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At least 343 records · Page 19

A Unified Theory of Fractional Nonlocal and Weighted Nonlocal Vector Calculus

Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are suitable for a broad class of engineering and scientific applications that feature multiscale or anomalous behavior. This has driven a desire for a vector calculus that includes nonlocal and fractional gradient, divergence and Laplacian type operators, as well as tools such as Green's identities, to model subsurface transport, turbulence, and conservation laws. In the literature, several independent definitions and theories of nonlocal and fractional vector calculus have been put forward. Some have been studied rigorously and in depth, while others have been introduced ad-hoc for specific applications. The goal of this work is to provide foundations for a unified vector calculus by (1) consolidating fractional vector calculus as a special case of nonlocal vector calculus, (2) relating unweighted and weighted Laplacian operators by introducing an equivalence kernel, and (3) proving a form of Green's identity to unify the corresponding variational frameworks for the resulting nonlocal volume-constrained problems. The proposed framework goes beyond the analysis of nonlocal equations by supporting new model discovery, establishing theory and interpretation for a broad class of operators, and providing useful analogues of standard tools from the classical vector calculus.

97 MATHEMATICS AND COMPUTING↗

Cross section measurements of deuteron electro-disintegration at very high recoil momenta and large 4-momentum transfers (Q^2)

The 2H(e,e'p)n cross sections have been measured at negative 4-momentum transfers of Q^2 = 4.5 +/- 0.5 (GeV/c)^2 and Q^2 = 3.5 +/- 0.5 (GeV/c)^2 reaching neutron recoil (missing) momenta up to p_r ?1.0 GeV/c. The data have been obtained at fixed neutron recoil angles 5 <= theta_nq <= 95 degrees with respect to the 3-momentum transfer q. The new data agree well with the previous data which reached p_r ?550 MeV/c. At theta_nq = 35 and 45 degrees, final state interactions (FSI), meson exchange currents (MEC) and isobar configurations (IC) are suppressed and the plane wave impulse approximation (PWIA) provides the dominant cross section contribution. The new data are compared to recent theoretical calculations, and a significant disagreement for recoil momenta p_r > 700 MeV/c is observed. The experiment was carried out in experimental Hall C at the Thomas Jefferson National Accelerator Facility (TJNAF) and formed part of a group of four experiments that were used to commission the new Super High Momentum Spectrometer (SHMS). The experiment consisted of a 10.6 GeV electron beam incident on a liquid deuterium target which resulted in the break-up of the deuteron into a proton and neutron. The scattered electrons were detected by the SHMS in coincidence with the knocked-out protons detected in the previously existing High Momentum Spectrometer (HMS) and the recoiling neutrons were reconstructed from energy-momentum conservation laws. To ensure that the 2H(e,e'p)n reaction channel was selected, we required the missing energy of the system to be the binding energy of the deuteron (?2.22 MeV). The spectrometers? central angles and momenta were set to measure three central missing momentum settings of the neutron corresponding to p_r = 80, 580 and 750 MeV/c, which required the SHMS central angle and momentum to be fixed and the HMS to be rotated from smaller to larger angles corresponding to the lower and higher missing momentum settings, respectively. The experiment was carried out in a time period of six days with typical electron beam currents of 45-60 uA at about 50% beam efficiency.

Yero, Carlos↗

Process-based Neural Network to Forecast Vegetation Dynamics

This white paper calls for an AI-based emulator of DOE’s dynamic vegetation model that is computationally efficient and accommodates/parameterizes the governing processes built in the model. This AI-based emulator is needed for model calibration, sensitivity analysis, prediction, uncertainty quantification, and decision making. This AI-based emulator will incorporate physics and biological information in the form of conservation laws and constitutive relationships.

