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At least 19 records

Approximating Two-Stage Chance-Constrained Programs with Classical Probability Bounds

We consider a joint-chance constraint (JCC) as a union of sets, and approximate this union using bounds from classical probability theory. When these bounds are used in an optimization model constrained by the JCC, we obtain corresponding upper and lower bounds on the optimal objective function value. We compare the strength of these bounds against each other under two different sampling schemes, and observe that a larger correlation between the uncertainties tends to result in more computationally challenging optimization models. We also observe the same set of inequalities to provide the tightest upper and lower bounds in our computational experiments.

97 MATHEMATICS AND COMPUTING↗

Calculation and interpretation of classical turning surfaces in solids

Abstract Classical turning surfaces of Kohn–Sham potentials separate classically allowed regions (CARs) from classically forbidden regions (CFRs). They are useful for understanding many chemical properties of molecules but need not exist in solids, where the density never decays to zero. At equilibrium geometries, we find that CFRs are absent in perfect metals, rare in covalent semiconductors at equilibrium, but common in ionic and molecular crystals. In all materials, CFRs appear or grow as the internuclear distances are uniformly expanded. They can also appear at a monovacancy in a metal. Calculations with several approximate density functionals and codes confirm these behaviors. A classical picture of conduction suggests that CARs should be connected in metals, and disconnected in wide-gap insulators, and is confirmed in the limits of extreme compression and expansion. Surprisingly, many semiconductors have no CFR at equilibrium, a key finding for density functional construction. Nonetheless, a strong correlation with insulating behavior can still be inferred. Moreover, equilibrium bond lengths for all cases can be estimated from the bond type and the sum of the classical turning radii of the free atoms or ions.

Chemistry↗

Machine Learning Classical Interatomic Potentials for Molecular Dynamics from First-Principles Training Data

The ever-increasing power of modern super-computers, along with the availability of highly scalable atomistic simulation codes, has begun to revolutionize predictive modeling of materials. In particular, molecular dynamics (MD) has led to breakthrough advances in diverse fields, including tribology, catalysis, sensing, and nanoparticle self-assembly. Furthermore, recent integration of MD simulations with X-ray characterization has demonstrated promise in real-time 3-D characterization of materials on the atomic scale. The popularity of MD is driven by its applicability at disparate length/time scales, ranging from ab initio MD (hundreds of atoms and tens of picoseconds) to all-atom classical MD (millions of atoms over microseconds), and coarse-grained (CG) models (micrometers and tens of microseconds). Nevertheless, a substantial gap persists between AIMD, which is highly accurate but restricted to extremely small sizes, and those based on classical force fields (atomistic and CG) with limited accuracy but access to larger length/time scales. The accuracy and predictive power of classical MD simulations is dictated by the empirical force fields, and their capability to capture the relevant physics. Here, we discuss some of our recent work on the use of machine learning (ML) to combine the accuracy and flexibility of electronic structure calculations with the speed of classical potentials. Our ML framework attempts to bridge the significant gulf that exists between the handful of research groups that develop new interatomic potential models (often requiring several years of effort), and the increasingly large user community from academia and industry that applies these models. Our data-driven approach represents significant departure from the status quo and involves several steps including generation and manipulation of extensive training data sets through electronic structure calculations, defining novel potential functional forms, employing state-of-the-art ML algorithms to formulate highly optimized training procedures, and subsequently developing user-friendly workflow tools integrating these algorithms on high-performance computers (HPCs). Our ML approach shows marked success in developing force fields for a wide range of materials from metals, oxides, nitrides, and heterointerfaces to two-dimensional (2D) materials.

Chan, Henry↗

A Comparison of Classical and Aggregation-Based Algebraic Multigrid Preconditioners for High-Fidelity Simulation of Wind Turbine Incompressible Flows

This paper presents a comparison of parallel strong scaling performance of classical and aggregation algebraic multigrid (AMG) preconditioners in the context of wind turbine simulations. Fluid motion is governed by the incompressible Navier--Stokes equations, discretized in space with control-volume finite elements and in time with an inexact projection scheme using an implicit integrator. A discontinuous-Galerkin sliding-mesh algorithm captures rotor motion. The momentum equations are solved with iterative Krylov methods, preconditioned by symmetric Gauss--Seidel (SGS) in Trilinos and $\ell_1$ SGS in hypre. The mass-continuity equation is solved with GMRES preconditioned by AMG and can account for the majority of simulation time. Reducing this continuity solve time is crucial. Wind turbine simulations present two unique challenges for AMG preconditioned solvers: the computational meshes include strongly anisotropic elements, and mesh motion requires matrix reinitialization and computation of preconditioners at each time step. Detailed timing profiles are presented and analyzed, and best practices are discussed for both classical and aggregation-based AMG. Results are presented for simulations of two different wind turbines with up to 6 billion grid points on two different computer architectures. For moving mesh problems that require linear-system reinitialization, the well-established strategy of amortizing preconditioner setup costs over a large number of time steps to reduce the solve time is no longer valid. Instead, results show that faster time to solution is achieved by reducing preconditioner setup costs at the expense of linear-system solve costs. Standard smoothed aggregation with Chebyshev relaxation was found to perform poorly when compared with classical AMG in terms of solve time and robustness. However, plain aggregation was comparable to classical AMG.

