From the resonance theory to the statistical model
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Toward a Parastatistics in Quantum Nonextensive Statistical Mechanics
On the basis of Bose quantum states in parastatistics the equations for the equilibrium distribution of quantum additive and nonextensive systems are determined. The fluctuations and variances of physical quantities for the equilibrium system are found. The Abelian group of microscopic entropies is determined for the composition law with a quadratic nonlinearity.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Improved approximations of non-Gaussian probability, force, and energy of a single polymer chain
The mechanical behavior of polymers such as their probability density function (PDF), strain energy, and entropic force, has long been described by the non-Gaussian statistical model. Non-Gaussian models are often approximated by the Kuhn-Grün (KG) distribution function, which is derived from the first-order approximation of the complex Rayleigh's exact Fourier integral distribution. Furthermore, the KG function is widely accepted in polymer physics, where the non-Gaussian theory is often used to describe energy of the chains with various flexibility ratios. However, the KG function is shown to be relevant only for long chains and becomes extremely inaccurate for chains with fewer than 40 segments. In comparison to the KG model, other approximations of the non-Gaussian statistical model are often less accurate, and those with higher accuracy are usually too complex to be implemented in large-scale simulations. Here a new accurate approximation of the non-Gaussian PDF, entropic force, and strain energy of a single chain subsequently is developed to describe the mechanics of a polymer chain. With a similar level of complexity, the presented approximations of non-Gaussian PDF, strain energy, and entropic force are at least 10 times more accurate than KG approximations and thus are an excellent alternative option to be used in micromechanical constitutive models.
42 ENGINEERING↗
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↗
Statistical Study of Solar Dimmings Using CoDiT
We present the results from analyzing the physical and morphological properties of 154 dimmings (transient coronal holes) and the associated flares and coronal mass ejections (CMEs). Each dimming in our 2013 catalog was processed with the semi-automated Coronal Dimming Tracker using Solar Dynamics Observatory AIA 193 Å observations and HMI magnetograms. Instead of the typically used difference images, we used our coronal hole detection algorithm to detect transient dark regions “directly” in extreme ultraviolet (EUV) images. This allowed us to study dimmings as the footpoints of CMEs—in contrast with the larger, diffuse dimmings seen in difference images that represent the projected view of the rising, expanding plasma. Studying the footpoint-dimming morphology allowed us to better understand the CME structure in the low corona. While comparing the physical properties of dimmings, flares, and CMEs we were also able to identify relationships between the different parts of this complex eruptive phenomenon. We found that larger dimmings are longer-lived, suggesting that it takes longer to “close down” large open magnetic regions. Also, during their growth phase, smaller dimmings acquire a higher magnetic flux imbalance (i. e., become more unipolar) than larger dimmings. Furthermore, we found that the EUV intensity of dimmings (indicative of local electron density) correlates with how much plasma was removed and how energetic the eruption was. Studying the morphology of dimmings (single, double, fragmented) also helped us identify different configurations of the quasi-open magnetic field.
79 ASTRONOMY AND ASTROPHYSICS↗
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↗
Load response of a floating wind turbine to turbulent atmospheric flow
The two turbulence-generation models [Kaimal Spectrum Exponential Coherence (KSEC) and Mann] specified in the international standard for wind turbine design assume neutral atmospheric conditions and are based on statistical and spectral methods. Mainly due to the lack of physics, the flow fields simulated with these models ultimately differ in their underlying structure, especially in terms of the spatial coherence of longitudinal velocity perturbations. While this may not be critical for smaller wind turbine rotors, it becomes important when rotor sizes increase. Furthermore, it might be especially important in the context of floating technologies as they are more sensitive to large turbulent coherent structures. Previous work found that these differences between KSEC and Mann can propagate to loads predictions and thereby affect the design space of the entire wind turbine system. It is therefore crucial to determine in which ways these two models are underperforming. Up until now, validation of these models had only been done in the vertical direction because it is extremely difficult to obtain atmospheric turbulence measurements separated laterally, and sampled at heights relevant to wind energy. In this work, we address the lack of measurements by using high-fidelity, high-resolution simulation data as a reference. We perform hour-long, large-eddy simulations of turbulent velocity fields that are stability-dependent and contain three-dimensional coherent structures. These flow fields are then used to investigate which stochastic model is a better predictor of loads on a realistic spar-system floating offshore wind turbine, and to quantify how the assumption of neutral stratification propagates to short-term load estimates. Both stochastic turbulence models are found to overpredict fatigue loading in high-wind scenarios (in some cases, by more than 25%) and underpredict it when the wind speed is low (by as much as 20%). The KSEC model matches the high-fidelity flow fields more closely than Mann at high wind speeds, and the opposite is true at low wind speeds. Finally, turbine loading is found to be sensitive to atmospheric stability even when the turbulence intensity remains fairly constant. This sensitivity is most pronounced at low wind speeds, when fatigue load estimates on the spar system can differ by 40%.
17 WIND ENERGY↗
Emission from quantum-dot high-β microcavities: transition from spontaneous emission to lasing and the effects of superradiant emitter coupling
Measured and calculated results are presented for the emission properties of a new class of emitters operating in the cavity quantum electrodynamics regime. The structures are based on high-finesse GaAs/AlAs micropillar cavities, each with an active medium consisting of a layer of InGaAs quantum dots (QDs) and the distinguishing feature of having a substantial fraction of spontaneous emission channeled into one cavity mode (high β-factor). This paper demonstrates that the usual criterion for lasing with a conventional (low β-factor) cavity, that is, a sharp non-linearity in the input–output curve accompanied by noticeable linewidth narrowing, has to be reinforced by the equal-time second-order photon autocorrelation function to confirm lasing. The article also shows that the equal-time second-order photon autocorrelation function is useful for recognizing superradiance, a manifestation of the correlations possible in high-β microcavities operating with QDs. In terms of consolidating the collected data and identifying the physics underlying laser action, both theory and experiment suggest a sole dependence on intracavity photon number. Evidence for this assertion comes from all our measured and calculated data on emission coherence and fluctuation, for devices ranging from light-emitting diodes (LEDs) and cavity-enhanced LEDs to lasers, lying on the same two curves: one for linewidth narrowing versus intracavity photon number and the other for g( 2 )(0) versus intracavity photon number.
36 MATERIALS SCIENCE↗
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↗
Mean force kinetic theory: A convergent kinetic theory for weakly and strongly coupled plasmas
A new closure of the BBGKY hierarchy is developed, which results in a convergent kinetic equation that provides a rigorous extension of plasma kinetic theory into the regime of strong Coulomb coupling. The approach is based on a single expansion parameter which enforces that the exact equilibrium limit is maintained at all orders. Because the expansion parameter does not explicitly depend on the range or the strength of the interaction potential, the resulting kinetic theory does not suffer from the typical divergences at short and long length scales encountered when applying the standard kinetic equations to Coulomb interactions. Here, the approach demonstrates that particles effectively interact via the potential of mean force and that the range of this force determines the size of the collision volume. When applied to a plasma, the collision operator is shown to be related to the effective potential theory [S. D. Baalrud and J. Daligault, Phys. Rev. Lett. 110, 235001 (2013)]. In addition to the collision operator, this systematic derivation reveals a second term that is related to the excess (nonideal) components of the pressure and internal energy in the hydrodynamic limit. The relationship between this and previous kinetic theories is discussed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