From the resonance theory to the statistical model
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Breaking the curse of dimensionality: Solving configurational integrals for crystalline solids by tensor networks
Accurately evaluating configurational integrals for dense solids remains a central and difficult challenge in the statistical mechanics of condensed systems. Here, we present a tensor network approach that reformulates the high-dimensional configurational integral for identical-particle crystals into a sequence of computationally efficient summations. We represent the integrand as a high-dimensional tensor and apply tensor-train (TT) decomposition together with a custom TT-cross interpolation. This approach circumvents the need to explicitly construct the full tensor. We introduce tailored rank-1 and rank-2 schemes optimized for sharply peaked Boltzmann probability densities, typical for identical-particle crystals. When applied to the calculation of internal energy and pressure-temperature curves for crystalline Cu and Ar at high (GPa) pressures, as well as the alpha-to-beta phase transition diagram of Sn, our method accurately reproduces molecular dynamics simulation results using tight-binding, machine learning, hierarchical interacting particle–neural network, and modified embedded atom method potentials,all within seconds of computation time.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Berry Phase Effects in Dipole Density and the Mott Relation
Here, we provide a unified semiclassical theory for thermoelectric responses of any observable represented by an operator $\hat{θ}$ that is well defined in periodic crystals. The Einstein and Mott relations are established generally in the presence of Berry phase effects for various physical realizations of $\hat{θ}$ in electronic systems, including the familiar case of the electric current as well as the currently controversial cases of the spin polarization and spin current. The magnetization current, which has been proven indispensable in the thermoelectric response of electric current, is generalized to the cases of various $\hat{θ}$. In our theory the dipole density of a physical quantity emerges and plays a vital role, which contains not only the statistical sum of the dipole moment of $\hat{θ}$ but also a Berry phase correction.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Physical conditions in the cool parts of prominences. II - The Mg triplet lines
The statistical equilibrium of Mg under prominence conditions is considered. It is shown that the principal lines of the triplet system can serve as an equivalent to the Na D lines for spectral diagnostic purposes. Like the Na D lines, these Mg lines are relatively easy to measure in prominences and exhibit small optical depths. It is demonstrated that potential complications due to possible radiative transfer effects in the Mg resonance transition (3 1S0 - 3 1P1) have little consequence for the triplet populations. The results are used to repeat the spectral analysis of Landman (1983) using the Mg multiplets in place of the Na ones. The results of the two analyses are in general agreement. The finding of a low degree of H ionization in the cool prominence regions and a correspondingly high gas pressure is confirmed.
Landman, D. A.↗
A Review and Reflections on the Sun-Climate Connection
The field of sun-climate is beset with an extraordinary number of numerical correlations attempting to relate various periodicities of solar activity with changes in the Earth's weather and climate. Signatures representing climatological variability have been sought for cycles as short as the solar 28-day rotational period up to Milankovich periods of thousands of years, although a majority of correlations have concentrated on the 11-year sunspot and 22-year Hale double sunspot cycles. For the shorter term, parameters including temperature, pressure, winds storm tracks, rainfall, and water levels in rivers and lakes, etc. have been correlated with solar variability. For longer periods, it has been necessary to seek more indirect evidence in ice cores, tree rings, and geologic deep sea cores. Other atmospheric parameters relating to atmospheric electricity and the global electric circuit have also been correlated in similar fashion. Unfortunately, few, if any, of this wide spectrum of numerical correlations have been associated with any viable physical explanation, making most studies in the field an exercise in numerical statistics. More recently, a few suggestions for plausible coupling processes have begun to appear. These, coupled with new and stronger correlations involving selective binning of climatological data sets have injected new life and hope to this field. An overview is given of the historical past and current perspectives, to evaluate possible avenues for defining physical linking processes in the future.
Goldberg, Richard A.↗
Improved HIRS2/MSU soundings using tropopause information
In the GLAS physical retrieval scheme, all temperature profiles are expressed as an expansion about a global mean using empirical orthogonal functions derived from a sample of radiosondes. Total ozone burden, a parameter highly correlated with tropopause height, should be useful in improving sounding accuracy. The ability to estimate tropopause information from layer mean temperatures suggests incorporating the layer mean temperatures estimated from the sounding itself to give estimates of tropopause pressure and temperature. While information completely independent of sounding and first guess data is preferable, additional information is in fact added to the system by the statistical relationships between tropopause temperature and pressure and layer mean temperature profiles. This should not be confused with use of statistical relationships between temperature profiles and satellite observations, which form the basis of a statistical retrieval system but is in no way used in the physical retrieval scheme.
