar neighborhood value is often applied across different galactic environments. To improve understanding of , we employ 3D magnetohydrodynamics simulations of the interstellar medium (ISM) in galactic disks with a large range of gas surface densities, allowing for varying metallicity, far-ultraviolet (FUV) radiation, and cosmic-ray ionization rate (CRIR). With the TIGRESS simulation framework we model the three-phase ISM with self-consistent star formation and feedback, and post-process outputs with chemistry and radiation transfer to generate synthetic CO (1–0) and (2–1) maps. Our models reproduce the observed CO excitation temperatures, line widths, and line ratios in nearby disk galaxies. decreases with increasing metallicity, with a power-law slope of −0.8 for the (1–0) line and −0.5 for the (2–1) line. also decreases at higher CRIR and is insensitive to the FUV radiation. As density increases, first decreases owing to increasing excitation temperature and then increases when the emission is fully saturated. We provide fits between and observable quantities such as the line ratio, peak antenna temperature, and line brightness, which probe local gas conditions. These fits, which allow for varying beam size, may be used in observations to calibrate out systematic biases. We also provide estimates of the CO-dark fraction at different gas surface densities, observational sensitivities, and beam sizes.

Prospectus on electron acceleration via magnetic reconnection

Many explosive plasma phenomena are powered by magnetic reconnection. Striking evidence of such events is found in short bursts of radiation from energetic electrons with energies much larger than what is typical of the ambient medium. Reconnection is a fundamentally multi-scale process that couples the global scale over which energy accumulates with small-scale dissipation. These macro- and micro-scales are bridged by a mesoscale of coherent magnetic structures that facilitate rapid energy conversion. Although there are many channels by which reconnection may release magnetic energy, a guiding-center approach distills electron energy gain into three basic mechanisms: parallel electric fields, Fermi reflection, and betatron acceleration. An efficient mechanism must scale strongly with the particle energy and operate over a globally significant region. These criteria favor the Fermi mechanism, which operates in volume-filling plasmoids. The guide field plays a critical role, facilitating three-dimensional transport that enables high-energy particles to continuously access acceleration sites, yet suppressing acceleration if the guide field is much larger than the reconnecting field. Open issues include the conditions necessary for power-law formation, the roles of scattering and plasma compression, and differences between the relativistic and nonrelativistic regimes. New high-resolution observations in the earth's magnetosphere offer a timely opportunity to test the predictions of numerical studies. On the other hand, understanding solar flares, where the global and dissipative scales are separated by many orders of magnitude, requires hybrid models that incorporate both the global evolution of the magnetic field and the self-consistent acceleration and feedback of energetic particles.

Superfluidity and pairing phenomena in ultracold atomic Fermi gases in one-dimensional optical lattices. I. Balanced case

The superfluidity and pairing phenomena in ultracold atomic Fermi gases have been of great interest in recent years, with multiple tunable parameters. Here we study the BCS-BEC crossover behavior of balanced two-component Fermi gases in a one-dimensional optical lattice, which is distinct from the simple three-dimensional (3D) continuum and a fully 3D lattice often found in a condensed matter system. We use a pairing fluctuation theory which includes self-consistent feedback effects at finite temperatures, and find widespread pseudogap phenomena beyond the BCS regime. As a consequence of the lattice periodicity, the superfluid transition temperature $T_c$ decreases with pairing strength in the BEC regime, where it approaches asymptotically $T_c = \pi an/2m$, with $a$ being the $s$-wave scattering length, and $n$ ($m$) the fermion density (mass). In addition, the quasi-two dimensionality leads to fast growing (absolute value of the) fermionic chemical potential $\mu$ and pairing gap $\Delta$, which depends exponentially on the ratio $d/a$. Importantly, $T_c$ at unitarity increases with the lattice constant $d$ and hopping integral $t$. The effect of the van Hove singularity on $T_c$ is identified. The superfluid density exhibits $T^{3/2}$ power laws at low $T$, away from the extreme BCS limit. These predictions can be tested in future experiments.

Self-consistent feedback mechanism for the sudden viscous dissipation of finite-Mach-number compressing turbulence.

