Theoretical Predictions Research Articles

Theoretical wavelet l1-norm from one-point probability density function prediction

Weak gravitational lensing, which results from the bending of light by matter along the line of sight, is a potent tool for exploring large-scale structures, particularly in quantifying non-Gaussianities. It is a pivotal objective for upcoming surveys. In the realm of current and forthcoming full-sky weak-lensing surveys, convergence maps, which represent a line-of-sight integration of the matter density field up to the source redshift, facilitate field-level inference. This provides an advantageous avenue for cosmological exploration. Traditional two-point statistics fall short of capturing non-Gaussianities, necessitating the use of higher-order statistics to extract this crucial information. Among the various available higher-order statistics, the wavelet $ has proven its efficiency in inferring cosmology. However, the lack of a robust theoretical framework mandates reliance on simulations, which demand substantial resources and time. Our novel approach introduces a theoretical prediction of the wavelet $ for weak-lensing convergence maps that is grounded in the principles of large-deviation theory. This method builds upon recent work and offers a theoretical prescription for an aperture mass one-point probability density function. We present for the first time a theoretical prediction of the wavelet $ for convergence maps that is derived from the theoretical prediction of their one-point probability distribution. Additionally, we explored the cosmological dependence of this prediction and validated the results on simulations. A comparison of our predicted wavelet $ with simulations demonstrates a high level of accuracy in the weakly non-linear regime. Moreover, we show its ability to capture cosmological dependence. This paves the way for a more robust and efficient parameter-inference process.

The imprint of the first stars on the faint end of the white dwarf luminosity function

Abstract Population III stars are characterized by extremely low metallicities as they are thought to be formed from a pristine gas in the early Universe. Although the existence of Population III stars is widely accepted, the lack of direct observational evidence hampers the study of the nature of the putative stars. In this article, we explore the possibilities of constraining the nature of the oldest stars by using the luminosity function of their remnants – white dwarfs. We study the formation and evolution of white dwarf populations by following star formation in a Milky Way-like galaxy using the semi-analytic model a-sloth. We derive the white dwarf luminosity function by applying a linear Initial-Final Mass Relation and Mestel’s cooling model. The obtained luminosity function is generally in agreement with available observations and theoretical predictions – with an exponential increase to a maximum of Mabs = 16 and a sudden drop for Mabs > 16. We explore the uncertainties of our model and compare them to the observational estimates. We adopt two different models of the initial mass function of Population III stars to show that the faint end of the luminosity function imprints the signature of Population III remnants. If the feature is detected in future observations, it would provide a clue to Population III stars and would also be an indirect evidence of low- to intermediate-mass Population III stars. We discuss the challenges and prospects for detecting the signatures.

Discrete Laplacian thermostat for flocks and swarms: the fully conservedInertial Spin Model

Abstract Experiments on bird flocks and midge swarms reveal that these natural systems are well described by an active theory in which conservation laws play a crucial role. By building a symplectic structure that couples the particles’ velocities to the generator of their internal rotations (spin), the Inertial Spin Model (ISM) reinstates a second-order temporal dynamics that captures many phenomenological traits of flocks and swarms. The reversible structure of the ISM predicts that the total spin is a constant of motion, the central conservation law responsible for all the novel dynamical features of the model. However, fluctuations and dissipation introduced in the original model to make it relax, violate the spin conservation law, so that the ISM aligns with the biophysical phenomenology only within finite-size regimes, beyond which the overdamped dynamics characteristic of the Vicsek model takes over. Here, we introduce a novel version of the ISM, in which the irreversible terms needed to relax the dynamics strictly respect the conservation of the spin. We perform a numerical investigation of the fully conservative model, exploring both the fixed-network case, which belongs to the equilibrium class of Model G, and the active case, characterized by self-propulsion of the agents and an out-of-equilibrium reshuffling of the underlying interaction network. Our simulations not only capture the correct spin wave phenomenology of the ordered phase, but they also yield dynamical critical exponents in the near-ordering phase that agree very well with the theoretical predictions.

