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At least 37 records · Page 2

Partitioned exponential methods for coupled multiphysics systems

Multiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the time integration of multiphysics problems. After a possible semi-discretization in space, the class of problems under consideration is modeled by a system of ordinary differential equations where the right-hand side is a summation of two component functions, each corresponding to a given set of physical processes. The partitioned-exponential methods proposed herein evolve each component of the system via an exponential integrator, and information between partitions is exchanged via coupling terms. Here, the traditional approach to constructing exponential methods, based on the variation-of-constants formula, is not directly applicable to partitioned systems. Rather, our approach to developing new partitioned-exponential families is based on a general-structure additive formulation of the schemes. Two method formulations are considered, one based on a linear-nonlinear splitting of the right hand component functions, and another based on approximate Jacobians. The paper develops classical (non-stiff) order conditions theory for partitioned exponential schemes based on particular families of T-trees and B-series theory. Several practical methods of third order are constructed that extend the Rosenbrock-type and EPIRK families of exponential integrators. Several implementation optimizations specific to the application of these methods to reaction-diffusion systems are also discussed. Numerical experiments reveal that the new partitioned-exponential methods can perform better than traditional unpartitioned exponential methods on some problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Sufficient conditions for a local minimum of the Bolza problem with a variable initial point

Sufficient conditions for a weak relative minimum of a form of the Bolza problem of variational calculus are derived. The variational problem considered includes arbitrary numbers of constraints on the initial and terminal points, but assumes no control constraints or interior point constraints. Testing of the second-order conditions requires the backward integration of fewer matrix elements than in the case of previously published sets of conditions. The derivation, though lengthy, is felt to be simpler in concept than previous derivations. The application of these conditions is demonstrated in the context of a simple geometric problem.

Wood, Lincoln J.↗

Boundary and Interface Conditions for High Order Finite Difference Methods Applied to the Euler and Navier-Strokes Equations

Boundary and interface conditions for high order finite difference methods applied to the constant coefficient Euler and Navier-Stokes equations are derived. The boundary conditions lead to strict and strong stability. The interface conditions are stable and conservative even if the finite difference operators and mesh sizes vary from domain to domain. Numerical experiments show that the new conditions also lead to good results for the corresponding nonlinear problems.

Nordstrom, Jan↗

Scaled Vecchia Approximation for Fast Computer-Model Emulation

Many scientific phenomena are studied using computer experiments consisting of multiple runs of a computer model while varying the input settings. Gaussian processes (GPs) are a popular tool for the analysis of computer experiments, enabling interpolation between input settings, but direct GP inference is computationally infeasible for large datasets. We adapt and extend a powerful class of GP methods from spatial statistics to enable the scalable analysis and emulation of large computer experiments. Specifically, we apply Vecchia’s ordered conditional approximation in a transformed input space, with each input scaled according to how strongly it relates to the computer-model response. The scaling is learned from the data by estimating parameters in the GP covariance function using Fisher scoring. Our methods are highly scalable, enabling estimation, joint prediction, and simulation in near-linear time in the number of model runs. In several numerical examples, our approach substantially outperformed existing methods.

97 MATHEMATICS AND COMPUTING↗

CRCNS US-France Research Proposal: Collaborative Research: Encoding reward expectation in Drosophilia

