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At least 523 records · Page 29
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DOE OSTI2021

Stability Analysis of Parameter Varying Genetic Toggle Switches Using Koopman Operators

The genetic toggle switch is a well known model in synthetic biology that represents the dynamic interactions between two genes that repress each other. The mathematical models for the genetic toggle switch that currently exist have been useful in describing circuit dynamics in rapidly dividing cells, assuming fixed or time-invariant kinetic rates. There is a growing interest in being able to model and extend synthetic biological function for growth conditions such as stationary phase or during nutrient starvation. As cells transition from one growth phase to another, kinetic rates become time-varying parameters. In this paper, we propose a novel class of parameter varying nonlinear models that can be used to describe the dynamics of genetic circuits, including the toggle switch, as they transition from different phases of growth. We show that there exists unique solutions for this class of systems, as well as for a class of systems that incorporates the microbial phenomena of quorum sensing. Further, we show that the domain of these systems, which is the positive orthant, is positively invariant. We also showcase a theoretical control strategy for these systems that would grant asymptotic monostability of a desired fixed point. We then take the general form of these systems and analyze their stability properties through the framework of time-varying Koopman operator theory. A necessary condition for asymptotic stability is also provided as well as a sufficient condition for instability. A Koopman control strategy for the system is also proposed, as well as an analogous discrete time-varying Koopman framework for applications with regularly sampled measurements.

Harrison, Jamiree (ORCID:0000000265351579)↗
DOE OSTI2025

The Principle of Maximum Conformality Correctly Resolves the Renormalization-Scheme-Dependence Problem

In this paper, we clarify a serious misinterpretation and consequent misuse of the Principle of Maximum Conformality (PMC), which also can serve as a mini-review of PMC. In a recently published article, P. M. Stevenson has claimed that “the PMC is ineffective and does nothing to resolve the renormalization-scheme-dependence problem”, concluding incorrectly that the success of PMC predictions is due to the PMC being a “laborious, ad hoc, and back-door” version of the Principle of Minimal Sensitivity (PMS). We show that such conclusions are incorrect, deriving from a misinterpretation of the PMC and an overestimation of the applicability of the PMS. The purpose of the PMC is to achieve precise fixed-order pQCD predictions, free from conventional renormalization schemes and scale ambiguities. We demonstrate that the PMC predictions satisfy all the self-consistency conditions of the renormalization group and standard renormalization-group invariance; the PMC predictions are thus independent of any initial choice of renormalization scheme and scale. The scheme independence of the PMC is also ensured by commensurate scale relations, which relate different observables to each other. Moreover, in the Abelian limit, the PMC dovetails into the well-known Gell-Mann–Low framework, a method universally revered for its precision in QED calculations. Due to the elimination of factorially divergent renormalon terms, the PMC series not only attains a convergence behavior far superior to that of its conventional counterparts but also deftly curtails any residual scale dependence caused by the unknown higher-order terms. This refined convergence, coupled with its robust suppression of residual uncertainties, furnishes a sound and reliable foundation for estimating the contributions from unknown higher-order terms. Anchored in the bedrock of standard renormalization-group invariance, the PMC simultaneously eradicates the factorial divergences and eliminates superfluous systematic errors, which inversely provides a good foundation for achieving high-precision pQCD predictions. Consequently, owing to its rigorous theoretical underpinnings, the PMC is eminently applicable to virtually all high-energy hadronic processes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

MOCMC: Method of Characteristics Moment Closure, a Numerical Method for Covariant Radiation Magnetohydrodynamics