Far field operator splitting and completion in inverse medium scattering

Abstract We study scattering of time-harmonic plane waves by compactly supported inhomogeneous objects in a homogeneous background medium. The far field operator associated to a fixed scatterer describes multi-static remote observations of scattered fields corresponding to arbitrary superpositions of plane wave incident fields at a single frequency. In this work we consider far field operators for systems of two well-separated scattering objects, and we discuss the nonlinear inverse problem to recover the far field operators associated to each of these two scatterers individually. This is closely related to the question whether the two components of the scatterer can be distinguished by means of inverse medium scattering in a stable way. We also study the restoration of missing or inaccurate components of an observed far field operator and comment on the benefits of far field operator splitting in this context. Both problems are ill-posed without further assumptions, but we give sufficient conditions on the diameter of the supports of the scatterers, the distance between them, and the size of the missing or corrupted data component to guarantee stable recovery whenever sufficient a priori information on the location of the unknown scatterers is available. We provide algorithms, error estimates, a stability analysis, and we demonstrate our theoretical predictions by numerical examples.

Minimal Einstein-Aether theory

We show that there is a phenomenologically and theoretically consistent limit of the generic Einstein-Aether theory in which the Einstein-Aether field equations reduce to Einstein field equations with a perfect fluid distribution sourced by the aether field. This limit is obtained by taking three of the coupling constants of the theory to be zero but keeping the expansion coupling constant to be nonzero. We then consider the further reduction of this limited version of Einstein-Aether theory by taking the expansion of the aether field to be constant (possibly zero), and thereby we introduce the Minimal Einstein-Aether theory that supports the Einstein metrics as solutions with a reduced cosmological constant. The square of the expansion of the unit-timelike aether field shifts the bare cosmological constant and thus provides, via local Lorentz symmetry breaking inherent in the Einstein-Aether theories, a novel mechanism for reconciling the observed, small cosmological constant (or dark energy) with the large theoretical prediction coming from quantum field theories. The crucial point here is that minimal Einstein-Aether theory does not modify the well-tested aspects of General Relativity such as solar system tests and black hole physics including gravitational waves.

Independent friction-restitution modeling of collisions: application to planar sphere rebound on a massive surface

Abstract The most widely used impulse-based description of impact events expresses it in terms of the coefficient of restitution (normal and tangential) and friction. This model leads to significant variations of the coefficients of tangential restitution and friction with the impact angle. An alternative formulation is presented based on the idea that friction and restitution can be treated as ‘mechanisms’ operating simultaneously but independently throughout the impact. The resulting independent friction restitution closure describes the impact for both stick and slip regimes using the same set of ‘constant’ coefficients of restitution (normal and tangential) and friction. The model yields theoretical predictions in agreement with reported experimental data including several results considered as ‘anomalous’ in the literature.

Analytical prediction of temperature effects on Lamb wave response in smart plates and its experimental verification

Abstract This article examines the effectiveness of a recently developed theoretical model for the generation and sensing of Lamb waves in thin plates with surface-bonded piezoelectric transducers in predicting temperature effects on Lamb waves and their time reversibility. In particular, the analytical model provides a closed-form solution, which incorporates both the shear-lag effect of the bonding layer and the system inertia in transducer-plate interaction modeling. Temperature-dependent material properties and thermal expansion of the system constituents are considered to predict the Lamb wave signal under a thermal environment. The accuracy of the theoretical prediction is assessed in comparison with experimental results obtained using an aluminum plate with adhesively bonded lead zirconate titanate transducers to its surface at different system temperatures ranging from 20°C to 75°C. Comparison is also made with experimental data and analytical solutions presented earlier without considering the inertia effect. The study reveals that the current solution accurately predicts the change in Lamb wave signal due to temperature variation, including the frequency dependency of the peak amplitude change with temperature rise. However, the theoretical model fails to predict the experimental trends when the inertia terms are neglected. The current model is also used to study the contributions of individual system parameters to the overall temperature effect on the time reversibility of Lamb waves and its dependence on the excitation frequency.

Deep learning-driven evaluation and prediction of ion-doped NASICON materials for enhanced solid-state battery performance

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Theoretical Prediction of Enhanced Hydrogen Evolution Reaction Electrocatalysts Based on Tantalum Phosphide.

Ta-based transition metal catalysts have shown significant catalytic activity for the hydrogen evolution reaction (HER) in recent studies. However, the application of tantalum phosphide (TaP) in the HER has not been documented. Herein, a systematic study of TaP catalysts was performed through density functional theory (DFT). The performance of TaP (004) for the HER was predicted. Thermodynamic analyses of Ta-terminated and P-terminated surfaces with adsorbed hydrogen atoms were conducted, and the HER mechanism on TaP (004) surfaces was carefully investigated. Theoretical results revealed that TaP (004) exhibits excellent HER activity (ΔGH* = 0.0456 eV), and both the Ta-terminated and P-terminated surfaces follow the Volmer-Heyrovsky mechanism under acidic conditions, with the Volmer step being the rate-determining step. A mixed surface strategy was also applied to explore the synergistic effects of Ta-terminated and P-terminated surfaces, which enhanced the HER activity. Additionally, the study screened dopants to assess their impact on the HER activity, revealing that doping with S, Ni, Co, Fe, and Cr could improve the HER performance.