Susskind, J.↗
Statistics of the charge spectrum of photo-multipliers and methods for absolute calibration
We derive the full expression for the shape of the charge spectrum that results from the illumination of a photo-multiplier tube. The derivation is for low intensity illumination with constant gain, a common condition for most nuclear and particle physics applications. Under these conditions, it is shown that an analytic expression can be formulated that describes details of the spectrum including the pedestal and dark noise with excellent fidelity to allow statistical fits to data. The derivation and full formula using either Gaussian or Poisson models for gain, and its limiting forms under various simplifying assumptions are presented with strategies on their use. The analytic description can be used to formulate data acquisition strategies to perform precise absolute calibration of photo-multipliers, the digitizers, and the data acquisition system.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Direct cross section measurement of 102 Pd (𝛾,𝑝) and 102 Pd (𝛾,𝛼) for the astrophysical 𝑝 process
Background: A handful of neutron-deficient stable nuclei, known as the “p nuclei,” cannot be produced through astrophysical neutron capture processes. Instead, some of these nuclei are proposed to be produced by 𝛾-induced reactions on existing r- and s-process seeds. The specific astrophysical site or sites are not yet identified, however, with uncertainties in the cross sections of these 𝛾-induced reactions playing a role. Databases of reaction rates for astrophysical simulations often rely on theoretical statistical model calculations, such as Hauser-Feshbach, for rates where no experimental information is known. However, reasonable variations in the choice of parametrizations of various nuclear properties can create order-of-magnitude variations in the final predicted cross sections and reaction rates, which are then propagated through the models to the predicted final abundances. Purpose: To better constrain these statistical model calculations and ultimately reduce the uncertainties from the nuclear physics on our understanding of the p nuclei, a measurement of the cross sections of 𝛾-induced reactions on the p-nucleus 102 Pd was undertaken. This work represents the first measurement of its kind, using segmented silicon detectors to measure prompt charged particle emission from 𝛾-induced reactions. Methods: Quasimonoenergetic gamma beams from the High Intensity 𝛾 Source facility bombarded an enriched 102 Pd target. A segmented silicon array was arranged to detect the particles emitted from (𝛾,𝑝) and (𝛾,𝛼) reactions. Results: Reaction cross sections were deduced at multiple 𝛾-beam energies between 10 and 19 MeV, and compared to statistical model calculations using talys-1.96. The 102 Pd (𝛾,𝑝) 101 Rh reaction cross section was reasonably well reproduced by a subset of photon strength functions and level densities, though the strength to the ground state of 101 Rh was underestimated at higher incident gamma energies. The 102 Pd (𝛾,𝛼) 98 Ru was in general overpredicted by the various alpha-nucleus optical model potentials. Conclusions: While the theoretical cross sections used to model the (𝛾,𝑝) reactions for the p process may be reasonable, a more careful approach is needed in the case of (𝛾,𝛼). Further work to probe gamma-induced reaction cross sections at and near the p nuclei is warranted.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Statistical significances and projections for proton decay experiments
Not Available
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Robust Strategy for Rocket Engine Health Monitoring
Monitoring the health of rocket engine systems is essentially a two-phase process. The acquisition phase involves sensing physical conditions at selected locations, converting physical inputs to electrical signals, conditioning the signals as appropriate to establish scale or filter interference, and recording results in a form that is easy to interpret. The inference phase involves analysis of results from the acquisition phase, comparison of analysis results to established health measures, and assessment of health indications. A variety of analytical tools may be employed in the inference phase of health monitoring. These tools can be separated into three broad categories: statistical, rule based, and model based. Statistical methods can provide excellent comparative measures of engine operating health. They require well-characterized data from an ensemble of "typical" engines, or "golden" data from a specific test assumed to define the operating norm in order to establish reliable comparative measures. Statistical methods are generally suitable for real-time health monitoring because they do not deal with the physical complexities of engine operation. The utility of statistical methods in rocket engine health monitoring is hindered by practical limits on the quantity and quality of available data. This is due to the difficulty and high cost of data acquisition, the limited number of available test engines, and the problem of simulating flight conditions in ground test facilities. In addition, statistical methods incur a penalty for disregarding flow complexity and are therefore limited in their ability to define performance shift causality. Rule based methods infer the health state of the engine system based on comparison of individual measurements or combinations of measurements with defined health norms or rules. This does not mean that rule based methods are necessarily simple. Although binary yes-no health assessment can sometimes be established by relatively simple rules, the causality assignment needed for refined health monitoring often requires an exceptionally complex rule base involving complicated logical maps. Structuring the rule system to be clear and unambiguous can be difficult, and the expert input required to maintain a large logic network and associated rule base can be prohibitive.