In this work, we present a conservative numerical method for radiation magnetohydrodynamics with frequency-dependent full transport in stationary spacetimes. This method is stable and accurate for both large and small optical depths and radiation pressures. The radiation stress–energy tensor is evolved in flux-conservative form, and closed with a swarm of samples that each transport a multigroup representation of the invariant specific intensity along a null geodesic. In each zone, the enclosed samples are used to efficiently construct a Delaunay triangulation of the unit sphere in the comoving frame, which in turn is used to calculate the Eddington tensor, average source terms, and adaptively refine the sample swarm. Furthermore, radiation four-forces are evaluated in the moment sector in a semi-implicit fashion. The radiative transfer equation is solved in invariant form deterministically for each sample. Since each sample carries a discrete representation of the full spectrum, the cost of evaluating the transport operator is independent of the number of frequency groups, representing a significant reduction of algorithmic complexity for transport in frequency-dependent problems. The major approximation we make in this work is performing scattering in an angle-averaged way. Local adaptivity in samples also makes this scheme more amenable to nonuniform meshes than a traditional Monte Carlo method. We describe the method and present results on a suite of test problems. We find that Method of Characteristics Moment Closure converges at least as ~N -1 , rather than the canonical Monte Carlo N -1/2 , where N is the number of samples per zone.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Thermodynamics of the Inner Heliosheath

We derive annual sky maps of the proton temperature in the inner heliosheath (IHS), and track their temporal evolution over the years 2009–2016 of Interstellar Boundary Explorer observations. Other associated thermodynamic parameters also determined are the density, kappa (the parameter that characterizes kappa distributions), temperature rate, polytropic index, and entropy. We exploit the theory of kappa distributions and their connection with polytropes, to (i) express a new polytropic quantity Π that remains invariant along streamlines where temperature and density may vary, (ii) parameterize the proton flux in terms of the Π invariant and kappa, and (iii) derive the temperature and density, respectively, from the slope and intercept of the linear relationship between kappa and logarithm of Π. We find the following thermodynamic characteristics: (1) temperature sky maps and histograms shifted to their lowest values in 2012 and their highest in 2015; (2) temperature negatively correlated with density, reflecting the subisothermal polytropic behavior; (3) temperature positively correlated with kappa, revealing characteristics of the mechanism responsible for generating kappa distributions; (4) processes in IHS are subisothermal tending toward isobaric, consistent with previously published results; (5) linear relationship between kappa and polytropic indices, revealing characteristics of the particle potential energy; and (6) entropy positively correlated with polytropic index, aligned with the underlying theory that entropy increases toward the isothermal state where the kappa distribution reduces to the Maxwell–Boltzmann description.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Reggeization of the Pion Exchange in Pion Photoproduction

At high energies, the production of light mesons induced by a photon beam interacting with a nucleon target is governed by the exchange of Regge trajectories in the t-channel. In charge-exchange reactions at small momentum transfer, unnatural parity exchanges, such as pion exchange, dominate. The point-like nature of the photon–pion interaction makes the pion photoproduction reaction an excellent way to study the pion exchange mechanism. However, the nucleon Born terms are required to ensure that the scattering amplitude is gauge invariant. The gauge invariance of the pion exchange amplitude is crucial in approaching its reggeization properly. Here we discuss a novel strategy to reggeize the pion pole which considers explicitly the exchange in the t-channel of all the mesons in the pion trajectory. Each of these exchanges contributes with a pole in spin, known as a Regge pole, and we perform their summation analytically.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Factorized visual representations in the primate visual system and deep neural networks

Object classification has been proposed as a principal objective of the primate ventral visual stream and has been used as an optimization target for deep neural network models (DNNs) of the visual system. However, visual brain areas represent many different types of information, and optimizing for classification of object identity alone does not constrain how other information may be encoded in visual representations. Information about different scene parameters may be discarded altogether (‘invariance’), represented in non-interfering subspaces of population activity (‘factorization’) or encoded in an entangled fashion. In this work, we provide evidence that factorization is a normative principle of biological visual representations. In the monkey ventral visual hierarchy, we found that factorization of object pose and background information from object identity increased in higher-level regions and strongly contributed to improving object identity decoding performance. We then conducted a large-scale analysis of factorization of individual scene parameters – lighting, background, camera viewpoint, and object pose – in a diverse library of DNN models of the visual system. Models which best matched neural, fMRI, and behavioral data from both monkeys and humans across 12 datasets tended to be those which factorized scene parameters most strongly. Notably, invariance to these parameters was not as consistently associated with matches to neural and behavioral data, suggesting that maintaining non-class information in factorized activity subspaces is often preferred to dropping it altogether. Thus, we propose that factorization of visual scene information is a widely used strategy in brains and DNN models thereof.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Data-Driven Operator Theoretic Methods for Global Phase Space Learning

