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At least 1,297 records · Page 72
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Integrable nonlinear evolution of the qubit

Highlights: •We study the nonlinear generalization of the von Neumann equation. •We discuss the nonlinear von Neumann equation for the qubit states. •We analyze solutions to the Riccati system corresponding to evolution of a qubit. -- Abstract: The nonlinear generalization of the von Neumann equation is studied. The global version of this equation preserves convexity of the space of states. The particular case of the evolution of pure states refers to the nonlinear Schrödinger equation discovered by Gisin. The concrete realization of the nonlinear von Neumann equation is investigated in detail for the density matrix representing the qubit states. Such equation reduces to the integrable classical Riccati system of nonlinear ordinary differential equations. An interesting property of the nonlinear dynamics described by this system is the global asymptotical stability of stationary solutions related to evolution from mixed states to pure states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Universal mass equation for equal-quantum excited-states sets I

The masses of fifteen baryon sets and twenty-four meson sets of three or more equal-quantum excited states, using Breit-Wigner PDG masses and their uncertainties at fixed J P for baryons and J PC for mesons, are fitted by a simple two-parameter logarithmic function, M n = αLn(n)+β, where n is the level of radial excitation. The conjecture is made that accurately measured masses of all equal-quantum baryons (including LHCb exotic P$_{c\bar{c}}^+$s) and meson excited states (including s$\bar{s}$, s$\bar{c}$, c$\bar{c}$, c$\bar{b}$, and b$\bar{b}$ states) are related by the logarithmic function used here; at least for the mass range of currently known excited states. The baryon “star” rating case is evaluated. The Cornell potential is an example of how a logarithmic behavior can be explained by an appropriate potential. Thus, a “universal mass equation” (UME) for equal-quantum excited-state sets is presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Preserving nonlinear constraints in variational flow filtering data assimilation

Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems of interest obey nonlinear physical constraints, and the corresponding dynamics is confined to a certain sub-manifold of the state space. Standard data assimilation techniques applied to such systems yield posterior states lying outside the manifold, violating the physical constraints. This work focuses on particle flow filters which use stochastic differential equations to evolve state samples from a prior distribution to samples from an observation-informed posterior distribution. The variational Fokker-Planck (VFP)—a generic particle flow filtering framework—is extended to incorporate non-linear, equality state constraints in the analysis. To this end, two algorithmic approaches that modify the VFP stochastic differential equation are discussed: (i) VFPSTAB, to inexactly preserve constraints with the addition of a stabilizing drift term, and (ii) VFPDAE, to exactly preserve constraints by treating the VFP dynamics as a stochastic differential-algebraic equation (SDAE). Additionally, an implicit-explicit time integrator is developed to evolve the VFPDAE dynamics. The strength of the proposed approach for constraint preservation in data assimilation is demonstrated on three test problems: the double pendulum, Korteweg-de-Vries, and the incompressible Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Evaluation of a quasi-steady-state approximation of the cloud droplet growth equation (QDGE) scheme for aerosol activation in global models using multiple aircraft data over both continental and marine environments

This research introduces a numerically efficient aerosol activation scheme and evaluates it by using stratus and stratocumulus cloud data sampled during multiple aircraft campaigns in Canada, Chile, Brazil, and China. The scheme employs a quasi-steady-state approximation of the cloud droplet growth equation (QDGE) to efficiently simulate aerosol activation, the vertical profile of supersaturation, and the activated cloud droplet number concentration (CDNC) near the cloud base. The calculated maximum supersaturation values using the QDGE scheme were compared with multiple parcel model simulations under various aerosol and environmental conditions. The differences are all below 0.18 %, indicating good performance and accuracy of the QDGE scheme. We evaluated the QDGE scheme by specifying observed environmental thermodynamic variables and aerosol information from 31 cloud cases as input and comparing the simulated CDNC with cloud observations. The average of mean relative error ($\overline{MRE}$) of the simulated CDNC for cloud cases in each campaign ranges from 17.30 % in Brazil to 25.90 % in China, indicating that the QDGE scheme successfully reproduces observed variations in CDNC over a wide range of different meteorological conditions and aerosol regimes. Additionally, we carried out an error analysis by calculating the maximum information coefficient (MIC) between the MRE and input variables for the individual campaigns and all cloud cases. MIC values were then sorted by aerosol properties, pollution level, environmental humidity, and dynamic condition according to their relative importance to MRE. Based on the error analysis, we found that the magnitude of MRE is more relevant to the specification of input aerosol pollution level in marine regions and aerosol hygroscopicity in continental regions than to other variables in the simulation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Platinum liquid-vapor phase boundary mapped by fluid flyer experiments