Previous work [Davidovits and Fisch, Phys. Rev. Lett. 116, 105004 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.105004] demonstrated that the compression of a turbulent field can lead to a sudden viscous dissipation of turbulent kinetic energy (TKE), and that paper suggested this mechanism could potentially be used to design new fast-ignition schemes for inertial confinement fusion (ICF). We expand on previous work by accounting for finite Mach numbers, rather than relying on a zero-Mach-limit assumption as previously done. The finite-Mach-number formulation is necessary to capture a self-consistent feedback mechanism in which dissipated TKE increases the temperature of the system, which in turn modifies the viscosity and thus the TKE dissipation itself. Direct numerical simulations with a tenth-order accurate Padé scheme were carried out to analyze this self-consistent feedback loop for compressing turbulence. Results show that, for finite Mach numbers, the sudden viscous dissipation of TKE still occurs, for both the solenoidal and dilatational turbulent fields. As the domain is compressed, oscillations in dilatational TKE are encountered due to the highly oscillatory nature of the pressure dilatation. An analysis of the source terms for the internal energy shows that the mechanical-work term dominates the viscous turbulent dissipation. As a result, the effect of the suddenly dissipated TKE on temperature is minimal for the Mach numbers tested. Moreover, an analytical expression is derived that confirms the dissipated TKE does not significantly alter the temperature evolution for low Mach numbers, regardless of compression speed. The self-consistent feedback mechanism is thus quite weak for subsonic turbulence, which could limit its applicability for ICF.

Unified quantum theory of elastic and inelastic atomic scattering from a physisorbed monolayer solid

A unified quantum theory of the elastic and inelastic scattering of low energy He atoms by a physisorbed monolayer solid in the one-phonon approximation is given. It uses a time-dependent wave packet with phonon creation and annihilation components and has a self-consistent feedback between the wave functions for elastic and inelastic scattered atoms. An attenuation of diffraction scattering by inelastic processes thus is inherent in the theory. The atomic motion and monolayer vibrations in the harmonic approximation are treated quantum mechanically and unitarity is preserved. The evaluation of specific one-phonon events includes contributions from diffuse inelastic scattering in other phonon modes. Effects of thermally excited phonons are included using a mean field approximation. The theory is applied to an incommensurate Xe/Pt(111) monolayer (incident energy ${E}_{i}=4--16$ meV), a commensurate Xe/graphite monolayer (${E}_{i}\ensuremath{\simeq}64$ meV), and an incommensurate Xe/Cu(001) monolayer (${E}_{i}\ensuremath{\simeq}8$ meV). The monolayers are very corrugated targets and there are transient closed diffraction and inelastic channels in the calculations. In many cases, the energy gain events have strengths comparable to the energy loss events.

Drifting States and Synchronization Induced Chaos in Autonomous Networks of Excitable Neurons.

The study of balanced networks of excitatory and inhibitory neurons has led to several open questions. On the one hand it is yet unclear whether the asynchronous state observed in the brain is autonomously generated, or if it results from the interplay between external drivings and internal dynamics. It is also not known, which kind of network variabilities will lead to irregular spiking and which to synchronous firing states. Here we show how isolated networks of purely excitatory neurons generically show asynchronous firing whenever a minimal level of structural variability is present together with a refractory period. Our autonomous networks are composed of excitable units, in the form of leaky integrators spiking only in response to driving currents, remaining otherwise quiet. For a non-uniform network, composed exclusively of excitatory neurons, we find a rich repertoire of self-induced dynamical states. We show in particular that asynchronous drifting states may be stabilized in purely excitatory networks whenever a refractory period is present. Other states found are either fully synchronized or mixed, containing both drifting and synchronized components. The individual neurons considered are excitable and hence do not dispose of intrinsic natural firing frequencies. An effective network-wide distribution of natural frequencies is however generated autonomously through self-consistent feedback loops. The asynchronous drifting state is, additionally, amenable to an analytic solution. We find two types of asynchronous activity, with the individual neurons spiking regularly in the pure drifting state, albeit with a continuous distribution of firing frequencies. The activity of the drifting component, however, becomes irregular in the mixed state, due to the periodic driving of the synchronized component. We propose a new tool for the study of chaos in spiking neural networks, which consists of an analysis of the time series of pairs of consecutive interspike intervals. In this space, we show that a strange attractor with a fractal dimension of about 1.8 is formed in the mentioned mixed state.

Self-consistent nonlocal feedback theory for electrocatalytic swimmers with heterogeneous surface chemical kinetics.

We present a self-consistent nonlocal feedback theory for the phoretic propulsion mechanisms of electrocatalytic micromotors or nanomotors. These swimmers, such as bimetallic platinum and gold rods catalyzing decomposition of hydrogen peroxide in aqueous solution, have received considerable theoretical attention. In contrast, the heterogeneous electrochemical processes with nonlocal feedback that are the actual "engines" of such motors are relatively neglected. We present a flexible approach to these processes using bias potential as a control parameter field and a locally-open-circuit reference state, carried through in detail for a spherical motor. While the phenomenological flavor makes meaningful contact with experiment easier, required inputs can also conceivably come from, e.g., Frumkin-Butler-Volmer kinetics. Previously obtained results are recovered in the weak-heterogeneity limit and improved small-basis approximations tailored to structural heterogeneity are presented. Under the assumption of weak inhomogeneity, a scaling form is deduced for motor speed as a function of fuel concentration and swimmer size. We argue that this form should be robust and demonstrate a good fit to experimental data.

