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Scaling Analysis of Two–Phase Flow in Fractal Permeability Fields
Fluid mixing in permeable media is essential in many practical applications. The mixing process is a consequence of velocity fluctuations owing to geological heterogeneities and mobility contrast of fluids. Heterogeneities in natural rocks are often spatially correlated, and their properties, such as permeability, may be described using fractal distributions. This work models the fractal characteristics of such permeability fields in which the covariance function is expressed as a power-law function. A generalized scaling relation is derived relating various fractal permeability fields using the magnitude of their fluctuations. Here, this relation reveals the self-similar behavior of two-phase flow in such permeable media. To that end, a recently developed, high-resolution numerical simulator is employed to validate the analytically derived scaling relations. Two flow problems are considered in which flow is governed by 1) a linear, and 2) a nonlinear transport equation. Due to the probabilistic representation of the fractal permeability fields, a sensitivity study is conducted for each flow scenario to determine the number of realizations required for statistical convergence. Scaling analysis is performed using ensemble averages of simulated saturation profiles and their mixing lengths. Results support the validity of the developed scaling relation across the range of investigated flow conditions at intermediate times. The dynamics of linear flow in the asymptotic regime is affected by the correlation structure of heterogeneity. In nonlinear flow, scaling behavior appears to be dominated by the degree of nonlinearity.
Revealing the hidden structure of disordered materials by parameterizing their local structural manifold
Abstract Durable interest in developing a framework for the detailed structure of glassy materials has produced numerous structural descriptors that trade off between general applicability and interpretability. However, none approach the combination of simplicity and wide-ranging predictive power of the lattice-grain-defect framework for crystalline materials. Working from the hypothesis that the local atomic environments of a glassy material are constrained by enthalpy minimization to a low-dimensional manifold in atomic coordinate space, we develop a generalized distance function, the Gaussian Integral Inner Product (GIIP) distance, in connection with agglomerative clustering and diffusion maps, to parameterize that manifold. Applying this approach to a two-dimensional model crystal and a three-dimensional binary model metallic glass results in parameters interpretable as coordination number, composition, volumetric strain, and local symmetry. In particular, we show that a more slowly quenched glass has a higher degree of local tetrahedral symmetry at the expense of cyclic symmetry. While these descriptors require post-hoc interpretation, they minimize bias rooted in crystalline materials science and illuminate a range of structural trends that might otherwise be missed.
Non-adiabatic approximations in time-dependent density functional theory: progress and prospects
Time-dependent density functional theory continues to draw a large number of users in a wide range of fields exploring myriad applications involving electronic spectra and dynamics. Although in principle exact, the predictivity of the calculations is limited by the available approximations for the exchange-correlation functional. In particular, it is known that the exact exchange-correlation functional has memory-dependence, but in practise adiabatic approximations are used which ignore this. Here we review the development of non-adiabatic functional approximations, their impact on calculations, and challenges in developing practical and accurate memory-dependent functionals for general purposes.
Linking structural and rheological memory in disordered soft materials
Linking the macroscopic flow properties and nanoscopic structure is a fundamental challenge to understanding, predicting, and designing disordered soft materials. Under small stresses, these materials are soft solids, while larger loads can lead to yielding and the acquisition of plastic strain, which adds complexity to the task. In this work, we connect the transient structure and rheological memory of a colloidal gel under cyclic shearing across a range of amplitudes via a generalized memory function using rheo-X-ray photon correlation spectroscopy (rheo-XPCS). Our rheo-XPCS data show that the nanometer scale aggregate-level structure recorrelates whenever the change in recoverable strain over some interval is zero. The macroscopic recoverable strain is therefore a measure of the nano-scale structural memory. We further show that yielding in disordered colloidal materials is strongly heterogeneous and that memories of prior deformation can exist even after the material has been subjected to flow.
Simulating sticky particles: A Monte Carlo method to sample a stratification
Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their equilibrium distribution, and there are several methods to sample probability distributions subject to fixed constraints. We introduce a Monte Carlo method to handle the case when constraints can break and form. More generally, the method samples a probability distribution on a stratification: a collection of manifolds of different dimensions, where the lower-dimensional manifolds lie on the boundaries of the higher-dimensional manifolds. We show several applications of the method in polymer physics, self-assembly of colloids, and volume calculation in high dimensions.