We report a direct measurement of the temperature and density of a metal along its liquid-vapor coexistence (L-V) curve. By shocking platinum to a high-pressure liquid, we imparted sufficient heat for subsequent isentropic release to place it in a state on the boundary between the liquid and vapor phases. Released material in the liquid phase acted as a high velocity flyer pinned to the L-V curve. We measured velocity and radiant emission of the flyer as well as the interface motion and transiting shock states induced in a downstream window material by its impact. We used these measurements to calculate temperature and density of the L-V curve state which we compare to density functional theory predictions.

Equations of state↗
DOE OSTI2026

Symmetry-energy expansion with strange dense matter

The quantum chromodynamics (QCD) phase diagram at large densities and low temperatures can be probed using both neutron stars and low-energy heavy-ion collisions. Heavy-ion collisions are nearly isospin-symmetric systems, whereas neutron stars are highly isospin asymmetric since they are neutron rich. The symmetry-energy expansion is used to connect these regimes across isospin asymmetry. However, the current symmetry-energy expansion does not account for strange particles. In this work, we include finite strangeness by redefining the isospin-asymmetry parameter and the symmetry-energy expansion in a way that is consistent with QCD SU(3) flavor symmetry. Furthermore, our new symmetry energy works well beyond typical neutron star central densities and admits a skewness term in the presence of strangeness for the case of weak equilibrium.

Equations of state of nuclear matter↗
DOE OSTI2020

Anisotropic time-dependent London approach: Application to the ac response in the Meissner state

The anisotropic London equations taking into account the normal currents are derived and applied to the problem of the surface impedance in the Meissner state of anisotropic materials. It is shown that the complex susceptibility of the anisotropic slab depends on the orientation of the applied microwave field relative to the crystal axes. In particular, the anisotropic sample in the microwave field is subject to a torque, unless the field is directed along one of the crystal principle axes.

36 MATERIALS SCIENCE↗
DOE OSTI2020

On the peridynamic effective force state and multiphase constitutive correspondence principle

This article concerns modeling unsaturated deformable porous media as an equivalent single-phase and single-force state peridynamic material through the effective force state. The balance equations of linear momentum and mass of unsaturated porous media are presented by defining relevant peridynamic states. The energy balance of unsaturated porous media is utilized to derive the effective force state for the solid skeleton that is an energy conjugate to the nonlocal deformation state of the solid, and the suction force state. Through an energy equivalence, a multiphase constitutive correspondence principle is built between classical unsaturated poromechanics and peridynamic unsaturated poromechanics. The multiphase correspondence principle provides a means to incorporate advanced constitutive models in classical unsaturated porous theory directly into unsaturated peridynamic poromechanics. Finally, numerical simulations of localized failure in unsaturated porous media under different matric suctions are presented to demonstrate the feasibility of modeling the mechanical behavior of such three-phase materials as an equivalent single-phase peridynamic material through the effective force state concept.

42 ENGINEERING↗
DOE OSTI2021

Shadow Lagrangian dynamics for superfluidity

Motivated by a similar approach for Born-Oppenheimer molecular dynamics, this paper proposes an extended "shadow" Lagrangian density for quantum states of superfluids. The extended Lagrangian contains an additional field variable that is forced to follow the wave function of the quantum state through a rapidly oscillating extended harmonic oscillator. By considering the adiabatic limit for large frequencies of the harmonic oscillator, we can derive the two equations of motions, a Schrödinger-type equation for the quantum state and a wave equation for the extended field variable. The equations are coupled in a nonlinear way, but each equation individually is linear with respect to the variable that it defines. The computational advantage of this new system is that it can be easily discretized using linear time stepping methods, where we propose to use a Crank-Nicolson-type approach for the Schrödinger equation and an extended leapfrog scheme for the wave equation. Furthermore, the difference between the quantum state and the extended field variable defines a consistency error that should go to zero if the frequency tends to infinity. By coupling the time-step size in our discretization to the frequency of the harmonic oscillator we can extract an easily computable consistency error indicator that can be used to estimate the numerical error without additional costs. The findings are illustrated in numerical experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Lifetime renormalization of driven weakly anharmonic superconducting qubits. II. The readout problem

