Temperature and concentration dependence of the ionic transport properties of poly(ethylene oxide) electrolytes
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25 ENERGY STORAGE↗
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Results for “solution theory”
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Deep Eutectic Solvents: A Review of Fundamentals and Applications
Deep eutectic solvents (DESs) are an emerging class of mixtures characterized by significant depressions in melting points compared to those of the neat constituent components. These green materials are promising for applications as inexpensive ’designer’ solvents exhibiting a host of tunable physicochemical properties. Here, a detailed review of the current literature reveals the lack of predictive understanding of the microscopic mechanisms that govern the structure-property relationships in this class of solvents. Complex hydrogen bonding behavior is postulated as the root cause of their melt-ing point depressions and physicochemical properties; to understand these hydrogen bonded networks, it is imperative to study these systems as dynamic entities using both simulations and experiments. This review emphasizes recent research efforts in order to elucidate the next steps needed to develop a fundamental framework for understanding DESs. It covers recent developments in DES research, frames outstanding scientific questions, and identifies gainful research thrusts that would advance the field towards predictive models and fundamental understanding of these solvents.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Morphology and Transport of Multivalent Cation-Exchanged Ionomer Membranes Using Perfluorosulfonic Acid–Ce Z+ as a Model System
Perfluorosulfonic acids (PFSAs) are commonly used as solid polymer electrolyte membranes (PEMs) in electrochemical energy devices, where they are vulnerable to attack by radical species during operation. A popular strategy to combat this problem is to introduce radical scavengers like cerium (Ce) ions that neutralize these species before they attack the PFSA. Such cation doping creates a multi-ion system, in which understanding the mechanisms of cation solvation and transport becomes important for the effective design and utilization of PFSA–cation systems. Ce ions also provide a representative model system for multication-exchanged ionomers in electrochemical systems. In this study, hydration and conductivity measurements, along with X-ray fluorescence and scattering, are employed to elucidate how Ce ion exchange alters PFSA’s ionic solvation, as well as nano- and mesoscale morphologies, which ultimately control its ion transport properties. A molecular transport model is used to deconvolute the impact of Ce ions on the local solvation structure of water in the membrane from mesoscale changes of the transport pathways. The combined experimental and theoretical analysis reveals a nonlinear decrease in conductivity driven by cation solvation at the molecular level and morphological changes at longer length scales. Migration–diffusion coupling, its nonlinear dependence on ion exchange and hydration, and its overall implications for ionomer performance are also discussed. Finally, these findings have the potential to be translated into other mixed cation–ionomer systems for a wide range of energy and environmental devices.
36 MATERIALS SCIENCE↗
Benchmark of few-level quantum theory vs ab initio numerical solutions for the strong-field Autler–Townes effect in photoionization of hydrogen
Abstract The temporal and spectral consequences of an intermediate resonance en route to photoionization are investigated theoretically in two ways: by solving few-level model equations and by ab initio numerical solution of the time-dependent Schrödinger equation, in both cases for hydrogen in three dimensions. The model consists of atomic states resonantly field-dressed in a three-level reduction of the hydrogen atom that consists of the 2 p –3 d (Balmer) transition and one energetically-distant continuum state. The model’s level occupation probabilities are derived from three Schrödinger amplitude equations and are benchmarked against an ab initio numerical solution for the hydrogen electron’s wavefunction under the same field. We examine contrasts between the results of the two approaches with a particular focus on Autler–Townes doublets that appear in the photoelectron spectrum.
