Complexity for link complement states in Chern-Simons theory
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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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Results for “Complexity theory”
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.
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Emergence of the polydeterminant in QCD
A generalization of the determinant appears in particle physics in effective Lagrangian interaction terms that model the chiral anomaly in quantum chromodynamics (Giacosa et al. in Phys Rev D 97(9):091901, 2018, Phys Rev D 109(7):L071502, 2024), in particular in connection to mesons. This polydeterminant function, known in the mathematical literature as a mixed discriminant, associates N distinct N x N complex matrices into a complex number and reduces to the usual determinant when all matrices are taken as equal. Here, we explore the main properties of the polydeterminant applied to (quantum) fields by using a formalism and a language close to high-energy physics approaches. We discuss its use as a tool to write down novel chiral anomalous Lagrangian terms and present an explicit illustrative model for mesons. Finally, the extension of the polydeterminant as a function of tensors is shown.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
A theory of supercritical wing sections, with computer programs and examples.
Mathematical methods for the design of supercritical wings, which depend on the numerical solution of the partial differential equations of two-dimensional gas dynamics, are developed. The main contribution is a computer program for the design of shockless transonic airfoils using the hodograph transformation and analytic continuation into the complex domain. The mathematical theory is described, and a manual for users of the programs is provided. Numerical examples are given and computational results are discussed, and the computer programs themselves are listed. The analysis routine can be used to ascertain whether the profiles behave well at off-design conditions, or to smooth coordinates and obtain a desirable shape more quickly when perfectly shockless flow is not essential.
Bauer, F.↗
Methods and Experiences for Developing Abstractions for Data-intensive, Scientific Applications
Developing software for scientific applications that require the integration of diverse types of computing, instruments, and data present challenges that are distinct from commercial software. These applications require scale, and the need to integrate various programming and computational models with evolving and heterogeneous infrastructure. Pervasive and effective abstractions for distributed infrastructures are thus critical; however, the process of developing abstractions for scientific applications and infrastructures is not well understood. While theory-based approaches for system development are suited for well-defined, closed environments, they have severe limitations for designing abstractions for scientific systems and applications. The design science research (DSR) method provides the basis for designing practical systems that can handle real-world complexities at all levels. In contrast to theory-centric approaches, DSR emphasizes both practical relevance and knowledge creation by building and rigorously evaluating all artifacts. In this work, we show how DSR provides a well-defined framework for developing abstractions and middleware systems for distributed systems. Specifically, we address the critical problem of distributed resource management on heterogeneous infrastructure over a dynamic range of scales, a challenge that currently limits many scientific applications. We use the pilot-abstraction, a widely used resource management abstraction for high-performance, high throughput, big data, and streaming applications, as a case study for evaluating the DSR activities. For this purpose, we analyze the research process and artifacts produced during the design and evaluation of the pilot-abstraction. We find DSR provides a concise framework for iteratively designing and evaluating systems. Finally, we capture our experiences and formulate different lessons learned.
97 MATHEMATICS AND COMPUTING↗
Stable vacua with realistic phenomenology and cosmology in heterotic M-theory satisfying Swampland conjectures
We recently described a protocol for computing the potential energy in heterotic M-theory for the dilaton, complex structure and Kähler moduli. This included the leading order non-perturbative contributions to the complex structure, gaugino condensation and worldsheet instantons assuming a hidden sector that contains an anomalous U(1) structure group embedded in E8. In this paper, we elucidate, in detail, the mathematical and computational methods required to utilize this protocol. These methods are then applied to a realistic heterotic M-theory model, the B – L MSSM, whose observable sector is consistent with all particle physics requirements. Within this context, it is shown that the dilaton and universal moduli can be completely stabilized at values compatible with every phenomenological and mathematical constraint — as well as with ΛCDM cosmology. We also show that the heterotic M-theory vacua are consistent with all well-supported Swampland conjectures based on considerations of string theory and quantum gravity, and we discuss the implications of dark energy theorems for compactified theories.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Engine health monitoring: An advanced system
The advanced propulsion monitoring system is described. The system was developed in order to fulfill a growing need for effective engine health monitoring. This need is generated by military requirements for increased performance and efficiency in more complex propulsion systems, while maintaining or improving the cost to operate. This program represents a vital technological step in the advancement of the state of the art for monitoring systems in terms of reliability, flexibility, accuracy, and provision of user oriented results. It draws heavily on the technology and control theory developed for modern, complex, electronically controlled engines and utilizes engine information which is a by-product of such a system.
