Variance-Reduced Splitting Schemes for Monotone Stochastic Generalized Equations
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Automation & Control Systems↗
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On the stability of systems with monotone and odd monotone nonlinearities.
Stability of feedback systems with monotone and odd monotone nonlinearities
TIME FACTOR↗
On a numerical sufficiency test for monotonic convergence of finite element models
Finite element analyses characterized by monotonic convergence include the discipline for meaningful measurements of convergence rate and consequently economical extrapolation. Few proposers of element models guarantee monotonic convergence for their elements. Thus, a need exists for an automatic test to classify available element models. This paper describes such a test - a test can be performed using a digital computer to guarantee that a particular element model imbues monotonicity. It describes the test and its basis. It examines seven element models for a rectangular membrane to illustrate the value of the tests. Besides confirming results already known, the application yields new data. It 'proves' monotonicity for two improved models, defines the range of element proportions for which another element can be guaranteed to exhibit monotonicity, and suggests that another element is deficient. In the special case of absolutely convergent membrane displacement models, proof of monotonicity is a necessary and sufficient condition to insure that upper bound estimates of strain energy are developed. Accordingly, the test furnishes a proof of bound solutions independently of requirements on displacement continuity the element basis may or may not satisfy.
Melosh, R. J.↗
Non-Monotonic Response of the Climate System to Abrupt CO2 Forcing
We explore the climate system response to abrupt CO2 forcing, spanning the range 1 × to 8×CO2, with two state-of-the-art coupled atmosphere-ocean-sea-ice-land models: the NASA Goddard Institute for Space Studies Model E2.1-G (GISS-E2.1-G) and the Community Earth System Model (CESM-LE). We find that the effective climate sensitivity is a non-monotonic function of CO2 in both models, reaching a minimum at 3×CO2 for GISS-E2.1-G, and 4×CO2 for CESM-LE. A similar non-monotonic response is found in Northern Hemisphere surface temperature, sea-ice, precipitation, the latitude of zero precipitation minus-evaporation, and the strength of the Hadley cell. Interestingly, the Atlantic meridional overturning circulation collapses when non-monotonicity appears and does not recover for larger CO2 forcings. Analyzing the climate response over the same CO2 range with slab ocean versions of the same models, we demonstrate that the climate system's non-monotonic response is linked to ocean dynamics.
Non-monotonic response↗
Accurate monotone cubic interpolation
Monotone piecewise cubic interpolants are simple and effective. They are generally third-order accurate, except near strict local extrema where accuracy degenerates to second-order due to the monotonicity constraint. Algorithms for piecewise cubic interpolants, which preserve monotonicity as well as uniform third and fourth-order accuracy are presented. The gain of accuracy is obtained by relaxing the monotonicity constraint in a geometric framework in which the median function plays a crucial role.
Huynh, Hung T.↗
Shape restricted additive hazards models: Monotone, unimodal, and U‐shape hazard functions
We consider estimation of the semiparametric additive hazards model with an unspecified baseline hazard function where the effect of a continuous covariate has a specific shape but otherwise unspecified. Such estimation is particularly useful for a unimodal hazard function, where the hazard is monotone increasing and monotone decreasing with an unknown mode. A popular approach of the proportional hazards model is limited in such setting due to the complicated structure of the partial likelihood. Our model defines a quadratic loss function, and its simple structure allows a global Hessian matrix that does not involve parameters. Thus, once the global Hessian matrix is computed, a standard quadratic programming method can be applicable by profiling all possible locations of the mode. However, the quadratic programming method may be inefficient to handle a large global Hessian matrix in the profiling algorithm due to a large dimensionality, where the dimension of the global Hessian matrix and number of hypothetical modes are the same order as the sample size. We propose the quadratic pool adjacent violators algorithm to reduce computational costs. The proposed algorithm is extended to the model with a time‐dependent covariate with monotone or U‐shape hazard function. In simulation studies, our proposed method improves computational speed compared to the quadratic programming method, with bias and mean square error reductions. We analyze data from a recent cardiovascular study.
Mathematical & Computational Biology↗
Monotone implicit algorithms for the small-disturbance and full potential equations applied to transonic flows
Numerical calculations of transonic flows by potential equations typically use algorithms that change the method of calculation for regions of subsonic and supersonic flow. In this paper, implicit approximate-factorization algorithms are modified to use the monotonic switch in the type of finite-differencing that was developed by Godunov for the Euler equations. Calculations of flows over airfoils by these algorithms are compared with calculations by other methods that are in common usage. For the small-disturbance potential equation, comparisons are made with the Murman-Cole method and the monotone method of Engquist and Osher for both steady and unsteady flows. For the full potential equation, comparisons are made with the methods of Jameson and of Holst and Ballhaus for steady flows. The comparisons show that the monotone methods are more stable. For steady flows, solutions are obtained for cases where the Murman-Cole switch requires a time step over ten times smaller in order for the calculations to remain stable. These improvements are achieved with no increase in computer storage and only minor modifications in current codes.