97 MATHEMATICS AND COMPUTING↗

Designing noise-robust quantum networks coexisting in the classical fiber infrastructure

The scalability of quantum networking will benefit from quantum and classical communications coexisting in shared fibers, the main challenge being spontaneous Raman scattering noise. We investigate the coexistence of multi-channel O-band quantum and C-band classical communications. We characterize multiple narrowband entangled photon pair channels across 1282 nm-1318 nm co-propagating over 48 km of installed standard fiber with record C-band power (>18 dBm) and demonstrate that some quantum-classical wavelength combinations significantly outperform others. We analyze the Raman noise spectrum, optimal wavelength engineering, multi-photon pair emission in entangled photon-classical coexistence, and evaluate the implications for future quantum applications.

Optics↗

Radiation reaction of classical hyperbolic oscillator: Experimental signatures

When accelerated by a constant force in the lab frame, a classical charge experiences no self force. In this case, the particle radiates without dissipating its kinetic and potential energy. But what happens when the particle enters another region with equal and opposite acceleration? Does the oscillating charge lose its mechanical energy similar to a radiating dipole, even though it seems to lose no mechanical energy within each region of constant acceleration? In this paper, I will show how mechanical energy is transferred to radiation energy via the Schott energy when the particle crosses the boundary between the two regions. In particular, I will show how preacceleration, which is usually regarded as an unphysical effect of the Lorentz–Abraham–Dirac self force, is essential for the energy transfer. Moreover, I will show that the commonly adopted Landau–Lifshitz approximation, which removes preacceleration, introduces second-order secular energy error. On a more fundamental level, the validity of classical electrodynamics is in fact questionable because quantum effects are likely important. The classical prediction can be tested experimentally by observing frequency chirping of radiation, whereby micro physics leaves signatures on macroscopic scales. The required experimental accuracy is estimated. Trap experiments of this type is complementary to collider experiments that endeavor to observe radiation reaction for elementary particles.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states

Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One powerful example of such a hybrid quantum-classical approach optimized for classically intractable eigenvalue problems is the variational quantum eigensolver, built to utilize quantum resources for the solution of eigenvalue problems and optimizations with minimal coherence time requirements by leveraging classical computational resources. These algorithms have been placed as leaders among the candidates for the first to achieve supremacy over classical computation. Here, we provide evidence for the conjecture that variational approaches can automatically suppress even nonsystematic decoherence errors by introducing an exactly solvable channel model of variational state preparation. Moreover, we develop a more general hierarchy of measurement and classical computation that allows one to obtain increasingly accurate solutions by leveraging additional measurements and classical resources. In conclusion, we demonstrate numerically on a sample electronic system that this method both allows for the accurate determination of excited electronic states as well as reduces the impact of decoherence, without using any additional quantum coherence time or formal error-correction codes.

McClean, Jarrod R.↗

Water Lone Pair Delocalization in Classical and Quantum Descriptions of the Hydration of Model Ions

Understanding the nature of ionic hydration at a fundamental level has eluded scientists despite intense interest for nearly a century. In particular, the microscopic origins of the asymmetry of ion solvation thermodynamics with respect to the sign of the ionic charge remains a mystery. Here, we determine the response of accurate quantum mechanical water models to strong nanoscale solvation forces arising from excluded volumes and ionic electrostatic fields. This is compared to the predictions of two important limiting classes of classical models of water with fixed point changes, differing in their treatment of “lone pair” electrons. Using the quantum water model as our standard of accuracy, we find that a single fixed classical treatment of lone pair electrons cannot accurately describe solvation of both apolar and cationic solutes, emphasizing the need for a more flexible description of local electronic effects in solvation processes. However, we explicitly show that all water models studied respond to weak long-ranged electrostatic perturbations in a manner that follows macroscopic dielectric continuum models, as would be expected. Here, we emphasize the importance of these findings in the context of realistic ion models, using density functional theory and empirical models, and discuss the implications of our results for quantitatively accurate reduced descriptions of solvation in dielectric media.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantum theory of the classical: quantum jumps, Born’s Rule and objective classical reality via quantum Darwinism

Here, the emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. In this paper, I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the environment. I begin with the derivation of preferred sets of states that help to define what exists—our everyday classical reality. They emerge as a result of the breaking of the unitary symmetry of the Hilbert space which happens when the unitarity of quantum evolutions encounters nonlinearities inherent in the process of amplification—of replicating information. This derivation is accomplished without the usual tools of decoherence, and accounts for the appearance of quantum jumps and the emergence of preferred pointer states consistent with those obtained via environment-induced superselection, or einselection . The pointer states obtained in this way determine what can happen—define events—without appealing to Born’s Rule for probabilities. Therefore, p k = |ψ k | 2 can now be deduced from the entanglement-assisted invariance, or envariance —a symmetry of entangled quantum states. With probabilities at hand, one also gains new insights into the foundations of quantum statistical physics. Moreover, one can now analyse the information flows responsible for decoherence. These information flows explain how the perception of objective classical reality arises from the quantum substrate: the effective amplification that they represent accounts for the objective existence of the einselected states of macroscopic quantum systems through the redundancy of pointer state records in their environment—through quantum Darwinism .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Floquet dynamics of classical and quantum cavity fields

