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DOE OSTI2016

Some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers of finite extent

As a part of the preliminary studies for the future space experiment (Zona-K) in the Russian module of the International Space Station, some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers filled with 10 cSt silicone oil have been numerically studied in this paper. As the laterally applied temperature difference is raised, variations in the spatial structure and temporal evolution of the thermocapillary convection and a complex sequence of transitions are observed. The results show that the finite extent of the liquid layer significantly influences the tempo-spatial evolution of the thermocapillary convection. Moreover, the bifurcation route of the thermocapillary convection changes very sensitively by the aspect ratio of the liquid layer. With the increasing Reynolds number (applied temperature difference), the steady thermocapillary convection experiences two consecutive transitions from periodic oscillatory state to quasi-periodic oscillatory state with frequency-locking before emergence of chaotic convection in a liquid layer of aspect ratio 14.25, and the thermocapillary convection undergoes period-doubling cascades leading to chaotic convection in a liquid layer of aspect ratio 13.0.

42 ENGINEERING↗

DOE OSTI2017

Discrete Adjoint Sensitivity Analysis of Hybrid Dynamical Systems With Switching [Discrete Adjoint Sensitivity Analysis of Hybrid Dynamical Systems]

Sensitivity analysis is an important tool for describing power system dynamic behavior in response to parameter variations. It is a central component in preventive and corrective control applications. The existing approaches for sensitivity calculations, namely, finite-difference and forward sensitivity analysis, require a computational effort that increases linearly with the number of sensitivity parameters. In this paper, we investigate, implement, and test a discrete adjoint sensitivity approach whose computational effort is effectively independent of the number of sensitivity parameters. The proposed approach is highly efficient for calculating sensitivities of larger systems and is consistent, within machine precision, with the function whose sensitivity we are seeking. This is an essential feature for use in optimization applications. Moreover, our approach includes a consistent treatment of systems with switching, such as dc exciters, by deriving and implementing the adjoint jump conditions that arise from state-dependent and time-dependent switchings. The accuracy and the computational efficiency of the proposed approach are demonstrated in comparison with the forward sensitivity analysis approach. In conclusion, this paper focuses primarily on the power system dynamics, but the approach is general and can be applied to hybrid dynamical systems in a broader range of fields.

42 ENGINEERING↗

DOE OSTI2018

Low-Temperature Behavior of the Multicomponent Widom–Rowlison Model on Finite Square Lattices

We consider the multicomponent Widom–Rowlison with Metropolis dynamics, which describes the evolution of a particle system where M different types of particles interact subject to certain hard-core constraints. Focusing on the scenario where the spatial structure is modeled by finite square lattices, we study the asymptotic behavior of this interacting particle system in the low-temperature regime, analyzing the tunneling times between its M maximum-occupancy configurations, and the mixing time of the corresponding Markov chain. In particular, we develop a novel combinatorial method that, exploiting geometrical properties of the Widom–Rowlinson configurations on finite square lattices, leads to the identification of the timescale at which transitions between maximum-occupancy configurations occur and shows how this depends on the chosen boundary conditions and the square lattice dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1992

The influence of bulges on boundary-layer instability

Local disturbances caused by a spanwise surface corrugation affect the position of the boundary-layer transition, and so the drag, of an object. This premature transition from laminar to turbulent flow is often associated with a separation of the laminar boundary-layer from its surface. Also the roughness-induced separation bubble provides an important link between the pressure and velocity fluctuations in the environment and the development of the disturbance in the laminar boundary-layer, i.e., the receptivity problem. To investigate the influence of a laminar separation bubble on boundary-layer instability, a separated flow generated by a velocity gradient over a flat plate was analyzed by direct numerical simulation using finite-difference solutions of the Navier-Stokes equations. The bubble acts as a strong amplifier of the instability waves and a highly nonlinear flow field is shown to develop downstream of the bubble. Consequently, the results of the direct numerical simulation differ noticeably from those of the classical linear stability theory proving the fact that the nonparallel effects together with the nonlinear interactions are crucial to this flow development. In the present paper, the effect of physical perturbations such as humps and hollows on boundary-layer instability is analyzed. This problem has been considered theoretically by several researchers (e.g., Nayfeh et al., 1987 and 1990; Cebeci et al., 1988). They used linear stability theory in their approach which does not include the nonparallel nor the nonlinear effects. Therefore, to account for these important effects in studying flow over humps and hollows the direct simulation technique is being implemented in generalized coordinates.