First Ab Initio Line Lists for Triatomic Sulfur-Containing Molecules: S2O and S3.

We present in this paper the first room temperature rovibrational line lists for the main isotopologues of disulfur monoxide (S2O) and thiozone (S3) variationally computed from newly developed ab initio potential energy and dipole moment surfaces (PESs and DMSs). S2O and S3 are supposed to be potential candidates for astronomical detection, especially in the Venusian atmosphere where sulfur chemistry plays a major role. Contrary to other stable sulfur-containing species like SO2 or H2S, there is much less experimental data for the short-lived reactive S2O and S3 molecules. Indeed, the infrared spectra of S2O and S3 are quite complicated to analyze without consistent theoretical predictions because they contain both high J (∼100) and a lot of hot band transitions, even at T = 296 K. In this work, we have constructed PESs based on the single-reference coupled cluster approach [CCSD(T)] and including corrections due to the scalar relativistic effects, DBOC, and highly excited Slater determinants. The structure of the excited electronic states of S3 was also discussed. The nuclear-motion Eckart-Watson Hamiltonian expressed in terms of normal-mode irreducible tensor operators was used to compute the energy levels. For line intensity calculation, ab initio DMSs were computed at the CCSD(T)/aug-cc-pV5Z level of the theory. Rotation-vibration patterns in the fundamental bands of S2O and S3 have been simulated taking into account the recent Fourier-transform spectra of S2O recorded at the SOLEIL synchrotron. The present work aims at providing line intensities of S2O and S3 that are missing in the literature as well as new spectroscopic support for atmospheric applications.

On the Strong Binding Affinity of Gold-Graphene Heterostructures with Heavy Metal Ions in Water: A Theoretical and Experimental Investigation.

Minimum energy configurations in 2D material-based heterostructures can enable interactions with external chemical species that are not observable for their monolithic counterparts. Density functional theory (DFT) calculations reveal that the binding energy of divalent toxic metal ions of Cd, Pb, and Hg on graphene-gold heterointerfaces is negative, in contrast to the positive value associated with free-standing graphene. The theoretical predictions are confirmed experimentally by Surface Plasmon Resonance (SPR) spectroscopy, where a strong binding affinity is measured for all the heavy metal ions in water. The results indicate the formation of a film of heavy metal ions on the graphene-gold (Gr/Au) heterointerfaces, where the adsorption of the ions follows a Langmuir isotherm model. The highest thermodynamic affinity constant K = 3.1 × 107 L mol-1 is observed for Hg2+@Gr/Au heterostructures, compared to 1.1 × 107 L mol-1 and 8.5 × 106 L mol-1 for Pb2+@Gr/Au and Cd2+@Gr/Au, respectively. In the case of Hg2+ ions, it was observed a sensitivity of about 0.01°/ppb and a detection limit of 0.7 ppb (∼3 nmol L-1). The combined X-ray photoelectron spectroscopy (XPS) and SPR analysis suggests a permanent interaction of all of the HMIs with the Gr/Au heterointerfaces. The correlation between the theoretical and experimental results indicates that the electron transfer from the graphene-gold heterostructures to the heavy metal ions is the key for correct interpretation of the enhanced sensitivity of the SPR sensors in water.

Striking a Balance: The Effect of Capability and Character Reputation Claims on Crowdfunding Performance

Drawing from expectancy violations theory, we examine the effect of entrepreneurs’ claims about their ventures’ capability reputation and character reputation on crowdfunding performance. We propose that capability reputation and character reputation claims benefit crowdfunding performance—but only up to a point—until crowdfunding backers begin to perceive it as over-claiming (inverted-U relationship). We also suggest the effect of entrepreneurs’ capability and character reputation claims are highly contingent upon whether the entrepreneur has launched a commercial or social campaign. Our analysis of 68,899 crowdfunding campaigns strongly supports our theoretical predictions.

