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The dispersion relation for the inverse hyperbolic potential is calculated in the classical limit. This is shown for both the low amplitude phonon branch and the high amplitude soliton branch. It is shown these results qualitatively follow that previously found for the inverse squared potential where explicit analytic solutions are known.
Methodologies for training machine learning potentials (MLPs) with quantum-mechanical simulation data have recently seen tremendous progress. Experimental data have a very different character than simulated data, and most MLP training procedures cannot be easily adapted to incorporate both types of data into the training process. Here, we investigate a training procedure based on iterative Boltzmann inversion that produces a pair potential correction to an existing MLP using equilibrium radial distribution function data. By applying these corrections to an MLP for pure aluminum based on density functional theory, we observe that the resulting model largely addresses previous overstructuring in the melt phase. Interestingly, the corrected MLP also exhibits improved performance in predicting experimental diffusion constants, which are not included in the training procedure. The presented method does not require autodifferentiating through a molecular dynamics solver and does not make assumptions about the MLP architecture. Our results suggest a practical framework for incorporating experimental data into machine learning models to improve the accuracy of molecular dynamics simulations.
Condensed algebraic forms for Maxwell's second- and third-order equations of transfer are developed for the case of molecules described by either elastic hard spheres, inverse-power potentials, or by Bird's variable hard-sphere model. These hardly reduced, yet exact, equations provide a new point of origin, when using the moment method, in seeking approximate solutions in the kinetic theory of gases for molecular models that are physically more realistic than that provided by the Maxwell model. An important by-product of the analysis when using these second- and third-order relations is that a clear mathematical connection develops between Bird's variable hard-sphere model and that for the inverse-power potential.
A heuristic estimate for the soliton production rate by a pulse is verified for the Korteweg - de Vries equation using inverse scattering. An observation from this result, which is shown to hold for some other nonlinear equations and for the case of the 'forced' nonlinear Schroedinger equation, is that production is determined by quantities that are invariant under rescaling of the original nonlinear equations. We speculate that this result may be useful to the development of an inverse scattering theory for 'forced' nonlinear systems.
Semiconductor photoelectrodes are regularly coupled to solid-state heterogeneous catalysts to perform solar-driven reduction of CO 2 . Less frequently, molecular catalysts are employed to better control the reactivity toward desired products, yet the development of robust semiconductor/molecule interfaces has proven challenging. Here, we demonstrate that a 2–3 nm thermal oxide layer on Si exhibits stability in aqueous solution, high photovoltage, and a photocurrent density of ∼10 mA/cm 2 for the solar-driven photoelectrochemical reduction of a homogeneous molecular catalyst, producing syngas with an ∼2:1 H 2 to CO ratio. Because of a low defect density, the oxide interface forms an electron inversion layer with metal-like electron density at cathodic potentials. This inversion layer facilitates electron transfer to redox-active molecules via tunneling even if the molecule’s reduction potential is beyond the semiconductor’s conduction band edge. Using an electrolyte solution composed of a homogeneous cobalt bis(terpyridine) catalyst in a water/organic solvent mixture, stable photoelectrochemistry was observed under 1-sun illumination, exhibiting an ∼30% Faradaic efficiency for CO that was similar to a glassy carbon electrode under comparable conditions. Furthermore, the results demonstrate that an ultrathin thermal oxide interface is a robust platform for development of aqueous-stable, molecule-driven photoelectrocatalysis.
An inverse numerical technique for designing transonic airfoils having a prescribed pressure distribution is presented. The method uses the full potential equation, inverse boundary conditions, and Cartesian coordinates. It includes simultaneous airfoil update and utilizes a direct-inverse approach that permits a logical method for controlling trailing edge closure. The method can also be used for the analysis of flowfields about specified airfoils. Comparison with previous results shows that accurate results can be obtained with a Cartesian grid. Examples show the application of the method to design aft-cambered and other airfoils specifically for transonic flight.
Several aspects of the kinetic models used in the collision phase of Monte Carlo direct simulations have been studied. Accurate molecular velocity distribution function predictions require a significantly increased number of computational cells in one maximum slope shock thickness, compared to predictions of macroscopic properties. The shape of the highly repulsive portion of the interatomic potential for argon is not well modeled by conventional interatomic potentials; this portion of the potential controls high Mach number shock thickness predictions, indicating that the specification of the energetic repulsive portion of interatomic or intermolecular potentials must be chosen with care for correct modeling of nonequilibrium flows at high temperatures. It has been shown for inverse power potentials that the assumption of variable hard sphere scattering provides accurate predictions of the macroscopic properties in shock waves, by comparison with simulations in which differential scattering is employed in the collision phase. On the other hand, velocity distribution functions are not well predicted by the variable hard sphere scattering model for softer potentials at higher Mach numbers.