Elli, S.↗

NASA NTRS2002

A Thermodynamic Theory Of Solid Viscoelasticity. Part 1: Linear Viscoelasticity.

The present series of three consecutive papers develops a general theory for linear and finite solid viscoelasticity. Because the most important object for nonlinear studies are rubber-like materials, the general approach is specified in a form convenient for solving problems important for many industries that involve rubber-like materials. General linear and nonlinear theories for non-isothermal deformations of viscoelastic solids are developed based on the quasi-linear approach of non-equilibrium thermodynamics. In this, the first paper of the series, we analyze non-isothermal linear viscoelasticity, which is applicable in a range of small strains not only to all synthetic polymers and bio-polymers but also to some non-polymeric materials. Although the linear case seems to be well developed, there still are some reasons to implement a thermodynamic derivation of constitutive equations for solid-like, non-isothermal, linear viscoelasticity. The most important is the thermodynamic modeling of thermo-rheological complexity , i.e. different temperature dependences of relaxation parameters in various parts of relaxation spectrum. A special structure of interaction matrices is established for different physical mechanisms contributed to the normal relaxation modes. This structure seems to be in accord with observations, and creates a simple mathematical framework for both continuum and molecular theories of the thermo-rheological complex relaxation phenomena. Finally, a unified approach is briefly discussed that, in principle, allows combining both the long time (discrete) and short time (continuous) descriptions of relaxation behaviors for polymers in the rubbery and glassy regions.

Freed, Alan D.↗

NASA NTRS2011

Generalized Fluid System Simulation Program, Version 5.0-Educational

The Generalized Fluid System Simulation Program (GFSSP) is a finite-volume based general-purpose computer program for analyzing steady state and time-dependent flow rates, pressures, temperatures, and concentrations in a complex flow network. The program is capable of modeling real fluids with phase changes, compressibility, mixture thermodynamics, conjugate heat transfer between solid and fluid, fluid transients, pumps, compressors and external body forces such as gravity and centrifugal. The thermofluid system to be analyzed is discretized into nodes, branches, and conductors. The scalar properties such as pressure, temperature, and concentrations are calculated at nodes. Mass flow rates and heat transfer rates are computed in branches and conductors. The graphical user interface allows users to build their models using the point, drag and click method; the users can also run their models and post-process the results in the same environment. The integrated fluid library supplies thermodynamic and thermo-physical properties of 36 fluids and 21 different resistance/source options are provided for modeling momentum sources or sinks in the branches. This Technical Memorandum illustrates the application and verification of the code through 12 demonstrated example problems.

Majumdar, A. K.↗

NASA NTRS2011

Generalized Fluid System Simulation Program, Version 5.0-Educational. Supplemental Information for NASA/TM-2011-216470

Majumdar, A. K.↗

DOE OSTI2019

A 2 × 1 all-optical multiplexer using Kerr nonlinear nano-plasmonic switch

In this paper, a novel surface plasmon polariton based 2 × 1 multiplexer, which is based on an adder module and an all-optical controllable nano-plasmonic switching module is presented. It is shown that by applying a pump light, the transmissions of the input signals into the output waveguide can be controlled. The operation of the proposed device is investigated through the use of coupled-mode theory and finite-difference time-domain method. In the proposed adder module, the transmissions of the input signals at the working wavelengths are about 0.7. Based on the simulation results, by applying a pump light intensity of 150 KW/cm{sup 2} the transmissions of input signals alter with the extinction ratio of 22.04 dB, which shows a significant switching effect. For a pump light intensity of 150 KW/cm{sup 2} the switching times of input signals are measured about 560 fs. It is expected that the proposed 2 × 1 multiplexer can be used in all-optical signal processing, nano-plasmonic circuits, communication, etc.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Relativistic model for anisotropic strange stars

