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At least 595 records · Page 33

A Scalable Reduced‐Order Model for the Steady Navier–Stokes Equations

Scaling up new scientific technologies from laboratory to industry often involves demonstrating performance on a larger scale. Computer simulations can accelerate design and predictions in the deployment process, though traditional numerical methods are computationally intractable even for intermediate pilot plant scales. Recently, the component reduced order modeling method has been developed to tackle this challenge by combining projection reduced order modeling and discontinuous Galerkin domain decomposition. However, while many scientific or engineering applications involve nonlinear physics, this method has only been demonstrated for various linear systems. In this work, the component reduced order modeling method is extended to steady Navier–Stokes flow, with application to general nonlinear physics in view. The large‐scale, global domain is decomposed into a combination of small‐scale unit component. Linear subspaces for flow velocity and pressure are identified via proper orthogonal decomposition over sample snapshots collected from each small‐scale unit component. Velocity bases are augmented with a pressure supremizer to satisfy the inf–sup condition for stable pressure prediction. Two different nonlinear reduced order modeling methods are employed and compared for efficient evaluation of nonlinear advection: A third‐order tensor projection operator and the empirical quadrature procedure. The proposed method is demonstrated on the flow over arrays of five different unit objects, achieving a 23‐fold speedup with less than 4% relative error in domains up to 256 times larger than the unit components. Furthermore, a numerical experiment with the pressure supremizer strongly indicates the need for a supremizer for stable pressure prediction. A comparison between the tensorial approach and the empirical quadrature procedure revealed a slight advantage of the empirical quadrature procedure. The framework is compared with an alternating Schwarz‐based reduced‐order approach, demonstrating improved efficiency and robustness for the DG‐based global solver while retaining flexibility for sub‐scale iterative solvers. The method is further extended to a coupled advection–diffusion and Navier–Stokes system, illustrating its applicability to multi‐physics problems and its potential for more general, inter‐coupled nonlinear systems.

42 ENGINEERING↗

A Father’s Day Tribute Father-son Nobel Prize-winning physicists worked together at the Lab

Partners in physics during the World War II years, father and son Niels and Aage Bohr worked side by side on the Lab’s top-secret effort to create the first atomic bombs. Arriving in Los Alamos in late 1943, Aage was just 21 years old. He had been studying physics to follow in the footsteps of his father, who had won a Nobel Prize in 1922. Aage’s higher education, however, had been interrupted by the rapid spread of Nazism in Europe. The Bohrs, who had Jewish heritage, fled their native Denmark to escape persecution, eventually arriving in Los Alamos to aid in the creation of weapons that would help end the war. Their story is part of the collections at the National Security Research Center, which is the Lab’s classified library and also houses unclassified historic materials. While at Los Alamos, Niels and Aage were accorded VIP status because of the family’s scientific renown and given new names to protect their identities: Aage was James Baker, while his father was Nicholas Baker, but the scientific community called him Uncle Nick. Whether called Niels and Aage or Nick and Jim, father and son were inseparable.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum Hall Effect and Langlands Program

Recent advances in the Langlands program shed light on a vast area of modern mathematics from an unconventional viewpoint, including number theory, gauge theory, representation, knot theory and etc. By applying to physics, these novel perspectives endow with a unified account of the (integer/ fractional) quantum Hall effect. The plateaus of the Hall conductance are described by Hecke eigensheaves of the geometric Langlands correspondence. Especially, the particle-vortex duality, which is explained by S-duality of Chern–Simons theory, corresponds to the Langlands duality in Wilson and Hecke operators. Moreover the Langlands duality in the quantum group associated with the Hamiltonian describes fractal energy spectrum structure, know as Hofstadter’s butterfly. These results suggest that the Langlands program has many physically realistic meanings.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Parametrizations of the spin density matrix

