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At least 1,603 records · Page 89

Multistate Landau-Zener models with all levels crossing at one point

Within this paper, we discuss common properties and reasons for integrability in the class of multistate Landau-Zener models with all diabatic levels crossing at one point. Exploring the Stokes phenomenon, we show that each previously solved model has a dual one, whose scattering matrix can be also obtained analytically. For applications, we demonstrate how our results can be used to study conversion of molecular into atomic Bose condensates during passage through the Feshbach resonance, and provide purely algebraic solutions of the bowtie and special cases of the driven Tavis-Cummings model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Synergistic Effects of Physical Aging and Damage on Long-Term Behavior of Polymer Matrix Composites

The research consisted of two major parts, first modeling and simulation of the combined effects of aging and damage on polymer composites and secondly an experimental phase examining composite response at elevated temperatures, again activating both aging and damage. For the simulation, a damage model for polymeric composite laminates operating at elevated temperatures was developed. Viscoelastic behavior of the material is accounted for via the correspondence principle and a variational approach is adopted to compute the temporal stresses within the laminate. Also, the effect of physical aging on ply level stress and on overall laminate behavior is included. An important feature of the model is that damage evolution predictions for viscoelastic laminates can be made. This allows us to track the mechanical response of the laminate up to large load levels though within the confines of linear viscoelastic constitutive behavior. An experimental investigation of microcracking and physical aging effects in polymer matrix composites was also pursued. The goal of the study was to assess the impact of aging on damage accumulation, in ten-ns of microcracking, and the impact of damage on aging and viscoelastic behavior. The testing was performed both at room and elevated temperatures on [+/- 45/903](sub s) and [02/903](sub s) laminates, both containing a set of 90 deg plies centrally located to facilitate investigation of microcracking. Edge replication and X-ray-radiography were utilized to quantify damage. Sequenced creep tests were performed to characterize viscoelastic and aging parameters. Results indicate that while the aging times studied have limited ]Influence on damage evolution, elevated temperature and viscoelastic effects have a profound effect on the damage mode seen. Some results are counterintuitive, including the lower strain to failure for elevated temperature tests and the catastrophic failure mode observed for the [+/- 45/9O3](sub s), specimens. The fracture toughness for transverse cracks increases with increasing temperature for both systems: transverse cracking was completely absent prior to failure in [+/- 45/903](sub s), and was suppressed for [02/903](sub s). No significant effect of damage on aging or viscoelastic parameters was observed.

Brinson, L. Cate↗

Increasing the power density when using inert matrix fuels to reduce production of transuranics

Reducing the production of transuranics is a goal of most advanced nuclear fuel cycles. One way to do this is to recycle the transuranics into the same reactors that are currently producing them using an inert matrix fuel. In previous work we have modeled such a reactor where 72%, of the core is comprised of standard enriched uranium fuel pins, with the remaining 28% fuel made from Yttria stabilized zirconium, in which transuranics are loaded. A key feature of this core is that all of the transuranics produced by the uranium fuel assemblies are later burned in inert matrix fuel assemblies. It has been shown that this system can achieve reductions in transuranic waste of more than 86%. The disadvantage of such a system is that the core power rating must be significantly lower than a standard pressurized water reactor. One reason for the lower power is that high burnup of the uranium fuel precludes a critical level of reactivity at the end of the campaign. Increasing the uranium enrichment and changing the pin pitch are two ways to increase burnup while maintaining criticality. In this paper we use MCNPX and a linear reactivity model to quantify the effect of these two parameters on the end of campaign reactivity. Importantly, we show that in the region of our proposed reactor, enrichment increases core reactivity by 0.02 per percent uranium 235 and pin pitch increases reactivity by 0.02 per mm. Reactivity is lost at a rate of 0.005 per MWd/kgIHM uranium burnup. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Distributions of off-diagonal scattering matrix elements: Exact results

Scattering is a ubiquitous phenomenon which is observed in a variety of physical systems which span a wide range of length scales. The scattering matrix is the key quantity which provides a complete description of the scattering process. The universal features of scattering in chaotic systems is most generally modeled by the Heidelberg approach which introduces stochasticity to the scattering matrix at the level of the Hamiltonian describing the scattering center. The statistics of the scattering matrix is obtained by averaging over the ensemble of random Hamiltonians of appropriate symmetry. We derive exact results for the distributions of the real and imaginary parts of the off-diagonal scattering matrix elements applicable to orthogonally-invariant and unitarily-invariant Hamiltonians, thereby solving a long standing problem. -- Highlights: •Scattering problem in complex or chaotic systems. •Heidelberg approach to model the chaotic nature of the scattering center. •A novel route to the nonlinear sigma model based on the characteristic function. •Exact results for the distributions of off-diagonal scattering-matrix elements. •Universal aspects of the scattering-matrix fluctuations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Exact diagonalization library for quantum electron models