ABSTRACT The leading explanation of the Fermi Galactic Centre γ-ray excess is the extended emission from an unresolved population of millisecond pulsars (MSPs) in the Galactic bulge. Such a population would, along with the prompt γ-rays, also inject large quantities of electrons/positrons (e±) into the interstellar medium. These e± could potentially inverse-Compton (IC) scatter ambient photons into γ-rays that fall within the sensitivity range of the upcoming Cherenkov Telescope Array (CTA). In this article, we examine the detection potential of CTA to this signature by making a realistic estimation of the systematic uncertainties on the Galactic diffuse emission model at TeV-scale γ-ray energies. We forecast that, in the event that e± injection spectra are harder than E−2, CTA has the potential to robustly discover the IC signature of a putative Galactic bulge MSP population sufficient to explain the Galactic Centre excess for e± injection efficiencies in the range of ≈2.9–74.1 per cent, or higher, depending on the level of mismodelling of the Galactic diffuse emission components. On the other hand, for spectra softer than E−2.5, a reliable CTA detection would require an unphysically large e± injection efficiency of ${\gtrsim} 158{{\ \rm per\ cent}}$. However, even this pessimistic conclusion may be avoided in the plausible event that MSP observational and/or modelling uncertainties can be reduced. We further find that, in the event that an IC signal were detected, CTA can successfully discriminate between an MSP and a dark matter origin for the radiating e±.
Data obtained from a numerical solution of the Boltzmann equation for shock-wave structure are used to test the accuracy of accepted approximate expressions for the two moments of the collision integral Delta (Q) for general intermolecular potentials in systems with a large translational nonequilibrium. The accuracy of the numerical scheme is established by comparison of the numerical results with exact expressions in the case of Maxwell molecules. They are then used in the case of hard-sphere molecules, which are the furthest-removed inverse power potential from the Maxwell molecule; and the accuracy of the approximate expressions in this domain is gauged. A number of approximate solutions are judged in this manner, and the general advantages of the numerical approach in itself are considered.
Functional soft materials, comprising colloidal and molecular building blocks that self-organize into complex structures as a result of their tunable interactions, enable a wide array of technological applications. Inverse methods provide a systematic means for navigating their inherently high-dimensional design spaces to create materials with targeted properties. Furthermore, while multiple physically motivated inverse strategies have been successfully implemented in silico, their translation to guiding experimental materials discovery has thus far been limited to a handful of proof-of-concept studies. In this perspective, we discuss recent advances in inverse methods for design of soft materials that address two challenges: (1) methodological limitations that prevent such approaches from satisfying design constraints and (2) computational challenges that limit the size and complexity of systems that can be addressed. Strategies that leverage machine learning have proven particularly effective, including methods to discover order parameters that characterize complex structural motifs and schemes to efficiently compute macroscopic properties from the underlying structure. We also highlight promising opportunities to improve the experimental realizability of materials designed computationally, including discovery of materials with functionality at multiple thermodynamic states, design of externally directed assembly protocols that are simple to implement in experiments, and strategies to improve the accuracy and computational efficiency of experimentally relevant models.
Time-resolved infrared (TRIR) and electrochemical impedance spectroscopy (EIS) were utilized to quantify surface states present at silicon oxide (SiO x ) protected crystalline p-Si electrolyte interfaces. The primary goal was to identify p-Si/SiO x photoelectrodes with both low surface recombination rates and efficient multi-electron transfer to an acceptor present in the external electrolyte. Three SiO x layers were investigated: native oxide (nOx), chemical oxide (cOx), and rapid thermal annealed (RTA) thermal oxide (tOx). Comparative study with [Ru(bpy) 3 ](PF 6 ) 2 as the electron acceptor indicated that tOx was most optimal with a small effective recombination rate, multi-electron transfer capability, and photovoltage of 500 ± 50 mV. A secondary goal was to analyze the surface recombination rates with the Shockley–Read–Hall (SRH) kinetic model. Two surface states were identified from this analysis, one closer to the CB edge (V t,1 ) and the other near the midgap (V t,2 ). EIS and SRH analyses revealed that a forming gas (5% H 2 /N 2 ) anneal (FGA) decreased surface recombination for tOx and nOx through a lower density of surface states. In the case of tOx, the infrared data indicated that V t,2 was completely removed. Here, the energetic positions of the band edges were correlated with the surface state density; low densities corresponded to more favorable potentials for inversion layer formation, which is expected to be most optimal for photocatalysis. Collectively this study indicates that the free carrier dynamics provided by TRIR represent a powerful in situ probe of the band edge and the surface state energetics in silicon based photoelectrochemical cells.
