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NASA NTRS1996

The Effects of Dissipation and Coarse Grid Resolution for Multigrid in Flow Problems

The objective of this paper is to investigate the effects of the numerical dissipation and the resolution of the solution on coarser grids for multigrid with the Euler equation approximations. The convergence is accomplished by multi-stage explicit time-stepping to steady state accelerated by FAS multigrid. A theoretical investigation is carried out for linear hyperbolic equations in one and two dimensions. The spectra reveals that for stability and hence robustness of spatial discretizations with a small amount of numerical dissipation the grid transfer operators have to be accurate enough and the smoother of low temporal accuracy. Numerical results give grid independent convergence in one dimension. For two-dimensional problems with a small amount of numerical dissipation, however, only a few grid levels contribute to an increased speed of convergence. This is explained by the small numerical dissipation leading to dispersion. Increasing the mesh density and hence making the problem over resolved increases the number of mesh levels contributing to an increased speed of convergence. If the steady state equations are elliptic, all grid levels contribute to the convergence regardless of the mesh density.

Eliasson, Peter↗

DOE OSTI2020

Stabilization of a Majorana zero mode through quantum frustration

We analyze a system in which a topological Majorana zero mode (tMZM) combines with a Majorana produced by quantum frustration (fMZM) to produce a novel ground state. The system that we study combines two parts, a grounded topological superconducting wire that hosts two tMZMs at its ends and an on-resonant quantum dot connected to two dissipative leads. The quantum dot with dissipative leads creates an effective two-channel Kondo (2CK) state in which quantum frustration yields an isolated fMZM at the dot. We find that coupling the dot to one end of the topological wire stabilizes the tMZM at the other end. Three routes are used to obtain these results: (i) calculation of the conductance through an auxiliary detector quantum dot, (ii) renormalization group (RG) arguments and the g theorem, and (iii) a fully nonequilibrium calculation of the I(V) curve and shot noise S(V) through the detector dot. In addition to providing a route to achieving an unpaired Majorana zero mode, this scheme provides a clear signature of the presence of the 2CK frustration-induced Majorana.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1989

Properties of earthquakes generated by fault dynamics

A model for fault dynamics consisting of a uniform chain of blocks and springs pulled slowly across a rough surface is presented. The only nonlinear element of the model is a slip-stick friction force between the blocks and the surface. It is found that this model gives rise to events of all sizes. The numerical evaluation of the distribution of earthquake magnitudes results in a power-law spectrum similar to what is observed in nature. Like certain other dissipative dynamical systems, the observed large fluctuations in earthquake magnitude persist because the system is in a state of marginal stability.

Carlson, J. M.↗

NASA NTRS1973

The use of superconductivity in magnetic balance design

The magnetic field and field gradient requirements for magnetic suspension in a Mach 3, 6-in. diameter wind tunnel are stated, along with the power requirements for gradient coil pairs wound of copper operating at room temperature and aluminum cooled to 20 K. The power dissipated is large enough that the use of superconductivity in the coil design becomes an attractive alternative. The problems of stability and ac losses are outlined along with the properties of stabilized superconductors. A brief review of a simplified version of the critical state model of C. P. Bean is presented, and the problems involved in calculations of the ac losses in superconducting coils are outlined. A summary of ac loss data taken on pancake coils wound of commercially available Nb3Sn partially stabilized tape is presented and shown as leading to the U.Va. gradient coil design. The actual coil performance is compared with predictions based on the BNL results. Finally, some remarks are presented concerning scaling of the ac losses to larger magnetic suspension systems as well as prospects for improved performance using newer multifilament superconductors.

Moss, F. E.↗

NASA NTRS1988

Extrema principles of entrophy production and energy dissipation in fluid mechanics

A survey is presented of several extrema principles of energy dissipation as applied to problems in fluid mechanics. An exact equation is derived for the dissipation function of a homogeneous, isotropic, Newtonian fluid, with terms associated with irreversible compression or expansion, wave radiation, and the square of the vorticity. By using entropy extrema principles, simple flows such as the incompressible channel flow and the cylindrical vortex are identified as minimal dissipative distributions. The principal notions of stability of parallel shear flows appears to be associated with a maximum dissipation condition. These different conditions are consistent with Prigogine's classification of thermodynamic states into categories of equilibrium, linear nonequilibrium, and nonlinear nonequilibrium thermodynamics; vortices and acoustic waves appear as examples of dissipative structures. The measurements of a typical periodic shear flow, the rectangular wall jet, show that direct measurements of the dissipative terms are possible.

