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At least 217 records · Page 12

Polymorphism and Negative Linear Compressibility in Pyrazine-d4

Pyrazine (1,4-diazine) is a widely used linker in coordination polymers, molecular magnets, and metal–organic frameworks, yet its solid-state polymorphism is controlled by weak C–H···N interactions. Using variable-temperature and high-pressure neutron diffraction, a previously unrecognized low-temperature transition to phase IV is identified, showing that the form stabilized under pressure can also be accessed below ∼90 K at ambient pressure in the perdeuterated compound. The transition from phase III → IV involves a symmetry-breaking lattice distortion driven by the reorganization of C–H···N hydrogen bonds, accompanied by negative linear compressibility, which is primarily accommodated through the reduction in void-space within the structure. Structural analysis reveals that while the overall monoclinic framework of phase IV is preserved under both temperature and pressure routes, the evolution of hydrogen-bonded network is distinct depending on the pathway taken. These results establish pyrazine as a model molecular solid for studying pressure–temperature polymorphism and demonstrate how weak directional interactions can produce anomalous mechanical responses in organic crystals.

Ridley, Christopher J. [Oak Ridge National Laborat↗

Exact restoration of Galilei invariance in density functional calculations with quantum Monte Carlo

We investigate some aspects of the connection between mean-field and ab-initio calculations for any-nucleon systems employing the Gogny effective interaction. In particular, we present variational Monte Carlo calculations of 4 He and 16 O, for which we extended the formalism of the linear method to the case of a density-dependent Hamiltonian. Monte Carlo calculations using an uncorrelated basis reduce to Hartree-Fock ones, but Galilean invariance can be preserved, contrary to the usual treatment. An analysis of the results obtained with the Gogny force when used in conjunction with correlated wave functions has also been performed. Here, the calculations show the collapse of the deuteron, leading to a set of unphysical predictions for the structure of heavier nuclei. This behavior remarks the different role of the Gogny effective interaction as compared to bare interactions typically used in fully microscopic calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Chain entanglements enable regeneration of high-performance thermosets

Thermoset plastics underpin structural materials, electronics and transportation, yet the permanent covalent networks that prevent flow and provide dimensional stability also make them difficult to recycle without sacrificing performance. In this work we show that high-performance thermosets can be built around dense chain entanglements, the physical interlacing of long polymer strands, rather than dense permanent crosslinks, with only a small number of selectively cleavable junctions preserving connectivity. Long, rigid, entangled polyolefin backbones generated by frontal polymerization form glassy polymers with high stiffness, high toughness and excellent creep suppression yet can be fully deconstructed into soluble, linear oligomers. Varying oligomer length and end-group chemistry enables their reuse as re-entangling building blocks that regenerate thermosets with thermal and mechanical properties that remain unchanged across generations. The strategy further extends to high-temperature fibre-reinforced composite matrices and additively manufactured structures, establishing chain entanglement as a design principle for durable, regenerable thermosets.

36 MATERIALS SCIENCE↗

A data-driven peridynamic continuum model for upscaling molecular dynamics

Nonlocal models, including peridynamics, often use integral operators that embed lengthscales in their definition. However, the integrands in these operators are difficult to define from the data that are typically available for a given physical system, such as laboratory mechanical property tests. In contrast, molecular dynamics (MD) does not require these integrands, but it suffers from computational limitations in the length and time scales it can address. To combine the strengths of both methods and to obtain a coarse-grained, homogenized continuum model that efficiently and accurately captures materials’ behavior, we propose a learning framework to extract, from MD data, an optimal Linear Peridynamic Solid (LPS) model as a surrogate for MD displacements. To maximize the accuracy of the learnt model we allow the peridynamic influence function to be partially negative, while preserving the well-posedness of the resulting model. To achieve this, we provide sufficient well-posedness conditions for discretized LPS models with sign-changing influence functions and develop a constrained optimization algorithm that minimizes the equation residual while enforcing such solvability conditions. This framework guarantees that the resulting model is mathematically well-posed, physically consistent, and that it generalizes well to settings that are different from the ones used during training. We illustrate the efficacy of the proposed approach with several numerical tests for single layer graphene. Our two-dimensional tests show the robustness of the proposed algorithm on validation data sets that include thermal noise, different domain shapes and external loadings, and discretizations substantially different from the ones used for training.