In this work, we propose to apply the recently developed Koopman operator techniques to explore the global phase space of a nonlinear system from time-series data. In particular, we address the problem of identifying various invariant subsets of a phase space from the spectral properties of the associated Koopman operator constructed from time-series data. Moreover, in the case when the system evolution is known locally in various invariant subspaces, then a phase space stitching result is proposed that can be applied to identify a global Koopman operator. A biological system, bistable toggle switch and a second-order nonlinear system example are considered to illustrate the proposed results. The construction of this global Koopman operator is very helpful in experimental works as multiple experiments can't be run at the same time starting from several initial conditions.

Nandanoori, Sai Pushpak↗
DOE OSTI2021

A Flexible Power Method for Solving Infinite Dimensional Tensor Eigenvalue Problems

We propose a flexible power method for computing the leftmost, i.e., algebraically smallest, eigenvalue of an infinite dimensional tensor eigenvalue problem, $H x = \lambda x$, where the infinite dimensional symmetric matrix $H$ exhibits a translational invariant structure. We assume the smallest eigenvalue of $H$ is simple and apply a power iteration of $e^{-H}$ with the eigenvector represented in a compact way as a translational invariant infinite Tensor Ring (iTR). Hence, the infinite dimensional eigenvector can be represented by a finite number of iTR cores of finite rank. In order to implement this power iteration, we use a small parameter $t$ so that the infinite matrix-vector operation $e^{-Ht}x$ can efficiently be approximated by the Lie product formula, also known as Suzuki--Trotter splitting, and we employ a low rank approximation through a truncated singular value decomposition on the iTR cores in order to keep the cost of subsequent power iterations bounded. We also use an efficient way for computing the iTR Rayleigh quotient and introduce a finite size iTR residual which is used to monitor the convergence of the Rayleigh quotient and to modify the timestep $t$. In this paper, we discuss 2 different implementations of the flexible power algorithm and illustrate the automatic timestep adaption approach for several numerical examples.

Beeumen, Roel Van↗
DOE OSTI2022

Study of Excited Cascade Baryons and Preliminary Cross-Sections for Ξ(1530) Using Data from the GlueX Experiment

The spectra of predicted particles from elementary quark models (CQMs) are expansive, accurate for the low-lying spectra, but incomplete. The GlueX experiment at Jefferson Lab is a vehicle to study medium energy photoproduction of hadronic states. The primary goal of the GlueX collaboration is to study Quantum Chromodynamics (QCD, also known as the strong nuclear force) and the nature of quark confinement. The GlueX collaboration uses a polarized photon beam incident on a liquid hydrogen target (LH 2 ) to investigate the aftermath of photon-proton interactions. The cascade baryons, denoted by Ξ, are defined by having two, second-generation, strange quarks with an additional first-generation light quark (u or d). Experimentally, few cascades have been discovered, which is the antithesis of what most models expect. The cascades have some favorable attributes but are difficult to detect because the production cross sections are small and direct production is unlikely. Fortunately, in the 12 GeV era of the GlueX experiment, there is sufficient energy, beam time and data analysis tools for the detection of excited cascade states and their properties. From the reaction γ p →Κ + Κ + Ξ - π 0 , the invariant mass spectra of Ξ - π 0 system was surveyed for new possible resonances. The invariant mass spectrum has a strong Ξ(1530) signal with other smaller resonances throughout the spectrum. Preliminary cross sections for the Ξ(1530) that was photoproduced from the proton are presented at energies never before explored. While the Ξ(1530) couples almost exclusively to the Ξπ channel, there is an easily identifiable Ξ(1690) signal decaying Ξπ. Through the use of a simultaneous fitting routing of the Ξ*- mass spectra, I was able to observe the Ξ(1690) decaying to the KΛ, as well as to the Ξ - π 0 branch. With additional statistics, a measurement of the branching ratio should be possible. Lastly, a partial wave analysis (PWA) was completed to verify that the total angular momentum of Ξ(1530) is J = 3/2 and consistent with having positive parity. Additionally, there is evidence of a potentially interesting feature slightly above the mass of the Ξ(1530) that should be more fully explored as new GlueX data becomes available.