Two-dimensional parametric design of short pulse laser driven iron opacity experiments
High intensity short pulse lasers are commonly used to create high temperature and high density plasmas. These plasmas are used to study fundamental properties such as the equation of state and opacity. The targets often use small-diameter, thin buried layers of the materials of interest, surrounded by a tamper of low atomic number material such as plastic. Computational modeling is used to design and interpret experiments with short pulse lasers. Most of the modeling to date has assumed one-dimensional plane-parallel geometry. In this paper, the effects of radial gradients in the irradiation of thin planar targets are studied with one- and two-dimensional radiation/hydrodynamic simulations. It is found that the main effect of radial gradients is the averaging of plasma conditions and x-ray emission over the pattern of irradiation. Additionally, differences between one- and two-dimensional simulations arise because the plasma conditions and x-ray emission are, in general, nonlinear functions of the temperature of the plasma and thereby also nonlinear functions of the irradiation intensity. The differences increase with the ratio of the buried layer radius to the laser spot radius. The root mean square difference in the inferred iron L-shell opacity is less than 30% when the ratio is less than 1.0 and about 70% when the ratio is 1.5.
Theory of the ion–electron temperature relaxation rate in strongly magnetized plasmas
Recent works have shown that strongly magnetized plasmas characterized by having a gyrofrequency greater than the plasma frequency exhibit novel transport properties. One example is that the friction force on a test charge shifts, obtaining components perpendicular to its velocity in addition to the typical stopping power component antiparallel to its velocity. Here, we apply a recent generalization of the Boltzmann equation for strongly magnetized plasmas to calculate the ion–electron temperature relaxation rate. Strong magnetization is generally found to increase the temperature relaxation rate perpendicular to the magnetic field and to cause the temperatures parallel and perpendicular to the magnetic field to not relax at equal rates. This, in turn, causes a temperature anisotropy to develop during the equilibration. Strong magnetization also breaks the symmetry of independence of the sign of the charges of the interacting particles on the collision rate, commonly known as the “Barkas effect.” Furthermore, it is found that the combination of oppositely charged interaction and strong magnetization causes the ion–electron parallel temperature relaxation rate to be significantly suppressed, scaling inversely proportional to the magnetic field strength.
How well do one-electron self-interaction-correction methods perform for systems with fractional electrons?
Recently developed locally scaled self-interaction correction (LSIC) is a one-electron SIC method that, when used with a ratio of kinetic energy densities (z σ ) as iso-orbital indicator, performs remarkably well for both thermochemical properties as well as for barrier heights overcoming the paradoxical behavior of the well-known Perdew–Zunger self-interaction correction (PZSIC) method. In this work, we examine how well the LSIC method performs for the delocalization error. Our results show that both LSIC and PZSIC methods correctly describe the dissociation of $H$$^{+}_{2}$ and $H$$^{+}_{2}$ but LSIC is overall more accurate than the PZSIC method. Likewise, in the case of the vertical ionization energy of an ensemble of isolated He atoms, the LSIC and PZSIC methods do not exhibit delocalization errors. For the fractional charges, both LSIC and PZSIC significantly reduce the deviation from linearity in the energy vs number of electrons curve, with PZSIC performing superior for C, Ne, and Ar atoms while for Kr they perform similarly. The LSIC performs well at the endpoints (integer occupations) while substantially reducing the deviation. The dissociation of LiF shows both LSIC and PZSIC dissociate into neutral Li and F but only LSIC exhibits charge transfer from Li + to F – at the expected distance from the experimental data and accurate ab initio data. Overall, both the PZSIC and LSIC methods reduce the delocalization errors substantially.
Peripheral positions encode transport specificity in the small multidrug resistance exporters
In secondary active transporters, a relatively limited set of protein folds have evolved diverse solute transport functions. Because of the conformational changes inherent to transport, altering substrate specificity typically involves remodeling the entire structural landscape, limiting our understanding of how novel substrate specificities evolve. In the current work, we examine a structurally minimalist family of model transport proteins, the small multidrug resistance (SMR) transporters, to understand the molecular basis for the emergence of a novel substrate specificity. We engineer a selective SMR protein to promiscuously export quaternary ammonium antiseptics, similar to the activity of a clade of multidrug exporters in this family. Using combinatorial mutagenesis and deep sequencing, we identify the necessary and sufficient molecular determinants of this engineered activity. Using X-ray crystallography, solid-supported membrane electrophysiology, binding assays, and a proteoliposome-based quaternary ammonium antiseptic transport assay that we developed, we dissect the mechanistic contributions of these residues to substrate polyspecificity. We find that substrate preference changes not through modification of the residues that directly interact with the substrate but through mutations peripheral to the binding pocket. Our work provides molecular insight into substrate promiscuity among the SMRs and can be applied to understand multidrug export and the evolution of novel transport functions more generally.