homogenization↗

Quantification of urinary uric acid in the presence of thymol and thimerosal by high-performance liquid chromatography

A high-performance liquid chromatographic method was developed as an alternative to automated enzymatic analysis of uric acid in human urine preserved with thymol and/or thimerosal. Uric acid (tR = 10 min) and creatinine (tR = 5 min) were separated and quantified during isocratic elution (0.025 M acetate buffer, pH 4.5) from a mu Bondapak C18 column. The uric-acid peak was identified chemically by incubating urine samples with uricase. The thymol/thimerosal peak appeared at 31 min during the washing step and did not interfere with the analysis. We validated the high-performance liquid chromatographic method for linearity, precision and accuracy, and the results were found to be excellent.

NASA Discipline Regulatory Physiology↗

An IIR median hybrid filter

A new class of nonlinear filters, the so-called class of multidirectional infinite impulse response median hybrid filters, is presented and analyzed. The input signal is processed twice using a linear shift-invariant infinite impulse response filtering module: once with normal causality and a second time with inverted causality. The final output of the MIMH filter is the median of the two-directional outputs and the original input signal. Thus, the MIMH filter is a concatenation of linear filtering and nonlinear filtering (a median filtering module). Because of this unique scheme, the MIMH filter possesses many desirable properties which are both proven and analyzed (including impulse removal, step preservation, and noise suppression). A comparison to other existing median type filters is also provided.

Bauer, Peter H.↗

Solutions of the benchmark problems by the dispersion-relation-preserving scheme

The 7-point stencil Dispersion-Relation-Preserving scheme of Tam and Webb is used to solve all the six categories of the CAA benchmark problems. The purpose is to show that the scheme is capable of solving linear, as well as nonlinear aeroacoustics problems accurately. Nonlinearities, inevitably, lead to the generation of spurious short wave length numerical waves. Often, these spurious waves would overwhelm the entire numerical solution. In this work, the spurious waves are removed by the addition of artificial selective damping terms to the discretized equations. Category 3 problems are for testing radiation and outflow boundary conditions. In solving these problems, the radiation and outflow boundary conditions of Tam and Webb are used. These conditions are derived from the asymptotic solutions of the linearized Euler equations. Category 4 problems involved solid walls. Here, the wall boundary conditions for high-order schemes of Tam and Dong are employed. These conditions require the use of one ghost value per boundary point per physical boundary condition. In the second problem of this category, the governing equations, when written in cylindrical coordinates, are singular along the axis of the radial coordinate. The proper boundary conditions at the axis are derived by applying the limiting process of r approaches 0 to the governing equations. The Category 5 problem deals with the numerical noise issue. In the present approach, the time-independent mean flow solution is computed first. Once the residual drops to the machine noise level, the incident sound wave is turned on gradually. The solution is marched in time until a time-periodic state is reached. No exact solution is known for the Category 6 problem. Because of this, the problem is formulated in two totally different ways, first as a scattering problem then as a direct simulation problem. There is good agreement between the two numerical solutions. This offers confidence in the computed results. Both formulations are solved as initial value problems. As such, no Kutta condition is required at the trailing edge of the airfoil.

Tam, Christopher K. W.↗

Accurate Monotonicity - Preserving Schemes With Runge-Kutta Time Stepping

A new class of high-order monotonicity-preserving schemes for the numerical solution of conservation laws is presented. The interface value in these schemes is obtained by limiting a higher-order polynominal reconstruction. The limiting is designed to preserve accuracy near extrema and to work well with Runge-Kutta time stepping. Computational efficiency is enhanced by a simple test that determines whether the limiting procedure is needed. For linear advection in one dimension, these schemes are shown as well as the Euler equations also confirm their high accuracy, good shock resolution, and computational efficiency.