Runaway electrons from a ‘beam-bulk’ model of streamer: application to TGFs

The generation of x- and gamma-rays in atmospheric discharges has been studied intensively since the discovery of terrestrial gamma-ray flashes (TGFs) by the Compton gamma-ray Observatory in 1991. Emissions are bremsstrahlung from high energy particles accelerated in large scale atmospheric electric fields associated with thunderstorms. Whereas observations now are many, both from lightning and the laboratory, the phases of the discharge where emissions are generated are still debated and several processes for electron acceleration have been put forward by theorists. This paper address the electron acceleration in streamer region of lightning. We present the first ‘beam-bulk’ model of self-consistent streamer dynamics and electron acceleration. The model combines a Monte Carlo Collision code that simulates the high-energy electrons (100 eV) and a fluid code that simulates the bulk of the low-energy electrons and ions. For a negative streamer discharge, we show how electrons are accelerated in the large electric field in the tip of the streamer and travel ahead of the streamer where they ionize the gas. In comparison to the results obtained with a classical fluid model for a negative streamer, the beam-bulk model predicts a decrease of the magnitude of the peak electric field and an increase of the streamer velocity. Furthermore, we show that a significant number of runaway electrons is lost by diffusion outside of the streamer tip. The results presented here do not yet include extra amplification nor acceleration far away from the streamer to explain the electron energies seen in TGFs. Still, in the light of those results, we emphasize that the production of runaway electrons from streamers needs to be simulated including the self-consistent feedback of runaways on the streamer. Simulations with a beam-bulk model may not only help to understand the fundamental atmospheric processes behind TGFs, but also pave the way for the interpretation of remote sensing of the most energetic discharges in the Earthʼs atmosphere and thus help to address their environmental impact.

Spin-up of a two-component superfluid: self-consistent container feedback

AbstractThe coupled dynamic response of a rigid container filled with a two-component superfluid undergoing Ekman pumping is calculated self-consistently. The container responds to the back-reaction torque exerted by the viscous component of the superfluid and an arbitrary external torque. The resulting motion is described by a pair of coupled integral equations for which solutions are easily obtained numerically. If the container is initially accelerated impulsively then set free, it relaxes quasi-exponentially to a steady state over multiple time scales, which are a complex combination of the Ekman number, superfluid mutual friction coefficients, the superfluid density fraction, and the varying hydrodynamic torque at different latitudes. The spin-down of containers with relatively small moments of inertia (compared with that of the contained fluid) depends weakly on the above parameters and occurs faster than the Ekman time. When the fluid components are initially differentially rotating, the container can ‘overshoot’ its asymptotic value before increasing again. When a constant external torque is applied, the superfluid components rotate differentially and non-uniformly in the long term. For an oscillating external torque, the amplitude and phase of the oscillation are most sensitive to the driving frequency for containers with relatively small moments of inertia. Applications to superfluid helium experiments and neutron stars are also discussed.

THE POWER-LAW SPECTRA OF ENERGETIC PARTICLES DURING MULTI-ISLAND MAGNETIC RECONNECTION

Power-law distributions are a near universal feature of energetic particle spectra in the heliosphere. Anomalous Cosmic Rays (ACRs), super-Alfv\'enic ions in the solar wind and the hardest energetic electron spectra in flares all have energy fluxes with power-laws that depend on energy $E$ approximately as $E^{-1.5}$. We present a new model of particle acceleration in systems with a bath of merging magnetic islands that self-consistently describes the development of velocity-space anisotropy parallel and perpendicular to the local magnetic field and includes the self-consistent feedback of pressure anisotropy on the merging dynamics. By including pitch-angle scattering we obtain an equation for the omni-directional particle distribution $f(v,t)$ that is solved in closed form to reveal $v^{-5}$ (corresponding to an energy flux varying as $E^{-1.5}$) as a near-universal solution as long as the characteristic acceleration time is short compared with the characteristic loss time. In such a state the total energy in the energetic particles reaches parity with the remaining magnetic free energy. More generally, the resulting transport equation can serve as the basis for calculating the distribution of energetic particles resulting from reconnection in large-scale inhomogeneous systems.

Steady-state spectra, current, and stability diagram of a quantum dot: A nonequilibrium variational cluster approach

We calculate steady-state properties of a strongly correlated quantum dot under voltage bias by means of non-equilibrium Cluster Perturbation Theory and the non-equilibrium Variational Cluster Approach, respectively. Results for the steady-state current are benchmarked against data from accurate Matrix Product State based time evolution. We show that for low to medium interaction strength, non-equilibrium Cluster Perturbation Theory already yields good results, while for higher interaction strength the self-consistent feedback of the non-equilibrium Variational Cluster Approach significantly enhances the accuracy. We report the current-voltage characteristics for different interaction strengths. Furthermore we investigate the non-equilibrium local density of states of the quantum dot and illustrate that within the variational approach a linear splitting and broadening of the Kondo resonance is predicted which depends on interaction strength. Calculations with applied gate voltage, away from particle hole symmetry, reveal that the maximum current is reached at the crossover from the Kondo regime to the doubly-occupied or empty quantum dot. Obtained stability diagrams compare very well to recent experimental data [Phys. Rev. B, 84, 245316 (2011)].