Santi, L. Michael↗
Diffusion Monte Carlo approaches for studying nuclear quantum effects in fluxional molecules
Abstract Diffusion quantum Monte Carlo (DMC) provides a powerful approach for obtaining the ground state energy and wave function of molecules, ions, and molecular clusters. The approach is uniquely well suited for studies of fluxional molecules, which undergo large amplitude vibrational motions even in their ground state. In contrast to the electronic structure problem, where the wave function must be antisymmetric with respect to exchange of any pair of electrons, the wave function for the ground vibrational state is nodeless. This greatly simplifies the application of DMC for vibrational problems. Because there is not a single potential function that can be used to describe the intramolecular and intermolecular interactions in all molecular systems, most methods that are used to describe nuclear quantum effects rely on a carefully chosen zero‐order description of the molecular vibrations. In contrast, DMC calculations can be performed in Cartesian coordinates, making the DMC algorithm easily transferable between different chemical systems. In this contribution, the theory that underlies DMC will be discussed along with important considerations for performing DMC calculations. Extensions for evaluating vibrationally excited states and molecular properties are also discussed. Insights that can be obtained from DMC calculations are illustrated in the context of the protonated water clusters. This article is categorized under: Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods Theoretical and Physical Chemistry > Spectroscopy
Chemistry↗
Active site design enables industrial scale H 2 O 2 electrosynthesis with metal-free catalysts
The electrosynthesis of hydrogen peroxide (H 2 O 2 ) via a two-electron oxygen reduction reaction enables decentralized H 2 O 2 production. While metal-free carbon catalysts are sustainable and low-cost, their performance is hindered by poorly defined active sites and uncontrolled defect states. Here, we resolve these challenges through active site design and catalyst screening using fluorine (F) and nitrogen (N) codoped carbons as model materials. Statistical analysis combined with density functional theoretical calculations reveals that F-induced structural modification and defect passivation optimize OOH* binding, with F-doping and adjacent F atoms predominantly lowering abs ΔG(OOH*). Experimental results confirm that semi-ionic C–F bonds passivate defects in nitrogen-doped carbon, enhancing catalytic activity and durability. The resulting (N, F)-codoped carbon achieves nearly 100% H 2 O 2 selectivity at 0.5–0.65 V versus the reversible hydrogen electrode and maintains > 95% across 0.01–0.65 V versus the reversible hydrogen electrode. In an electrolyzer, (N, F)-codoped carbon exhibits an H 2 O 2 yield rate of 74.35 mol g cat. −1 h -1 and sustains 300 mA cm -2 for 105 hours with ~95% faradaic efficiency. Coupling the two-electron oxygen reduction reaction with methanol oxidation further reduces cell voltage and enhances productivity. This work provides a means to design efficient catalysts for industrial H 2 O 2 electrosynthesis.
