Second-order Contributions Research Articles

Aggregation Rules of Short Peptides.

The elucidation of aggregation rules for short peptides (e.g., tetrapeptides and pentapeptides) is crucial for the precise manipulation of aggregation. In this study, we derive comprehensive aggregation rules for tetrapeptides and pentapeptides across the entire sequence space based on the aggregation propensity values predicted by a transformer-based deep learning model. Our analysis focuses on three quantitative aspects. First, we investigate the type and positional effects of amino acids on aggregation, considering both the first- and second-order contributions. By identifying specific amino acids and amino acid pairs that promote or attenuate aggregation, we gain insights into the underlying aggregation mechanisms. Second, we explore the transferability of aggregation propensities between tetrapeptides and pentapeptides, aiming to explore the possibility of enhancing or mitigating aggregation by concatenating or removing specific amino acids at the termini. Finally, we evaluate the aggregation morphologies of over 20,000 tetrapeptides, regarding the morphology distribution and type and positional contributions of each amino acid. This work extends the existing aggregation rules from tripeptide sequences to millions of tetrapeptide and pentapeptide sequences, offering experimentalists an explicit roadmap for fine-tuning the aggregation behavior of short peptides for diverse applications, including hydrogels, emulsions, or pharmaceuticals.

Coherent electron phase-space manipulation by combined elastic and inelastic light-electron scattering

Abstract Photon-Induced Near-field Electron Microscopy (PINEM), Kapitza-Dirac (KD) gratings, and ponderomotive phase plates are examples of techniques in which the wave function of an electron in free space is manipulated using light fields: Free Electron Quantum Optics (FEQO). These effects are usually treated in separate theoretical frameworks. In this paper we present a unified, two-pronged framework that can be used to describe and numerically evaluate the performance of a number of FEQO-based electron-optical elements. The first part is an extension of an existing analytical treatment of PINEM, based on solving a relativistically corrected Schrödinger equation. The extension covers both second-order contributions to PINEM and the Kapitza-Dirac effect. The second, novel element of the approach is based on electron wavefront reconstruction by evaluating the quantum mechanical phase along a bundle of classical electron trajectories. The quasi-classical (but fully relativistic) approach lends itself to simulating a wide variety of FEQO devices, including the examples mentioned. We apply both approaches to a few specific experimental configurations: mirror-based first-order PINEM, second-order PINEM in very high laser intensity, and Kapitza-Dirac diffraction. The results show excellent agreement between the analytical results and the quasi-classical simulations. Finally, we propose a setup that combines KD and PINEM to allow for simultaneous coherent energy and transverse momentum shaping of an electron beam, and present simulation results thereof.

Local clustering of relic neutrinos: comparison of kinetic field theory and the Vlasov equation

Gravitational clustering in our cosmic vicinity is expected to lead to an enhancement of the local density of relic neutrinos. We derive expressions for the neutrino density, using a perturbative approach to kinetic field theory and perturbative solutions of the Vlasov equation up to second order. Our work reveals that both formalisms give exactly the same results and can thus be considered equivalent. Numerical evaluation of the local relic neutrino density at first and second order provides some fundamental insights into the frequently applied approach of linear response to neutrino clustering (also known as the Gilbert equation). Against the naive expectation, including the second-order contribution does not lead to an improvement of the prediction for the local relic neutrino density but to a dramatic overestimation. This is because perturbation theory breaks down in a momentum-dependent fashion and in particular for densities well below unity.

Contributions beyond direct random-phase approximation in the binding energy of solid ethane, ethylene, and acetylene

The random-phase approximation (RPA) includes a subset of higher than second-order correlation-energy contributions, but stays in the same complexity class as the second-order Møller–Plesset perturbation theory (MP2) in both Gaussian-orbital and plane-wave codes. This makes RPA a promising ab initio electronic structure approach for the binding energies of molecular crystals. Still, some issues stand out in practical applications of RPA. Notably, compact clusters of nonpolar molecules are poorly described, and the interaction energies strongly depend on the reference single-determinant state. Using the many-body expansion of the binding energy of a crystal, we investigate those issues and the effect of beyond-RPA corrections. We find the beneficial effect of quartic-scaling exchange and non-ring coupled-cluster doubles corrections. The nonadditive interactions in compact trimers of molecules are improved by using the self-consistent Hartree–Fock orbitals instead of the usual Kohn–Sham states, but this kind of orbital input also leads to underestimated dimer energies. Overall, a substantial improvement over the RPA with a renormalized singles approach is possible at a modest quartic-scaling cost, which encourages further research into additional RPA corrections.