We present an exact diagonalization C++ template library (EDLib) for solving quantum electron models,including the single-band finite Hubbard cluster and the multi-orbital impurity Anderson model. Theobservables that can be computed using EDLib are single particle Green’s functions and spin–spincorrelation functions. This code provides three different types of Hamiltonian matrix storage that canbe chosen based on the model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Interrelated rotordynamic effects of cylindrical and conical whirl of annular seal rotors

In the present comprehensive method for annular-seal dynamic coefficients computations, the rotor-excitation effects of the uniform lateral-eccentricity mode and the angular eccentricity are treated as interrelated, by recognizing the fluid-exerted moments resulting from each. The computational procedure is a FEM perturbation model in which the zeroth-order, undisplaced-rotor flow solution in the clearance gap is obtained through a Petrov-Galerkin approach. The full matrix of rotordynamic coefficients is obtained. The computational model is verified against a bulk-flow model for a simple case involving a straight annular seal.

Baskharone, E. A.↗

Mixed quantum/classical theory of rotationally and vibrationally inelastic scattering in space-fixed and body-fixed reference frames

We formulated the mixed quantum/classical theory for rotationally and vibrationally inelastic scattering process in the diatomic molecule + atom system. Two versions of theory are presented, first in the space-fixed and second in the body-fixed reference frame. First version is easy to derive and the resultant equations of motion are transparent, but the state-to-state transition matrix is complex-valued and dense. Such calculations may be computationally demanding for heavier molecules and/or higher temperatures, when the number of accessible channels becomes large. In contrast, the second version of theory requires some tedious derivations and the final equations of motion are rather complicated (not particularly intuitive). However, the state-to-state transitions are driven by real-valued sparse matrixes of much smaller size. Thus, this formulation is the method of choice from the computational point of view, while the space-fixed formulation can serve as a test of the body-fixed equations of motion, and the code. Rigorous numerical tests were carried out for a model system to ensure that all equations, matrixes, and computer codes in both formulations are correct.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Analysis of transverse shear strains in pre-twisted thick beams using variational asymptotic method

The cross-sectional stiffness matrix is derived for a pre-twisted, moderately thick beam made of transversely isotropic materials and having rectangular cross sections. An asymptotically-exact methodology is used to model the anisotropic beam from 3-D elasticity, without any further assumptions. The beam is allowed to have large displacements and rotations, but small strain is assumed. The strain energy is computed making use of the beam constitutive law and kinematical relations derived with the inclusion of geometrical nonlinearities and an initial twist. The energy functional is minimized making use of the Variational Asymptotic Method (VAM), thereby reducing the cross section to a point on the beam reference line with appropriate properties, forming a 1-D constitutive law. VAM is a mathematical technique employed in the current problem to rigorously split the 3-D analysis of beams into two: a 2-D analysis over the beam cross-sectional domain, which provides a compact semi-analytical form of the properties of the cross sections, and a nonlinear 1-D analysis of the beam ref-erence curve. In this method, as applied herein, the cross-sectional analysis is performed asymptotically by taking advantage of a material small parameter and two geometric small parameters. 3-D strain components are derived using kinematics and arranged in orders of the small parameters. Closed-form expressions are derived for the 3-D non-linear warping and stress fields. Warping functions are obtained by the minimization of strain energy subject to certain set of constraints that render the 1-D strain measures well-defined. The zeroth-order 3-D warping field thus yielded is then used to integrate the 3-D strain energy density over the cross section, resulting in the 1-D strain energy density, which in turn helps identify the corresponding cross-sectional stiffness matrix. The model is capable of predicting interlaminar and transverse shear stresses accurately up to first order.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Clay, Water, and Salt: Controls on the Permeability of Fine-Grained Sedimentary Rocks