59 BASIC BIOLOGICAL SCIENCES↗

The REDTOP experiment: Rare $\eta/\eta^{\prime}$ Decays To Probe New Physics

The $\eta$ and $\eta^{\prime}$ mesons are nearly unique in the particle universe since they are almost Goldstone bosons and the dynamics of their decays are strongly constrained. The integrated $\eta$-meson samples collected in earlier experiments amount to $\sim10^{9}$ events. A new experiment, REDTOP (Rare Eta Decays To Probe New Physics), is being proposed, with the intent of collecting a data sample of order 10$^{14}$ $\eta$ (10$^{12}$ $\eta^{\prime}$) for studying very rare decays. Such statistics are sufficient for investigating several symmetry violations, and for searching for particles and fields beyond the Standard Model. In this work we present several studies evaluating REDTOP sensitivity to processes that couple the Standard Model to New Physics through all four of the so-called \emph{portals}: the Vector, the Scalar, the Axion and the Heavy Lepton portal. The sensitivity of the experiment is also adequate for probing several conservation laws, in particular $CP$, $T$ and Lepton Universality, and for the determination of the $\eta$ form factors, which is crucial for the interpretation of the recent measurement of muon $g-2$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Combining DPG in space with DPG time-marching scheme for the transient advection-reaction equation

In this article, we present a general methodology to combine the Discontinuous PetrovGalerkin (DPG) method in space and time in the context of methods of lines for transient advection-reaction problems. We first introduce a semidiscretization in space with a DPG method redefining the ideas of optimal testing and practicality of the method in this context. Then, we apply the recently developed DPG-based time-marching scheme, which is of exponential-type, to the resulting system of Ordinary Differential Equations (ODEs). We also discuss how to efficiently compute the action of the exponential of the matrix coming from the space semidiscretization without assembling the full matrix. Finally, we verify the proposed method for 1D+time advection-reaction problems showing optimal convergence rates for smooth solutions and more stable results for linear conservation laws comparing to the classical exponential integrators.

97 MATHEMATICS AND COMPUTING↗

Differential geometric approaches to momentum-based formulations for fluids [Slides]

This SAND report documents CIS Late Start LDRD Project 22-0311, "Differential geometric approaches to momentum-based formulations for fluids". The project primarily developed geometric mechanics formulations for momentum-based descriptions of nonrelativistic fluids, utilizing a differential geometry/exterior calculus treatment of momentum and a space+time splitting. Specifically, the full suite of geometric mechanics formulations (variational/Lagrangian, Lie-Poisson Hamiltonian and Curl-Form Hamiltonian) were developed in terms of exterior calculus using vector-bundle valued differential forms. This was done for a fairly general version of semi-direct product theory sufficient to cover a wide range of both neutral and charged fluid models, including compressible Euler, magnetohydrodynamics and Euler-Maxwell. As a secondary goal, this project also explored the connection between geometric mechanics formulations and the more traditional Godunov form (a hyperbolic system of conservation laws). Unfortunately, this stage did not produce anything particularly interesting, due to unforeseen technical difficulties. There are two publications related to this work currently in preparation, and this work will be presented at SIAM CSE 23, at which the PI is organizing a mini-symposium on geometric mechanics formulations and structure-preserving discretizations for fluids. The logical next step is to utilize the exterior calculus based understanding of momentum coupled with geometric mechanics formulations to develop (novel) structure-preserving discretizations of momentum. This is the main subject of a successful FY23 CIS LDRD "Structure-preserving discretizations for momentum-based formulations of fluids".

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Magnetoelectronic phenomena due to quantum magnetization fluctuations

The goal of the project was to identify techniques to study magnetoelectronic phenomena such as spin transfer (ST) that stem from the quantum-mechanical nature of magnetization, and utilize them to characterize these quantum phenomena. The first such technique, electronic measurements based on the dependence of resistance on the population of spin-wave quanta (magnons) in a magnetic nanostructure, was shown by detailed measurements to be significantly influenced by the current-driven generation of a highly nonequilibrium phonon distribution by electrical current. This previously unrecognized phenomenon adds to the understanding of current-induced heating phenomena, qualitatively changes the methodology of analysis of current-induced heating common in scientific studies and engineering of current-carrying nanostructures. It benefits the public by providing a new direction for mitigation of Joule heating effects in electronic devices. The project also included quantum simulations of current-induced effects in magnetic nanostructures, which revealed that linear momentum and energy conservation are important for ST. Only angular momentum conservation was previously believed to be important. This finding is important for the fundamental understanding of ST, and for the design of efficient magnetoelectronic devices taking advantage of these conservation laws. Simulations also showed that non-classical ST is dominant in antiferromagnets, which will transform the understanding of ST in these systems. Finally, experimental studies of spin-transfer in ultrathin transition metal films revealed very large non-classical effects which were traced to the quantum origins of magnetism associated in the studied systems with the formation of an orbital liquid state. These findings i) transform the understanding of "conventional" transition-metal magnetism, ii) open a new field of studies in magnetism and a new method for the electronic control of magnetic properties and magnetism itself, and iii) provide a new approach to the development of efficient magnetoelectronic devices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Physics Informed Neural Networks as Computational Physics Emulators