Highlights: We find exact solutions for the Einstein field equations for anisotropic strange stars. Maximum anisotropy at the surface is an inherent property for the singularity free compact stars. Maximum value for the mass and radius is presented for the corresponding values of the bag constants. Using observed value of mass different physical parameters for the strange stars are predicted. - Abstract: In this article, we attempt to find a singularity free solution of Einstein’s field equations for compact stellar objects, precisely strange (quark) stars, considering Schwarzschild metric as the exterior spacetime. To this end, we consider that the stellar object is spherically symmetric, static and anisotropic in nature and follows the density profile given by Mak and Harko (2002) , which satisfies all the physical conditions. To investigate different properties of the ultra-dense strange stars we have employed the MIT bag model for the quark matter. Our investigation displays an interesting feature that the anisotropy of compact stars increases with the radial coordinate and attains its maximum value at the surface which seems an inherent property for the singularity free anisotropic compact stellar objects. In this connection we also perform several tests for physical features of the proposed model and show that these are reasonably acceptable within certain range. Further, we find that the model is consistent with the energy conditions and the compact stellar structure is stable with the validity of the TOV equation and Herrera cracking concept. For the masses below the maximum mass point in mass vs radius curve the typical behavior achieved within the framework of general relativity. We have calculated the maximum mass and radius of the strange stars for the three finite values of bag constant B{sub g}.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

A compatible high-order meshless method for the Stokes equations with applications to suspension flows

A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. Here in this work, we present a discretization that couples a staggered scheme for pressure approximation with a divergence-free velocity reconstruction to obtain an adaptive, high-order, finite difference-like discretization that can be efficiently solved with conventional algebraic multigrid techniques. We use analytic benchmarks to demonstrate equal-order convergence for both velocity and pressure when solving problems with curvilinear geometries. In order to study problems in dense suspensions, we couple the solution for the flow to the equations of motion for freely suspended particles in an implicit monolithic scheme. The combination of high-order accuracy with fully-implicit schemes allows the accurate resolution of stiff lubrication forces directly from the solution of the Stokes problem without the need to introduce sub-grid lubrication models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Martensitic transformation in superlattices of two non-transforming metals

A number of studies have shown that the coherent integration of a second non-transforming phase in martensitic materials results in unprecedented thermo-mechanical properties. We demonstrate the possibility of martensitic transformation by epitaxially combining two non-transforming materials, Mg (hexagonal closed packed) and MgLi (body centered cubic). Density functional theory calculations predict that MgLi/Mg superlattices undergo a transformation crystallographically equivalent to MgSc alloys and can be expected to result in finite temperature shape memory behavior. We predict the zero-temperature energy of the martensite phase to be 9.3 meV/atom lower than austenite for a 50–50 at. % MgLi/Mg nanolaminate, which is expected to result in a martensitic transformation temperature of approximately 150 K. This energy difference can be tuned between 4.9 and 18.1 meV/atom by varying the fraction of the pure Mg phase in the superlattice, potentially enabling the transformation from cryogenic to room and higher temperatures. While Li diffusion might limit the applications of the systems proposed, this work opens the door to a new approach to create martensitic materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

An unstructured body-of-revolution electromagnetic particle-in-cell algorithm with radial perfectly matched layers and dual polarizations

