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Implementation in the programming language Julia of the Restricted Alternating Anderson Picard (AAP) acceleration for (non)-linear fixed point iterations.
Abstract Unusual electrical transport properties associated with weak or strong localization are sometimes found in disordered electronic materials. Here, we report experimental observation of a crossover of electronic behavior from weak localization to enhanced weak localization due to the spatial influence of disorder induced by ZrO 2 nanopillars in (La 2/3 Sr 1/3 MnO 3 ) 1− x :(ZrO 2 ) x ( x = 0, 0.2, and 0.3) nanocomposite films. The spatial strain regions, identified by scanning transmission electron microscopy and high-resolution x-ray diffraction, induce a coexistence of two-dimentional (2D) and three-dimentional (3D) localization and switches to typical 2D localization with increasing density of ZrO 2 pillars due to length scale confinement, which interestingly accords with enhancing vertically interfacial strain. Based on the excellent agreement of our experimental results with one-parameter scaling theory of localization, the enhanced weak localization exists in metal range close to the fixed point. These films provide a tunable experimental model for studying localization in particular the transition regime by appropriate choice of the second epitaxial phase. Graphical Abstract
This data package contains observation-based and model-simulated datasets (all provided in NetCDF format) for evaluating how wintertime lake-ice representation affects regional weather and climate over the Laurentian Great Lakes (freshwater lake ecosystem) during the high–ice-cover winter of 2009. The observational component includes: (1) Stage IV gridded precipitation at 4 km, hourly resolution for January–February 2009 over the Great Lakes region (radar–gauge multisensor precipitation analyses); (2) Great Lakes Surface Environmental Analysis (GLSEA) satellite-derived lake-ice coverage at 1.3 km, daily resolution for the 2009 winter months, providing ice coverage over Lakes Superior, Michigan, Huron, Erie, and Ontario; and (3) in situ measurements at the Standard Rock site on Lake Superior from the Great Lakes Evaporation Network (GLEN) at hourly resolution, including near-surface atmospheric variables and sensible and latent heat fluxes (air–lake exchange) at a fixed point location. The modeling component provides corresponding fields from two simulations, both archived at 4 km, hourly resolution: a standalone Weather Research Forecasting model (WRF) run driven by the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis 5 (ERA5), and a two-way coupled model using WRF and the Finite Volume Community Ocean Model (WRF-FVCOM, a 3-D hydrodynamic lake model). These outputs include variables relevant to air–lake interaction and lake-effect processes (e.g., near-surface temperature, humidity, wind, precipitation, and surface turbulent fluxes), enabling direct comparison with the observational datasets. Users can analyze and visualize these NetCDF files with common tools such as Python (e.g., xarray, netCDF4, numpy, pandas), NCO/CDO, Panoply, or ncview; NetCDF variables can also be converted to other formats (e.g., CSV, GeoTIFF) using these utilities.
Our objective is to improve the view of the seismicity in the Caucasus region using instrumental data between 1951 and 2019. To create a comprehensive catalog, we combine the bulletins of local agencies and the International Seismological Centre, and use an advanced single-event location algorithm, iLoc, to obtain better locations. We show that relocations with iLoc, using travel-time predictions from the 3D upper mantle velocity model, Regional Seismic Travel Time, improve the locations. Then, using the iLoc results as initial locations and the ground-truth events identified in the iLoc results as fix points, we apply Bayesloc, a multiple-event location algorithm, to simultaneously relocate the entire seismicity of the Caucasus region. Here we demonstrate that the simultaneous relocation of the seismicity with Bayesloc clarifies the location and geometry of major active structures accommodating ongoing convergence between the Arabian and Eurasian continents between the Black and Caspian Seas. Among our major findings is the confirmation of widespread seismicity in the mantle beneath the northern flank of the Greater Caucasus and central Caspian, resulting from north-dipping subduction of the Kura and South Caspian basins and the identification of a discrete band of crustal seismicity beneath the southern flank of the Greater Caucasus.
We consider a UV-complete field-theoretic model in general dimensions, including d=2+1, which consists of two copies of the long-range vector models, with O(m) and O(N-m) global symmetry groups, perturbed by double-trace operators. Using conformal perturbation theory we find weakly-coupled IR fixed points for N\geq 6 N ≥ 6 that reveal a spontaneous breaking of global symmetry. Namely, at finite temperature the lower rank group is broken, with the pattern persisting at all temperatures due to scale-invariance. We provide evidence that the models in question are unitary and invariant under full conformal symmetry. Furthermore, we show that this model exhibits a continuous family of weakly interacting field theories at finite N.