Suresh, A.↗

A Technique for Mapping Characteristic Lengths to Preserve Energy Dissipated via Strain Softening in a Multiscale Analysis

It is often advantageous to account for the microstructure of the material directly using multiscale modeling. For computational tractability, an idealized repeating unit cell (RUC) is used to capture all of the pertinent features of the microstructure. Typically, the RUC is dimensionless and depends only on the relative volume fractions of the different phases in the material. This works well for non-linear and inelastic behavior exhibiting a positive-definite constitutive response. Although, once the material exhibits strain softening, or localization, a mesh objective failure theories, such as smeared fracture theories, nodal and element enrichment theories (XFEM), cohesive elements or virtual crack closure technique (VCCT), can be utilized at the microscale, but the dimensions of the RUC must then be defined. One major challenge in multiscale progressive damage modeling is relating the characteristic lengths across the scales in order to preserve the energy that is dissipated via localization at the microscale. If there is no effort to relate the size of the macroscale element to the microscale RUC, then the energy that is dissipated will remain mesh dependent at the macroscale, even if it is regularized at the microscale. Here, a technique for mapping characteristic lengths across the scales is proposed. The RUC will be modeled using the generalized method of cells (GMC) micromechanics theory, and local failure in the matrix constituent subcells will be modeled using the crack band theory. The subcell characteristic lengths used in the crack band calculations will be mapped to the macroscale finite element in order to regularize the local energy in a manner consistent with the global length scale. Examples will be provided with and without the regularization, and they will be compared to a baseline case where the size and shape of the element and RUC are coincident (ensuring energy is preserved across the scales).

softening↗

Data-driven modeling and control of dynamical systems using Koopman and Perron-Frobenius operators

This dissertation studies the data-driven modeling and control problem of nonlinear systems by exploiting the linear operator theoretic framework involving Koopman and Perro-Frobenius operator. A systematic linear-operator based controller design procedure has been established, which can be used to solve a variety of nonlinear control problems, including feedback stabilization using control Lyapunov functions, optimal quadratic regulation using Koopman eigenfunctions and convex optimization formulation of optimal control problem using P-F and Koopman operator approximation. As the core of data-driven modeling, we first propose a new algorithm for the finite-dimensional approximation of the linear transfer Koopman and Perron-Frobenius operator from time-series data. We argue that the existing approach for the finite-dimensional approximation of these transfer operators such as Dynamic Mode Decomposition (DMD) and Extended Dynamic Mode Decomposition (EDMD) do not capture two important properties of these operators, namely positivity and Markov property. The algorithm we propose preserves these two properties. We call the proposed algorithm as naturally structured DMD (NSDMD) since it retains the inherent properties of these operators. Naturally structured DMD algorithm leads to a better approximation of the steady-state dynamics of the system regarding computing Koopman and Perron- Frobenius operator eigenfunctions and eigenvalues. However, preserving positivity property is critical for capturing the real transient dynamics of the system. This positivity property of the transfer operators and it's finite-dimensional approximation play an important role for controller and estimator design of nonlinear systems. To solve the feedback stabilization problem for nonlinear control systems, we tried to take advantage of the Koopman operator framework. The Koopman operator approach provides a linear representation for a nonlinear dynamical system and a bilinear representation for a nonlinear control system. The problem of feedback stabilization of a nonlinear control system is then transformed to the stabilization of a bilinear control system. We propose a control Lyapunov function (CLF)-based approach for the design of stabilizing feedback controllers for the bilinear system. The search for finding a CLF for the bilinear control system is formulated as a convex optimization problem. This leads to a schematic procedure for designing CLF-based stabilizing feedback controllers for the bilinear system and hence the original nonlinear system. Another advantage of the proposed controller design approach outlined in this dissertation is that it does not require explicit knowledge of system dynamics. In particular, the bilinear representation of a nonlinear control system in the Koopman eigenfunction space can be obtained from time-series data. Next, we study the optimal quadratic regulation problem for nonlinear systems. The linear operator theoretic framework involving the Koopman operator is used to lift the dynamics of nonlinear control system to an infinite-dimensional bilinear system. The optimal quadratic regulation problem for nonlinear system is formulated in terms of the finite-dimensional approximation of the bilinear system. A convex optimization-based approach is proposed for solving the quadratic regulator problem for bilinear system. We applied a variety of examples and compared the simulation results between our framework and conventional LQR control using linearized model. For more general optimal control problems, we provide a density-function based convex formulation for the optimal control problem of the nonlinear system. The convex formulation relies on the duality result in the stability theory of a dynamical system involving density function and Perron-Frobenius operator. The optimal control problem is formulated as an infinite-dimensional convex optimization program. The finite-dimensional approximation of the optimization problem relies on the recent advances made in the data-driven computation of the Koopman operator, which is dual to the Perron-Frobenius operator. Simulation results are presented to demonstrate the application of the developed framework.