Dyson, R. J. E.↗
Fully unsteady subsonic and supersonic potential aerodynamics for complex aircraft configurations for flutter applications
A general theory for study, oscillatory or fully unsteady potential compressible aerodynamics around complex configurations is presented. Using the finite-element method to discretize the space problem, one obtains a set of differential-delay equations in time relating the potential to its normal derivative which is expressed in terms of the generalized coordinates of the structure. For oscillatory flow, the motion consists of sinusoidal oscillations around a steady, subsonic or supersonic flow. For fully unsteady flow, the motion is assumed to consist of constant subsonic or supersonic speed for time t or = 0 and of small perturbations around the steady state for time t 0.
Tseng, K.↗
Deep reinforcement learning for complex evaluation of one-loop diagrams in quantum field theory
In this paper we present a technique based on deep reinforcement learning that allows for numerical analytic continuation of integrals that are often encountered in one-loop diagrams in quantum field theory. To extract certain quantities of two-point functions, such as spectral densities, mass poles or multiparticle thresholds, it is necessary to perform an analytic continuation of the correlator in question. At one-loop level in Euclidean space, this results in the necessity to deform the integration contour of the loop integral in the complex plane of the square of the loop momentum, to avoid nonanalyticities in the integration plane. Using a toy model for which an exact solution is known, we train a reinforcement learning agent to perform the required contour deformations. We report our study shows great promise for an agent to be deployed in iterative numerical approaches used to compute nonperturbative two-point functions, such as the quark propagator Dyson-Schwinger equation, or more generally, Fredholm equations of the second kind, in the complex domain.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Formulation and closure of compressible turbulence equations in the light of kinetic theory
Fluid-dynamic moment equations, based on a kinetic hierarchy system, are derived governing the interaction between turbulent and thermal fluctuations. The kinetic theory is shown to reduce the inherent complexity of the conventional formalism of compressible turbulence theory and to minimize arbitrariness in formulating the closure condition.
Tsuge, S.↗
Self-organizing biochemical cycles
I examine the plausibility of theories that postulate the development of complex chemical organization without requiring the replication of genetic polymers such as RNA. One conclusion is that theories that involve the organization of complex, small-molecule metabolic cycles such as the reductive citric acid cycle on mineral surfaces make unreasonable assumptions about the catalytic properties of minerals and the ability of minerals to organize sequences of disparate reactions. Another conclusion is that data in the Beilstein Handbook of Organic Chemistry that have been claimed to support the hypothesis that the reductive citric acid cycle originated as a self-organized cycle can more plausibly be interpreted in a different way.
NASA Discipline Exobiology↗
The 3-D inelastic analysis methods for hot section components: Brief description
Advanced 3-D inelastic structural/stress analysis methods and solution strategies for more accurate yet more cost-effective analysis of components subjected to severe thermal gradients and loads in the presence of mechanical loads, with steep stress and strain gradients are being developed. Anisotropy, time and temperature dependent plasticity and creep effects are also addressed. The approach is to develop four different theories, one linear and three higher order theories (polynomial function, special function, general function). The theories are progressively more complex from linear to general function in order to provide streamlined analysis capability with increasing accuracy for each hot section component and for different parts of the same component according to the severity of the local stress, strain and temperature gradients associated with hot spots, cooling holes and surface coating cracks. To further enhance the computational effectiveness, the higher order theories will have embedded singularities (cooling passages, for example) in the generic modeling region. Each of the four theories consists of three formulation models derivable from independent theoretical formulations. These formulation models are based on: (1) mechanics of materials; (2) special finite elements; and (3) an advanced formulation to be recommended by the contractor.