Highlights: • Proposed two methods for parametrizing the SDM of spinning, unstable particles. • All non-negativity conditions fulfilled; adaptability to various constraints. • First method: based on a theorem; applicable in a simple and flexible way. • Second method: particularly suitable for especial conditions. • Applications: two of them interesting in the search for new physics. We propose for the spin density matrix two parametrizations which automatically fulfill the non-negativity conditions, without setting any bound on the parameters. The first one relies on a theorem, that we prove, and it is rather simple and easily adaptable to some specific reactions, where, for example, parity is conserved or angular momentum conservation entails selection rules. Moreover, in the case when the rank is less than the order of the density matrix, we show how to improve the fits to the data, either by implementing previous suggestions, or by elaborating an alternative method, for which we prove a second theorem. Our second parametrization is a variant of previous treatments, it appears suitable for some particular processes. Moreover, we discuss about the possibility of inferring the elements of the density matrix from the differential decay width. Last, we illustrate various examples of current interest, both in strong and weak decays; some of them may be helpful in the investigation of physics beyond the standard model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Bloch decomposition-based stochastic Galerkin method for quantum dynamics with a random external potential

In this paper, we consider the numerical solution of the one-dimensional Schrödinger equation with a periodic lattice potential and a random external potential. This is an important model in solid state physics where the randomness results from complicated phenomena that are not exactly known. Here we generalize the Bloch decomposition-based time-splitting pseudospectral method to the stochastic setting using the generalized polynomial chaos with a Galerkin procedure so that the main effects of dispersion and periodic potential are still computed together. We prove that our method is unconditionally stable and numerical examples show that it has other nice properties and is more efficient than the traditional method. Finally, we give some numerical evidence for the well-known phenomenon of Anderson localization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

'Who Thinks Abstractly?': Quantum Theory and the Architecture of Physical Concepts

Beginning with its introduction by W. Heisenberg, quantum mechanics was often seen as an overly abstract theory, mathematically and physically, vis-a-vis classical physics or relativity. This perception was amplified by the fact that, while the quantum-mechanical formalism provided effective predictive algorithms for the probabilistic predictions concerning quantum experiments, it appeared unable to describe, even by way idealization, quantum processes themselves in space and time, in the way classical mechanics or relativity did. The aim of the present paper is to reconsider the nature of mathematical and physical abstraction in modern physics by offering an analysis of the concept of ''physical fact'' and of the concept of 'physical concept', in part by following G. W. F. Hegel's and G. Deleuze's arguments concerning the nature of conceptual thinking. In classical physics, relativity, and quantum physics alike, I argue, physical concepts are defined by the following main features - 1) their multi-component multiplicity; 2) their essential relations to problems; 3) and the interactions between physical, mathematical, and philosophical components within each concept. It is the particular character of these interactions in quantum mechanics, as defined by its essentially predictive (rather than descriptive) nature, that distinguishes it from classical physics and relativity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Subleading effects in QCD global fits

I discuss several corrections to leading twist calculation of nucleon structure functions which are needed to include experimental data at large parton fractional momentum x and at low scale Q{sup 2} in global fits of parton distribution functions. In particular I discuss the results of the CTEQ6X global fit, and some work in progress. Topics covered include the interplay of target mass and higher-twist corrections, the importance of nuclear corrections for deuterium target data, and applications to the study of quark-hadron duality. Implications for collider physics are highlighted.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Evidence for a bound H-dibaryon using lattice QCD

The H-dibaryon, a J = 0 state with the valence quark content udsuds, has long been hypothesized to exist because of the attractive nature of color magnetic gluon exchange in the flavor- singlet channel. Using lattice QCD the NPLQCD collaboration have investigated this system and evidence is presented for the existence of a stable H-dibaryon, albeit at a quark mass somewhat larger than that in nature. This calculation is reviewed and combined with subsequent calculations by the HALQCD collaboration at the SU(3) flavor symmetric point to identify bounds on the H-dibaryon mass at the physical quark masses.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Models of isospin violating ADM