We identify the unique stress tensor deformation which preserves zero-birefringence conditions in non-linear electrodynamics, which is a 4d 4 d version of the T\overline{T} T T ¯ operator. We study the flows driven by this operator in the three Lagrangian theories without birefringence - Born-Infeld, Plebanski, and reverse Born-Infeld - all of which admit ModMax-like generalizations using a root- T\overline{T} T T ¯ -like flow that we analyse in our paper. We demonstrate one way of making this root- T\overline{T} T T ¯ -like flow manifestly supersymmetric by writing the deforming operator in \mathcal{N} = 1 𝒩 = 1 superspace and exhibit two examples of superspace flows. We present scalar analogues in d = 2 d = 2 with similar properties as these theories of electrodynamics in d = 4 d = 4 . Surprisingly, the Plebanski-type theories are fixed points of the classical T\overline{T} T T ¯ -like flows, while the Born-Infeld-type examples satisfy new flow equations driven by relevant operators constructed from the stress tensor. Finally, we prove that any theory obtained from a classical stress-tensor-squared deformation of a conformal field theory gives rise to a related “subtracted” theory for which the stress-tensor-squared operator is a constant.
We consider the problem of the development of steady states in one-dimensional Bose gas tubes that are weakly coupled to one another through a density-density interaction. We analyze this development through a Boltzmann collision integral approach. We argue that when the leading order of the collision integral, where single particle-hole excitations are created in individual gases, is dominant, the state of the gas evolves first to a non-thermal fixed point, i.e. a prethermalization plateau. This order is dominant when a pair of tubes are inequivalent with, say, different temperatures or different effective interaction parameters, \gamma γ . When both tubes are in the strongly interacting regime we additionally characterize this non-thermal prethermalization plateau by constructing the quasi-conserved quantities that control the existence of this plateau as well as the associated generalized Gibbs ensemble.
Projective symmetries are ubiquitous in quantum lattice models and can be leveraged to constrain their phase diagram and entanglement structure. In this paper, we investigate the consequences of projective algebras formed by non-invertible symmetries and lattice translations in a generalized 1+1 1 + 1 D quantum XY model based on group-valued qudits. This model is specified by a finite group G G and enjoys a projective \mathsf{Rep}(G)× Z(G) 𝖱 𝖾 𝗉 ( G ) × Z ( G ) and translation symmetry, where symmetry operators obey a projective algebra in the presence of symmetry defects. For invertible symmetries, such projective algebras imply Lieb-Schultz-Mattis (LSM) anomalies. However, this is not generally true for non-invertible symmetries, and we derive a condition on G G for the existence of an LSM anomaly. When this condition is not met, we prove an SPT-LSM theorem: any unique and gapped ground state is necessarily a non-invertible weak symmetry protected topological (SPT) state with non-trivial entanglement, for which we construct an example fixed-point Hamiltonian. The projectivity also affects the dual symmetries after gauging \mathsf{Rep}(G)× Z(G) 𝖱 𝖾 𝗉 ( G ) × Z ( G ) sub-symmetries, giving rise to non-Abelian and non-invertible dipole symmetries, as well as non-invertible translations. We complement our analysis with the SymTFT, where the projectivity causes it to be a topological order non-trivially enriched by translations. Throughout the paper, we develop techniques for gauging \mathsf{Rep}(G) 𝖱 𝖾 𝗉 ( G ) symmetry and inserting its symmetry defects on the lattice, which are applicable to other non-invertible symmetries.
In a physical system with conformal symmetry, observables depend on cross-ratios, measures of distance invariant under global conformal transformations (conformal geometry for short). We identify a quantum information-theoretic mechanism by which the conformal geometry emerges at the gapless edge of a 2+1D quantum many-body system with a bulk energy gap. We introduce a novel pair of information-theoretic quantities (\mathfrak{c}_{\textrm{tot}}, \eta) ( 𝔠 tot , η ) that can be defined locally on the edge from the wavefunction of the many-body system, without prior knowledge of any distance measure. We posit that, for a topological groundstate, the quantity \mathfrak{c}_{\textrm{tot}} 𝔠 tot is stationary under arbitrary variations of the quantum state, and study the logical consequences. We show that stationarity, modulo an entanglement-based assumption about the bulk, implies (i) \mathfrak{c}_{\textrm{tot}} 𝔠 tot is a non-negative constant that can be interpreted as the total central charge of the edge theory. (ii) \eta η is a cross-ratio, obeying the full set of mathematical consistency rules, which further indicates the existence of a distance measure of the edge with global conformal invariance. Thus, the conformal geometry emerges from a simple assumption on groundstate entanglement. We show that stationarity of \mathfrak{c}_{\textrm{tot}} 𝔠 tot is equivalent to a vector fixed-point equation involving \eta η , making our assumption locally checkable. We also derive similar results for 1+1D systems under a suitable set of assumptions.
