Fusion Diagrams Research Articles

Unifying O(3) equivariant neural networks design with tensor-network formalism

Many learning tasks, including learning potential energy surfaces from ab initio calculations, involve global spatial symmetries and permutational symmetry between atoms or general particles. Equivariant graph neural networks are a standard approach to such problems, with one of the most successful methods employing tensor products between various tensors that transform under the spatial group. However, as the number of different tensors and the complexity of relationships between them increase, maintaining parsimony and equivariance becomes increasingly challenging. In this paper, we propose using fusion diagrams, a technique widely employed in simulating SU(2)-symmetric quantum many-body problems, to design new spatial equivariant components for neural networks. This results in a diagrammatic approach to constructing novel neural network architectures. When applied to particles within a given local neighborhood, the resulting components, which we term ‘fusion blocks,’ serve as universal approximators of any continuous equivariant function defined on the neighborhood. We incorporate a fusion block into pre-existing equivariant architectures (Cormorant and MACE), leading to improved performance with fewer parameters on a range of challenging chemical problems. Furthermore, we apply group-equivariant neural networks to study non-adiabatic molecular dynamics of stilbene cis-trans isomerization. Our approach, which combines tensor networks with equivariant neural networks, suggests a potentially fruitful direction for designing more expressive equivariant neural networks.

Probing anomalous off-shell electroweak dipole moment of the top quark

A possibility to search for anomalous Wtb interaction ∂μWμ−b¯ f W L P L + f W R P R t is considered for the first time. Despite such couplings do not contribute to both pair top quark production or three main electroweak production modes, they could provide non-zero contributions to associated single top quark production with W or Z bosons or in association with two forward light jets via electroweak fusion diagrams.

Enhanced charged Higgs production through W -Higgs fusion in W -b scattering

We study the associated production of a charged Higgs boson with a bottom quark and a light quark at the LHC via p p \to H^\pm\,b\,j in the Two Higgs Doublet Models (2HDMs). Using the effective W approximation, we show that there is exact cancellation among various Feynman diagrams in high energy limit. This may imply that the production of charged Higgs can be significantly enhanced in the presence of large mass differences among the neutral Higgs bosons via W^\pm-Higgs fusion in the p p \to H^\pm\,b\,j process. Particularly, we emphasize the potential enhancement due to a light pseudoscalar boson $A$, which is still allowed by the current data by which we explicitly calculate the allowed regions in (M_A,\,\tan\beta) plane, and show that the production cross section can be as large as 0.1 pb for large $\tan\beta$. We also show that the transverse momentum distribution of the b quark can potentially distinguish the W^\pm-A fusion diagram from the top diagram. Finally, we point out further enhancement when we go beyond the 2HDMs.

Derivation of basic equations for phase miscibility in melts of systems with exchange interaction

Thermodynamically justified basic equations for isothermal crystallization and immiscibility equilibria in high-temperature phase systems with exchange interaction are derived; these equations are relatively simple and available for thorough analysis. Two dimensionless energy characteristics are found to be the initial parameters responsible for phase equilibria in these systems: one of those is related to the Gibbs energy of exchange interaction, and the other is related to the chemical potential of the equilibrium phase. Three possible applications of these basic equations are outlined: calculations of high-temperature thermodynamic parameters according to the fusion diagrams of systems, calculations of diagrams based on thermodynamic data, and a meticulous examination of relationships between phase solubility and thermodynamic parameters of reciprocal systems.

Salicylamide cocrystals: screening, crystal structure, sublimation thermodynamics, dissolution, and solid-state DFT calculations.

A new cocrystal of 2-hydroxybenzamide (A) with 4-acetamidobenzoic acid (B) has been obtained by the DSC screening method. Thermophysical analysis of the aggregate [A:B] has been conducted and a fusion diagram has been plotted. Cocrystal formation from melts was studied by using thermomicroscopy. A cocrystal single-crystal was grown and its crystal structure was determined. The pattern of noncovalent interactions has been quantified using the solid-state DFT computations coupled with the Bader analysis of the periodic electron density. The sublimation processes of A-B cocrystal have been studied and its thermodynamic functions have been calculated. The classical method of substance transfer by inert gas-carrier was chosen to investigate sublimation processes experimentally. The lattice energy is found to be 143 ± 4 kJ/mol. It is lower than the sum of the corresponding values of the cocrystal pure components. The theoretical value of the lattice energy, 156 kJ/mol, is in reasonable agreement with the experimental one. A ternary phase diagram of solubility (A-B-ethanol) has been plotted and the areas with solutions for growing thermodynamically stable cocrystals have been determined.