The isospin violating dark matter (IVDM) scenario offers an interesting possibility to reconcile conflicting results among direct dark matter search experiments for a mass range around 10 GeV. We consider two simple renormalizable IVDM models with a complex scalar dark matter and a Dirac fermion dark matter, respectively, whose stability is ensured by the conservation of “dark matter number.” Although both models successfully work as the IVDM scenario with destructive interference between effective couplings to proton and neutron, the dark matter annihilation cross section is found to exceed the cosmological/astrophysical upper bounds. Then, we propose a simple scenario to reconcile the IVDM scenario with the cosmological/astrophysical bounds, namely, the IVDM being asymmetric. We also discuss collider experimental constraints on the models and an implication to Higgs boson physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum mechanical derivation of the Wallis formula for π

A famous pre-Newtonian formula for π is obtained directly from the variational approach to the spectrum of the hydrogen atom in spaces of arbitrary dimensions greater than one, including the physical three dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Exact Parent Hamiltonian for the Quantum Hall States in a Lattice

We study lattice models of charged particles in uniform magnetic fields. We show how longer range hopping can be engineered to produce a massively degenerate manifold of single-particle ground states with wave functions identical to those making up the lowest Landau level of continuum electrons in a magnetic field. We find that in the presence of local interactions, and at the appropriate filling factors, Laughlin's fractional quantum Hall wave function is an exact many-body ground state of our lattice model. The hopping matrix elements in our model fall off as a Gaussian, and when the flux per plaquette is small compared to the fundamental flux quantum one only needs to include nearest and next-nearest neighbor hoppings. We suggest how to realize this model using atoms in optical lattices, and describe observable consequences of the resulting fractional quantum Hall physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

On time-optimal NMR control of states of qutrits represented by quadrupole nuclei with the spin I = 1

Elementary logical operators (selective rotation, Fourier transform, controllable phase shift, and SUM gate) are considered for a quantum computer based on three-level systems (qutrits) represented by nuclear spins I = 1 under nuclear magnetic resonance conditions. The computer simulation of the realization of these operators by means of simple and composite selective radiofrequency (RF) pulses and optimized RF pulses is performed. The time dependence of the amplitude of last pulses is found by numerical optimization at different durations. Two variants are proposed for realization of a two-qutrit SUM gate by using one-qutrit or two-qutrit optimized RF pulses. The calculated time dependences of realization errors were used to study the time optimality of different methods for obtaining gates, proposed earlier and in this paper. The advantages and disadvantages of each of the methods are evaluated for different values of physical parameters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quartet states of the lepton sector

A holistic study of the lepton sector is fulfilled in the framework of rigorous restrictions by five input suppositions. All leptons are divided into three classes on the structure of their equations. They are singlets, doublets and quartets. The quartet states are the most interesting among them from the point of view of their properties and possible physical interpretations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

N.N. Bogoliubov’s contribution to nonequilibrium statistical mechanics (1937–1945)

It is shown that many important and still relevant results in the field of nonequilibrium statistical mechanics were derived by Bogoliubov (jointly with N.M. Krylov) early in the prewar years and were completely published in a still insufficiently known monograph of 1945. Among these findings were the concept of time hierarchy for stochastic evolution, the concept of quasi-averages that remove symmetry relative to time inversion, and the mechanism of dynamic relaxation of a physical object in a thermostat.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

TeV-Scale Strings

This article discusses the status of string physics where the string tension is around the TeV scale. Here, the article covers model building basics for perturbative strings, based on D-brane configurations. The effective low energy physics description of such string constructions is analyzed: how anomaly cancellation is implemented, how fast proton decay is avoided and how D-brane models lead to additional Z' particles. This review also discusses direct search bounds for strings at the TeV scale, as well as theoretical issues with model building related to flavor physics and axions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Simple Algorithms for a Physics Code Base

Project 1: Developing a container for state variables in a physics code. Project 2: Setting up near-continuous performance and usage metrics monitoring of a physics code.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