H2O2 electrosynthesis↗
Temperature and density dependent pair potential for deuterium under shock
Large-scale classical molecular dynamics (CMD) simulations naturally include the microscopic physics necessary for atomistic modeling of shock release at the ablator-fuel interface in an inertial confinement fusion (ICF) capsule. Here, the multi-megabar shocks utilized in ICF experiments can drive the deuterium fuel from ambient to electron volt temperatures (T) and multi-fold compression. Modeling interatomic interactions over such an extreme range of conditions is challenging for empirical bond order potentials. We generate a pair potential for deuterium with explicit temperature and mass density dependence from ab initio density functional theory molecular dynamics using the iterative Boltzmann inversion method. This potential accurately reproduces the radial distribution functions and pressures from DFT in CMD equilibrium simulations across a wide range of thermodynamic conditions, yet fails to return the expected Hugoniot relations when used in direct CMD shock simulations.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Calculation of self-diffusion coefficients in supercritical carbon dioxide using mean force kinetic theory
This paper presents an application of mean force kinetic theory (MFT) to the calculation of the self-diffusivity of CO 2 in the supercritical fluid regime. Two modifications to the typical application of MFT are employed to allow its application to a system of molecular species. Therefore, the first is the assumption that the inter-particle potential of mean force can be obtained from the molecule center-of-mass pair correlation function, which in the case of CO 2 is the C–C pair correlation function. The second is a new definition of the Enskog factor that describes the effect of correlations at the surface of the collision volume. The new definition retains the physical picture that this quantity represents a local density increase, resulting from particle correlations, relative to that in the zero density homogeneous fluid limit. These calculations are facilitated by the calculation of pair correlation functions from molecular dynamics (MD) simulations using the FEPM2 molecular CO2 model. The self-diffusivity calculated from theory is in good agreement with that from MD simulations up to and slightly beyond the density at the location of the Frenkel line. The calculation is compared with and is found to perform similarly well to other commonly used models but has a greater potential for application to systems of mixed species and to systems of particles with long range interatomic potentials due to electrostatic interactions.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Inverse design of equilibrium cluster fluids applied to a physically informed model
Inverse design strategies have proven highly useful for the discovery of interaction potentials that prompt self-assembly of a variety of interesting structures. However, often the optimized particle interactions do not have a direct relationship to experimental systems. In this work, we show that Relative Entropy minimization is able to discover physically meaningful parameter sets for a model interaction built from depletion attraction and electrostatic repulsion that yield self-assembly of size-specific clusters. Here, we then explore the sensitivity of the optimized interaction potentials with respect to deviations in the underlying physical quantities, showing that clustering behavior is largely preserved even as the optimized parameters are perturbed.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Quadrupole-mediated dielectric response and the charge-asymmetric solvation of ions in water
Treating water as a linearly responding dielectric continuum on molecular length scales allows very simple estimates of the solvation structure and thermodynamics for charged and polar solutes. While this approach can successfully account for basic length and energy scales of ion solvation, computer simulations indicate not only its quantitative inaccuracies but also its inability to capture some basic and important aspects of microscopic polarization response. Here, we consider one such shortcoming, a failure to distinguish the solvation thermodynamics of cations from that of otherwise-identical anions, and we pursue a simple, physically inspired modification of the dielectric continuum model to address it. The adaptation is motivated by analyzing the orientational response of an isolated water molecule whose dipole is rigidly constrained. Its free energy suggests a Hamiltonian for dipole fluctuations that accounts implicitly for the influence of higher-order multipole moments while respecting constraints of molecular geometry. Finally, we propose a field theory with the suggested form, whose nonlinear response breaks the charge symmetry of ion solvation. An approximate variational solution of this theory, with a single adjustable parameter, yields solvation free energies that agree closely with simulation results over a considerable range of solute size and charge.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
On the molecular correlations that result in field-dependent conductivities in electrolyte solutions
Employing recent advances in response theory and nonequilibrium ensemble reweighting, we study the dynamic and static correlations that give rise to an electric field-dependent ionic conductivity in electrolyte solutions. We consider solutions modeled with both implicit and explicit solvents, with different dielectric properties, and at multiple concentrations. Implicit solvent models at low concentrations and small dielectric constants exhibit strongly field-dependent conductivities. We compare these results to Onsager-Wilson theory of the Wien effect, which provides a qualitatively consistent prediction at low concentrations and high static dielectric constants but is inconsistent away from these regimes. The origin of the discrepancy is found to be increased ion correlations under these conditions. Explicit solvent effects act to suppress nonlinear responses, yielding a weakly field-dependent conductivity over the range of physically realizable field strengths. By decomposing the relevant time correlation functions, we find that the insensitivity of the conductivity to the field results from the persistent frictional forces on the ions from the solvent. Our findings illustrate the utility of nonequilibrium response theory in rationalizing nonlinear transport behavior.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