74 ATOMIC AND MOLECULAR PHYSICS↗
Continuum Description of the Role of Negative Transference Numbers on Ion Motion in Polymer Electrolytes
New experimental techniques such as electrophoretic NMR (eNMR) are emerging as powerful methods for directly measuring ion velocities in electrolytes under applied electric fields. The aim of this theoretical study is to predict the spatial- and temporal-dependence of these velocities of ions as a function of the magnitude of the applied field and salt concentration. It has recently been shown that mixtures of poly(ethylene oxide)-based (PEO) and lithium bis(trifluoromethanesulfonyl) imide (LiTFSI) electrolytes exhibit negative cation transference numbers in a certain salt concentration range. In this range, the cation motion at early times is directed to the positive electrode at all locations in the cell; ion migration dominates in this regime. As time progresses, the cation velocity in finite zones near both the electrodes changes sign. These zones grow rapidly with time, reflecting the increasing importance of diffusion, and a point in time is reached beyond which the cation velocity in the entire cell is directed toward the negative electrode. Overall, our work reveals the limited time window over which the results of eNMR can be used to determine the transference number. More importantly, it shows how to account for the effect of diffusional flux in such experiments.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Prediction of Redox Potentials for Ac, Th, and Pa in Aqueous Solution
Density functional theory in conjunction with small core pseudopotentials and the associated basis sets was used to calculate potentials for multiple redox couples, covering a range of oxidation states for Ac (0 to III), Th (0 to IV), and Pa (0 to V) in aqueous solution. Solvation effects were incorporated using a supermolecule-continuum approach, with 30 water molecules representing two solvation shells, and the COSMO and SMD implicit solvation models. The calculated geometries for Ac(III), Th(IV), and Pa(V) were in reasonable agreement with the available experimental data. Using the COSMO model with the B3LYP functional, the calculated redox potentials were within ± 0.2 V from experiment for most redox couples. Several pathways were explored for the Pa(V/IV) redox couple for different forms of Pa(V) and Pa(IV). Most Pa(V/IV) redox couples have very similar potentials, ranging from 0 to -0.4 V up to a pH of 1.4. At pH = 1.4, the potentials shift to values that are more negative than -0.7 V, reflecting the growing unfavorable nature of the redox process at higher pH levels. The calculated values for An(III/II) potentials were consistent with prior estimates and the available experimental data. The predicted redox potentials for An(II/I) were highly negative, as expected. For An(I/0) potentials, Th and Pa exhibited positive values, contrasting with the negative values calculated for Ac. Furthermore, the An +m /An(0) potentials agreed better with the experimental data when using the COSMO solvation model as compared to the SMD model.
Chemical calculations↗
Dynamics of E6 chiral gauge theories
We present exact nonperturbative vacuum solutions to chiral gauge theories based on the gauge group and several matter fermions in the fundamental -dimensional representation. They are obtained when supersymmetric versions are perturbed by small supersymmetry breaking by anomaly mediation. The universality classes obtained are very different from what can be conjectured by the tumbling hypothesis. In particular, the case with three may have an unbroken SU(3) symmetry with massless composite fermions in of SU(3). For this case, we employed numerical techniques to obtain the exact ground state.
Goh, Andrew↗
Bounce-averaged theory in arbitrary multi-well plasmas: solution domains and the graph structure of their connections
Bounce-averaged theories provide a framework for simulating relatively slow processes, such as collisional transport and quasilinear diffusion, by averaging these processes over the fast periodic motions of a particle on a closed orbit. This procedure dramatically increases the characteristic time scale and reduces the dimensionality of the modelled system. The natural coordinates for such calculations are the constants of motion (COM) of the fast particle motion, which by definition do not change during an orbit. However, for sufficiently complicated fields – particularly in the presence of local maxima of the electric potential and magnetic field – the COM are not sufficient to specify the particle trajectory. In such cases, multiple domains in COM space must be used to solve the problem, with boundary conditions enforced between the domains to ensure continuity and particle conservation. Previously, these domains have been imposed by hand, or by recognising local maxima in the fields, limiting the flexibility of bounce-averaged simulations. Here, we present a general set of conditions for identifying consistent domains and the boundary condition connections between the domains, allowing the application of bounce-averaged theories in arbitrarily complicated and dynamically evolving electromagnetic field geometries. We also show how the connections between the domains can be represented by a directed graph, which can help to succinctly represent the trajectory bifurcation structure.
fusion plasma↗
The Kalai-Smorodinsky solution for many-objective Bayesian optimization
An ongoing aim of research in multiobjective Bayesian optimization is to extend its applicability to a large number of objectives. While coping with a limited budget of evaluations, recovering the set of optimal compromise solutions generally requires numerous observations and is less interpretable since this set tends to grow larger with the number of objectives. We thus propose to focus on a specific solution originating from game theory, the Kalai-Smorodinsky solution, which possesses attractive properties. In particular, it ensures equal marginal gains over all objectives. We further make it insensitive to a monotonic transformation of the objectives by considering the objectives in the copula space. A novel tailored algorithm is proposed to search for the solution, in the form of a Bayesian optimization algorithm: sequential sampling decisions are made based on acquisition functions that derive from an instrumental Gaussian process prior. Our approach is tested on four problems with respectively four, six, eight, and nine objectives. The method is available in the R package GPGame available on CRAN at https://cran.r-project.org/package=GPGame.