Numerical analysis of the bistable propagation of lean premixed hydrogen flames

Premixed hydrogen-air flames that propagate in slender channels have been recently found to be bistable in the limit of fuel-lean mixtures and non-negligible heat losses. Specifically, two stable configurations conformed by either a circular or a double-cell flame front arise for the same combination of controlling parameters (fuel mixture, heat transfer). Nevertheless, this multiplicity of solutions lacks a satisfactory explanation that predicts the formation of either one or another structure given a particular ignition transient. In this work, the analysis of a set of numerical simulations is offered to unveil the underlying physics controlling the bistable behavior. The formulation employed here proves that simplified one-step Arrhenius reaction and quasi-two-dimensional equations suffice to reproduce the complex dynamics, rendering three-dimensional effects and detailed chemical kinetics as second-order contributions that may be important, however, to provide exact quantitative results. Specifically, the initial temperature profiles and subsequent expansion of the flow field prescribe the growth of the flame front leading to different curvatures and sizes of the kernel that control the evolution into one of the canonical structures. Moreover, the achievement of double-cell flames require splitting and reorientation processes prior to pairing of isolated flames, which call for specific initialization conditions that enable these transient dynamics.

CRRfast: an emulator for the cosmological recombination radiation with effects from inhomogeneous recombination

ABSTRACT The cosmological recombination radiation (CRR) is one of the guaranteed ΛCDM spectral distortion (SD) signals. Even if very small in amplitude, it provides a direct probe of the three recombination eras, opening the path for testing one of the key pillars in our cosmological interpretation of the measured CMB anisotropies. Here, we develop a new emulator, CRRfast, to quickly and accurately represent the CRR for a wide range of cosmologies, using the state-of-the-art CosmoSpec code as a reference. CRRfast has been made publicly available both as stand-alone code and as part of class, thereby completing the set of average ΛCDM sources of SDs that can be modelled with class. With this newly developed pipeline we investigate the full constraining power of SDs within ΛCDM and highlight possible future applications to experimental design optimization. Furthermore, we show that the inhomogeneous evolution of the recombination process imprints second-order contributions to the CRR spectrum, leading to a broadening and shifting of the CRR features. These second-order terms are naturally captured by the emulator and allow us to evaluate the contribution of the ΛCDM primordial perturbations to the average CRR as well as to illustrate the effect of perturbed recombination due to Primordial Magnetic Fields (PMFs). As it turns out, while the second-order ΛCDM signal can be neglected, it could be significantly enhanced in the beyond-ΛCDM models. In particular in the case of PMFs, we demonstrate that through these non-linear terms the parameter space relevant to the Hubble tension could be tested with future CMB spectrometers.

Spectral characteristics of particle preferential concentration in turbulence computed by Eulerian and Lagrangian methods

This study conducts a comprehensive analysis of the Fourier spectra characteristics of particle preferential concentration in turbulent flows obtained by Eulerian and Lagrangian modelling approaches for different Stokes numbers. Particle preferential concentration is characterized by clusters and voids in the spatial particle distributions formed in turbulent flows and can significantly influence processes such as droplet coalescence, evaporation, and gas-particle reactions. The research primarily focuses on comparing the performance of two Eulerian models—one with and one without second-order velocity moments—and one Lagrangian model, which are used to predict particle dispersion. Key findings include the impact of artificial diffusion in Eulerian methods, the superiority of methods incorporating second-order velocity moments contributions at higher Stokes numbers, and the sensitivity of the Lagrangian method to Poisson statistics. Notably, the study reveals minimal variation in mean velocity spectra across different Stokes numbers, as opposed to the marked variations in particle concentration, momentum, and energy spectra. Grid resolution emerges as a crucial factor in enhancing spectral energy predictions in Eulerian methods. The research underscores the nuanced distinctions between Eulerian and Lagrangian methods in modelling preferential concentration, providing a detailed spectral comparison of particle concentration, velocity, momentum, and energy, highlighting the importance of method selection based on specific modelling needs.

Revisiting the spin effects induced by thermal vorticity* *Supported in part by the National Natural Science Foundation of China (12175123, 11890710, 11890713), and the Major Program of Natural Science Foundation of Shandong Province, China (ZR2020ZD30)

We revisit the spin effects induced by thermal vorticity by calculating them directly from the spin-dependent distribution functions. For spin-1/2 particles, we provide the polarization up to the first order of thermal vorticity and compare it with the usual results calculated from the spin vector. For spin-1 particles, we show that all the non-diagonal elements vanish and there is no spin alignment up to the first order of thermal vortcity. We present the spin alignment at second-order contribution from thermal vorticity. We also show that the spin effects for both Dirac and vector particles receive an extra contribution when the spin direction is associated with the momentum of the particle.