This report is a brief overview and evaluation of Physics Informed Neural Networks (PINNs). Karniadakis and co-workers, e.g., Karniadakis et al. (2021) assert that the PINNs approach integrates seamlessly both data and mathematical physics models, even in partially understood, uncertain and high-dimensional contexts. They further claim that PINNs are effective and efficient for ill-posed and inverse problems, and when combined with domain decomposition, are scalable to large problems and a tool to discover hidden physics. While they demonstrate the capabilities in specific academic instances, their overarching claims about PINNs seem to be an overstatement, at least at the current time. We have briefly considered a few of the limitations of PINNs in this investigation. It is not clear to us if the PINNs approach can ever be competitive with approaches that use specialized algorithms to achieve high-accuracy solutions of governing equations and other techniques that can combine observational data with such solutions. As an example of the latter, consistent with the principles of Bayesian inference, data assimilation, or more generally data-model fusion, is a process that fuses observational data typically with a computational model that respects certain constraints such as conservation laws. For example, improvements in observational network combined with data assimilation have been key in improving weather predictions over the past four decades Kalnay (2003).

97 MATHEMATICS AND COMPUTING↗

Parallel Implicit Hydrodynamics with Material Strength for High Explosive Burn Calculations

High explosives are almost always evolving in some form of metal containment vessel. This fact requires that a materials model for the evolution of the metal containment vessel be part of any simulation of the HE. Since the actual form of the strength model to be used is an open question, we incorporate the material strength properties in a relatively agnostic fashion, which will accommodate many strength models. The only restriction is that the stress components be a function of density, specific internal energy and velocities. In addition, the timescales and rates of the chemical reactions in the HE vary between thousands of seconds and nanoseconds. A hydrodynamics capable of operating in anticipation of the eventual violent release of energy via these chemical reactions is a necessity. The central issue in creating a hydrodynamics capable of spanning these timescales is to forgo the use of a Courant time step control necessary in an explicit hydrodynamics. The Courant time-step arises because of characteristic velocities associated with the material, such as the sound speed or, in materials with strength, characteristic longitudinal and transverse speeds associated with compression and shear. The method used to circumvent the need for a Courant time-step limit is to develop an implicit calculation of the advanced particle pressure and shear modulus derived from the conservation laws of mass, momentum and specific internal energy. This process creates the implicit hydrodynamics needed for the HE calculations of interest to this study.

36 MATERIALS SCIENCE↗

Searching for Muon to Electron Transition [Slides]

Summary : Searches for violations of fundamental symmetries and conservation laws - Powerful Probes of physics beyond the Standard Model (BSM); Charged Lepton Flavor violation : Mu to E conversion; 4-orders of magnitude improvements in BR; SD process can dominate the conversion process in ALP models; fa > O(100)TeV can be achieved, complementary role.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Ab initio equation of state for vanadium

Accurate materials’ equations of state (EOS) are essential for understanding materials properties as well as for use in multiphysics simulations. In particular, hydrodynamics simulations are based on three fundamental conservation laws (mass, momentum and energy) that form an under-determined system of equations. The equation of state serves as an additional closure relation between thermodynamic variables for a given material that enables numerical hydrodynamics simulation. In this report, we focus on the development of an ab initio EOS for the body centered cubic (BCC) phase of Vanadium (V) for eventual integration into a multiphase EOS in the OpenSesame EOS database.