Improving acoustic vehicle classification by information fusion

We present an information fusion approach for ground vehicle classification based on the emitted acoustic signal. Many acoustic factors can contribute to the classification accuracy of working ground vehicles. Classification relying on a single feature set may lose some useful information if its underlying sound production model is not comprehensive. To improve classification accuracy, we consider an information fusion diagram, in which various aspects of an acoustic signature are taken into account and emphasized separately by two different feature extraction methods. The first set of features aims to represent internal sound production, and a number of harmonic components are extracted to characterize the factors related to the vehicle’s resonance. The second set of features is extracted based on a computationally effective discriminatory analysis, and a group of key frequency components are selected by mutual information, accounting for the sound production from the vehicle’s exterior parts. In correspondence with this structure, we further put forward a modified Bayesian fusion algorithm, which takes advantage of matching each specific feature set with its favored classifier. To assess the proposed approach, experiments are carried out based on a data set containing acoustic signals from different types of vehicles. Results indicate that the fusion approach can effectively increase classification accuracy compared to that achieved using each individual features set alone. The Bayesian-based decision level fusion is found to be improved than a feature level fusion approach.

Measurement and prediction of phase diagrams of the enantiomeric 3-chloromandelic acid system

The identification of racemic species of enantiomeric 3-chloromandelic acid (3-ClMA) as well as ternary solubility measurement in a mixture of water and isopropanol (IPA) was studied in this paper. Thermal analyses were carried out for mixtures of the two enantiomers with different compositions. The binary fusion diagram suggested the presence of a racemic compound for racemate 3-ClMA. It was verified with the ternary solubility phase diagram by dissolving various mixtures into the H 2O/IPA solution. Ternary phase diagram revealed a strong temperature dependency of solubility for the 3-ClMA system. In order to shorten the experimental time in the solubility measurement, a semi-empirical thermodynamic model (UNIQUAC) was used to predict the solubility of various compositions of enantiomers at different temperatures. Results indicate that UNIQUAC model can provide good predictions in the solubility of racemate, eutectic and (R)-3-ClMA in both pure water and H 2O/IPA (9/1 weight ratio) system. In addition, structures of racemate and pure (R)-3-ClMA were also studied using a powder X-ray diffractometer. Thermodynamic prediction, thermal analysis, and structural study are in excellent agreement for identifying the enantiomeric 3-ClMA system as a racemic compound forming system.

Al–Co–W fusion diagram in the Co–CoAl–W part

Al–Co–W fusion diagram in the Co–CoAl–W part

Parametric design of fusion diagrams and solubility of phases

Relationships between the fusion diagrams and the thermodynamic characteristics of the phases involved are analyzed using a relatively simple, thermodynamically substantiated equation of salt crystallization isotherms. The dimensionless parameters \(\begin{gathered} {\text{RMn}}_{\text{2}} {\text{O}}_{\text{5}} {\text{ = RMnO}}_{\text{3}} + \frac{1}{3}{\text{RMn}}_{\text{3}} {\text{O}}_{\text{4}} + \frac{1}{3}{\text{O}}_{\text{2}} \hfill \\ \frac{{\Delta G}}{{RT}} \hfill \\ \end{gathered} \) and \(\frac{{\Delta Z_{{\text{AX}}} }}{{RT}}\) are shown to be basic to the thermodynamics of liquid–solid and liquid–liquid phase equilibria. A number of techniques for evaluating thermodynamic constants from fusion diagrams and calculating elements of fusion diagrams from thermodynamic data are described and exemplified by particular systems. The effects of the basic parameters on the solubility of phases and phase equilibria are examined, and critical values of these parameters are determined for the first time. Parametric criteria for liquid immiscibility in salt systems are established.