Coupling the atmosphere with interior dynamics: Implications for the resurfacing of Venus

We calculated 2D and 3D mantle convection models for Venus using digitized atmosphere temperatures from the model of Bullock and Grinspoon (Bullock, M.A., Grinspoon, D.H. [2001]. Icarus 150, 19–37) to study the interaction between interior dynamics and atmosphere thermal evolution. The coupling between atmosphere and interior occurs through mantle degassing and the effect of varying concentrations of the greenhouse gas H 2O on the surface temperature. Exospheric loss of hydrogen to space is accounted for as a H 2O sink. The surface temperature enters the mantle convection model as a boundary condition. Our results suggest a self-consistent feedback mechanism between the interior and the atmosphere resulting in spatial–temporal surface renewal. Greenhouse warming of the atmosphere results in an increase in the surface temperature. Whenever the surface temperature reaches a critical value, the viscosity difference across the lithosphere becomes smaller than about 10 5 and the surface becomes locally mobile. The critical surface temperature depends on the activation energy for mantle creep, the stress exponent in the non-Newtonian mantle rheology law, and the mantle temperature. Surface renewal together with surface lava flow may explain why the surface of Venus is young on average, i.e. not older than a few hundred million years. The mobilization of the near-surface lithosphere increases the rate of heat removal from the mantle and thereby the interior cooling rate. The enhanced cooling results in a reduction of the water outgassing rates. As a consequence of decreasing water concentrations in the atmosphere, the surface temperature decreases. Our model calculations suggest that Venus should have been geologically active until recently. This is in agreement with several lines of observational evidence from thermal emissivity measurements and crater distribution analyses.

Retracted: When failure feels better than success: Self-salience, self-consistency, and affect

People like self-consistent feedback because it induces feelings of predictability and control, but they like positive feedback because it induces positive self-esteem. We show that self-salience determines whether people are more consistency- or positivity-driven. When self-knowledge is salient, people's primary responses (i.e., under load) are consistency-driven (people with low self-esteem feel better after negative feedback than after positive feedback, whereas people with high self-esteem feel better after positive feedback than after negative feedback) and controlled responses are positivity-driven (people feel better after positive feedback than after negative feedback, regardless of self-consistency). Without salient self-knowledge this pattern reverses: people's primary responses are positivity-driven, whereas people's controlled responses are consistency-driven.

Coupled Land–Atmosphere Intraseasonal Variability of the West African Monsoon in a GCM

Abstract Recent observational studies have suggested a role for soil moisture and land–atmosphere coupling in the 15-day westward-propagating mode of intraseasonal variability in the West African monsoon. This hypothesis is investigated with a set of three atmospheric general circulation model experiments. 1) When soil moisture is fully coupled with the atmospheric model, the 15-day mode of land–atmosphere variability is clearly identified. Precipitation anomalies lead soil moisture anomalies by 1–2 days, similar to the results from satellite observations. 2) To assess whether soil moisture is merely a passive response to the precipitation, or an active participant in this mode, the atmospheric model is forced with a 15-day westward-propagating cycle of regional soil moisture anomalies based on the fully coupled mode. Through a reduced surface sensible heat flux, the imposed wet soil anomalies induce negative low-level temperature anomalies and increased pressure (a cool high). An anticyclonic circulation then develops around the region of wet soil, enhancing northward moisture advection and precipitation to the west. Hence, in a coupled framework, this soil moisture–forced precipitation response would provide a self-consistent positive feedback on the westward-propagating soil moisture anomaly and implies an active role for soil moisture. 3) In a final sensitivity experiment, soil moisture is again externally prescribed but with all intraseasonal fluctuations suppressed. In the absence of soil moisture variability there are still pronounced surface sensible heat flux variations, likely due to cloud changes, and the 15-day westward-propagating precipitation signal is still present. However, it is not as coherent as in the previous experiments when interaction with soil moisture was permitted. Further examination of the soil moisture forcing experiment in GCM experiment 2 shows that this precipitation mode becomes phase locked to the imposed soil moisture anomalies. Hence, the 15-day westward-propagating mode in the West African monsoon can exist independently of soil moisture; however, soil moisture and land–atmosphere coupling act to feed back on the atmosphere and further enhance and organize it.