Huang, Bowen↗

Using Strassen's algorithm to accelerate the solution of linear systems

Strassen's algorithm for fast matrix-matrix multiplication has been implemented for matrices of arbitrary shapes on the CRAY-2 and CRAY Y-MP supercomputers. Several techniques have been used to reduce the scratch space requirement for this algorithm while simultaneously preserving a high level of performance. When the resulting Strassen-based matrix multiply routine is combined with some routines from the new LAPACK library, LU decomposition can be performed with rates significantly higher than those achieved by conventional means. We succeeded in factoring a 2048 x 2048 matrix on the CRAY Y-MP at a rate equivalent to 325 MFLOPS.

Bailey, David H.↗

Feature learning and generalization in deep networks with orthogonal weights

Fully-connected deep neural networks with weights initialized from independent Gaussian distributions can be tuned to criticality, which prevents the exponential growth or decay of signals propagating through the network. However, such networks still exhibit fluctuations that grow linearly with the depth of the network, which may impair the training of networks with width comparable to depth. We show analytically that rectangular networks with tanh activations and weights initialized from the ensemble of orthogonal matrices have corresponding preactivation fluctuations which are independent of depth, to leading order in inverse width. Moreover, we demonstrate numerically that, at initialization, all correlators involving the neural tangent kernel (NTK) and its descendants at leading order in inverse width—which govern the evolution of observables during training—saturate at a depth of ~20, rather than growing without bound as in the case of Gaussian initializations. We speculate that this structure preserves finite-width feature learning while reducing overall noise, thus improving both generalization and training speed in deep networks with depth comparable to width. We provide some experimental justification by relating empirical measurements of the NTK to the superior performance of deep non-linear orthogonal networks trained under full-batch gradient descent on the MNIST and CIFAR-10 classification tasks.

97 MATHEMATICS AND COMPUTING↗

Anomalous superconducting diode effect in a polar superconductor

A superconductor with broken time-reversal and inversion symmetry may exhibit nonreciprocal charge transport, including a nonreciprocal critical current, also known as superconducting diode effect. Here, we report an intrinsic superconducting diode effect in a polar strontium titanate film. Differential resistance measurements reveal a superconducting state whose depairing current is polarity dependent. There is, however, no measurable deviation from Ohmic behavior, implying that this state does not arise from a bulk magnetochiral anisotropy. In the entire measurement range, the only deviation from linearity in the differential resistance is on the edge of the superconducting transition at high magnetic fields, likely due to the motion of flux vortices. Furthermore, the magnitude of the effect is preserved even when the in-plane magnetic field is oriented parallel to the current, indicating that this effect truly does not originate from a bulk magnetochiral anisotropy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A high resolution atlas of the galactic plane at 12 microns and 25 microns

High resolution images of the 12 micron and 25 micron IRAS survey data from each HCON crossing the Galactic Plane are being created for those regions that the original IRAS processing labeled as confused. This encompasses the area within 100 deg longitude of the Galactic Center and within 3 deg to 10 deg of the Plane. The procedures used to create the images preserve the spatial resolution inherent in the IRAS instrument. The images are separated into diffuse and point source components and candidate sources are extracted from the point source image after non-linear spatial sharpening. Fluxes are estimated by convolving the candidate sources with the point response function and cross-correlating with the original point source image. A source is considered real if it is seen on at least two HCON's with a rather generous flux match but a stringent position criterion. A number of fields spanning a range of source densities from low to high have been examined. Initial analysis indicates that the imaging and extraction works quite well up to a source density of about 100 sources per square degree or down to roughly 0.8 Janskys.