Game theory↗
Transient solute drag and strain aging of dislocations
The transient drag force exerted by mobile solutes on a moving dislocation is computed using continuum theory. These mobile solutes form so-called Cottrell atmospheres around dislocations during static and dynamic strain aging. We evaluate the evolution of the drag force exerted by the atmosphere under two velocity time-histories: impulsive acceleration to a chosen velocity and a constant acceleration rate. A particular focus is on the conditions under which the stationary limit assumed by theories of dynamic strain aging is obeyed. According to our results, two conditions—one on the dislocation velocity and one on the acceleration rate—must be satisfied for the stationary limit to hold. Using the Orowan relation and a line tension model, we obtain estimates for the temperature, stress, strain rate, and dislocation density regimes where the stationary limit is valid, and compare these results with experiments for a few material systems.
36 MATERIALS SCIENCE↗
SU(n) and Quantum SU(n) Symmetries in Physical Systems [Slides]
Presence of SU(n) or other Lie group symmetry in a physical system is its powerful, usually underutilized property. In many cases it allows for finding analytical solutions to nonlinear differential equations describing this system. Power of the method is presented on diversified examples from mathematical physics: Lie-group symmetries in finding solutions of generalized, multidimensional theory of gravity; analytical Dirac–equation solutions for description of conducting polymers; stability of qubit states in quantum computers; spatial defects in condensed matter; reconstruction of 3D object from its 2D tomographic image; significant improvement of numerical solutions stability for Euler equations. The next question after obtaining such Lie group symmetric solution is: does a generalized solution with appropriate quantum group symmetry exists for the given physical system, and if yes what is the physical meaning of the deformation parameter q introduced by such solution. In many cases it can be identified. Any SU(n) solution is by its nature singular, assuming a perfect symmetry of the physical system discussed. Such solution gives a powerful insight to theoretical physics, yet the assumption may be too demanding for experimental applications. Deformation parameter q from a quantum group symmetry allows for a continuum of solutions, more applicable to experiments.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Nucleon decay search with DUNE
Grand Unification and Supersymmetry are appealing theories that offer solutions to important problems of modern physics. A key prediction of both theories is the decay of protons and bound neutrons, for which no evidence has been found yet. The dominant proton decay mode in favored supersymmetric theories is $p \rightarrow \bar{\nu} K^+$ and the predicted lifetimes range between $10^{32} - 10^{35} \, \text{years}$. In this report, a sensitivity study for $p \rightarrow \bar{\nu} K^+$ is presented for the Deep Underground Neutrino Experiment (DUNE). At an exposure of $400 \, \text{kiloton} \cdot \text{years}$, DUNE will be able to constrain the proton lifetime to $\tau / \text{Br} \left( p \rightarrow \bar{\nu} K^+ \right) > 1.3 \times 10^{34} \, \text{years}$ at $90 \, \%$ confidence level if no proton decay is observed.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Exact solution of burst pressure for thick-walled pipes using the flow theory of plasticity
This paper develops an exact solution of burst pressure for defect-free, thick-walled pipes using the flow theory of plasticity in terms of the average shear stress yield criterion (or Zhu-Leis yield criterion). The pipe steel is assumed to obey the power-law strain hardening rule, and large plastic deformation is described by the finite strain theory. On this basis, internal pressure is obtained as a power series function of the effective strains on the inside and outside surfaces of the thick-walled pipe with use of the second Bernoulli numbers. At burst failure, the Zhu-Leis flow solution of burst pressure is determined as a power series solution, and the burst effective strains, the burst effective stresses, and the burst pressure are functions of the diameter ratio (D o / D i ), strain hardening exponent (n), and ultimate tensile strength (UTS). Similarly, the Tresca and von Mises flow solutions of burst pressure are also determined as a power series solution in terms of the Tresca and von Mises yield criteria. A general closed-from exact solution of burst pressure is then proposed for the three yield criteria, and the results showed that the proposed exact solution matches well with the power series solution for each yield criterion. Moreover, the von Mises flow solution is an upper bound prediction, the Tresca flow solution is a lower bound prediction, and the Zhu-Leis flow solution is an intermediate prediction that agrees well with the finite element analysis results of burst pressure for thick-walled pipes. Furthermore, two datasets of full-scale burst tests are then utilized to evaluate and validate the proposed flow solutions of burst pressure for both thin and thick-walled pipes.