Centuries ago, the prolific mathematician Leonhard Euler (1707–1783) wrote down the equations of motion (EOM) for the heavy symmetrical top with one point fixed. The resulting set of equations turned out to be nonlinear and had a limited number of closed-form solutions. Today, tools such as transfer matrix and finite elements enable the calculation of the rotor dynamic properties for rotor-bearing systems. Some of these tools rely on the “linearized” version of the EOM to calculate the eigenvalues, unbalance response, or transients in these systems. In fact, industry standards mandate that rotors be precisely balanced to have safe operational characteristics. However, in some cases, the nonlinear aspect of the EOM should be considered. The purpose of this paper is to show examples of how the linear vs. nonlinear formulations differ. This paper will also show how excessive unbalance is capable of dramatically altering the behavior of the system and can produce chaotic motions associated with the “jump” phenomenon.
This is the final technical report for the grant Three Dimensional Equilibrium Reconstruction and MHD Studies in Stellarators. The major goals of this project were to: further develop V3FIT code capabilities, continue to support experiments using the V3FIT code, continue theoretical support for the CTH experiment at Auburn, particularly in the area of NIMROD simulations of CTH discharges. Dr. Lopez Ortiz has made significant progress on his analysis of NIMROD simulations of CTH MHD phenomena. In particular, his study has focused on the fixed point dynamics and energy flow amongst toroidal Fourier modes in sawtooth oscillations simulations.
Wide-spread adoption of machine learning and distributed energy production has the potential to fundamentally change behaviours of energy markets. In practice, along with the benefits, previously unseen instabilities have begun emerging in markets currently embracing these technologies. In this report we study electricity markets as dynamical systems arising in smooth games, where energy consumers are modelled as gradient-based learners who interact on a graph through distributed energy producers. We give simple examples of how instabilities can arise even when the consumers’ local objectives seem reasonable and how these instabilities can be remedied. Drawing insights from these examples, we begin developing a general model of optimization-driven electricity market dynamics and give conditions for ensuring local Nash equilibria of the system are stable fixed points of the dynamics. Our results demonstrate how models of electricity market dynamics might be used for deriving formal guarantees in order to stabilize markets and enact regulatory policies in the face of market shocks.
This is probably the first thing I’d suggest anyone learns about adiabatic transitions because it tells you how a linear system reacts to an arbitrary forcing function. Not all systems are linear but they are usually locally linear near their stable fixed point. I think Scott Berg pointed out the relation to the Fourier transform to me and there’s probably literature about this under generic dynamical systems.
UT contribution in this Tokamak Disruption Simulation (TDS) is to develop a parallel high‐order hybridized Discontinuous Galerkin (HDG) methods for large‐s cale MHD simulations. The following are the major goals: 1) Construction of HDG methods for linearized MHD, 2) Rigorous analysis for the HDG formulations for linearized MHD, 3) 2D and 3D simulations to verify the convergent of the HDG methods for linearized MHD, 4) multigrid solvers/preconditioners for HDG formulations, 5) HDG for reconnection problems, 6) Divergence cleaning with HDG, 7) HDG formulations for nonlinear MHD, 8) Picard fixed point HDG approach, 9) IMEX HDG‐DG for nonlinear HDG; 10) parallel large‐scale HDG for linear and nonlinear MHD simulations.
A definition of partonic jet flavor that is both theoretically well-defined and experimentally robust would have profound implications for measurements and predictions especially for heavy flavor applications. Recently, a definition of jet flavor was introduced as the net flavor flowing along the direction of the Winner-Take-All axis of a jet which is soft safe to all orders, but not collinear safe. Here, we exploit the lack of collinear safety and propose a factorization theorem of perturbative flavor fragmentation functions that resum collinear divergences and describe the evolution of flavor from the short distance of jet production to the long distance at which hadronization occurs. Collinear flavor evolution is governed by a small modification of the DGLAP equations. We present a detailed all-orders analysis and identify exact relations that must hold amongst the various anomalous dimensions by probability conservation and the existence of fixed points of the renormalization group flow. We explicitly validate the factorization theorem at one-loop order, and demonstrate its consistency at two loops in particular flavor channels. Starting at two-loops, constraints on phase space imposed by flavor measurements potentially allow for non-trivial soft contributions, but we demonstrate that they are scaleless and so explicitly vanish, ensuring that soft particles are summed inclusively and all divergences are exclusively collinear in nature. This factorization theorem opens the door to precision calculations with identified flavor in the infrared.