A novel electromagnetic particle-in-cell algorithm has been developed for fully kinetic plasma simulations on unstructured (irregular) meshes in complex body-of-revolution geometries. The algorithm, implemented in the BORPIC++ code, utilizes a set of field scalings and a coordinate mapping, reducing the Maxwell field problem in a cylindrical system to a Cartesian finite element Maxwell solver in the meridian plane. The latter obviates the cylindrical coordinate singularity in the symmetry axis. The choice of an unstructured finite element discretization enhances the geometrical flexibility of the BORPIC++ solver compared to the more traditional finite difference solvers. Symmetries in Maxwell’s equations are explored to decompose the problem into two dual polarization states with isomorphic representations that enable code reuse. The particle-in-cell scatter and gather steps preserve charge conservation at the discrete level. Our previous algorithm (BORPIC+) discretized the E and B field components of TE Φ and TM Φ polarizations on the finite element (primal) mesh. Here, we employ a new field-update scheme. Using the same finite element (primal) mesh, this scheme advances two sets of field components independently: (1) E and B of TE Φ polarized fields, (E z , E ρ , B Φ ) and (2) D and H of TM Φ polarized fields, (D Φ , H z , H ρ ). Since these field updates are not explicitly coupled, the new field solver obviates the coordinate singularity, which otherwise arises at the cylindrical symmetric axis, ρ = 0 when defining the discrete Hodge matrices (generalized finite element mass matrices). Here, a cylindrical perfectly matched layer is implemented as a boundary condition in the radial direction to simulate open space problems, with periodic boundary conditions in the axial direction. We investigate effects of charged particles moving next to the cylindrical perfectly matched layer. We model azimuthal currents arising from rotational motion of charged rings, which produce TMΦ polarized fields. Several numerical examples are provided to illustrate the first application of the algorithm.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2013

Generalized Fluid System Simulation Program, Version 6.0

The Generalized Fluid System Simulation Program (GFSSP) is a finite-volume based general-purpose computer program for analyzing steady state and time-dependant flow rates, pressures, temperatures, and concentrations in a complex flow network. The program is capable of modeling real fluids with phase changes, compressibility, mixture thermodynamics, conjugate heat transfer between solid and fluid, fluid transients, pumps, compressors and external body forces such as gravity and centrifugal. The thermo-fluid system to be analyzed is discretized into nodes, branches, and conductors. The scalar properties such as pressure, temperature, and concentrations are calculated at nodes. Mass flow rates and heat transfer rates are computed in branches and conductors. The graphical user interface allows users to build their models using the 'point, drag, and click' method; the users can also run their models and post-process the results in the same environment. The integrated fluid library supplies thermodynamic and thermo-physical properties of 36 fluids, and 24 different resistance/source options are provided for modeling momentum sources or sinks in the branches. This Technical Memorandum illustrates the application and verification of the code through 25 demonstrated example problems.

Majumdar, A. K.↗

DOE OSTI2015

Stochastic differential equation model to Prendiville processes

The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Electron-phonon coupling and superconductivity in the doped topological crystalline insulator ( Pb 0.5 Sn 0.5 ) 1 – x In x Te

Here, we present a neutron-scattering study of phonons in single crystals of ( Pb 0.5 Sn 0.5 ) 1 – x In x Te with x = 0 (metallic, but nonsuperconducting) and x = 0.2 (nonmetallic normal state, but superconducting). We map the phonon dispersions (more completely for x = 0 ) and find general consistency with theoretical calculations, except for the transverse and longitudinal optical (LO) modes at the Brillouin-zone center. At low temperature, both modes are strongly damped but sit at a finite energy ( ≈ 4 meV in both samples), shifting to higher energy at room temperature. These modes are soft due to a proximate structural instability driven by the sensitivity of Pb-Te and Sn-Te p -orbital hybridization to off-center displacements of the metal atoms. The impact of the soft optical modes on the low-energy acoustic modes is inferred from the low thermal conductivity, especially at low temperature. Given that the strongest electron-phonon coupling is predicted for the LO mode, which should be similar for both studied compositions, it is intriguing that only the In-doped crystal is superconducting. In addition, we observe elastic diffuse (Huang) scattering that is qualitatively explained by the difference in Pb-Te and Sn-Te bond lengths within the lattice of randomly distributed Pb and Sn sites. We also confirm the presence of anomalous diffuse low-energy atomic vibrations that we speculatively attribute to local fluctuations of individual Pb atoms between off-center sites.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Nonequilibrium effects on stability of hybrid stars with first-order phase transitions

