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At least 55 records · Page 3

Resurgence and dynamics of O(N) and Grassmannian sigma models

Here, we study the non-perturbative dynamics of the two dimensional O( N ) and Grassmannian sigma models by using compactification with twisted boundary conditions on R× S 1 , semi-classical techniques and resurgence. While the O(N) model has no instantons for N > 3, it has (non-instanton) saddles on R 2 , which we call 2d-saddles. On R× S 1 , the resurgent relation between perturbation theory and non-perturbative physics is encoded in new saddles, which are associated with the affine root system of the o( N ) algebra. These events may be viewed as fractionalizations of the 2d-saddles. The first beta function coefficient, given by the dual Coxeter number, can then be intepreted as the sum of the multiplicities (dual Kac labels) of these fractionalized objects. Surprisingly, the new saddles in O( N ) models in compactified space are in one-to-one correspondence with monopole-instanton saddles in SO( N ) gauge theory on R 3 ×S 1 . The Grassmannian sigma models Gr( N , M ) have 2d instantons, which fractionalize into N kink-instantons. The small circle dynamics of both sigma models can be described as a dilute gas of the one-events and two-events, bions. One-events are the leading source of a variety of non-perturbative effects, and produce the strong scale of the 2d theory in the compactified theory. We show that in both types of sigma models the neutral bion emulates the role of IR-renormalons. We also study the topological theta angle dependence in both the O (3) model and Gr( N , M ), and describe the multi-branched structure of the observables in terms of the theta-angle dependence of the saddle amplitudes, providing a microscopic argument for Haldane’s conjecture.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Orbital perturbations of the Galilean satellites during planetary encounters

The Nice model of the dynamical instability and migration of the giant planets can explain many properties of the present solar system, and can be used to constrain its early architecture. In the jumping-Jupiter version of the Nice model, required from the terrestrial planet constraint and dynamical structure of the asteroid belt, Jupiter has encounters with an ice giant. Here, we study the survival of the Galilean satellites in the jumping-Jupiter model. This is an important concern because the ice-giant encounters, if deep enough, could dynamically perturb the orbits of the Galilean satellites and lead to implausible results. We performed numerical integrations where we tracked the effect of planetary encounters on the Galilean moons. We considered three instability cases from Nesvorný and Morbidelli that differed in the number and distribution of encounters. We found that in one case, where the number of close encounters was relatively small, the Galilean satellite orbits were not significantly affected. In the other two, the orbital eccentricities of all moons were excited by encounters, Callisto's semimajor axis changed, and, in a large fraction of trials, the Laplace resonance of the inner three moons was disrupted. The subsequent evolution by tides damps eccentricities and can recapture the moons in the Laplace resonance. A more important constraint is represented by the orbital inclinations of the moons, which can be excited during the encounters and not appreciably damped by tides. We find that one instability case taken from Nesvorný and Morbidelli clearly does not meet this constraint. This shows how the regular satellites of Jupiter can be used to set limits on the properties of encounters in the jumping-Jupiter model, and help us to better understand how the early solar system evolved.

79 ASTRONOMY AND ASTROPHYSICS↗

The Vertical Momentum Budget of Shallow Cumulus Convection: Insights From a Lagrangian Perspective

A Lagrangian Particle Dispersion Model is embedded into large eddy simulations to diagnose the responses of shallow cumulus convection to a small-amplitude large-scale temperature perturbation. The Lagrangian framework allows for a decomposition of the vertical momentum budget and diagnosis of the forces that regulate cloudy updrafts. The results are used to shed light on the parameterization of vertical velocity in convective schemes, where the treatment of the effects of entrainment as well as buoyancy-induced and mechanically induced pressure gradients remains highly uncertain. We show that both buoyancy-induced and mechanically induced pressure gradients are important for the vertical momentum budget of cloudy updrafts, whereas the entrainment dilution term is relatively less important. Based on the analysis of the dominant force balance, we propose a simple model to derive the perturbation pressure gradient forces. We further illustrate that the effective buoyancy and dynamic perturbation pressure can be approximated to a good extent using a simple cylindrical updraft model given the cloud radius. This finding has the potential for improving the parameterization of vertical velocity in convective schemes and the development of a unified scheme for cumulus convection.