Sumner, Brandon↗
DOE OSTI2022

Search for the NΔ resonance in the 𝛾𝑑 → 𝑑𝜋 +𝜋 − reaction

A dibaryon which is an object with baryon number B = 2 has been studied for a long time. Dyson and Xuong classified non-strangeness dibaryon states based on SU(6) symmetries in 1960?s. In the framework, the deuteron is classified as one of the sextet states of dibaryons. Although dibaryon have been an interesting subject of research for a long time, most of the experimental studies up to the early 2000?s were unsuccessful. The CELCIUS/WASA collaboration reported this state via the double-pionic fusion reaction (?= ! 3c0c0) in 2009. Thereafter, the WASA-at-COSY collaboration revealed properties of the isoscaler resonance state via the ?= ! 3c0c0 reaction in 2011. The dibaryon resonance state with isospin ? = 0 and spin ( = 3 thought to be a ?03 which was predicted by Dyson and Xuong at 2.35 GeV?22 with a configuration of ??. The reported mass and width of that state were 2?37 GeV?22 and 0?07 GeV?22, espectively. The mass was ?0?08 GeV?22 smaller than that of 2?, the width was narrower than that of single ?. This surprising result made dibaryon study come back into the limelight. ?12 is one of the dibaryon states classified by Dyson and Xuong with isospin ? = 1, spin ( = 2. This state can be regarded as an s-wave #? resonance. ?12 is an interesting state from the point of view of the possibilities of existence as an internal structure of ?03 and contribution to many-body effects in nuclei. Though there were some experimental clues and theoretical studies of this state, it was unclear whether the obtained experimental results represented a real resonance or not due to the difficulty of separation from kinematical effects. Very recently, the FOREST group at Tohoku University reported a photoproduced isovector dibaryon state at mass of 2.14 GeV?22 in the 3c0 invariant mass spectra of the W3 ! 3c0c0 reaction. The most probable ?% configuration was 2¸ although they didn?t exclude the possibility of ?% = 1¸ or 3?. They separated the dibaryon production process from conventional pion production process for the first time using angular distribution of deuteron. We investigated the W3 ! 3c¸c? reaction for study of a possible #? dibaryon state using a deuterium target at the Research Center for Electron Photon Science, Tohoku University, Japan. In the experiment, ?3 ? 1012 tagged photon beam at energies ranging from 0.8 to 1.1 GeV was impinged to the liquid deuterium target (?520 mg?cm2) and the charged particles in the final state: deuteron, c¸, and c?, were detected by a magnetic spectrometer with a large solid angle named NKS2. NKS2 had capabilities of reconstructing momentum of charged particles, multi-track analysis, and ??c separation. We performed two different analyses named 2-track analysis and 3-track analysis. The 2-track (3-track) analysis was for events in which two (three) particles of 3c¸c? in the final state, including deuteron, were detected by NKS2. In the 3-track and 2-track analysis, ?2000? ?15000 events were identified as the W3 ! 3c¸c? reaction events, respectively. The 2-track analysis with higher statistics was mainly used to derive the cross sections, and the 3-track analysis was used to check the consistency of the 2-track analysis. In this thesis, we have shown the total cross section, the differential cross sections of the W3 ! 3c¸c? reaction in the region of jC j ¡ 0?15 GeV2. This is the world?s first measurement of this reaction in this energy region. Dibaryon resonance structures were observed below the #? threshold in the differential cross section of the invariant mass of 3c?. The mass and width of the structure were consistent with these of ?12 measured by the W3 ! 3c0c0 reaction. The mechanism of the production process was discussed based on the angular distribution of emitted deuteron.