Goorjian, P. M.↗
Accurate upwind-monotone (nonoscillatory) methods for conservation laws
The well known MUSCL scheme of Van Leer is constructed using a piecewise linear approximation. The MUSCL scheme is second order accurate at the smooth part of the solution except at extrema where the accuracy degenerates to first order due to the monotonicity constraint. To construct accurate schemes which are free from oscillations, the author introduces the concept of upwind monotonicity. Several classes of schemes, which are upwind monotone and of uniform second or third order accuracy are then presented. Results for advection with constant speed are shown. It is also shown that the new scheme compares favorably with state of the art methods.
Huynh, Hung T.↗
Matrix cracking in laminated composites under monotonic and cyclic loadings
An analytical model based on the internal state variable (ISV) concept and the strain energy method is proposed for characterizing the monotonic and cyclic response of laminated composites containing matrix cracks. A modified constitution is formulated for angle-ply laminates under general in-plane mechanical loading and constant temperature change. A monotonic matrix cracking criterion is developed for predicting the crack density in cross-ply laminates as a function of the applied laminate axial stress. An initial formulation for a cyclic matrix cracking criterion for cross-ply laminates is also discussed. For the monotonic loading case, a number of experimental data and well-known models are compared with the present study for validating the practical applicability of the ISV approach.
Allen, David H.↗
Comparison of Mode II and III Monotonic and Fatigue Delamination Onset Behavior for Carbon/Toughened Epoxy Composites
Monotonic and fatigue tests were performed to compare the Mode II and III interlaminar fracture toughness and fatigue delamination onset for Tenax-HTA/R6376 carbon/toughened epoxy composites. The Mode II interlaminar fracture toughness and fatigue delamination onset were characterized using the end-notched flexure (ENF) test while the Mode III interlaminar fracture toughness and fatigue delamination onset were characterized by using the edge crack torsion (ECT) test. Monotonic tests show that the Mode III fracture toughness is higher than the Mode II fracture toughness. Both Mode II and III cyclic loading greatly increases the tendency for a delamination to grow relative to a single monotonically increasing load. Under fatigue loading, the Mode III specimen also has a longer life than the Mode II specimen.
Li, Jian↗
19.31% binary organic solar cell and low non-radiative recombination enabled by non-monotonic intermediate state transition
Non-fullerene acceptors based organic solar cells represent the frontier of the field, owing to both the materials and morphology manipulation innovations. Non-radiative recombination loss suppression and performance boosting are in the center of organic solar cell research. Here, we developed a non-monotonic intermediate state manipulation strategy for state-of-the-art organic solar cells by employing 1,3,5-trichlorobenzene as crystallization regulator, which optimizes the film crystallization process, regulates the self-organization of bulk-heterojunction in a non-monotonic manner, i.e., first enhancing and then relaxing the molecular aggregation. As a result, the excessive aggregation of non-fullerene acceptors is avoided and we have achieved efficient organic solar cells with reduced non-radiative recombination loss. In PM6:BTP-eC9 organic solar cell, our strategy successfully offers a record binary organic solar cell efficiency of 19.31% (18.93% certified) with very low non-radiative recombination loss of 0.190 eV. And lower non-radiative recombination loss of 0.168 eV is further achieved in PM1:BTP-eC9 organic solar cell (19.10% efficiency), giving great promise to future organic solar cell research.
14 SOLAR ENERGY↗
Non-monotonic size-dependent exciton radiative lifetime in CsPbBr3 nanocrystals
Lead halide perovskite nanocrystals have attracted intense interest due to their desirable optical properties, diverse structural features, and size-tunable excitonic structure. Here we show that, under ambient conditions, a non-monotonic trend in radiative lifetime emerges from the interplay of size, lattice symmetry and excitonic structure. Small nanocrystals exhibit long radiative lifetimes due to weakly emissive excitons, but the oscillator strength increases and shortens the lifetime for nanocrystals approaching intermediate confinement. For larger nanocrystals with higher exciton density of states (DOS), the radiative lifetime is lengthened due to depopulation of the bright exciton manifold into thermally accessible dim states. A size-dependent structural symmetry lowering transition from cubic to orthorhombic is observed by XRD and MD simulations, and the non-monotonic radiative lifetime trend emerges only in lower symmetry structures with an increased dim exciton DOS. These findings shed light on the impact of nanocrystal size and structure on radiative lifetime and pave the way for tailored optical materials in various optical applications.