The stability of hybrid stars with first-order phase transitions as determined by calculating fundamental radial oscillation modes is known to differ from the predictions of the widely used Bardeen-Thorne-Meltzer criterion. We consider the effects of out-of-chemical-equilibrium physics on the radial modes and hence stability of these objects. For a barotropic equation of state, this is done by allowing the adiabatic sound speed to differ from the equilibrium sound speed. We show that doing so extends the stable branches of stellar models, allowing stars with rapid phase transitions to support stable higher-order stellar multiplets similarly to stars with multiple slow phase transitions. We also derive a new junction condition to impose on the oscillation modes at the phase transition. Termed the reactive condition, it is physically motivated, consistent with the generalized junction conditions between two phases, and has the common rapid and slow conditions as limiting cases. Unlike the two common cases, it can only be applied to nonbarotropic stars. Here, we apply this junction condition to hybrid stellar models generated using a two-phase equation of state consisting of nuclear matter with unpaired quark matter at high densities joined by a first-order phase transition and show that, like in the slow limiting case, stars that are classically unstable are stabilized by a finite chemical reaction speed.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2002

3D Finite Element Analysis of Particle-Reinforced Aluminum

Deformation in particle-reinforced aluminum has been simulated using three distinct types of finite element model: a three-dimensional repeating unit cell, a three-dimensional multi-particle model, and two-dimensional multi-particle models. The repeating unit cell model represents a fictitious periodic cubic array of particles. The 3D multi-particle (3D-MP) model represents randomly placed and oriented particles. The 2D generalized plane strain multi-particle models were obtained from planar sections through the 3D-MP model. These models were used to study the tensile macroscopic stress-strain response and the associated stress and strain distributions in an elastoplastic matrix. The results indicate that the 2D model having a particle area fraction equal to the particle representative volume fraction of the 3D models predicted the same macroscopic stress-strain response as the 3D models. However, there are fluctuations in the particle area fraction in a representative volume element. As expected, predictions from 2D models having different particle area fractions do not agree with predictions from 3D models. More importantly, it was found that the microscopic stress and strain distributions from the 2D models do not agree with those from the 3D-MP model. Specifically, the plastic strain distribution predicted by the 2D model is banded along lines inclined at 45 deg from the loading axis while the 3D model prediction is not. Additionally, the triaxial stress and maximum principal stress distributions predicted by 2D and 3D models do not agree. Thus, it appears necessary to use a multi-particle 3D model to accurately predict material responses that depend on local effects, such as strain-to-failure, fracture toughness, and fatigue life.

Shen, H.↗

DOE OSTI2015

Modified Heisenberg model for the zig-zag structure in multiferroic RMn{sub 2}O{sub 5}

The class of RMn{sub 2}O{sub 5} (R = Ho, Tb, Y, Eu) compounds offers multiferroic properties where the refined magnetic zig-zag order breaks the inversion symmetry. Varying the temperature, the system undergoes a magnetic and a subsequent ferroelectric phase transition where the ferroelectricity is magnetically induced. We propose a modified anisotropic Heisenberg model that can be used as a tractable analytical model studying the properties of those antiferromagnetic zig-zag spin chains. Based on a finite temperature Green's function method, it is shown that the polarization is induced solely by different exchange couplings of the two different Mn{sup 4+} and Mn{sup 3+} magnetic ions. We calculate the excitation energy of the spin system for finite temperatures, which for its part determines the temperature dependent magnetization and polarization. The ferroelectric phase transition is manifested as a kink in the excitation energy. The variation of the polarization by an external magnetic field depends strongly on the direction of that field. Whereas, the polarization in b-direction increases with an external magnetic field as well in b-direction it can be switched for strong fields in a-direction. The results based on that modified Heisenberg model are in qualitative agreement with experimental data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