Wave Modulation in a Strong Tidal Current and Its Impact on Extreme Waves

Abstract Accurate estimates of extreme waves are central for maritime activities, and stochastic wave models are the best option available for practical applications. However, the way currents influence the statistics of space–time extremes in spectral wave models has not been properly assessed. Here we demonstrate impacts of the wave modulation caused by one of the world’s strongest open ocean tidal currents, which reaches speeds of at least 3 m s−1. For a bimodal swell and wind sea state, we find that most intense interactions occur when the wind sea opposes the tidal current, with an increase in significant wave height and spectral steepness up to 45% and 167%, respectively. The steepness modulation strengthens the second-order Stokes contribution for the normalized extreme crests, which increases between 5% and 14% during opposing wind sea and current. The normalized extreme wave heights have a strong dependence on the narrow-bandedness parameter, which is sensitive to the variance distribution in the bimodal spectrum, and we find an increase up to 12% with currents opposing the wind sea. In another case of swell opposing a tidal jet, we find the spectral steepness to exceed the increase predicted by a simplified modulation model. We find support in single-point observations that using tidal currents as forcing in wave models improves the representation of the expected maximum waves, but that action must be taken to close the gap of measurements in strong currents. Significance Statement The purpose of this study is to investigate how a very strong tidal current affects the surface wave field, and how it changes the stochastic extreme waves formulated for a space–time domain. Our results suggest that the expected maximum waves become more realistic when tidal currents are added as forcing in wave models. Here, the expected extremes exceed traditional model estimates, i.e., without current forcing, by more than 10%. These differences have implications for maritime operations, both in terms of planning of marine structures and for navigational purposes. However, there is a significant lack of observations in environments with such strong currents, which are needed to further verify our results.

Delving into theoretical and computational considerations for accurate calculation of chemical shifts in paramagnetic transition metal systems using quantum chemical methods.

The chemical shielding tensor for a paramagnetic system has been derived from the macroscopically observed magnetization using the perturbation theory. An approach to calculate the paramagnetic chemical shifts in transition metal systems based on the spin-only magnetic susceptibility directly evaluated from the ab initio Hilbert space of the electronic Zeeman Hamiltonian has been discussed. Computationally, several advantages are associated with this approach: (a) it includes the state-specific paramagnetic Curie (first-order) and Van Vleck (second-order) contributions of the paramagnetic ion to the paramagnetic chemical shifts; (b) thus it avoids the system-specific modeling and evaluating effectively in terms of the electron paramagnetic resonance (EPR) spin Hamiltonian parameters of the magnetic moment of the paramagnetic ion formulated previously; (c) it can be utilized both in the point-dipole (PD) approximation (in the long-range) and with the quantum chemical (QC) method based the hyperfine tensors (in the short-range). Additionally, we have examined the predictive performance of various density functional theory (DFT) functionals of different families and commonly used core-augmented basis sets for nuclear magnetic resonance (NMR) chemical shifts. A selection of transition metal ion complexes with and without first-order orbital contributions, namely the [M(AcPyOx)3(BPh)]+ complexes of M = Mn2+, Ni2+ and Co2+ ions and CoTp2 complex and their reported NMR chemical shifts are studied from QC methods for illustration.

Assembly of MnIII ions into di-, tetra-, deca-nuclear coordination complexes, zero- to three-dimensional molecular frameworks: molecular spin flop to and short-range bulk magnetic spin flop ordering

Octahedral MnIII ions possess significant magnetic anisotropy due to second-order orbital contribution combined with Jahn–Teller distortion.

Elucidation of the exchange interaction in photoexcited three-spin systems - a second-order perturbational approach.

Photogenerated three-spin systems show great potential for applications in the field of molecular spintronics. In these systems, the exchange interaction in the electronically excited state dictates their magnetic properties. To design such molecules for specific applications, it is thus important to understand how the sign and magnitude of the exchange interaction can be controlled. For this purpose, we developed a perturbational approach, based on previous work by the groups of de Loth and Malrieu, that allows for the direct calculation of the exchange interaction and its individual contributions up to the second order and implemented it within the ORCA program package. Within this manuscript, we present the derivation of the individual second-order contributions, provide an overview of the implementation of the code and illustrate its performance. We show that, using this perturbational approach in combination with state-averaged orbitals from minimal active space calculations, accurate values for the exchange interaction can be computed for organic nitroxides. Further, we demonstrate that the weight of the ionic determinants in the orbital optimisation of the CASSCF procedure is crucial for the computation of accurate exchange couplings. In the case of photoexcited chromophore-radical systems, we find that the dynamic spin polarisation effect constitutes the most important contribution to the exchange interaction, whereby the sign of this contribution determines the sign of the exchange interaction.