36 MATERIALS SCIENCE↗

Self-Similarity, Fractality and Entropy Principle in Collisions of Hadrons and Nuclei at Tevatron, RHIC and LHC

$z$-Scaling of inclusive spectra as a manifestation of self-similarity and fractality of hadron interactions is illustrated.The scaling for negative particle production in $Au+Au$ collisionsfrom BES-I program at RHIC is demonstrated. The scaling variable $z$ depends on the momentum fractions of the colliding objects carried by the interacting constituents, and momentum fractions of the produced objects in the scattered and recoil directions, which carries the inclusive particle and its counterpart, respectively. Structures of the colliding objects and fragmentation processes in final stateare expressed by fractal dimensions. Medium produced in the collisions is described by a specific heat. The scaling function $\psi(z)$ reveals energy, angular, multiplicity, and flavor independence.It has a power behavior at high $z$ (high $p_T$). Based on entropy principle and $z$-scaling, energy loss as a function of the collision energy, centrality and transverse momentum of inclusive particle is estimated.New conservation law including fractal dimensions is found. Quantization of fractal dimensions is discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Plasma Dynamics in Low-Electron-Beta Environments

Recent in situ measurements by the MMS and Parker Solar Probe missions bring interest to small-scale plasma dynamics (waves, turbulence, magnetic reconnection) in regions where the electron thermal energy is smaller than the magnetic one. Examples of such regions are the Earth’s magnetosheath and the vicinity of the solar corona, and they are also encountered in other astrophysical systems. In this brief review, we consider simple physical models describing plasma dynamics in such low-electron-beta regimes, discuss their conservation laws and their limits of applicability.

79 ASTRONOMY AND ASTROPHYSICS↗

Increasing Extractable Work in Small Qubit Landscapes

An interesting class of physical systems, including those associated with life, demonstrates the ability to hold thermalization at bay and perpetuate states of high free-energy compared to a local environment. In this work we study quantum systems with no external sources or sinks for energy, heat, work, or entropy that allow for high free-energy subsystems to form and persist. We initialize systems of qubits in mixed, uncorrelated states and evolve them subject to a conservation law. We find that four qubits make up the minimal system for which these restricted dynamics and initial conditions allow an increase in extractable work for a subsystem. On landscapes of eight co-evolving qubits, interacting in randomly selected subsystems at each step, we demonstrate that restricted connectivity and an inhomogeneous distribution of initial temperatures both lead to landscapes with longer intervals of increasing extractable work for individual qubits. We demonstrate the role of correlations that develop on the landscape in enabling a positive change in extractable work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Multiscale Models for Fibril Formation: Rare Events Methods, Microkinetic Models, and Population Balances

Amyloid fibrils are thought to grow by a two-step dock-lock mechanism. However, previous simulations of fibril formation (i) overlook the bi-molecular nature of the docking step and obtain rates with first-order units, or (ii) superimpose the docked and locked states when computing the potential of mean force for association and thereby muddle the docking and locking steps. Here, we developed a simple microkinetic model with separate locking and docking steps and with the appropriate concentration dependences for each step. We constructed a simple model comprised of chiral dumbbells that retains qualitative aspects of fibril formation. We used rare events methods to predict separate docking and locking rate constants for the model. The rate constants were embedded in the microkinetic model, with the microkinetic model embedded in a population balance model for “bottom-up” multiscale fibril growth rate predictions. These were compared to “top-down” results using simulation data with the same model and multiscale framework to obtain maximum likelihood estimates of the separate lock and dock rate constants. We used the same procedures to extract separate docking and locking rate constants from experimental fibril growth data. Our multiscale strategy, embedding rate theories, and kinetic models in conservation laws should help to extract docking and locking rate constants from experimental data or long molecular simulations with correct units and without compromising the molecular description.

Shayesteh Zadeh, Armin (ORCID:0000000299896710)↗

The Search for μ+ → e+γ with 10–14 Sensitivity: The Upgrade of the MEG Experiment

The MEG experiment took data at the Paul Scherrer Institute in the years 2009–2013 to test the violation of the lepton flavor conservation law, which originates from an accidental symmetry that the Standard Model of elementary particle physics has, and published the most stringent limit on the charged lepton flavor violating decay μ+→e+γ: BR(μ+→e+γ) <4.2×10−13 at 90% confidence level. The MEG detector has been upgraded in order to reach a sensitivity of 6×10−14. The basic principle of MEG II is to achieve the highest possible sensitivity using the full muon beam intensity at the Paul Scherrer Institute (7×107 muons/s) with an upgraded detector. The main improvements are better rate capability of all sub-detectors and improved resolutions while keeping the same detector concept. In this paper, we present the current status of the preparation, integration and commissioning of the MEG II detector in the recent engineering runs.

physics beyond the Standard Model↗