Photothermal-assisted magnetic recoverable Cd0.9Zn0.1S/NiCoB heterojunction with extraordinary photocatalytic hydrogen evolution

Easily recyclable photocatalysts hold great potential in the field of photocatalysis. Guided by rational theoretical predictions, this study designs a novel tetrapod-like Cd0.9Zn0.1S/NiCoB (CZS/NCB) Schottky heterojunction with magnetic and photothermal properties, and demonstrates its excellent photocatalytic hydrogen evolution performance. Under the combined effects of the photothermal properties and the Schottky heterojunction, the photocatalytic hydrogen evolution rate extraordinarily reaches 108.39 mmol g−1 h−1 after 3 h of visible light irradiation, which is 4.69 times that of pure CZS. Additionally, photocatalytic hydrogen evolution tests conducted using infrared thermography and alternating visible and visible plus infrared light irradiation have confirmed the material’s outstanding photothermal properties. In-depth density functional theory (DFT) calculations reveal potential charge transfer pathways and confirm the formation of the Schottky heterojunction. This work provides guidance for the rational construction of magnetic recoverable photocatalysts with practical application.

Synthetic rotational Doppler shift on transmission lines and it’s microwave applications

Rotational Doppler shift of a circularly polarized wave impinging normally on a rotating anisotropic surface, causes scattered waves with frequency shift equals twice the surface rotation frequency. We show that virtual rotational Doppler shift can be realized in transmission line platforms through a time-varying junction. In a system consisting of a pair of decoupled but identical transmission lines, voltage waves with a 90-degree phase difference between the two lines mimic a circularly polarized wave. A junction, comprising three time-varying capacitors and a static two-port network, connects the two lines and acts as a synthetically rotating anisotropic surface. As a result, the reflected and transmitted voltage (or current) waves undergo a frequency shift equal to twice the synthetic rotation frequency. Utilizing this effect, a full frequency converter is then proposed by augmenting the synthetically rotating capacitive junction with a dispersive phase shifter, followed by a short circuit. The system efficiently converts the incident tone into a single down- or up-converted tone, with amplification observed in the case of up-conversion. The frequency converter is subsequently employed to design a magnetic-free isolator. Circuit simulations with both ideal and switch-based time-varying capacitors match theoretical predictions.

Are government budgets a visible stabilizer? Evidence from China since the tax-assignment reform

PurposeThis study quantitatively examines the relationship between economic fluctuations and government budget size in the context of China’s fiscal decentralization, drawing inspiration from theoretical predictions of the Keynesian view and empirical studies on other economies.Design/methodology/approachThe panel comprises 31 provinces or equivalents in mainland China, spanning from 1994 to 2019. Diverse estimation strategies including two-way fixed effect regression, the generalized method of moments (GMM) and threshold regressions are, utilized.FindingsThe results suggest that under the “tax-assignment system”, neither the central government’s fiscal transfers nor the provincial budgetary revenues or expenditures help reduce economic volatility. Surprisingly, some regression outcomes suggest that government size measures destabilize business cycles.Originality/valueWhile the study does not provide supportive evidence for the stabilizing effect of public budgets in Chinese provinces, it promotes a rethinking of the government’s intricate role in macroeconomic stabilization in the context of China’s fiscal decentralization.

Amorphous Structure Benefits in MgV2O4/V2O3 Composites for Zinc-Ion Storage: An Integration of Computational and Experimental Studies.

This study investigates the electrochemical properties of MgV2O4/V2O3 composites for Aqueous Zinc-Ion Batteries (AZIBs) using both Density Functional Theory (DFT) calculations and experimental validation. DFT analysis reveals significant electron mobility and reactivity at the MgV2O4/V2O3 interface, enhancing Zn2+ storage capabilities. This theoretical prediction is confirmed experimentally by synthesizing a novel MgV2O4/V2O3 composite that demonstrates superior electrochemical performance compared to pristine phases. Notably, the transition of the MgV2O4/V2O3 composite into an amorphous structure during electrochemical cycling is pivotal, providing enhanced diffusion pathways and increased conductivity. The composite delivers a consistent specific capacity of 330.2 mAh g-1 over 50 cycles at 0.1 A g-1 and maintains 152.7 mAh g-1 at an elevated current density of 20 A g-1 after 2000 cycles, validating the synergy between DFT insights and experimental outcomes, and underscoring the potential of amorphous structures in enhancing battery performance.