We show that the time-dependence of electromagnetic field in a periodically modulated cavity can be effectively analyzed using a Floquet map. The map relates the field states separated by one period of the drive; iterative application of the map allows to determine field configuration after arbitrary number of drive periods. For resonant and near-resonant drives, the map has stable and unstable fixed points, which are the loci of infinite energy concentration in the long time limit. The Floquet map method can be applied both to classical and quantum massless field problems, including the dynamical Casimir effect. The stroboscopic time evolution implemented by the map can be interpreted in terms of the wave propagation in a curved space, with the fixed points of the map corresponding to the black hole and white hole horizons. More practically, the map can be used to design protocols for signal compression/decompression, cooling, and sensing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Instability in dynamic fracture and the failure of the classical theory of cracks

Cracks, the major vehicle for material failure, undergo a micro-branching instability at ~40% of their sonic limiting velocity in three dimensions. Recent experiments showed that in thin systems cracks accelerate to nearly their limiting velocity without micro-branching, until undergoing an oscillatory instability. Despite their fundamental importance, these dynamic instabilities are not explained by the classical theory of cracks, which is based on linear elasticity and an extraneous local symmetry criterion to predict crack paths. We develop a two-dimensional theory for predicting arbitrary paths of ultrahigh-speed cracks, which incorporates elastic nonlinearity without extraneous criteria. We show that cracks undergo an oscillatory instability controlled by small-scale, near crack-tip, elastic nonlinearity. This instability occurs above an ultrahigh critical velocity and features an intrinsic wavelength proportional to the ratio of the fracture energy to the elastic modulus, in quantitative agreement with experiments. As a result, this ratio emerges as a fundamental scaling length assumed to play no role in the classical theory of cracks, but shown here to strongly influence crack dynamics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Recent experimental explorations of non-classical nucleation

Nucleation, the early stage of crystallization, is a key step in producing functional materials, but nucleation processes have yet to be understood in detail. Recent advanced characterization techniques, especially atomic force microscopy, liquid-cell transmission electron microscopy (TEM) and cryo-TEM, enable scientists to observe previously inaccessible nucleation details at the nanoscale. In this review, we summarize newly suggested non-classical nucleation models with respect to mechanistic understanding from experimental views, which highlight multi-step nucleation mechanisms. Different intermediated phases such as clusters at the pre-nucleation stage, liquid-like precursors, amorphous phases and even oligomers have been revealed, which play vital roles in nucleation and structure control. Moreover, these intermediated phases practically contribute in general to the structural variances of materials for nanoscience and nanotechnology. Overall, these studies ultimately enable us to control nucleation processes for materials synthesis.

Jin, Biao↗

Li + solvation and kinetics of Li + –BF 4 - /PF 6 - ion pairs in ethylene carbonate. A molecular dynamics study with classical rate theories

Using our polarizable force-field models and employing classical rate theories of chemical reactions, we examine the ethylene carbonate (EC) exchange process between the first and second solvation shells around Li+ and the dissociation kinetics of ion pairs Li+-[BF4] and Li+-[PF6] in this solvent. We calculate the exchange rates using transition state theory and correct them with transmission coefficients computed by the reactive flux; Impey, Madden, and McDonald approaches; and Grote-Hynes theory. We found the residence times of EC around Li+ ions varied from 70 to 450 ps, depending on the correction method used. We found the relaxation times changed significantly from Li+-[BF4] to Li+-[PF6] ion pairs in EC. Our results also show that, in addition to affecting the free energy of dissociation in EC, the anion type also significantly influence the dissociation kinetics of ion pairing. This work was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences. The calculations were carried out using computer resources provided by the Office of Basic Energy Sciences.

Chang, Tsun-Mei↗

Pulse-noise approach for classical spin systems

For systems of classical spins interacting with the bath via damping and thermal noise, a technique is suggested to replace the white noise by a pulse noise acting at regular time intervals Δ t , within which the system evolves conservatively. The method is working well in the typical case of a small dimensionless damping constant λ and allows a considerable speedup of computations by using high-order numerical integrators with a large time step δ t (up to a fraction of the precession period), while keeping δ t ≪ Δ t to reduce the relative contribution of noise-related operations. In cases when precession can be discarded, δ t can be increased up to a fraction of the relaxation time ∝ 1 / λ that leads to a further speedup. This makes equilibration speed comparable with that of the Metropolis Monte Carlo method. The pulse-noise approach is tested on single-spin and multispin models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