We report that the ability to predict the permeability of fine-grained soils, sediments, and sedimentary rocks is a fundamental challenge in the geosciences with potentially transformative implications in subsurface hydrology. In particular, fine-grained sedimentary rocks (shale, mudstone) constitute about two-thirds of the sedimentary rock mass and play important roles in three energy technologies: petroleum geology, geologic carbon sequestration, and radioactive waste management. The problem is a challenging one that requires understanding the properties of complex natural porous media on several length scales. One inherent length scale, referred to hereafter as the mesoscale, is associated with the assemblages of large grains of quartz, feldspar, and carbonates over distances of tens of micrometers. Its importance is highlighted by the existence of a threshold in the core scale mechanical properties and regional scale energy uses of shale formations at a clay content X clay ≈ 1/3, as predicted by an ideal packing model where a fine-grained clay matrix fills the gaps between the larger grains. A second important length scale, referred to hereafter as the nanoscale, is associated with the aggregation and swelling of clay particles (in particular, smectite clay minerals) over distances of tens of nanometers. Mesoscale phenomena that influence permeability are primarily mechanical and include, for example, the ability of contacts between large grains to prevent the compaction of the clay matrix. Nanoscale phenomena that influence permeability tend to be chemomechanical in nature, because they involve strong impacts of aqueous chemistry on clay swelling. The second length scale remains much less well characterized than the first, because of the inherent challenges associated with the study of strongly coupled nanoscale phenomena. Advanced models of the nanoscale properties of fine-grained media rely predominantly on the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, a mean field theory of colloidal interactions that accurately predicts clay swelling in a narrow range of conditions (low salinity, low compaction, Na + counterion). An important feature of clay swelling that is not predicted by these models is the coexistence, in most conditions of aqueous chemistry and dry bulk density, of two types of pores between parallel smectite particles: mesopores with a pore width of >3 nm that are controlled by long-range interactions (the osmotic swelling regime) and nanopores with a pore width <1 nm that are controlled by short-range interactions (the crystalline swelling regime). Finally, nanogeochemical characterization and simulation techniques, including coarse-grained and all-atom molecular dynamics simulations, hold significant promise for the development of advanced constitutive relations that predict this coexistence and its dependence on aqueous chemistry.

58 GEOSCIENCES↗

Study of modal coupling procedures for the shuttle: A matrix method for damping synthesis

The damping method was applied successfully to real structures as well as analytical models. It depends on the ability to determine an appropriate modal damping matrix for each substructure. In the past, modal damping matrices were assumed diagonal for lack of being able to determine the coupling terms which are significant in the general case of nonproportional damping. This problem was overcome by formulating the damped equations of motion as a linear perturbation of the undamped equations for light structural damping. Damped modes are defined as complex vectors derived from the complex frequency response vectors of each substructure and are obtained directly from sinusoidal vibration tests. The damped modes are used to compute first order approximations to the modal damping matrices. The perturbation approach avoids ever having to solve a complex eigenvalue problem.

Hasselman, T. K.↗

Algorithmic Patterns for $$\mathcal {H}$$-Matrices on Many-Core Processors

In this work, we consider the reformulation of hierarchical ( \(\mathcal {H}\) ) matrix algorithms for many-core processors with a model implementation on graphics processing units (GPUs). \(\mathcal {H}\) matrices approximate specific dense matrices, e.g., from discretized integral equations or kernel ridge regression, leading to log-linear time complexity in dense matrix–vector products. The parallelization of \(\mathcal {H}\) matrix operations on many-core processors is difficult due to the complex nature of the underlying algorithms. While previous algorithmic advances for many-core hardware focused on accelerating existing \(\mathcal {H}\) matrix CPU implementations by many-core processors, we here aim at totally relying on that processor type. As main contribution, we introduce the necessary parallel algorithmic patterns allowing to map the full \(\mathcal {H}\) matrix construction and the fast matrix–vector product to many-core hardware. In this work, crucial ingredients are space filling curves, parallel tree traversal and batching of linear algebra operations. The resulting model GPU implementation hmglib is the, to the best of the authors knowledge, first entirely GPU-based Open Source \(\mathcal {H}\) matrix library of this kind. We investigate application examples as present in kernel ridge regression, Gaussian Process Regression and kernel-based interpolation. In this context, an in-depth performance analysis and a comparative performance study against a standard multi-core CPU \(\mathcal {H}\) matrix library highlights profound speedups of our many-core parallel approach.

97 MATHEMATICS AND COMPUTING↗

Time–series Analysis of Volume Change at Brady Hot Springs, Nevada, USA using Geodetic Data from 2003 – 2018

Brady Hot Springs geothermal field has exhibited subsidence, as measured by interferometric synthetic aperture radar (InSAR). Previous studies have examined both the temporal evolution of the deformation from 2004 through 2016 and the spatial extent of the deformation, directly relating the observed subsidence to volumetric changes below the surface. We extend the modeling at Brady to analyze a data set of interferometric pairs spanning from the end of 2003 through 2018. We examine spatial and temporal trends in the observed deformation by time–series analysis of each of the 1656 cubic voxels in a parameterized elastic dislocation model to identify areas where the subsurface volume changes as a function of time. Joint time–series analysis of Global Positioning System and InSAR pairs confirm significant changes in rates of volume change during time intervals when well operations were varied. Here, the rate of subsidence increases with increased injection, consistent with the identification of thermal contraction of the rock matrix as the dominant driving mechanism. Conversely, the modeled volume increases when pumping ceases, suggesting thermal expansion of the rock matrix.