54 ENVIRONMENTAL SCIENCES↗

Stability Analysis of the Flow Over a Swept Forward-Facing Step Using PIV Base Flows

Step excrescences are a type of surface imperfection encountered on swept wings of commercial aircraft, commonly because accessibility requirements prevent creating the wing’s surface from a single panel. If the step height is too large, super-critical, the flow can undergo an early transition to turbulence, which can be highly detrimental for the performance of the wing. In the case of a forward-facing step on a swept wing in a low-disturbance environment, stationary crossflow vortices can develop a significant amplitude upstream of the step and hence dominate the structure of the boundary-layer flow over the step. The main goal of the present investigation is to illuminate the path to transition supported by the fascinatingly complex flow field in the direct downstream vicinity of a step with a super critical height. The high-resolution, stereographic Particle Image Velocimetry (PIV) measurement dataset presently available for this flow field provides a complete description of the laminar flow for the execution of BiGlobal stability analysis in a plane parallel to the step. Although the notorious sensitivity of stability results to the description of the base flow demands a very careful uncertainty analysis of those results, it is argued that this very fact can be leveraged to produce new insight into the supported perturbation dynamics. In performing the analysis, several unsteady mode families are discovered that display the explosive perturbation expected for early transition to be induced. In considering domain widths equal to an integer-multiple of the incident crossflow-vortex wavelength and analyzing an extent of 5 crossflow-vortex wavelengths parallel to the step, it is found that the stability results converge while increasing the domain width. It is demonstrated, moreover, that the results for the wider domains can be approximated by appropriately averaging the results on neighboring single-crossflow-vortex-wavelength domains covering the same region. Besides being useful for computational purposes, this observed property suggests interpreting the instability mechanism as a distorted primary mechanism rather than a “proper” secondary mechanism. This follows in the context of the secondary in-stability analysis of three-dimensional boundary layers, because the secondary mechanism is usually characterized by being localized in a pocket of strong shear, while the distorted primary mechanism typically has an infinite support in the direction parallel to the step. Even though the growth rates are found to be sensitive to the interrogation-window size inherent to the PIV post-processing procedure, the spatial structure of the eigenfunctions is found to be relatively insensitive. Lastly, the spatial structure of the eigenfunctions corresponding to all velocity components are matched with the shape functions determined by computing the Spectral Proper Orthogonal Decomposition (SPOD) of a time-resolved measurement of the perturbation content.

forward-facing step↗

Modal techniques for analyzing airplane dynamics

A series of techniques are presented for analyzing airplane control and output characteristics. State-space matrix equations describing the linear perturbation dynamics are transformed from physical coordinates into scaled, modal coordinates. Techniques for analyzing the impacts of system inputs on the fundamental modes of motion and the appearance of these modes in the system outputs are explained. Scaled modal matrices are used to compute steady-state control inputs which optimize the steady-state response of selected system outputs. Graphics which promote quick understanding of the analysis are presented to display the resulting vectors and matrices. The defined analysis techniques are applied to an example airplane model, illustrating the insight which can be acquired using the described modal techniques.

Arbuckle, P. Douglas↗

Multidimensional characterization of stochastic dynamical systems based on multiple perturbations and measurements

Generalized nonlinear response theory is presented for stochastic dynamical systems. Experiments in which multiple measurements of dynamical quantities are used along with multiple perturbations of parameters of dynamical systems are described by generalized response functions (GRFs). These constitute a new type of multidimensional measures of stochastic dynamics either in the time or the frequency domains. Closed expressions for GRFs in stochastic dynamical systems are derived and compared with numerical non-equilibrium simulations. Several types of perturbations are considered: impulsive and periodic perturbations of temperature and impulsive perturbations of coordinates. The present approach can be used to study various types of stochastic processes ranging from single-molecule conformational dynamics to chemical kinetics of finite-size reactors such as biocells.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Deriving super-horizon curvature perturbations from the dynamics of preheating

We present a framework for calculating super-horizon curvature perturbation from the dynamics of preheating, which gives a reasonable match to the lattice results. Hubble patches with different initial background field values evolve differently. From the bifurcation of their evolution trajectories we find curvature perturbation using Lyapunov theorem and δ N formulation. In this way we have established a connection between the finer dynamics of preheating and the curvature perturbation produced in this era. From the calculated analytical form of the curvature perturbation we have derived the effective super-horizon curvature perturbation smoothed out on large scales of CMB. The order of the amount of local form non-gaussianity generated in this process has been calculated and problems regarding the precise determination of it have been pointed out.

79 ASTRONOMY AND ASTROPHYSICS↗

High-quality axion from exact SUSY chiral dynamics

We use supersymmetric chiral dynamics perturbed by anomaly-mediated supersymmetry breaking to obtain a high-quality, composite axion that solves the strong problem. The strong dynamics arises from a supersymmetric SU(10) chiral gauge theory with massless matter chiral superfields. This leads to a stable, nonsupersymmetric vacuum, calculated exactly, where a spontaneously broken global symmetry, identified with the Peccei-Quinn (PQ) symmetry, gives rise to a composite QCD axion. The chiral gauge theory also admits a discrete (or ) gauge symmetry that forbids PQ-violating operators up to dimension eight. An extension to an chiral gauge theory incorporates grand unification where the unification scale is identified with the PQ-breaking scale and PQ-violating operators are forbidden up to dimension 20. The supersymmetry breaking scale, near 100 TeV, ameliorates the Higgs hierarchy problem, while colored Nambu–Goldstone bosons may be detected at future colliders via decays to gluons or form heavy isotopes.