Horne, W. Clifton↗

NASA NTRS1988

Extrema principles of entropy production and energy dissipation in fluid mechanics

A survey is presented of several extrema principles of energy dissipation as applied to problems in fluid mechanics. An exact equation is derived for the dissipation function of a homogeneous, isotropic, Newtonian fluid, with terms associated with irreversible compression or expansion, wave radiation, and the square of the vorticity. By using entropy extrema principles, simple flows such as the incompressible channel flow and the cylindrical vortex are identified as minimal dissipative distributions. The principal notions of stability of parallel shear flows appear to be associated with a maximum dissipation condition. These different conditions are consistent with Prigogine's classification of thermodynamic states into categories of equilibrium, linear nonequilibrium, and nonlinear nonequilibrium thermodynamics; vortices and acoustic waves appear as examples of dissipative structures. The measurements of a typical periodic shear flow, the rectangular wall jet, show that direct measurements of the dissipative terms are possible.

Horne, W. Clifton↗

NASA NTRS2009

Construction of Low Dissipative High Order Well-Balanced Filter Schemes for Non-Equilibrium Flows

The goal of this paper is to generalize the well-balanced approach for non-equilibrium flow studied by Wang et al. [26] to a class of low dissipative high order shock-capturing filter schemes and to explore more advantages of well-balanced schemes in reacting flows. The class of filter schemes developed by Yee et al. [30], Sjoegreen & Yee [24] and Yee & Sjoegreen [35] consist of two steps, a full time step of spatially high order non-dissipative base scheme and an adaptive nonlinear filter containing shock-capturing dissipation. A good property of the filter scheme is that the base scheme and the filter are stand alone modules in designing. Therefore, the idea of designing a well-balanced filter scheme is straightforward, i.e., choosing a well-balanced base scheme with a well-balanced filter (both with high order). A typical class of these schemes shown in this paper is the high order central difference schemes/predictor-corrector (PC) schemes with a high order well-balanced WENO filter. The new filter scheme with the well-balanced property will gather the features of both filter methods and well-balanced properties: it can preserve certain steady state solutions exactly; it is able to capture small perturbations, e.g., turbulence fluctuations; it adaptively controls numerical dissipation. Thus it shows high accuracy, efficiency and stability in shock/turbulence interactions. Numerical examples containing 1D and 2D smooth problems, 1D stationary contact discontinuity problem and 1D turbulence/shock interactions are included to verify the improved accuracy, in addition to the well-balanced behavior.

Wang, Wei↗

NASA NTRS1983

Finite element formulation for transient heat treat problems

The macrothermomechanical behavior of materials subjected to rapid thermal or mechanical loading such as occurs in most heat treatments is described. The equations are developed for Lagrangian, Eulerian, and intermediary kinematic descriptions and are independent of the constitutive laws and the equation of state; they can be solved numerically for a specified material and boundary conditions. The coupled transport effects between dissipation and energy are included. The conventional linearized stability approach indicates the numerical procedure to be stable, with certain restriction on the time step size.

Mullen, R. L.↗

DOE OSTI2026

Inverter-Based Power Systems From an Electric Circuit Perspective

This presentation reports a twin circuit theory that enables us to interpret power system dynamics from a electric circuit perspective. Our proposed twin circuit theory can roughly prove the dissipating energy flow (DEF) method, and shows the positive impacts of well-designed grid-forming (GFM) inverters on power systems stability.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Nanoscale imaging of He-ion irradiation effects on amorphous TaO x toward electroforming-free neuromorphic functions

Resistive switching in thin films has been widely studied in a broad range of materials. Yet, the mechanisms behind electroresistive switching have been persistently difficult to decipher and control, in part due to their non-equilibrium nature. Here, we demonstrate new experimental approaches that can probe resistive switching phenomena, utilizing amorphous TaO x as a model material system. Specifically, we applied scanning microwave impedance microscopy and cathodoluminescence (CL) microscopy as direct probes of conductance and electronic structure, respectively. These methods provide direct evidence of the electronic state of TaO x despite its amorphous nature. For example, CL identifies characteristic impurity levels in TaO x , in agreement with first principles calculations. We applied these methods to investigate He-ion-beam irradiation as a path to activate conductivity of materials and enable electroforming-free control over resistive switching. However, we find that even though He-ions begin to modify the nature of bonds even at the lowest doses, the films' conductive properties exhibit remarkable stability with large displacement damage and they are driven to metallic states only at the limit of structural decomposition. Finally, we show that electroforming in a nanoscale junction can be carried out with a dissipated power of <20 nW, a much smaller value compared to earlier studies and one that minimizes irreversible structural modifications of the films. Importantly, the multimodal approach described here provides a new framework toward the theory/experiment guided design and optimization of electroresistive materials.