The fruit fly Drosophila melanogaster has been a valuable model for investigating the genetic and neural bases that underlie learning and memory. Early and most current studies use basic behavior conditioning protocols to study learning in controlled laboratory settings. More recently, the ability to transgenically manipulate many of the brain neurons in the fruit fly with exquisite specificity, and the recent knowledge of the synaptic ‘connectome’ of the fruit fly brain, makes these animals almost unique as a comprehensive model for studies of learning, memory and motivated behavior. In fact, the connectome has revealed many types of new connections that had until now been overlooked. Within this context, the thesis of this proposal is that studies of learning and memory will be greatly enhanced by using more sophisticated means for evaluating memory representations, such as have been developed in vertebrates, and combining those studies with information from the connectome guided by computational modelling. We propose to push beyond the boundaries of existing conditioning protocols for fruit flies to investigate more complex memory representations. In particular, we will investigate the function of reinforcement pathways in relation to the absence of expected reinforcement. More specifically, we propose a series of experiments designed to investigate the memory representations in fruit flies when an expected consequence of a Conditioned Stimulus (CS) fails to occur. Although studies have evaluated how this failure can establish extinction memory for the CS, our studies will go beyond studying extinction. Specifically, we predict that in Drosophila when a CS is associated with a failed expectation of an appetitive food reinforcement it will acquire aversive value, and vice versa for a failed expectation of an aversive reinforcer. We combine these studies with manipulations of reinforcement pathways in the CNS inspired from the connectome, iteratively knitted in with established computational models. Intellectual Merit: The concept of reinforcement expectation and incentive contrast have been influential in the development of studies of associative learning in mammals. These questions are particularly challenging to answer in vertebrates because they require exquisite cellular, temporal, and genetic specificity of experimental manipulations. The recent development of work with identified neurons and their connectomes makes the larval and adult fly brains ripe as models for pushing our understanding of neural bases for these higher- order conditioning phenomena. Broader Impacts: Public health: These analyses and the conceptual framework of prediction error processing underlying them have a profound impact on our understanding of reinforcement-related behavior in humans, including monetary rewards and the mnemonic consequences of traumatic experiences, and for pathologies of the dopamine reinforcement system. Educational: This project will provide interdisciplinary training for postdoctoral researchers, Ph.D. and undergraduate students. The PIs will act as co-supervisors or mentors of students working in the different labs via face-to-face and internet-based technologies. We will also work with ASU’s award-winning Ask- A-Biologist program. This is an online science program designed to enrich the learning experiences of students of all ages and to provide classroom material for use by K-12 teachers. We will develop an extension of a game developed under a prior NSF award, and the new game will include modules to teach K-12 students about how insects learn. We will also integrate into the AAB site a program developed by a collaborator (B Gerber) at the Leibniz Institut für Neurobiologie, Magdeburg, and now in use in schools in Germany, to teach K-12 students how to train animals using the fruit fly larval learning paradigm. Underrepresented groups: All PIs will work with their university offices of Academic Diversity and Equal Opportunity for reaching underrepresented students.

59 BASIC BIOLOGICAL SCIENCES↗

Multirate linearly-implicit GARK schemes

Many complex applications require the solution of initial-value problems where some components change fast, while others vary slowly. Multirate schemes apply different step sizes to resolve different components of the system, according to their dynamics, in order to achieve increased computational efficiency. The stiff components of the system, fast or slow, are best discretized with implicit base methods in order to ensure numerical stability. To this end, linearly implicit methods are particularly attractive as they solve only linear systems of equations at each step. This paper develops the Multirate GARK-ROS/ROW (MR-GARK-ROS/ROW) framework for linearly-implicit multirate time integration. The order conditions theory considers both exact and approximative Jacobians. The effectiveness of implicit multirate methods depends on the coupling between the slow and fast computations; an array of efficient coupling strategies and the resulting numerical schemes are analyzed. Multirate infinitesimal step linearly-implicit methods, that allow arbitrarily small micro-steps and offer extreme computational flexibility, are constructed. The new unifying framework includes existing multirate Rosenbrock(-W) methods as particular cases, and opens the possibility to develop new classes of highly effective linearly implicit multirate integrators.

97 MATHEMATICS AND COMPUTING↗

A unified formulation of splitting-based implicit time integration schemes

Splitting-based time integration approaches such as fractional step, alternating direction implicit, operator splitting, and locally one dimensional methods partition the system of interest into components, and solve individual components implicitly in a cost-effective way. Here this work proposes a unified formulation of splitting time integration schemes in the framework of general-structure additive Runge–Kutta (GARK) methods. Specifically, we develop implicit-implicit (IMIM) GARK schemes, provide the order conditions for this class, and explain their application to partitioned systems of ordinary differential equations. We show that classical splitting methods belong to the IMIM GARK family, and therefore can be studied in this unified framework. New IMIM-GARK splitting methods are developed and tested using parabolic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Reactions of hydrazine with the amidogen radical and atomic hydrogen

The rate coefficient k 1 for NH 2 + N 2 H 4 was measured to be (5.4 ± 0.4) × 10 –14 cm 3 molecule –1 s –1 at 296 K. NH 2 was generated by pulsed laser photolysis of NH 3 at 193 nm, and monitored as a function of time by pulsed laser-induced fluorescence excited at 570.3 nm under pseudo-first order conditions in the presence of excess N 2 H 4 in an Ar bath gas. This reaction was also investigated computationally, with geometries and scaled frequencies obtained with M06-2X/6-311+G(2df,2p) theory, and single-point energies from CCSD(T)-F12b/cc-pVTZ-F12 theory, plus a term to correct approximately for electron correlation through CCSDT(Q). Three connected transition states are involved and rate constants were obtained via Multistructural Improved Canonical Variational Transition State Theory with Small Curvature Tunneling. Combination of experiment and theory leads to a recommended rate coefficient for hydrogen abstraction of k 1 = 6.3 × 10 –23 T 3.44 exp(+289 K/T) cm 3 molecule –1 s –1 . The minor channel for H + N 2 H 4 forming NH 2 + NH 3 was characterized computationally as well, to yield 5.0 × 10 –19 T 2.07 exp(-4032 K/T) cm 3 molecule –1 s –1 . Finally, these results are compared to several discordant prior estimates, and are employed in an overall mechanism to compare with measurements of half-lives of hydrazine in a shock tube.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Master equation study of hydrogen abstraction from HCHO by OH via a chemically activated intermediate