Toyama, Yuichi↗
DOE OSTI2022

Well-Balanced Second-Order Convex Limiting Technique for Solving the Serre–Green–Naghdi Equations

In this article, we introduce a numerical method for approximating the dispersive Serre–Green–Naghdi equations with topography using continuous finite elements. The method is an extension of the hyperbolic relaxation technique introduced in Guermond et al. (J Comput Phys 450:110809, 2022). It is explicit, second-order accurate in space, third-order accurate in time, and is invariant-domain preserving. It is also well balanced and parameter free. Special attention is given to the convex limiting technique when physical source terms are added in the equations. The method is verified with academic benchmarks and validated by comparison with laboratory experimental data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Physics of the Inverted Harmonic Oscillator: From the lowest Landau level to event horizons

In this work, we present the inverted harmonic oscillator (IHO) Hamiltonian as a paradigm to understand the quantum mechanics of scattering and time-decay in a diverse set of physical systems. As one of the generators of area preserving transformations, the IHO Hamiltonian can be studied as a dilatation generator, squeeze generator, a Lorentz boost generator, or a scattering potential. In establishing these different forms, we demonstrate the physics of the IHO that underlies phenomena as disparate as the Hawking–Unruh effect and scattering in the lowest Landau level (LLL) in quantum Hall systems. We derive the emergence of the IHO Hamiltonian in the LLL in a gauge invariant way and show its exact parallels with the Rindler Hamiltonian that describes quantum mechanics near event horizons. This approach of studying distinct physical systems with symmetries described by isomorphic Lie algebras through the emergent IHO Hamiltonian enables us to reinterpret geometric response in the lowest Landau level in terms of relativistic effects such as Wigner rotation. Further, the analytic scattering matrix of the IHO points to the existence of quasinormal modes (QNMs) in the spectrum, which have quantized time-decay rates. We present a way to access these QNMs through wave packet scattering, thus proposing a novel effect in quantum Hall point contact geometries that parallels those found in black holes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Generalized multifractality at spin quantum Hall transition

Generalized multifractality characterizes scaling of eigenstate observables at Anderson-localization critical points. We explore generalized multifractality in 2D systems, with the main focus on the spin quantum Hall (SQH) transition in superconductors of symmetry class C. Relations and differences with the conventional integer quantum Hall (IQH) transition are also studied. Using the field-theoretical formalism of non-linear sigma-model, we derive the pure-scaling operators representing generalizing multifractality and then “translate” them to the language of eigenstate observables. Performing numerical simulations on network models for SQH and IQH transitions, we confirm the analytical predictions for scaling observables and determine the corresponding exponents. Remarkably, the generalized-multifractality exponents at the SQH critical point strongly violate the generalized parabolicity of the spectrum, which implies violation of the local conformal invariance at this critical point.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Subcell limiting strategies for discontinuous Galerkin spectral element methods