Chamis, C. C.↗
A NASA initiative: Software engineering for reliable complex systems
The objective is the development of methods, technology, and skills that will enable NASA to cost-effectively specify, build, and manage reliable software which can evolve and be maintained over an extended period. The need for such software is rooted in the increasing integration of software and computing components into NASA systems. Current NASA Software Engineering expertise was applied toward some of the largest reliable systems including: shuttle launch; ground support; shuttle simulation; minor control; satellite tracking; and scientific data systems. Unfortunately, no theory exists for reliable complex software systems. NASA is seeking to fill this theoretical gap through a number of approaches. One such approach is to conduct research on theoretical foundations for managing complex software systems. It includes: communication models, new and modified paradigms, and life-cycle models. Another approach is research in the theoretical foundations for reliable software development and validation. It focuses upon formal specifications, programming languages, software engineering systems, software reuse, formal verification, and software safety. Further approaches involve benchmarking a NASA software environment, experimentation within the NASA context, evolution of present NASA methodology, and transfer of technology to the space station software support environment.
Holcomb, Lee B.↗
Biaxial experiments supporting the development of constitutive theories for advanced high-temperature materials
Complex states of stress and strain are introduced into components during service in engineering applications. It follows that analysis of such components requires material descriptions, or constitutive theories, which reflect the tensorial nature of stress and strain. For applications involving stress levels above yield, the situation is more complex in that material response is both nonlinear and history dependent. This has led to the development of viscoplastic constitutive theories which introduce time by expressing the flow and evolutionary equation in the form of time derivatives. Models were developed here which can be used to analyze high temperature components manufactured from advanced composite materials. In parallel with these studies, effort was directed at developing multiaxial testing techniques to verify the various theories. Recent progress in the development of constitutive theories from both the theoretical and experimental viewpoints are outlined. One important aspect is that material descriptions for advanced composite materials which can be implemented in general purpose finite element codes and used for practical design are verified.
Ellis, J. R.↗
Connected three-body terms in single-reference unitary many-body theories: Iterative and perturbative approximations
This work introduces various approaches to include connected three-body terms in unitary many-body theories, focusing on the driven similarity renormalization group (DSRG). Starting from the least approximate method—the linearized DSRG truncated to one-, two-, and three-body operators [LDSRG(3)]—we develop several approximate LDSRG(3) models with reduced computational cost. Through a perturbative analysis, we motivate a family of iterative LDSRG(3)-n and -n' (n = 1, 2, 3, 4) methods that contain a subset of the LDSRG(3) diagrams. Among these variants, the LDSRG(3)-2 scheme has the same computational complexity of coupled cluster theory with singles, doubles, and triples (CCSDT), but it outperforms CCSDT in the accuracy of the predicted correlation energies. We also propose and implement two perturbative triples corrections based on the linearized DSRG truncated to one- and two-body operators augmented with recursive semi-quadratic commutators [qDSRG(2)]. Overall, the resulting qDSRG(2)+(T) approach matches the accuracy of the “gold-standard” coupled cluster theory with singles, doubles, and perturbative triples model on the energetics of twenty-eight closed-shell atoms and small molecules.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Proliferation transitions from a topological phase in 2+1 dimensions
We consider phase transitions out of a general topological phase in 2+1 dimensions. We assume that the transition is triggered by a single Abelian anyon, which becomes light near the transition and whose worldlines proliferate after the transition. (This proliferation is often referred to as “condensation.”) We describe the transition using a continuum field theory obtained by coupling the corresponding topological quantum field theory (TQFT) to a single complex scalar field associated with this anyon. With these assumptions, we find the most general relativistic field theory for such a transition. Even though for a given TQFT and a choice of anyon, there are infinitely many such field theories, the transition theory depends on only a single additional integer parameter. We analyze all these theories, their global symmetries, and their phases. In generic cases, the theory after the transition can be related to the original one via an Abelian hierarchy construction. In special cases, the theory after the transition is gapless, and with a particular deformation, it is related to the original TQFT by gauging an anomaly-free one-form global symmetry. We also explore the enrichment of this setup by a global U(1) symmetry. In some cases, enriching the original TQFT is incompatible with the full transition theory. Lastly, we demonstrate our construction with many specific examples.