Abstract Even before its role in electroweak symmetry breaking, the Anderson-Higgs mechanism was introduced to explain the Meissner effect in superconductors. Spontaneous symmetry-breaking yields massless phase modes representing the low-energy excitations of the Mexican-Hat potential. Only in superconductors the phase mode is shifted towards higher energies owing to the gauge field of the charged condensate. This results in a low-energy excitation spectrum governed by the Higgs mode. Consequently, the Bardeen-Cooper-Schrieffer-like Meissner effect signifies a macroscopic quantum condensate in which a photon acquires mass, representing a one-to-one analogy to high-energy physics. We report on an innovative spectroscopic technique to study symmetries and energies of the Higgs modes in the high-temperature superconductor Bi 2 Sr 2 CaCu 2 O 8 after a soft quench of the Mexican-Hat potential. Population inversion induced by an initial laser pulse leads to an additional anti-Stokes Raman-scattering signal, which is consistent with polarization-dependent Higgs modes. Within Ginzburg-Landau theory, the Higgs-mode energy is connected to the Cooper-pair coherence length. Within a Bardeen-Cooper-Schrieffer weak-coupling model we develop a quantitative and coherent description of single-particle and two-particle channels. This opens the avenue for Higgs Spectroscopy in quantum condensates and provides a unique pathway to control and explore Higgs physics.
As buildings age, retrofits are becoming an increasingly important topic for the ever-growing and aging existing building stock. To compare designs or evaluate in-service building envelopes, thermal modeling is utilized to evaluate the thermal performance of envelope assemblies; however, it can be difficult to model the thermal performance of as-built assemblies due to degradation or missing documentation. To address this issue, inverse modeling can be applied to infer the properties of as-built envelope assemblies. This paper presents a review of the literature and published methods to model and infer the transient conductive performance of building envelopes. This review serves as a survey of existing transient conduction algorithms to evaluate performance, computational speed, and relevance for inverse modeling applications. In addition to the literature review, this work also evaluates the computational performance of the most prevalent transient conduction algorithms against the ASHRAE 1052RP toolkit to assess inverse modeling potential. This methodology serves as a foundation for future research to characterize the transient thermal performance of as-built building envelope assemblies.
Abstract The construction of a better exchange-correlation potential in time-dependent density functional theory (TDDFT) can improve the accuracy of TDDFT calculations and provide more accurate predictions of the properties of many-electron systems. Here, we propose a machine learning method to develop the energy functional and the Kohn–Sham potential of a time-dependent Kohn–Sham (TDKS) system is proposed. The method is based on the dynamics of the Kohn–Sham system and does not require any data on the exact Kohn–Sham potential for training the model. We demonstrate the results of our method with a 1D harmonic oscillator example and a 1D two-electron example. We show that the machine-learned Kohn–Sham potential matches the exact Kohn–Sham potential in the absence of memory effect. Our method can still capture the dynamics of the Kohn–Sham system in the presence of memory effects. The machine learning method developed in this article provides insight into making better approximations of the energy functional and the Kohn–Sham potential in the TDKS system.
Here, in this work, we consider a “reverse-engineering” approach to construct confining potentials that support exact, constant density kovaton solutions to the classical Gross-Pitaevskii equation (GPE) also known as the nonlinear Schr¨odinger equation (NLSE). In the one-dimensional case, the exact solution is the sum of stationary kink and anti-kink solutions, i.e. a kovaton, and in the overlapping region, the density is constant. In higher dimensions, the exact solutions are generalizations of this wave function. In the absence of self-interactions, the confining potential is similar to a smoothed out finite square well with minima also at the edges. When self-interactions are added, a term proportional to ±gψ*ψ gets added to the confining potential and ±gM, where M is the norm, gets added to the total energy. In the realm of stability analysis, we find (linearly) stable solutions in the case with repulsive self-interactions which also are stable to self-similar deformations. For attractive interactions, however, the minima at the edges of the potential get deeper and a barrier in the center forms as we increase the norm. This leads to instabilities at a critical value of M (related to the number of particles in the BEC). Comparing the stability criteria from Derrick’s theorem and Bogoliubov-de Gennes analysis stability results, we find that both predict stability for repulsive self-interactions and instability at a critical mass M for attractive interactions. However, the numerical analysis gives a much lower critical mass. The numerical analysis shows further that the initial instabilities violate the symmetry x → -x assumed by Derrick’s theorem.