With the rise of artificial intelligence, the popularization of deep learning, and a constantly evolving industry, the demand for flexible and efficient tools has never been greater. As algorithms grow more complex, their runtime and energy consumption increase exponentially. Customized hardware accelerators, long used for specific mathematical operations, remain essential for managing modern applications' computational and power demands. Hardware accelerators can speed up complex computations by orders of magnitude, but their manual design and verification processes are often challenging and time-consuming. High-Level Synthesis (HLS) provides a solution by transforming high-level algorithm descriptions, typically written in C++ or SystemC, into synthesizable RTL suitable for hardware implementation. This approach reduces development time for RTL engineers while offering flexibility beyond what traditional handwritten RTL can provide. We extended this capability to the machine-learning domain with the open-source framework hls4ml, which allows neural networks trained in Python frameworks like Tensorflow or PyTorch to be synthesized into efficient hardware representations for the traditional FPGA and ASIC flows. This breakthrough addresses the growing need for reduced design turnaround and easy verification of ML hardware accelerators with low latency and power efficiency constraints. During this tutorial, we will demonstrate how Python complements HLS by simplifying the ML design process, bridging the gap between software and hardware development. Attendees will explore how we translate neural networks modeled in Python into fixed-point C++ models suitable for HLS workflows. We will dive into strategies like Value-Range Analysis and Quantization-Aware Training, which optimize these designs for deployment and evaluate their accuracy, power consumption, and energy efficiency. To exemplify these concepts, experts from Fermilab will share their experiences applying this technology to high-energy physics experiments, where real-time, low-latency processing is critical. Over the years, Fermilab engineers have demonstrated how deep neural networks, optimized for hardware using hls4ml, can meet the stringent requirements of trigger systems at the CERN Large Hadron Collider. These systems rely on rapid decision-making to process immense data volumes while retaining only the most relevant events for further analysis. The application of hls4ml has also been extended to innovative technologies like smart pixel arrays. These smart pixels integrate ML inference capabilities directly into sensor devices, enabling localized data processing at the pixel level. This approach drastically reduces the need to transmit raw data to external processing units, significantly decreasing power consumption and latency. By embedding neural networks within the pixel architecture, the smart pixels can identify and prioritize relevant data in real time, providing a highly efficient solution for edge computing in scenarios such as particle detectors and imaging systems. Fermilab's work highlights the potential of hardware-accelerated ML in scenarios where both speed and power efficiency are mission-critical. Through this tutorial, attendees will gain valuable insights into the challenges and solutions of deploying ML in hardware. Understanding how HLS and hls4ml streamline the development of neural network-based hardware accelerators is fundamental for the industry's future. Participants will learn how these technologies are shaping the future of AI and scientific computing.
The objective of this campaign was to complement the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) User Facility’s Cloud And Precipitation Experiment at kennaook (CAPE-k) in northwest Tasmania by deploying scanning, fixed pointing angle, and in situ aerosol, cloud, and precipitation remote-sensing instruments during the last six months of the experiment. These instruments provided a three-dimensional (3D) context to the second ARM Mobile Facility (AMF2) vertically pointing observations collected at the kennaook Cape Grim (KCG) site and captured a portion of the life cycle of the clouds before and after the passage over the AMF2 vertical column. These 3D cloud measurements will be used in the near future to 1) investigate how the vertical profiles of aerosol and cloud properties are representative of the broader area and how these properties evolve during the portion of the cloud life cycle captured by the scanning instruments, 2) quantify how accurate the cloud fraction derived with assumptions from vertically pointing observations are compared with direct 3D cloud fraction measurements, 3) evaluate cloud fraction and liquid water path in the Australian Community Climate and Earth-System Simulator–Convective-scale (ACCESS-C) forecast model, and 4) evaluate aerosol and cloud products from the European Space Agency/Japanese Aerospace Exploration Agency (ESA/JAXA) Earth Cloud Aerosol Radiation Explorer (EarthCARE) mission using the scanning measurements, offering more chances of exact collocation, thereby complementing the statistical approach we are planning to employ with AMF2 observations for that same purpose.
The studies of adiabatic island generation through tracking near the quarter integer resonance and separately, through phase modulation was conducted using the accelerator code BLonD. Parameters from the Hadron Storage Ring (HSR) were used in the model. The demonstration of resonance island formation through phase modulation will help to understand this possible source of beam dilution during the store and further control of the bunch shaping. In this document, an algorithm to calculate the 5 th , 7 th , and N th order resonances is given, tracking results are presented, and the stable fixed point calculations with comparison to Poincaré contours are given.