The abstraction reaction of hydrogen from formaldehyde by OH radical plays an important role in formaldehyde oxidation. The reaction involves a bimolecular association to form a chemically activated hydrogen-bonded reaction complex followed by a unimolecular reaction of the complex to generate the products. The reaction rate is usually considered to be pressure-independent by assuming equilibrium between the reactants and the complex. However, our nonequilibrium calculations based on the chemically significant eigenmode of the master equation, carried out with our recently developed TUMME program, indicate that the reaction complex makes the rate constant dependent on pressure at low temperatures (T < 200 K). The calculations include anharmonicity, variational effects, and multi-dimensional tunneling. We find that the reaction rate constant reaches a low-pressure limit at pressures below 10 Torr over the whole investigated temperature range (20–1800 K), which explains why the available low-temperature experiments, which are for pressures below 2 Torr, did not observe the pressure dependence. A new extension of the TUMME master-equation program is used to explore the time evolutions of the concentrations of the OH radical and the complex under pseudo-first-order conditions. The time-dependent evolution of the concentrations of the complex at a low temperature provide direct evidence for the stabilization of the reaction complex at high pressures, and it shows the negligible role of the stabilized reaction complex at low pressures. Finally, the picture that emerges is qualitatively consistent with our previous study of the reaction of methanol with OH in that the tunneling in the unimolecular step from the complex to the products affects the phenomenological reaction rate constants differently at high and low pressures and leads to a significant pressure effect.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Low-Density Parity-Check Stabilizer Codes as Gapped Quantum Phases: Stability under Graph-Local Perturbations

We generalize the proof of stability of topological order, due to Bravyi, Hastings, and Michalakis, to stabilizer Hamiltonians corresponding to low-density parity-check (LDPC) codes without the restriction of geometric locality in Euclidean space. We consider Hamiltonians 𝐻 0 defined by ⟦𝑁,𝐾,𝑑⟧ LDPC codes, which obey certain topological quantum order conditions: (i) code distance 𝑑 ≥ 𝑐⁢log (𝑁), implying local indistinguishability of ground states, and (ii) a mild condition on local and global compatibility of ground states—these include good quantum LDPC codes and the toric code on a hyperbolic lattice, among others. We consider stability under weak perturbations that are quasilocal on the interaction graph defined by 𝐻 0 and that can be represented as sums of bounded-norm terms. As long as the local perturbation strength is smaller than a finite constant, we show that the perturbed Hamiltonian has well-defined spectral bands originating from the 𝑂⁡(1) smallest eigenvalues of 𝐻 0 . The band originating from the smallest eigenvalue has 2 𝐾 states, is separated from the rest of the spectrum by a finite energy gap, and has exponentially narrow bandwidth 𝛿 =𝐶⁢𝑁⁢𝑒 −Θ⁡(𝑑) , which is tighter than the best-known bounds even in the Euclidean case. We also obtain that the new ground-state subspace is related to the initial-code subspace by a quasilocal unitary, allowing one to relate their physical properties. Our proof uses an iterative procedure that performs successive rotations to eliminate non-frustration-free terms in the Hamiltonian. Our results extend to quantum Hamiltonians built from classical LDPC codes, which give rise to stable symmetry-breaking phases. These results show that LDPC codes very generally define stable gapped quantum phases, even in the non-Euclidean setting, initiating a systematic study of such phases of matter.

mathematical physics↗

Absolute rate parameters for the reaction of atomic hydrogen with hydrazine

Absolute rate parameters for the reaction of atomic hydrogen with hydrazine H + N2H4 yields H2 + N2H3 have been determined in a direct manner using flash photolysis of dilute mixtures of hydrazine in helium and time dependent observation of H via resonance fluorescence. By measuring the H-atom decay under pseudo-first-order conditions, the bimolecular rate constant K sub 1 was obtained over the temperature range 228-400 K. The data were fitted with good linearity to the Arrhenius expression K sub 1 = (9.87 plus or minus 1.17) x 10 to the -12th exp(-2380 plus or minus 100/RT) cu cm/molecule/s. The data were shown to be free of any contributions from secondary reactions involving H as a reactant or product.

Stief, L. J.↗

The rate constant for the reaction of O/3P/ atoms with ClONO2

Experiments were conducted in a conventional fast flow apparatus to study the rate constant and the activation energy for the reaction O(3P) + ClONO2. The air-afterglow technique was used for the detection of oxygen atoms under pseudo first order conditions. A value of (3.4 plus or minus 0.6) x 10 to the -12th exp/(-840 plus or minus 60)T/cu cm/molecule/s was obtained for the rate constant. The observed rate is sufficiently slow so that oxygen atom attack is of minor importance in the stratosphere compared to photolysis.