optical materials↗
MHD stability of spherical tokamak equilibria with non-monotonic q-profiles
We use the 3D magnetohydrodynamic (MHD) code M3D-C1 [Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)] to examine the MHD stability and subsequent evolution of NSTX shot 129169. This discharge had a period with a non-monotonic safety factor profile, q (reversed shear), which was terminated by a MHD event that abruptly lowered the central safety factor, q0, and greatly reduced the peakedness of the pressure profile. We show that the equilibrium just before the MHD event occurred was linearly unstable to many pressure-driven infernal modes. Modes with toroidal mode number n≥3 all had rational surfaces very close to the minimum value of q. However, a non-resonant pressure-driven (1, 1) mode was also present, and this dominated the nonlinear evolution. The final state in the simulation, after the MHD activity subsided, had a reduced and flattened pressure profile and a nearly monotonic q-profile, in qualitative agreement with experimental results. The initial state was also unstable to the resistive interchange criteria in the reversed-shear region, but the final state was stable everywhere. The “double tearing mode” (DTM) does not appear to play a role in the MHD activity of this discharge. In Appendix A, we show that in a torus, the DTM is strongly stabilized by pressure, but it is destabilized in cylindrical geometry (which has been the most extensively analyzed in the literature).
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Nonlinear Alfvén instability simulation and EP transport for ITER reversed shear (steady-state) and monotonic q-profile regimes *
The nonlinear evolution and dynamics of energetic particle (EP) driven instabilities in both steady-state (reversed shear q-profile) and monotonic q-profile regimes of ITER are examined using the global gyro-Landau closure model FAR3d. Both neutral beam and alpha components are included, leading to synergistic effects between the two populations. In order to maintain computational feasibility, the present nonlinear simulation includes all toroidal mode numbers ranging from n = 0 to 15. It cannot be excluded that n’s above this range could introduce larger linear growth rates; however, as indicated from the results, the n = 0 to 15 range is sufficient to provide a strong linear drive and significant nonlinear transport effects. While the toroidal mode numbers n = 6,13 dominate the linear instability growth phase, nonlinear energy transfers in the saturated phase reverse this trend, leading to the dominance of lower n’s in the saturated phase of the simulation. Zonal flow structure generation and EP density flattening are further consequences of the nonlinear phase. The density profile flattening is caused by collectively driven EP radial transport fluxes, which have non-local characteristics. Instantaneous alpha particle transport fluxes are significant (Γ α ~ 2 x 10 20 m –2 s –1 ) for the reversed shear regime and lower (Γ α ~ 1.1 x 10 20 m –2 s –1 ) for the monotonic q-profile case.
AE↗
Strategies for conservative and non-conservative monotone remapping on the sphere
Abstract. Monotonicity is an important property of remapping operators for coupled weather and climate models. However, it is often challenging to design highly accurate operators that avoid the generation of new extrema or keep a remapped field between physically prescribed bounds. To that end, this paper explores several traditional and novel approaches for both conservative and non-conservative monotone remapping on the sphere. The accuracy and effectiveness of these algorithms are evaluated in the context of several different real and idealized fields and meshes.
54 ENVIRONMENTAL SCIENCES↗
Applications of partial orderings to the study of positive definiteness, monotonicity, and convergence of iterative methods for linear systems.
Most of the known results concerning convergence of iterative methods for solving linear systems involve either positive definiteness or monotonicity. In this paper a new concept, called K-semipositivity, is introduced, which provides a link between convergence theory, monotonicity, and positive definiteness. By using this concept, together with partial orderings in Euclidean n-space, several new convergence theorems are proved. Application to Jacobi's methods and the theory of regular splittings shows the usefulness of these new results.
Vandergraft, J. S.↗
Life prediction of materials exposed to monotonic and cyclic loading: Bibliography
This bibliography is comprised of approximately 1200 reference citations related to the mechanics of failure in aerospace structures. Most of the references are for information on life prediction for materials exposed to monotonic and cyclic loading in elevated temperature environments such as that in the hot end of a gas turbine engine. Additional citations listed are for documents on the thermal and mechanical effects on solar cells in the cryogenic vacuum environment; radiation effects on high temperature mechanical properties; and high cycle fatigue technology as applicable to gas turbine engine bearings. The bibliography represents a search of the literature published in the period April 1962 through April 1974 and is largely limited to documents published in the United States. It is a companion volume to NASA CR-134750, Life Prediction of Materials Exposed to Monotonic and cyclic Loading - A Technology Survey.
Carpenter, J. L., Jr.↗
Finite-element analysis of crack growth under monotonic and cyclic loading
An elastic-plastic (incremental) finite-element analysis, in conjunction with a crack-growth criterion, was used to study crack-growth behavior under monotonic and cyclic loading. The crack-growth criterion was based on crack-tip strain. Whenever the crack-tip strain equals or exceeds a critical strain value, the crack grows. The effects of element-mesh size, critical strain, strain hardening, and specimen type (tension or bending) on crack growth under monotonic loading were investigated. Crack growth under cyclic loading (constant amplitude and simple variable amplitude) were also studied. A combined hardening theory, which incorporates features of both isotropic and kinematic hardening under cyclic loading, was also developed for smooth yield surfaces and was used in the analysis.
Newman, J. C., Jr.↗