36 MATERIALS SCIENCE↗

NASA NTRS1974

Possible histories of the obliquity of Mercury

Possible evolutionary paths of the spin axis of Mercury are studied theoretically in terms of generalized Cassini's laws using the Hamiltonian approach. Three stable positions (Cassini states) of the spin axis are discerned. The Cassini states in which the spin axis remains fixed in the frame rotating with the orbit precession are extremes in the tide-free Hamiltonian under the condition of constant angular momentum. The stability of the 3/2 spin resonance for Mercury as a function of obliquity is discussed, and it is shown how control of the resonance is passed from one to another term in the averaged potential as the obliquity is increased with a corresponding loss of stability at each transfer. A sampling technique is used to infer the evolution due to tidal interaction. Two tidal models are used - one with a constant value of the specific dissipation function Q and the other with Q inversely proportional to frequency. An approximate analytic solution for precession trajectories very close to a Cassini state is developed.

Peale, S. J.↗

NASA NTRS1994

Proposed law of nature linking impacts, plume volcanism, and Milankovitch cycles to terrestrial vertebrate mass extinctions via greenhouse-embryo death coupling

A greenhouse-physiological coupling killing mechanism active among mammals, birds, and reptiles has been identified. Operating via environmental thermal effects upon the maternal core-skin blood flow critical to the survival and development of embryos, it reduces the flow of blood to the uterine tract. Today, during hot summers, this phenomena kills embryos on a vast, global scale. Because of sensitivity of many mammals to modern heat, a major modern greenhouse could reduce population numbers on a global scale, and potentially trigger population collapses in the more vulnerable parts of the world. In the geological past, the killing mechanism has likely been triggered into action by greenhouse warming via impact events, plume volcanism, and Earth orbital variations (Milankovitch cycles). Earth's biosphere is maintained and molded by the flow of energy from the solar energy source to Earth and on to the space energy sink (SES). This SES energy flow maintains Earth's biosphere and its living components, as open, intermediate, dissipative, nonequilibrium systems whose states are dependent upon the rate of energy flowing through them. Greenhouse gases such as CO2 in the atmosphere influence the SES energy flow rate. Steady-state flow is necessary for global ecological stability (autopoiesis). Natural fluctuations of the C cycle such as rapid releases of CO2 from the mantle, or oceans, disrupt steady-state SES flow. These fluctuations constantly challenge the biosphere; slowdown of SES energy flow drives it toward thermodynamical equilibrium and stagnation. Fluctuations induced by impact event, mantle plume volcanism, and Milankovitch cycles can grow into structure-breaking waves triggering major perturbations of Earth's C cycle and mass extinctions. A major C cycle perturbation involves readjustment of the outer physiochemical spheres of the Earth: the atmosphere, hydrosphere, and lithosphere; and by necessity, the biosphere. A greenhouse, one manifestation of a major C cycle perturbation, is the most dangerous natural phenomenon that life on Earth can experience. Greenhouse conditions existed during the KT mass extinctions of 65 m.y. ago, and the Pleistocene-Holocene (P-H) mammalian extinctions of 10,000-12,000 yr ago. Coupling climatology to reproductive physiology via effects of ambient air temperature upon uterine blood flow to developing embryos accounts for the extinctions via established physiological principles.

Mclean, D. M.↗

NASA NTRS1990

A high-order compact numerical algorithm for supersonic flows

A dissipative compact two-four scheme (second-order time, fourth-order space) similar to the original MacCormack scheme has been developed, that exhibits greater accuracy than conventional fourth-order schemes. The dissipative nature of the scheme allows it to resolve weak discontinuities without artificial damping. A derivation of the scheme is presented, as well as the theoretical stability characteristics. The temporal scheme is then generalized into a steady-state formulation which achieves fourth-order spatial accuracy at steady-state. Several test problems are used to show that the scheme is more accurate than the traditional MacCormack scheme, and is nearly as efficient.