Taking into account the influence of correlations on the system dynamics in the reduced description method

A complex of issues related to using the Peletminsky–Yatsenko model for the study of non-equilibrium processes is investigated. The problems are associated with the inability of performing the calculation of necessary averages when system states are described by a new, wider set of reduced description parameters, in particular, fluctuations. A matter system interacting with a non-equilibrium system of bosons is considered. The substance is described by two reduced description parameters η1 , η2 and calculations with the quasi-equilibrium statistical operator corresponding to these parameters are technically impossible; at the same time, the calculations can be performed with such operator in the case of the only parameter η1 . Overcoming this problem by considering only small values δη2 of the other reduced description parameter is proposed. An exact definition of δη2 is given, and the theory of perturbations by powers δη2 is developed for the calculation of the initial quasi-equilibrium statistical operator with accuracy up to second-order contributions. Since all further averages are calculated only with the named operator including only η1 , the simplified calculation procedure is carried out for it.On this basis, the theory of non-equilibrium processes in the system of two-level emitters interacting with the boson field is developed. The emitter system is described by excitation degree η1 and the value of emitter correlations η2. The system is considered as a system of spins. The mathematically identical Dicke model describing superradiance and Wagner model introduced for the analogous acoustic phenomenon description are studied. The quasi-equilibrium statistical operator calculation is constructed.

Group Contribution Method for the Residual Entropy Scaling Model for Viscosities of Branched Alkanes

In this work it is shown how the entropy scaling paradigm introduced by Rosenfeld (Phys Rev A 15:2545–2549, 1977, https://doi.org/10.1103/PhysRevA.15.2545) can be extended to calculate the viscosities of branched alkanes by group contribution methods (GCM), making the technique more predictive. Two equations of state (EoS) requiring only a few adjustable parameters (Lee–Kesler–Plöcker and PC-SAFT) were used to calculate the thermodynamic properties of linear and branched alkanes. These EOS models were combined with first-order and second-order group contribution methods to obtain the fluid-specific scaling factor allowing the scaled viscosity values to be mapped onto the generalized correlation developed by Yang et al. (J Chem Eng Data 66:1385–1398, 2021, https://doi.org/10.1021/acs.jced.0c01009) The second-order scheme offers a more accurate estimation of the fluid-specific scaling factor, and overall the method yields an AARD of 10 % versus 8.8 % when the fluid-specific scaling factor is fit directly to the experimental data. More accurate results are obtained when using the PC-SAFT EoS, and the GCM generally out-performs other estimation schemes proposed in the literature for the fluid-specific scaling factor.

Oceanographic wave buoy motion as a 3D-vector field: Spectra, linear components and bound harmonics

This study analyses time history data measured by a widely used type of oceanographic buoy. The motion of the buoy is recorded as a three-component displacement vector with one vertical and two horizontal components. Focusing on the average shapes of the large events in the time series, we investigate the linear and nonlinear structure of the displacements and their inherent relationships. All three displacements show clear evidence of both linear and second-order contributions. Two types of nonlinear contributions are identified: the difference term representing slow oscillation on the mooring system, and the sum term oscillating at roughly twice the frequency of the linear waves. These terms are small vertically but larger horizontally. We examine the coupled structure of the vertical and horizontal motions with a conditioning analysis. The averaged time histories associated with large waves are found to obey a simple reciprocal relationship, and the average shape of the motion in space associated with large waves in the sea-state resembles that in a localised steep wave-group. The power spectrum of the vertical motion can be transformed into those in the horizontal plane. This work demonstrates that, as well as providing accurate spectral information of the sea state, oceanographic wave buoys can provide internally consistent time series for the vector displacement field with little observable distortion from the mooring system.

Non-Abelian gauge structure and flavor mixing in quantum field theory1

The quantum field theory formalism describing the phenomenon of neutrino mixing and oscillations is reviewed in its essential aspects. The condensate structure of the flavor vacuum state is considered and its non-perturbative nature is discussed within the existence in the quantum field theory of the manifold of unitarily inequivalent representations of the anticommutation relations. The Poincaré structure of the theory is discussed in connection with the gauge theory features of neutrino mixing, where the possibility arises to describe flavored neutrinos as on-shell fields with definite masses. The flavor vacuum state may be thought of as a refractive medium where different refraction indexes are related to the different neutrino masses. Neglecting the condensate structure of the flavor vacuum implies neglecting second-order contributions in the gauge field coupling and leads to experimentally inconsistent results.