Price, Stephan D.↗

Regional surrogates for predictive control of digital twins

Digital twins of complex systems must involve a model that is fast, generalizable, and usable for real-time control. For example, high-fidelity nonlinear multiphysics simulations can capture laser-material interactions, but are too slow for optimization or model predictive control (MPC). Reduced-order models, used to accelerate such computation, frequently fail to generalize to unseen inputs or control states. We show theoretically that this failure is intrinsic, i.e., that a learned model is non-unique outside the sampled subspace when its low-rank structure arises from limited excitation and clustered eigenvalues, rather than from a user-imposed truncation alone. Motivated by this result, we propose a control-ready regional surrogate-construction framework for both autonomous and nonautonomous dynamics; it employs Koopman lifting to represent nonlinearities, while preserving spatial locality. We illustrate our approach by constructing a control-ready surrogate for the digital twin of a thermal component of additive-manufacturing process. Our surrogate, localized in space through a von Neumann stencil, is learned from noisy high-fidelity simulations that emulate thermal-camera images collected during the manufacturing. It is linear in thermo-physically augmented states so that MPC reduces to a convex quadratic program. The surrogate requires no online correction, generalizes to unseen scan paths and power profiles of the laser, and is more than three orders of magnitude faster than a finite-difference solver. Furthermore, when the MPC sequence computed on the digital twin is applied to this solver, closed-loop temperature regulation is recovered, showing that the surrogate preserves control-relevant input-output behavior.

Data-driven model↗

Impact of Advection Schemes on Tracer Interrelationships in Large-Eddy Simulations of Deep Convection

This study investigates the preservation of tracer interrelationships during advection in large-eddy simulations of an idealized deep convective cloud, which is particularly relevant to chemistry, aerosol, and cloud microphysics models. Employing the Cloud Model 1, advection is represented using third-, fifth-, and seventh-order weighted essentially non-oscillatory schemes. As a simplified analogy for cloud hydrometeors and aerosols, several inert passive tracers following linear and nonlinear relationships are initialized after the cloud reaches ~6-km depth. Numerical mixing in the simulated turbulent convective clouds leads to significant deviations from the initial nonlinear relationships between tracers. In these simulations, a considerable fraction of the grid points where the tracers’ nonlinear relationships are altered from advection are classified as unrealistic (e.g., ~13% for the environmental tracers on average), including errors from range-preserving unmixing and overshooting. Errors in the sum of three tracers are also relatively large, ranging between ~1% and 16% for 5% of the grid points in and near the cloud. The magnitude of unrealistic mixing and errors in the sum of three tracers generally increase with the order of accuracy of the advection scheme. These results are consistent across model grid spacings ranging from 50 to 200 m, and across three different flow realizations for each combination of grid spacing and advection scheme tested. Tests employing a previously proposed scalar normalization procedure show substantially reduced errors in the sum of three tracers with a relatively small negative impact on other tracer relationships. This analysis, therefore, suggests efficacy of the normalization procedure when applied to turbulent three-dimensional cloud simulations.

54 ENVIRONMENTAL SCIENCES↗

Structure preserving and energy dissipative contact approaches for implicit dynamics

In this work, several structure preserving and energy dissipative contact approaches are proposed and evaluated. The time integration schemes considered are general with regard to the version of constraint type, but here the emphasis was on mortar contact. The proposed mortar contact approach conserves both linear and angular momentum for mortar contact in a novel way. The proposed time integration scheme can conserve energy or provide strict contact dissipation. In addition, the proposed scheme enforces both gap constraints and gap velocity constraints (i.e., persistency). Using a midstep time integrator often causes energy dissipation during initial impact, here this energy can be recovered in a novel way. Enforcing the gap velocity constraint mitigates the contact chatter of the contact pressure and nodes in many problems. Whereas some approaches enforce the persistency condition and gap constraints simultaneously during the solution of the equations of motion (EOM) requiring multipliers for both constraints included in the equation set, here the gap constraint is solved through the equations of motion and the persistency condition is satisfied in the time integration scheme by the velocity update after the equations of motion. It is shown that this approach is strictly dissipative in that a plastic contact condition can be achieved. Analogous to a coefficient of restitution for rigid bodies, any dissipated energy can then be returned upon release if energy conservation is desired. Structure preserving methods are good for long-time dynamics simulations and energy conserving and strictly dissipative methods can overcome stability issues associated with standard time integration algorithms such as the Newmark method.

42 ENGINEERING↗