Gherghetta, Tony↗

Multi-Flight-Phase GPS Navigation Filter Applications to Terrestrial Vehicle Navigation and Positioning

A candidate onboard space navigation filter demonstrated excellent performance (less than 8 meter level RMS semi-major axis accuracy) in performing orbit determination of a low-Earth orbit Explorer satellite using single-frequency real GPS data. This performance is significantly better than predicted by other simulation studies using dual-frequency GPS data. The study results revealed the significance of two new modeling approaches evaluated in the work. One approach introduces a single-frequency ionospheric correction through pseudo-range and phase range averaging implementation. The other approach demonstrates a precise axis-dependent characterization of dynamic sample space uncertainty to compute a more accurate Kalman filter gain. Additionally, this navigation filter demonstrates a flexibility to accommodate both perturbational dynamic and observational biases required for multi-flight phase and inhomogeneous application environments. This paper reviews the potential application of these methods and the filter structure to terrestrial vehicle and positioning applications. Both the single-frequency ionospheric correction method and the axis-dependent state noise modeling approach offer valuable contributions in cost and accuracy improvements for terrestrial GPS receivers. With a modular design approach to either 'plug-in' or 'unplug' various force models, this multi-flight phase navigation filter design structure also provides a versatile GPS navigation software engine for both atmospheric and exo-atmospheric navigation or positioning use, thereby streamlining the flight phase or application-dependent software requirements. Thus, a standardized GPS navigation software engine that can reduce the development and maintenance cost of commercial GPS receivers is now possible.

Park, Young W.↗

From the Upper Troposphere Through the Stratosphere: How Satellite Measurements Help Us Decode the Past to Better Project the Future

Decades of observations of key chemical species are allowing us to more fully understand processes important to transport and composition from the upper troposphere through the stratosphere. This talk will focus on a few examples and how they are informing our understanding of variability, trends, and future projections. The growth of the Antarctic ozone hole (late 1970s – mid 1990s) caused a dynamical perturbation to the Southern Hemisphere stratospheric circulation visible in ozone, one of our longest and best observed chemical constituents, and illustrates the connection between chemical change and the coupled radiative and dynamical response that challenges chemistry-climate models (CCMs). The quasi-biennial oscillation (QBO) is the dominant mode of interannual variability in the tropical stratosphere, however its impacts on stratospheric circulation and composition can be traced globally. The QBOs timing with respect to the seasonal cycle in each hemisphere is significant in understanding its impact on up to decadal scale variability. The El Nino Southern Oscillation (ENSO), which dominates tropical tropospheric interannual variability, also affects the stratosphere and its influence is visible in our growing record of tropospheric and stratospheric composition measurements. I will discuss how our knowledge of response has grown and how representation of these observed responses in CCMs is key both to understanding recent trends and to reducing uncertainty in future changes of composition.

Luke David Oman↗

Uncertainty quantification for generalized Langevin dynamics

Here, we present efficient finite difference estimators for goal-oriented sensitivity indices with applications to the generalized Langevin equation (GLE). In particular, we apply these estimators to analyze an extended variable formulation of the GLE where other well known sensitivity analysis techniques such as the likelihood ratio method are not applicable to key parameters of interest. These easily implemented estimators are formed by coupling the nominal and perturbed dynamics appearing in the finite difference through a common driving noise or common random path. After developing a general framework for variance reduction via coupling, we demonstrate the optimality of the common random path coupling in the sense that it produces a minimal variance surrogate for the difference estimator relative to sampling dynamics driven by independent paths. In order to build intuition for the common random path coupling, we evaluate the efficiency of the proposed estimators for a comprehensive set of examples of interest in particle dynamics. These reduced variance difference estimators are also a useful tool for performing global sensitivity analysis and for investigating non-local perturbations of parameters, such as increasing the number of Prony modes active in an extended variable GLE.

97 MATHEMATICS AND COMPUTING↗

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↗

Management of Vortices Trailing Flapped Wings via Separation Control

A pilot study was conducted on a flapped semi-span model to investigate the concept and viability of near-wake vortex management via separation control. Passive control was achieved by means of a simple fairing and active control was achieved via zero mass-flux blowing slots. Vortex sheet strength, estimated by integrating surface pressure ports, was used to predict vortex characteristics by means of inviscid rollup relations. Furthermore, vortices trailing the flaps were mapped using a seven-hole probe. Separation control was found to have a marked effect on vortex location, strength, tangential velocity, axial velocity and size over a wide range of angles of attack and control conditions. In general, the vortex trends were well predicted by the inviscid rollup relations. Manipulation of the separated flow near the flap edges exerted significant control over both outboard and inboard edge vortices while producing negligible lift excursions. Dynamic separation and attachment control was found to be an effective means for dynamically perturbing the vortex from arbitrarily long wavelengths down to wavelengths less than a typical wingspan. In summary, separation control has the potential for application to time-independent or time-dependent wake alleviation schemes, where the latter can be deployed to minimize adverse effects on ride-quality and dynamic structural loading.