Recent experiments in superconducting qubit systems have shown an unexpectedly strong dependence of the qubit relaxation rate on the readout drive power. This phenomenon limits the maximum measurement strength and thus the achievable readout speed and fidelity. We address this problem here and provide a plausible mechanism for drive-power dependence of relaxation rates. To this end we introduce a two-parameter perturbative expansion in qubit anharmonicity and the drive amplitude through a unitary transformation technique introduced in Part I. This approach naturally reveals number-nonconserving terms in the Josephson potential as a fundamental mechanism through which applied microwave drives can activate additional relaxation mechanisms. Here, we present our results in terms of an effective master equation with renormalized state- and drive-dependent transition frequency and relaxation rates. Comparison of numerical results from this effective master equation to those obtained from a Lindblad master equation which only includes number-conserving terms (i.e., Kerr interactions) shows that number-nonconserving terms can lead to significant drive-power dependence of the relaxation rates. The systematic expansion technique introduced here is of general applicability to obtaining effective master equations for driven-dissipative quantum systems that contain weakly nonlinear degrees of freedom.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Including the parallel mass flow in calculating the steady-state solutions and stability of the momentum balance equations for a quasisymmetric stellarator

The Helically Symmetric Experiment (HSX) is a quasisymmetric stellarator with minimal parallel viscous damping in a helical direction. The parallel flow (Vǁ) along the magnetic field is similarly weakly damped by viscosity. In this paper, the self-consistent steady-state parallel and poloidal momentum balance equations are used to show that a large Vǁ on the order of the ion thermal velocity can increase the ion resonant radial electric field (Er) beyond the value calculated using the typical approximation that Vǁ is zero. By altering the damping of Vǁ, either by degrading the quasisymmetry or varying the neutral density, the ion resonant Er can shift in a controllable fashion. It is shown explicitly that there exist stable and unstable steady-state solutions in the two-dimensional space of Vǁ and Er. A stability analysis of each solution is performed by calculating the eigenvalues and eigenvectors of the Jacobian. The unstable solution corresponds to a saddle point in which the eigenvalues have opposite signs. The analysis leads to the conclusion that unstable solutions occur when the derivative of the total poloidal damping with respect to Er is positive. A hysteresis in Er and Vǁ is observed when the radial current density is linearly increased to a maximum and then decreased back to zero. Jumps in the radial electric field and the parallel flow are observed as the radial current density drives the evolution from one stable point to the next. This result is similar to experimental data observed on several devices.

Physics↗
DOE OSTI2021

Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering

Here we present an error analysis for the discontinuous Galerkin (DG) method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation with isotropic scattering. Under some mild assumptions, we show that the DG method converges uniformly with respect to a scaling parameter which characterizes the strength of scattering in the system. However, the rate is not optimal and can be polluted by the presence of boundary layers. In one-dimensional slab geometries, we demonstrate optimal convergence when boundary layers are not present and analyze a simple strategy for balance interior and boundary layer errors. Some numerical tests are also provided in this reduced setting.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Dual Representations and H ∞ -Optimal Control of Partial Differential Equations

We consider H ∞ -optimal state-feedback control of the class of linear Partial Differential Equations (PDEs) which admit a Partial Integral Equation (PIE) representation. While linear matrix inequalities are commonly used for optimal control of Ordinary Differential Equations (ODEs), the absence of a universal state-space representation and suitable dual form prevents such methods from being applied to optimal control of PDEs. Specifically, for ODEs, the controller synthesis problem is defined in state-space, and duality is used to resolve the bilinearity of that synthesis problem. Recently, the PIE representation was proposed as a universal state-space representation for linear PDE systems. In this paper, we show that any PDE system represented by a PIE admits a dual PIE with identical stability and I/O properties. This result allows us to reformulate the stabilizing and optimal state-feedback control problems as convex optimization over the cone of positive Partial Integral (PI) operators. Operator inversion formulae then allow us to construct feedback gains for the original PDE system. The results are verified through application to several canonical problems in optimal control of PDEs and indicate the resulting bounds on H ∞ norm are not conservative.