Anyons↗
Classification of all $\mathcal{N}\geq 3$ moduli space orbifold geometries at rank 2
We classify orbifold geometries which can be interpreted as moduli spaces of four-dimensional \mathcal{N}\geq 3 𝒩 ≥ 3 superconformal field theories up to rank 2 (complex dimension 6). The large majority of the geometries we find correspond to moduli spaces of known theories or discretely gauged version of them. Remarkably, we find 6 geometries which are not realized by any known theory, of which 3 have an \mathcal{N}=2 𝒩 = 2 Coulomb branch slice with a non-freely generated coordinate ring, suggesting the existence of new, exotic \mathcal{N}=3 𝒩 = 3 theories.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Photodissociation and Infrared Spectroscopy of Uranium–Nitrogen Cation Complexes
Laser vaporization of uranium in a pulsed supersonic expansion of nitrogen is used to produce complexes of the form U + (N 2 ) n (n = 1–8). These ions are mass selected in a reflectron time-of-flight spectrometer and studied with visible and UV laser fixed-frequency photodissociation and with tunable infrared laser photodissociation spectroscopy. The dissociation patterns and spectroscopy of U + (N 2 ) n indicate that N 2 ligands are intact molecules and that there is no insertion chemistry resulting in UN + or NUN + . Fixed frequency photodissociation at 532 and 355 nm indicate that the U + –N 2 bond dissociation energy varies little with changing coordination. The photon energy and the number of ligands eliminated allow an estimate of the average U + –N 2 dissociation energy of 12 kcal/mol. Infrared bands are observed for these complexes near the N–N stretch vibration via elimination of N 2 molecules. These resonances are observed to be shifted about 130 cm–1 to the red from the free-N 2 frequency for complexes with n = 3–8. Density functional theory indicates that U + is most stable in the sextet state in these complexes and that N 2 molecules bind in end-on configurations. Furthermore, the fully coordinated complex is predicted to be U + (N 2 ) 8 , which has a cubic structure. The vibrational frequencies predicted by theory are consistently lower than those in the experiment, independent of the isomeric structure or spin state of the complexes. Despite its failure to reproduce the infrared spectra, theory provides an average U + –N 2 dissociation energy of 11.8 ± 0.5 kcal/mol, in good agreement with the value from the experiments.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Achieving designed texture and flows in bulk active nematics using optimal control theory
Being intrinsically nonequilibrium, active materials can potentially perform functions that would be thermodynamically forbidden in passive materials. However, active systems have diverse local attractors that correspond to distinct dynamical states, many of which exhibit chaotic turbulent-like dynamics and thus cannot perform work or useful functions. Designing such a system to choose a specific dynamical state is a formidable challenge. Motivated by recent advances enabling optogenetic control of experimental active materials, we describe an optimal control theory framework that identifies a spatiotemporal sequence of light-generated activity that drives an active nematic system toward a prescribed dynamical steady state. Active nematics are unstable to spontaneous defect proliferation and chaotic streaming dynamics in the absence of control. We demonstrate that optimal control theory can compute activity fields that redirect the dynamics into a variety of alternative dynamical programs and functions. This includes dynamically reconfiguring between states, selecting and stabilizing emergent behaviors that do not correspond to attractors, and are hence unstable in the uncontrolled system. Furthermore, our results provide a roadmap to leverage optical control methods to rationally design structure, dynamics, and function in a wide variety of active materials.
Complex systems theory↗