Analysis of a preQ1-I riboswitch in effector-free and bound states reveals a metabolite-programmed nucleobase-stacking spine that controls gene regulation
Abstract Riboswitches are structured RNA motifs that recognize metabolites to alter the conformations of downstream sequences, leading to gene regulation. To investigate this molecular framework, we determined crystal structures of a preQ1-I riboswitch in effector-free and bound states at 2.00 Å and 2.65 Å-resolution. Both pseudoknots exhibited the elusive L2 loop, which displayed distinct conformations. Conversely, the Shine-Dalgarno sequence (SDS) in the S2 helix of each structure remained unbroken. The expectation that the effector-free state should expose the SDS prompted us to conduct solution experiments to delineate environmental changes to specific nucleobases in response to preQ1. We then used nudged elastic band computational methods to derive conformational-change pathways linking the crystallographically-determined effector-free and bound-state structures. Pathways featured: (i) unstacking and unpairing of L2 and S2 nucleobases without preQ1—exposing the SDS for translation and (ii) stacking and pairing L2 and S2 nucleobases with preQ1—sequestering the SDS. Our results reveal how preQ1 binding reorganizes L2 into a nucleobase-stacking spine that sequesters the SDS, linking effector recognition to biological function. The generality of stacking spines as conduits for effector-dependent, interdomain communication is discussed in light of their existence in adenine riboswitches, as well as the turnip yellow mosaic virus ribosome sensor.
Conductance of a dissipative quantum dot: Nonequilibrium crossover near a non-Fermi-liquid quantum critical point
In this work, we find the nonlinear conductance of a dissipative resonant level in the nonequilibrium steady state near its quantum critical point. The system consists of a spin-polarized quantum dot connected to two resistive leads that provide ohmic dissipation. We focus on the crossover from the strong-coupling, non-Fermi-liquid regime to the weak-coupling, Fermi-liquid ground state, a crossover driven by the instability of the quantum critical point to hybridization asymmetry or detuning of the level in the dot. We show that the crossover properties are given by tunneling through an effective single barrier described by the boundary sine-Gordon model. The nonlinear conductance is then obtained from thermodynamic Bethe ansatz results in the literature, which were developed to treat tunneling in a Luttinger liquid. The current-voltage characteristics are thus found for any value of the resistance of the leads. For the special case of lead resistance equal to the quantum resistance, we find mappings onto, first, the two-channel Kondo model and, second, an effectively noninteracting model from which the nonlinear conductance is found analytically. A key feature of the general crossover function is that the nonequilibrium crossover driven by applied bias is different from the crossover driven by temperature---we find that the nonequilibrium crossover is substantially sharper. Finally, we compare to experimental results for both the bias and temperature crossovers: the agreement is excellent.
The Optics of Deterrence: How Science Assures the Nuclear Stockpile's Reliability In Lieu of Testing
When designing a product intended to perform a certain function and satisfy some set of criteria, the standard engineering method to assess its ability to perform is to test it. This nearly universal concept works consistently, assuring proper function and generally avoiding or mitigating the consequence of failure to within acceptable limits. What would happen if the product developers were told that they must continue to certify and validate the performance without testing it, that the landscape in which the product must serve its purpose is constantly evolving, and that the product in question is the United States’ nuclear weapons stockpile? This is the position the National Nuclear Security Administration (NNSA) finds itself in; the reliability of the stockpile must be verified without actually testing it to see if it works as intended.
Primer for OTERR Core Reloading Optimization
OTERR (Optimization of Test Reactor Reloading) is a software tool which assists in finding optimal fuel assembly reloading patterns for nuclear reactors. It was created specifically to support the Versatile Test Reactor (VTR) program, but its functionality is general enough to be applied to most fast spectrum reactors which use hexagonal prismatic fuel elements. This document is meant to be a primer for new users of OTERR to walk through example workflows for core reloading optimization cases. Simple cases are followed step-by-step to discuss what needs to be done to complete a reloading optimization sequence. Note that the intent of this document is to provide practical examples for users to follow along with so they can quickly start using OTERR and then make changes to fit their own modeling needs. Detail is limited in terms of addressing additional features not used in these examples and especially lacking in discussion of theory used in the code. To better address these points, users are highly encouraged to refer to the OTERR User Manual and the OTERR Theory Manual.