Molina, L. T.↗

Absolute rate constant of the reaction between chlorine /2P/ atoms and hydrogen peroxide from 298 to 424 K

The absolute rate constant of the reaction between chlorine (2P) atoms and hydrogen peroxide was determined from 298 to 424 K, using the discharge flow resonance fluorescence technique. Pseudo-first-order conditions were used with hydrogen peroxide in large excess. A fast flow-sampling procedure limited hydrogen peroxide decomposition to less than 5% over the temperature range studied. At 298 K, the rate constant is (4.1 plus or minus 0.2) x 10 to the minus 13th cu cm/molecule-sec.

Keyser, L. F.↗

Temperature dependence of the reaction O/3P/ + OH/2 Pi/ yields O2 + H

Measurements of the absolute rate and temperature dependence of the rate constant for the reaction of ground state atomic oxygen with hydroxyl radicals to yield molecular oxygen and hydrogen atoms over the temperature range 211-499 K are presented. The reaction was monitored in a low-pressure discharge flow resonance fluorescence apparatus under pseudo-first-order conditions in which the oxygen concentration was greater than the hydroxyl concentration. An expression for the temperature dependence of the rate constant is derived from a least-squares fit to the observed bimolecular rate constants, which were found to range from 3.21 to 2.77 x 10 to the -11th cu cm/molecule per sec for temperatures from 211 to 499 K, indicative of a slight negative temperature dependence. Results are compared with those of previous workers, and the significance of the lower value of the rate constant obtained in the present study to models of HO(x) in the upper stratosphere is indicated.

Lewis, R. S.↗

Absolute rate constant of the reaction OH + HO2 yields H2O + O2

The absolute rate constant of the reaction OH + HO2 yields H2O + O2 was determined by using the discharge-flow resonance fluorescence technique at 299 K and 1-torr total pressure. Pseudo-first-order conditions were used with HO2 concentrations in large excess over OH. Secondary reactions of atomic oxygen and atomic hydrogen were shown not to interfere under the conditions used. The result is (6.4 plus or minus 1.5) x 10 to the -11th cu cm/molecule s where the error limits are twice the standard deviation. The overall experimental error is estimated to be plus or minus 30%.

Keyser, L. F.↗

Kinetics of the reaction OH + HO2 yields H2O + O2 from 254 to 382 K

The discharge-flow resonance fluorescence technique has been used to determine the absolute rate constant for the reaction OH + HO2 yields H2O + O2 from 254 to 382 K at a total pressure of 1 Torr. Pseudo-=first-order conditions were used with HO2 in large excess over OH. The rate constant was obtained directly from observed decays of OH and measured concentrations of HO2. Since the observed rate constant was found to be very sensitive to small background concentrations of O and H atoms, NO2 was used to remove both atom species from the system. With added NO2 the result at 299 K is (1.1 + or - 0.3) x 10 to the -10th cu cm/molecule where the error limits are one standard deviation and include an estimate of overall experimental uncertainty. The temperature dependence expressed in Arrhenius form is (4.8 + or - 0.8) x 10 to the -11th exp (250 + or - 50)/T. The results are independent of the type of reactor surface and the precursor used to produce OH and HO2. The present results agree well with earlier measurements near 1-atm total pressure and suggest that this rate constant exhibits little or no pressure dependence between 1 and 1000 Torr.

Keyser, Leon F.↗

A Subband Coding Method for HDTV

This paper introduces a new HDTV coder based on motion compensation, subband coding, and high order conditional entropy coding. The proposed coder exploits the temporal and spatial statistical dependencies inherent in the HDTV signal by using intra- and inter-subband conditioning for coding both the motion coordinates and the residual signal. The new framework provides an easy way to control the system complexity and performance, and inherently supports multiresolution transmission. Experimental results show that the coder outperforms MPEG-2, while still maintaining relatively low complexity.

Chung, Wilson↗

Analytical and Computational Aspects of Collaborative Optimization

Bilevel problem formulations have received considerable attention as an approach to multidisciplinary optimization in engineering. We examine the analytical and computational properties of one such approach, collaborative optimization. The resulting system-level optimization problems suffer from inherent computational difficulties due to the bilevel nature of the method. Most notably, it is impossible to characterize and hence identify solutions of the system-level problems because the standard first-order conditions for solutions of constrained optimization problems do not hold. The analytical features of the system-level problem make it difficult to apply conventional nonlinear programming algorithms. Simple examples illustrate the analysis and the algorithmic consequences for optimization methods. We conclude with additional observations on the practical implications of the analytical and computational properties of collaborative optimization.

Alexandrov, Natalia M.↗