58 GEOSCIENCES↗

Nonequilibrium optical response of a one-dimensional Mott insulator

We define, compute, and analyze the nonequilibrium differential optical conductivity of the one-dimensional extended Hubbard model at half-filling after applying a pump pulse, using the time-dependent density matrix renormalization group method. The melting of the Mott insulator is accompanied by a suppression of the local magnetic moment and ensuing photogeneration of doublon-holon pairs. The differential optical conductivity reveals (i) mid-gap states related to parity-forbidden optical states and (ii) strong renormalization and hybridization of the excitonic resonance and the absorption band, yielding a Fano resonance. We offer evidence and interpret such a resonance as a signature of nonequilibrium optical excitations resembling excitonic strings, (bi)excitons, and unbound doublon-holon pairs, depending on the magnitude of the intersite Coulomb repulsion. We discuss our results in the context of pump and probe spectroscopy experiments on organic Mott insulators.

1-dimensional systems↗

Pair density wave in the doped three-band Hubbard model on two-leg square cylinders

A pair density wave (PDW) is a superconducting (SC) state with a spatially modulated order parameter. Although much is known about the properties of the PDW state, its realization in microscopic models with divergent susceptibility has been challenging. Here, in this work, we report a density-matrix renormalization group study of a three-band Hubbard model (also known as the Emery model) for cuprates on long two-leg square cylinders. Upon light doping, we find that the ground state of the system is consistent with that of a PDW state with mutually commensurate and power-law SC, charge (CDW), and spin (SDW) density wave correlations. The SC correlations are dominant between neighboring Cu sites with d-wave pairing symmetry. Interestingly, we find that the near-neighbor interactions, especially the near-neighbor attractive V pd interaction between neighboring Cu and oxygen sites, can notably enhance the SC correlations while simultaneously suppressing the CDW correlations. For a modestly strong attractive V pd , the SC correlations become quasi-long-ranged with a divergent PDW susceptibility.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

The accuracy of approximate solutions in the analysis of fracture of composites

This paper concerns the accuracy of three related mathematical models (developed by Hedgepeth, Eringen and Sendeckyj and Jones) used in the stress analysis and in fracture studies of continuous-fiber composites. These models have particular application in the investigation of fiber and matrix stresses in unidirectional composites in the region near a crack tip. The interest in such models is motivated by the desire to be able to simplify the equations of elasticity to the point that they can be solved in a relatively easy manner.

Goree, J. G.↗

The accuracy of approximate solutions in the analysis of fracture of composites

This paper concerns the accuracy of three related mathematical models (developed by Hedgepeth, Eringen and Sendeckyj and Jones) used in the stress analysis and in fracture studies of continuous-fiber composites. These models have particular application in the investigation of fiber and matrix stresses in unidirectional composites in the region near a crack tip. The interest in such models is motivated by the desire to be able to simplify the equations of elasticity to the point that they can be solved in a relatively easy manner.

Goree, J. G.↗

Distinct critical behaviors from the same state in quantum spin and population dynamics perspectives

There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations—within simple models, both are obtained from the principal eigenvector of the same matrix. However, that vector is the wave-function amplitude in the quantum spin model, whereas it is the probability itself in the population model. We show that this seemingly minor difference has significant consequences: Phase transitions that are discontinuous in the spin system become continuous when viewed through the population perspective, and transitions that are continuous become governed by new critical exponents. We introduce a more general class of models that encompasses both cases and that can be solved exactly in a mean-field limit. Numerical results are also presented for a number of one-dimensional chains with power-law interactions. We see that well-worn spin models of quantum statistical mechanics can contain unexpected new physics and insights when treated as population-dynamical models and beyond, motivating further studies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Finite element implementation of viscoplastic models

A brief description of the implementation in MARK, the general purpose finite element structural analysis code, of two viscoplastic models developed by Robinson is given. One model is for isotropic materials and the other is for metal matrix composites. Also presented are analytical results obtained for hot section components using these models.

Arya, V. K.↗