42 ENGINEERING↗
Investigations about iso-geometric analysis for self-shielding calculations with the subgroup method
The implementation of a self-shielding method for a neutron transport calculation code based on the iso-geometric analysis (IGA) method that can resolve the multi-group neutron transport equation for arbitrary spatial domain, is presented. The self-shielding model based on the subgroup theory is adopted because the subgroup method can be used to perform calculations for any arbitrary geometrical domain which is the main purpose of our IGA code. Some basic theory of the subgroup method is given. A self-shielding calculation based on the PWR fuel pin composed of MOX fuel is presented and compared with a Monte Carlo calculation. The result is that the combination of SN transport theory, IGA and the subgroup method gives correctly shielded cross sections. Validation of the combination of the IGA method and SN neutron transport for subgroup calculations in two steps are presented: the first step is to ascertain the correctness of the IGA solutions compared to a known analytical solution in diffusion theory; the second step is a validation of the IGA solutions compared to a reference calculation in SN transport theory. The relation between the settings for the IGA solver and the accuracy of the results are elucidated. (authors)
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
Covariant color-kinematics duality
We show that color-kinematics duality is a manifest property of the equations of motion governing currents and field strengths. For the nonlinear sigma model (NLSM), this insight enables an implementation of the double copy at the level of fields, as well as an explicit construction of the kinematic algebra and associated kinematic current. As a byproduct, we also derive new formulations of the special Galileon (SG) and Born-Infeld (BI) theory. For Yang-Mills (YM) theory, this same approach reveals a novel structure — covariant color-kinematics duality — whose only difference from the conventional duality is that 1/$\square$ is replaced with covariant 1/D 2 . Remarkably, this structure implies that YM theory is itself the covariant double copy of gauged biadjoint scalar (GBAS) theory and an F 3 theory of field strengths encoding a corresponding kinematic algebra and current. Directly applying the double copy to equations of motion, we derive general relativity (GR) from the product of Einstein-YM and F 3 theory. This exercise reveals a trivial variant of the classical double copy that recasts any solution of GR as a solution of YM theory in a curved background. Covariant color-kinematics duality also implies a new decomposition of tree-level amplitudes in YM theory into those of GBAS theory. Using this representation we derive a closed-form, analytic expression for all BCJ numerators in YM theory and the NLSM for any number of particles in any spacetime dimension. By virtue of the double copy, this constitutes an explicit formula for all tree-level scattering amplitudes in YM, GR, NLSM, SG, and BI.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Explicit kink solutions in several one-parameter families of higher-order field theory models
Here, we present several one-parameter families of higher-order field theory models some of which admit explicit kink solutions with an exponential tail while others admit explicit kink solutions with a power-law tail. Various properties of these families of kink solutions are examined in detail. Further, by applying the recent Manton formalism, we provide estimates for the kink–kink (KK) and antikink–kink (AK-K) acceleration and hence the ratio of the corresponding AK-K and KK forces.
97 MATHEMATICS AND COMPUTING↗
The Newman-Penrose map and the classical double copy
Gauge-gravity duality is arguably our best hope for understanding quantum gravity. Considerable progress has been made in relating scattering amplitudes in certain gravity theories to those in gauge theories — a correspondence dubbed the double copy. Recently, double copies have also been realized in a classical setting, as maps between exact solutions of gauge theories and gravity. We present here a novel map between a certain class of real, exact solutions of Einstein’s equations and self-dual solutions of the flat-space vacuum Maxwell equations. This map, which we call the Newman-Penrose map, is well-defined even for non-vacuum, non-stationary spacetimes, providing a systematic framework for exploring gravity solutions in the context of the double copy that have not been previously studied in this setting. To illustrate this, we present here the Newman- Penrose map for the Schwarzschild and Kerr black holes, and Kinnersley’s photon rocket.
79 ASTRONOMY AND ASTROPHYSICS↗
Length scales and scale-free dynamics of dislocations in dense solid solutions
The fundamental interactions between an edge dislocation and a random solid solution are studied by analyzing dislocation line roughness profiles obtained from molecular dynamics simulations of Fe 0.70 Ni 0.11 Cr 0.19 over a range of stresses and temperatures. These roughness profiles reveal the hallmark features of a depinning transition. Namely, below a temperature-dependent critical stress, the dislocation line exhibits roughness in two different length scale regimes which are divided by a so-called correlation length. This correlation length increases with applied stress and at the critical stress (depinning transition or yield stress) formally goes to infinity. Above the critical stress, the line roughness profile converges to that of a random noise field. Motivated by these results, a physical model is developed based on the notion of coherent line bowing over all length scales below the correlation length. Above the correlation length, the solute field prohibits such coherent line bow outs. Using this model, we identify potential gaps in existing theories of solid solution strengthening and show that recent observations of length-dependent dislocation mobilities can be rationalized.
36 MATERIALS SCIENCE↗