Abstract. Recent studies suggested significant impacts of boreal cryosphere changes on wintertime air stagnation and haze pollution extremes in China. However, the underlying mechanisms of such a teleconnection relationship remains unclear. Here we use the Whole Atmosphere Community Climate Model (WACCM) to investigate dynamic processes leading to atmospheric circulation and air stagnation responses to Arctic sea ice changes. We conduct four climate sensitivity experiments by perturbing sea ice concentrations (SIC) and corresponding sea surface temperature (SST) in autumn and early winter over the whole Arctic and three subregions in the climate model. The results indicate distinct responses in circulation patterns and regional ventilation to the region-specific Arctic changes, with the largest increase of both the probability (by 132 %) and the intensity (by 30 %) of monthly air stagnation extremes being found in the experiment driven by SIC and SST changes over the Pacific sector of the Arctic (the East Siberian and Chukchi seas). The increased air stagnation extremes are mainly driven by an amplified planetary-scale atmospheric teleconnection pattern that resembles the negative phase of the Eurasian (EU) pattern. Dynamical diagnostics suggest that convergence of transient eddy forcing in the vicinity of Scandinavia in winter is largely responsible for the amplification of the teleconnection pattern. Transient eddy vorticity fluxes dominate the transient eddy forcing and produce a barotropic anticyclonic anomaly near Scandinavia and wave train propagation across Eurasia to the downstream regions in East Asia. The piecewise potential vorticity inversion analysis reveals that this long-range atmospheric teleconnection of Arctic origin takes place primarily via the middle and upper troposphere. The anomalous ridge over East Asia in the middle and upper troposphere worsens regional ventilation conditions by weakening monsoon northwesterlies and enhancing temperature inversions near the surface, leading to more and stronger air stagnation and pollution extremes over eastern China in winter. Ensemble projections based on state-of-the-art climate models in the Coupled Model Intercomparison Project Phase 6 (CMIP6) corroborate this teleconnection relationship between high-latitude environmental changes and midlatitude weather extremes, though the tendency and magnitude vary considerably among each participating model.
Reducing uncertainties in regional carbon balances requires a better understanding of CO 2 transport in synoptic weather systems. Here, we apply the Patient Rule Induction Method (PRIM), a data-mining method to identify high-density regions for a target-class within an input parameter space, to airborne observations of potential temperature, wind speed, water vapor mixing ratio, and CO 2 dry mol fraction gathered during the Atmospheric Carbon and Transport (ACT)-America Summer 2016 and Winter 2017 campaigns. ACT observations were targeted at expert-designated cases of fair weather and near-frontal warm and cold sector air at atmospheric boundary-layer, lower-, and higher free tropospheric levels (ABL, LFT, and HFT, respectively). We investigate atmospheric characteristics of these pre-defined cases and associated CO 2 model-observation-differences in the mesoscale WRF-Chem model. PRIM results separate winter- and summertime observations as well as observations from ABL, LFT, and HFT with enrichment factors of 4.0–20.5 inside the PRIM box compared to the entire dataset but cannot distinguish between near-frontal warm and cold sector observations in the higher free troposphere. Analyzing of the parameter space constrained by PRIM, we find that large magnitude model observation differences preferentially associated with times when atmospheric conditions are less typical. This association suggests that PRIM could provide a useful tool for isolating atmospheric conditions with large-magnitude and non-Gaussian CO 2 -residuals for targeted transport model evaluation and to potentially improve inversion results during synoptically active periods.
Expressions for the diffusion coefficient of ions in gas mixtures are obtained from momentum transfer theory, and are given in terms of the diffusion coefficients and drift velocities of the ions in the pure component gases. Blanc's law holds exactly at all field strengths if the mean free time between collisions is independent of velocity (Maxwell model), but otherwise there may be either positive or negative deviations from Blanc's law at high fields. Such deviations are of comparable magnitude for the diffusion coefficients and the mobility, but are not identical. Specific cases of inverse-power potentials are treated in further detail, and some numerical examples are given for rigid-sphere interactions.