Core Model Proposal #373: Add Exogenous Shutdown Decider
This core model proposal adds an exogenous shutdown decider that can scale the output of a vintaged technology in years after its initial operating period. The output can be scaled above or below the technology vintage's original output. This proposal also includes code changes to disable the behavior of the s-curve shutdown decider and profit shutdown decider in calibration periods. The proposal does not include any changes to data to utilize the new exogenous shutdown decider (it only introduces the capability). It should be noted that the exogenous shutdown decider and s-curve shutdown decider serve similar functions and generally should not be used together; however, the exogenous shutdown decider and profit shutdown decider reflect different dynamics and can be used in combination.
Innovation of heterochromatin functions drives rapid evolution of essential ZAD-ZNF genes in Drosophila
Contrary to dogma, evolutionarily young and dynamic genes can encode essential functions. We find that evolutionarily dynamic ZAD-ZNF genes, which encode the most abundant class of insect transcription factors, are more likely to encode essential functions in Drosophila melanogaster than ancient, conserved ZAD-ZNF genes. We focus on the Nicknack ZAD-ZNF gene, which is evolutionarily young, poorly retained in Drosophila species, and evolves under strong positive selection. Yet we find that it is necessary for larval development in D. melanogaster. We show that Nicknack encodes a heterochromatin-localizing protein like its paralog Oddjob, also an evolutionarily dynamic yet essential ZAD-ZNF gene. We find that the divergent D. simulans Nicknack protein can still localize to D. melanogaster heterochromatin and rescue viability of female but not male Nicknack-null D. melanogaster. Our findings suggest that innovation for rapidly changing heterochromatin functions might generally explain the essentiality of many evolutionarily dynamic ZAD-ZNF genes in insects.
Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory
We present a general approach to converge excited state solutions to any quantum chemistry orbital optimization process, without the risk of variational collapse. The resulting square gradient minimization (SGM) approach only requires analytic energy/Lagrangian orbital gradients and merely costs 3 times as much as ground state orbital optimization (per iteration), when implemented via a finite difference approach. SGM is applied to both single determinant ΔSCF and spin-purified restricted open-shell Kohn-Sham (ROKS) approaches to study the accuracy of orbital optimized DFT excited states. It is found that SGM can converge challenging states where the maximum overlap method (MOM) or analogues either collapse to the ground state or fail to converge. We also report that ΔSCF/ROKS predict highly accurate excitation energies for doubly excited states (which are inaccessible via TDDFT). Singly excited states obtained via ROKS are also found to be quite accurate, especially for Rydberg states that frustrate (semi)local TDDFT. Our results suggest that orbital optimized excited state DFT methods can be used to push past the limitations of TDDFT to doubly excited, charge-transfer, or Rydberg states, making them a useful tool for the practical quantum chemist's toolbox for studying excited states in large systems.
Importance of imposing gauge invariance in time-dependent density functional theory calculations with meta-generalized gradient approximations
It has been known for more than a decade that the gauge variance of the kinetic energy density τ leads to additional terms in the magnetic orbital rotation Hessian used in linear-response time-dependent density functional theory (TDDFT), affecting excitation energies obtained with τ-dependent exchange–correlation functionals. While previous investigations found that a correction scheme based on the paramagnetic current density has a small effect on benchmark results, we report more pronounced effects here, in particular, for the popular M06-2X functional and for some other meta-generalized gradient approximations (mGGAs). In the first part of this communication, this is shown by a reassessment of a set of five Ni(II) complexes for which a previous benchmark study that did not impose gauge invariance has found surprisingly large errors for excitation energies obtained with M06-2X. These errors are more than halved by restoring gauge invariance. The variable importance of imposing gauge invariance for different mGGA-based functionals can be rationalized by the derivative of the mGGA exchange energy integrand with respect to τ. In the second part, a large set of valence excitations in small main-group molecules is analyzed. For M06-2X, several selected n → π* and π→π$^{*}_{⊥}$ excitations are heavily gauge-dependent with average changes of –0.17 and –0.28 eV, respectively, while π→π$^{*}_{∥}$ excitations are marginally affected (–0.04 eV). Similar patterns, but of the opposite signs, are found for SCAN0. Here, the results suggest that reevaluation of previous gauge variant TDDFT results based on M06-2X and other mGGA functionals is warranted.