Greenblatt, David↗

Theoretical assessment of the nuclear quantum effects on polymer crystallinity via perturbation theory and dynamics

As seen in experiments with poly(3-hexylthiophene), substitution of hydrogen with deuterium on the main chain alone decreases crystallinity. To understand this effect, a general formalism for analysis of the dipole moments and polarizabilities incorporating quantum nuclei, is developed in this paper. The formalism, based on quantum dynamics of the proton/deuteron and on the perturbative analysis of the dipole interaction energy, accounts for the anharmonicity of a potential energy surface and for the anisotropy of molecular dipole moments. The formalism is implemented within the Discrete Variable Representation and the Density Functional Theory describing, respectively, the quantum proton/deuteron on the thiophene ring and the electronic structure of the 27-atom model polymer chain, embedded into a larger crystalline environment. Finally, the isotope effect is mainly attributed to the differences in the zero-point energy of the CH/CD bonds and to the isotope-dependence of the dipole-dipole inter-chain interactions.

36 MATERIALS SCIENCE↗

Seasonal Change on Saturn from Cassini/CIRS Observations, 2004-2009

Five years of thermal infrared spectra from the Cassini Composite Infrared Spectrometer (CIRS) are analyzed to determine the response of Saturn's atmosphere to seasonal changes in insolation. Hemispheric mapping sequences at 15.0 cm-1 spectral resolution are used to retrieve the variation in the zonal mean temperatures in the stratosphere (0.5-5.0 mbar) and upper troposphere (75-800 mbar) between October 2004 (shortly after the summer solstice in the southern hemisphere) and July 2009 (shortly before the autumnal equinox). Saturn's northern mid-latitudes show signs of dramatic warming in the stratosphere (by 6-10 K) as they emerge from ring-shadow into springtime conditions, whereas southern mid-latitudes show evidence for cooling (4-6 K). The 40-K asymmetry in stratospheric temperatures between northern and southern hemispheres (at 1 mbar) slowly decreased during the timespan of the observations. Tropospheric temperatures also show temporal variations but with a smaller range, consistent with the increasing radiative time constant of the atmospheric response with increasing pressure. The tropospheric response to the insolation changes shows the largest magnitude at the locations of the broad retrograde jets. Saturn's warm south-polar stratospheric hood has cooled over the course of the mission, but remains present. Stratospheric temperatures are compared to a radiative climate model which accounts for the spatial distribution of the stratospheric coolants. The model successfully predicts the magnitude and morphology of the observed changes at most latitudes. However, the model fails at locations where strong dynamical perturbations dominate the temporal changes in the thermal field, such as the hot polar vortices and the equatorial semi-annual oscillation (Orton, G., and 27 colleagues [2008]. Nature 453, 196-198). Furthermore, observed temperatures in Saturn's ring-shadowed regions are larger than predicted by all radiative-climate models to date due to the incomplete characterization of the dynamical response to the shadow. Finally, far-infrared CIRS spectra are used to demonstrate variability of the para-hydrogen distribution over the 5-year span of the dataset, which may be related to observed changes in Saturn's tropospheric haze in the spring hemisphere.

Fletcher, Leigh N.↗

Dynamic Electric Field Assisted CO 2 Methanation

Energy-efficient advanced chemical reactions are essential for accelerating the growth of hydrocarbon economy. Sabatier reaction stands out for its potential to effectively transform carbon dioxide into valuable hydrocarbons and is an asset for long-duration Mars missions. This study explores a novel catalytic approach that harnesses electric field-assisted catalysis to substantially enhance the efficiency of the Sabatier reaction. Application of a dynamically perturbed electric field at 1000 Hz resulted in remarkable enhancements, increasing methane formation rates by over 100% at 350 °C and by 74% at 400 °C. Post-reaction catalyst characterization further revealed reduced blockage of active catalytic surface area under the applied electric field, emphasizing improved catalytic longevity and sustained activity. These results underscore the potential of tailored electric field waveforms to dynamically modulate elementary reaction kinetics and surface processes, positioning electric field-assisted catalysis as a transformative strategy for energy-efficient, cost-effective chemical manufacturing and energy conversion technologies.

42 - ENGINEERING↗