Here, we present a general family of subcell limiting strategies to construct robust high-order accurate nodal discontinuous Galerkin (DG) schemes. The main strategy is to construct compatible low order finite volume (FV) type discretizations that allow for convex blending with the high-order variant with the goal of guaranteeing additional properties, such as bounds on physical quantities and/or guaranteed entropy dissipation. For an implementation of this main strategy, four main ingredients are identified that may be combined in a flexible manner: (i) a nodal high-order DG method on Legendre–Gauss–Lobatto nodes, (ii) a compatible robust subcell FV scheme, (iii) a convex combination strategy for the two schemes, which can be element-wise or subcell-wise, and (iv) a strategy to compute the convex blending factors, which can be either based on heuristic troubled-cell indicators, or using ideas from flux-corrected transport methods. By carefully designing the metric terms of the subcell FV method, the resulting methods can be used on unstructured curvilinear meshes, are locally conservative, can handle strong shocks efficiently while directly guaranteeing physical bounds on quantities such as density, pressure or entropy. We further show that it is possible to choose the four ingredients to recover existing methods such as a provably entropy dissipative subcell shock-capturing approach or a sparse invariant domain preserving approach. We test the versatility of the presented strategies and mix and match the four ingredients to solve challenging simulation setups, such as the KPP problem (a hyperbolic conservation law with non-convex flux function), turbulent and hypersonic Euler simulations, and MHD problems featuring shocks and turbulence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A high-order explicit Runge-Kutta approximation technique for the shallow water equations

Here, we introduce a high-order space–time approximation of the Shallow Water Equations with sources that is invariant-domain preserving (IDP), well-balanced with respect to rest states, and employs a novel explicit Runge–Kutta (ERK) introduced in Ern and Guermond (SIAM J. Sci. Comput. 44(5), A3366–A3392, 2022) for systems of non-linear conservation equations. The resulting method is then numerically illustrated through verification and validation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Robust second-order approximation of the compressible Euler equations with an arbitrary equation of state

Here, this paper is concerned with the approximation of the compressible Euler equations supplemented with an arbitrary or tabulated equation of state. The proposed approximation technique is robust, formally second-order accurate in space, invariant-domain preserving, and works for every equation of state, tabulated or analytic, provided the pressure is nonnegative. An entropy surrogate functional that grows across shocks is proposed. The numerical method is verified with novel analytical solutions and then validated with several computational benchmarks seen in the literature including problems with composite waves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Observation of three-proton-decaying resonant states in 21 Al

The structure of the proton-unbound nucleus 21 Al has been studied via proton transfer from a 9 Be target to a 20 Mg beam at E/A = 103 MeV. Three resonant states in 21 Al are identified by the invariant-mass reconstruction of 18 Ne + 3p events. The decay-energy spectra for the two subsystems of 21 Al , i.e. 18 Ne+ 1 p and 18 Ne+ 2 p , indicate that the observed resonant state with the lowest energy has decay branches consisting of three sequential steps of one-proton decay. Based on the ab initio and the distorted-wave Born approximation (DWBA) calculations, this resonant state at Ε ⁎ = 6.09(11) MeV likely has a spin-parity of (1/2 + - 7/2 + ). Meanwhile, the possibility that the observed resonant peak represents an admixture of several states cannot be ruled out. The good isospin-symmetry of the low-lying states with d 5/2 , d 3/2 configurations in the 21 Al- 21 O pair and the ab initio calculations indicate weak configuration mixing between the s - and d -orbital components. The systematics of experimental energy differences between the 5/2 + ground state and lowest-lying 3/2 + excited state for isotopes (isotones) of Z(N) = 13 suggest a likely semimagic nature of 21 Al.

21Al↗
DOE OSTI2026

Transverse orbital angular momentum in the proton

Using the equations of motion of QCD and Lorentz invariance relations, we show a new, more direct way of obtaining the decomposition of the proton's quark transverse angular momentum into its spin and orbital components. The new decomposition can be understood as a twist-three relation, with the quark transverse spin described by the parton distribution g T . We find that the orbital component can be expressed in terms of a moment in the quark transverse momentum, k T , of the generalized transverse momentum-dependent distribution F 12 , or alternatively in terms of the twist-three generalized parton distributions H 2T and $\tilde{E}$ 2T .

Lorentz invariance relations↗