Asymptotic theory of Mack-mode receptivity in hypersonic boundary layers due to interaction of a heating/cooling source and a freestream sound wave

In this paper, we study the local receptivity of the inviscid Mack modes in hypersonic boundary layers induced by the interaction between a surface heating or cooling source (HCS) and a freestream acoustic wave. The asymptotic analysis reveals that among the three distinguished layers, i.e. the main, wall and Stokes layers, the leading-order receptivity is attributed to the interaction of the HCS-induced mean-flow distortion and the acoustic signature in the wall layer; the second-order contribution appears in the Stokes layer; the third-order contribution appears in both the main and wall layers. Interestingly, at a moderate Reynolds number, the third-order contribution to the receptivity efficiency may be quantitatively greater than the second-order one, but this does not lead to breakdown of this asymptotic theory. Assuming the HCS intensity to be sufficiently weak, the asymptotic predictions are made for four representative cases involving different Mach numbers and wall temperatures, which are compared with the results obtained by the finite-Reynolds-number theory based on either the extended compressible Orr–Sommerfeld equations or the harmonic linearised Navier–Stokes (HLNS) calculations. Taking into account the first three orders of the receptivity efficiency, the asymptotic predictions are confirmed to be sufficiently accurate even when the Reynolds number is a few thousands, and the agreement with the finite-Reynolds-number calculations is better when the wall temperature of the base flow approaches the adiabatic wall temperature. The HLNS calculations are also conducted for moderate HCS intensities. It is found that the nonlinearity does not affect the receptivity coefficient much even when the temperature distortion of the HCS reaches $80\,\%$ of the temperature at the wall.

An improved Nicolai map for super Yang–Mills theory

Adding a topological theta term to the action of N=1D=4 super Yang–Mills theory modifies its Nicolai map. For the BPS value of the theta angle a chiral version of the map emerges, which allows for a considerable simplification compared to the non-chiral formulation. We exhibit these improvements to all orders in perturbation theory and compute the map to fourth order in the coupling on the Laudau-gauge hypersurface. The second-order contribution vanishes, and antisymmetrizations are more manifest. All checks are verified to third order.

An experimental analysis of component contributions to shock absorption performance in third generation sport artificial turf

The increasing use of artificial turf across all levels of sports play has been hypothesized to contribute to an increase in athlete injuries. Current testing standards evaluate the shock absorbing performance of artificial turf surfaces through a single measure of acceleration after a drop test impact. However, these standards focus on the performance of the aggregate turf system, thereby neglecting the component-level contributions of the shock pad, carpet, and infill constituents. The purpose of this study was to explore a novel testing methodology that has the potential to isolate first-order and second-order contributions of components to total system performance. Various subsystems of the traditional, three layer artificial turf were treated as energy absorbing surfaces. A series of no-fatigue and fatigue tests were performed using a custom-built apparatus to characterize each energy absorbing surface at five different drop heights. During no-fatigue testing, it was found that the complete three-layer system outperformed all subsystems by mitigating resultant acceleration and force compared to the baseline. However, any energy absorbing subsystem that contained rubber infill outperformed any subsystem that included shock pad, the designated energy dissipating layer in third generation artificial turf. For fatigue testing, it was observed that energy absorbing surfaces began to deteriorate in as few as 20 impacts. In comparison to existing standards, the inclusion of a second data acquisition instrument yielded more accurate calculations of shock absorption. By capturing an input and output measurement during the impact, calculation of the surface’s characteristic transfer function is attainable and therefore, more information in gleaned from the impact test. Additional research is required to be able to deploy this testing methodology on-site, with fully installed artificial turf systems.

Second-order productivity, second-order payoffs, and the Owen value

We introduce the concepts of the components’ second-order productivities in cooperative games with transferable utility (TU games) with a coalition structure (CS games) and of the components’ second-order payoffs for one-point solutions for CS games as generalizations of the players’ second-order productivities in TU games and of the players’ second-order payoffs for one-point solutions for TU games (Casajus in Discrete Appl Math 304:212–219, 2021). The players’ second-order productivities are conceptualized as second-order marginal contributions, that is, how one player affects another player’s marginal contributions to coalitions containing neither of them by entering these coalitions. The players’ second-order payoffs are conceptualized as the effect of one player leaving the game on the payoff of another player. Analogously, the components’ second-order productivities are conceptualized as their second-order productivities in the game between components; the components’ second-order payoffs are conceptualized as their second-order payoffs in the game between components. We show that the Owen value is the unique efficient one-point solution for CS games that reflects the players’ and the components’ second-order productivities in terms of their second-order payoffs.