Carpenter, M. H.↗

NASA NTRS1983

Preferred orbit planes in the gravitational field of a tumbling spheroidal galaxy

An analytic method is described by means of which the preferred planes into which gas will settle by dissipative differential precession in a slightly nonspherical, nonstatic potential can be determined. Attention is given to the analysis of circular orbit precession in the external potential of a slightly prolate spheroidal mass that is tumbling about a short axis, providing a crude model for barred spiral galaxies as well as for prolate elliptical ones. The results obtained agree with previous work on the existence, orientation, and stability of periodic orbits in triaxial potentials. Depending on the source and injection geometry of the gas and on the nature of dissipation in the gas, the orbital dynamics presented could lead to enhanced, or even catastrophic, radial inflow and to steady state warped structures.

Durisen, R. H.↗

DOE OSTI2026

Third-body stabilization of supercritical CO 2 in CO oxidation: development and application of a ReaxFF force field for the CO/O/CO 2 system

Supercritical CO 2 (scCO 2 ) plays a crucial role as a solvent in separation processes, advanced power cycles, and materials processing. Nonetheless, the atomistic comprehension of how the dense scCO 2 matrix influences the fundamental reaction of carbon monoxide (CO) is still insufficiently explored. Experimental studies and molecular dynamics (MD) simulations frequently fail to detect the highly reactive, transient intermediates, such as atomic oxygen (O), that drive these reactions. Here, to address this issue, we have developed a novel ReaxFF reactive force field for the CO 2 /CO/O system. The force field parameters were calibrated using density functional theory and second-order Møller-Plesset calculations to model CO 2 crystal properties, intermolecular interactions, bond dissociation curves, and reaction energy barriers. The force field reproduces the cohesive energy of the CO 2 crystal, the pressure characteristics of bulk scCO 2 , the equation-of-state behavior over a wide pressure–density range, the pressure dependence of the C–O bond length under compression, and the structural properties of liquid and scCO 2 , as documented by experiments, ab-initio MD, and prominent non-reactive models. The force field was subsequently applied to study the CO + O → CO 2 reaction. In a dilute environment, the reaction is inefficient as the newly formed CO 2 rapidly dissociates due to excess kinetic and potential energy acquired from the exothermic reaction. Conversely, in a dense scCO 2 environment, the surrounding matrix acts as an efficient third body, stabilizing the emerging CO2 product via molecular collisions. Statistical analysis confirms an average excess energy dissipation of 133.9 ± 3.6 kcal/mol over 112.4 ± 17.9 ps. Kinetic energy decomposition reveals that ∼ 92% of the excess kinetic energy is stored in internal (rotational and vibrational) degrees of freedom. This ReaxFF force field establishes a mechanistic foundation for third-body stabilization in dense reactive environments.

Chowdhury, Emdadul Haque [Pennsylvania State Univ.↗

NASA NTRS1983

Protostellar rotation - Turbulence and heating of molecular clouds

The formation of rapidly rotating protostellar objects in turbulent and clumpy molecular clouds is analyzed. It is shown that the early dissipation of the protostellar rotational energy via a rotationally driven wind can keep their parent molecular clouds at the observed temperatures and in the observed turbulent state. The model requires a low space density of protostellar shells in order to provide the energy requirements to stabilize molecular clouds against gravitational collapse in regions of star formation. The dependence of this mechanism on the star formation rate suggests that the star formation is self-regulated.

Franco, J.↗

NASA NTRS1984

A numerical simulation of barotropic instability. I Wave-mean flow interaction

A numerical model is used to study the evolution of the barotropic point jet instability as it interacts with the mean flow. The linearized instability solution agrees well with the recent analytical solutions of Lindzen. Stabilization of the point jet instability occurs as the mean flow is modified by wave vorticity transport. Assuming stabilization occurs when the meridional gradient of the zonal mean vorticity is no longer negative, the maximum integrated wave enstrophy can be predicted. In addition, an estimate of the integrated wave enstrophy at steady state can be made by balancing the generation of vorticity against dissipation. These limits are found to be in good agreement with the numerical results.

Schoeberl, M. R.↗

NASA NTRS1990

The effects of oppositely sloping boundaries with Ekman dissipation in a nonlinear baroclinic system

The present analytical and numerical examination of the effect of the slope Delta with dissipation delta on baroclinic flows in linear and nonlinear systems uses a modified Eady channel model with oppositely sloping top and bottom Ekman layers, and truncates the spectral wave solution up to six components. Comparisons are made wherever possible with results from beta-plane dissipative systems. In the linear system, the combined effect of Delta and delta strongly stabilizes long waves. In a nonlinear system without wave-wave interaction, Delta stabilizes the flow even for small delta and reduces the domain of vacillation while enlarging the domain of single-wave steady state.

Weng, H.-Y.↗