Towards a universal analytical model for Population III star formation: interplay between feedback and fragmentation

ABSTRACT JWST has brought us new insights into Cosmic Dawn with tentative detection of the unique signatures of metal-free Population III (Pop III) stars, such as strong He II emission, extremely blue ultraviolet spectrum, and enhanced nitrogen abundance. Self-consistent theoretical predictions of the formation rates, sites, and masses of Pop III stars are crucial for interpreting the observations, but are challenging due to complex physical processes operating over the large range of length-scales involved. One solution is to combine analytical models for the small-scale star formation process with cosmological simulations that capture the large-scale physics such as structure formation, radiation backgrounds, and baryon-dark matter streaming motion that regulate the conditions of Pop III star formation. We build an analytical model to predict the final masses of Pop III stars/clusters from the properties of star-forming clouds, based on the key results of small-scale star formation simulations and stellar evolution models. Our model for the first time considers the interplay between feedback and fragmentation and covers different modes of Pop III star formation ranging from ordinary small ($\sim\!{10{-}2000}\ \rm M_\odot$) clusters in molecular-cooling clouds to massive ($\gtrsim\!{10^{4}}\ \rm M_\odot$) clusters containing supermassive ($\sim\!{10^{4}{-}3}\times 10^{5}\ \rm M_\odot$) stars under violent collapse of atomic-cooling clouds with large gas accretion rates of $\gtrsim\!{0.1}\ \rm M_\odot \ yr^{-1}$. As an example, the model is applied to the Pop III star-forming clouds in the progenitors of typical haloes hosting high-z luminous quasars ($M_{\rm h}\sim 10^{12}\ \rm M_\odot$ at $z\sim 6$), which shows that formation of Pop III massive clusters is common ($\sim\!{20{-}70}{{\ \rm per\ cent}}$) in such biased ($\sim\!{4}\sigma$) regions, and the resulting heavy black hole seeds from supermassive stars can account for a significant fraction of observed luminous ($\gtrsim\!{10^{46}}\ \rm erg\ s^{-1}$) quasars at $z\sim 6$.

Use of third generation data for the pure elements to model the thermodynamics of binary alloy systems: Part 3 – The theoretical prediction of the Al–Si–Zn system

In a previous paper a method was developed to define Einstein temperatures for metastable phases of the elements and their relation to the so-called lattice stabilities used in the past, and also the variation of the Einstein temperature with composition to account for the composition dependence of the excess entropy. This approach was demonstrated successfully for the Al–Zn system. In this paper this approach is extended to cover the Al–Si and Si–Zn binary systems. The phase diagram for the Al–Si–Zn ternary system was then predicted from the thermodynamic description of the binary subsystems only without any ternary interaction parameters. Agreement with the experimental data is shown to be very good.

Theoretical prediction of holes and electrons mobility in coronene and perchlorocoronene crystals: Application of the Marcus–Jortner–Levich Theory

The study focused on theoretically predicting charge carrier mobilities in coronene and perchlorocoronene crystals using the Marcus–Levich–Jortner approach. By analyzing charge transfer integrals and considering hopping pathways, significant anisotropy in charge transfer was observed. Density functional theory (DFT) calculations at the B3LYP-D3/6-311++G(d,p) and ωB97X-D/6-311++G(d,p) levels were employed to assess the impact of normal modes on reorganization energies and charge transfer rates. Results indicated that perchlorination reduced mobility for both holes and electrons. Notably, maximum mobilities were observed at the melting points: 0.0120 cm2 V−1 s−1 for electrons and 0.0798 cm2 V−1 s−1 for holes in coronene at 455 K, and 0.0032 cm2 V−1 s−1 for electrons and 0.0426 cm2 V−1 s−1 for holes in perchlorocoronene at 560 K. This suggests that both crystals exhibit favorable charge transport characteristics near their respective melting points.

Free energy and extension of stiff polymer chains confined in nanotubes with diverse cross-sectional shapes

The statistical mechanics of stiff polymer chains confined within narrow tubes is a foundational topic in polymer physics, extensively analyzed in prior research. For cylindrical, rectangular, and slit-like confinements, the chains’ free energy and extension adhere to a scaling law consistent with the Odijk theory. While this scaling law may not apply to tubes with different cross-sectional geometries, there is a lack of research examining the behavior of stiff chains in tubes with intricate cross-sectional shapes. In this study, we investigate the partition function of a stiff chain confined within an elliptic tube using the path integral approach, deriving a deflection length in a concise closed form through dimensional analysis. This length scale facilitates straightforward expressions for the chain's free energy and extension. Notably, we discover a shape-independent property of these expressions applicable to tubes with a wide variety of cross-sectional geometries. Extensive numerical simulations are conducted using a biased chain-growth Monte Carlo method, incorporating the Pruned and Enriched Rosenbluth algorithm, to validate the theoretical predictions on the confinement free energy and extension of chains in tubes with differing shapes.