42 ENGINEERING↗
DOE OSTI2023

Probability of Initiation in Neutron Transport

We discuss the numerical solution of the nonlinear integro-differential equation for the probability of a divergent neutron chain in a stationary system (i.e., the probability of initiation (POI)). We follow the development described in Bell’s classic paper on the stochastic theory of neutron transport. As noted by Bell, the linearized form of this equation resembles the linear adjoint neutron transport equation. A matrix formalism for the discretized steady state (or forward) neutron equation in slab geometry is first developed and is then used to derive the discrete adjoint equation. A main advantage of this discrete development is that the resulting discrete adjoint equation does not depend upon how the multigroup cross sections for the forward problem are obtained. That is, we derive the discrete adjoint directly from the discrete forward equations rather than discretizing directly the adjoint equation. This also guarantees that the discrete adjoint operator is consistent with the inner product used to define the adjoint operator. We discuss three approaches for the numerical solution of the POI equations, and present numerical results on several test problems. The three solution methods are a simple fixed-point iteration, a second approach that is akin to a nonlinear Power iteration, and a third approach which uses a Newton-Krylov nonlinear solver. We also give sufficient conditions to guarantee the existence and uniqueness of nontrivial solutions to our discrete POI equations when the discrete system is supercritical, and that only the trivial solution exists when the discrete system is subcritical. Our approach is modeled after the analysis presented for the continuous POI equations by Mokhtar-Kharroubi and Jarmouni-Idrissi, and by Pazy and Rabinowitz.

42 ENGINEERING↗
DOE OSTI2024

Lax-Oleinik-Type Formulas and Efficient Algorithms for Certain High-Dimensional Optimal Control Problems

Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimension. In this paper, we provide analytical solutions to certain optimal control problems whose running cost depends on the state variable and with constraints on the control. We also provide Lax-Oleinik-type representation formulas for the corresponding Hamilton-Jacobi partial differential equations with state-dependent Hamiltonians. Additionally, we present an efficient, grid-free numerical solver based on our representation formulas, which is shown to scale linearly with the state dimension, and thus, to overcome the curse of dimensionality. Using existing optimization methods and the min-plus technique, we extend our numerical solvers to address more general classes of convex and nonconvex initial costs. We demonstrate the capabilities of our numerical solvers using implementations on a central processing unit (CPU) and a field-programmable gate array (FPGA). In several cases, our FPGA implementation obtains over a 10 times speedup compared to the CPU, which demonstrates the promising performance boosts FPGAs can achieve. Furthermore, our numerical results show that our solvers have the potential to serve as a building block for solving broader classes of high-dimensional optimal control problems in real-time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

An exploratory steady–state redox model of photosynthetic linear electron transport for use in complete modelling of photosynthesis for broad applications

A photochemical model of photosynthetic electron transport (PET) is needed to integrate photophysics, photochemistry, and biochemistry to determine redox conditions of electron carriers and enzymes for plant stress assessment and mechanistically link sun-induced chlorophyll fluorescence to carbon assimilation for remotely sensing photosynthesis. Towards this goal, we derived photochemical equations governing the states and redox reactions of complexes and electron carriers along the PET chain. These equations allow the redox conditions of the mobile plastoquinone pool and the cytochrome b 6 f complex (Cyt) to be inferred with typical fluorometry. The equations agreed well with fluorometry measurements from diverse C 3 /C 4 species across environments in the relationship between the PET rate and fraction of open photosystem II reaction centres. We found the oxidation of plastoquinol by Cyt is the bottleneck of PET, and genetically improving the oxidation of plastoquinol by Cyt may enhance the efficiency of PET and photosynthesis across species. Redox reactions and photochemical and biochemical interactions are highly redundant in their complex controls of PET. Although individual reaction rate constants cannot be resolved, they appear in parameter groups which can be collectively inferred with fluorometry measurements for broad applications. The new photochemical model developed enables advances in different fronts of photosynthesis research.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