Modeling of Thermodynamic Properties and Fusion Diagrams of Ternary Oxosulfide Systems

Three different approximations are used to determine the thermodynamic properties of components and fusion diagrams of ternary oxosulfide systems FeS-FeO-Cu2S and FeS-FeO-Ni3S2. The coordinates of eutectic points and eutectic temperatures are obtained, and equations for calculating the thermodynamic activities of the components are derived for the system FeS-FeO-Cu2S.

Experimental Analysis and Thermodynamic Calculation of the Structural Regularities in the Fusion Diagram of the System of Alloys Al-Mg-Si

Experimental Analysis and Thermodynamic Calculation of the Structural Regularities in the Fusion Diagram of the System of Alloys Al-Mg-Si

Experimental analysis and thermodynamic calculation of the structural regularities in the fusion diagram of the system of alloys Al-Mg-Si

Sections of the phase diagram Al-Mg-Si with up to 35 at.% magnesium and 35 at.% silicon are constructed. The thermodynamic calculation and experimental analysis have shown that the conode of three-phase eutectic equilibrium L ⇔ α-Al+Mg2Si, corresponding to the maximum temperature of eutectic transformation, does not coincide with the stoichiometric cross section between Al and Mg2Si in the Al-Mg-Si ternary system, but rather occurs toward the magnesium-rich side of the ternary diagram. A polythermal cross section, corresponding to this conode, has been constructed. Concentration-temperature parameters of the univariant eutectic transformation L ⇔ α-Al+Mg2Si, as well as the boundaries of the domain of existence of alloys crystallizing with the formation of only two phases, namely, α-Al and Mg2Si, were determined. Modeling of phase equilibria involving solid and liquid phases in the ternary system Al-Mg-Si was carried out. The topology of the phase diagram is stable against a wide range variation of the adjustable parameters; the inherent form of the diagram seems well established. The reasons for this are discussed.

Simulation of Calorimetric Melting Processes—A Useful Tool for Enantiomeric Purity Determination

Simulation of calorimetric fusion curves was introduced as a new technique in calorimetric purity analysis and has now been tested for its applicability to enantiomeric purity determination. The system investigated was the enantiomeric pair (S)-(+)-1-Indanol/(R)-(-)-1-Indanol. The racemic form of this system either exists as a conglomerate or as a racemic compound. The binary fusion diagrams of both forms of enantiomeric mixtures were built up from melting investigations and were compared with calculations. The results obtained show that the simulation method is suitable to determine enantiomeric purities by an accuracy of better than 10% within a concentration range 80… 100% ee which is the important range for purity analysis.

Fusion diagram for the pseudosystem CaO�Al2O3-MgO�Al2O3-MgO

The use of statistical methods will considerably reduce the number of experiments needed to construct fusion diagrams, and yield good results.

Fusion diagram in the SrO-Al2O3-HfO2 system

Determination des temperatures de fusion, par calcul et experimentalement. Construction des lignes de temperatures sur le diagramme de fusion

Inclusive ϕ meson production, the parton fusion model and strange quark structure functions

The parton fusion model is used to describe the longitudinal differential cross section (dσ/dxF) of hadronic ϕ production. Thedσ/dxF for ϕ production in π±p,\(\mathop p\limits^{( - )} p\) andK±p interactions is evaluated in the model by using structure functions for the constituents of the interacting particles. A comparison between the model and high statistics data in the Feynmanx range 0.0<xF(ϕ)<0.4 allows the determination of the strange valence quark distribution inK mesons and the strange sea quark distribution in π mesons, which appears to be harder than the light sea quark distribution. The comparison also shows that a significant part of inclusive ϕ production is due to the OZI allowed fusion of strange quarks, while the OZI inhibited fusion diagrams are strongly suppressed.

Higgs-boson photoproduction at very high energy

The photoproduction cross section of Higgs bosons with very-high-energy $\mathrm{ep}$ colliding beams is calculated. The fusion diagram $\ensuremath{\gamma}g\ensuremath{\rightarrow}q\overline{q}H$, where $q$ is a heavy quark, is shown to be dominant. The resulting cross section, although larger than estimates performed in the leading-logarithm approximation, turns out to be rather small.

Method for determining the retrograde solubility of solid solutions

A method was proposed for determining fusion diagrams with retrograde solubility from the dependence of the equilibrium distribution coefficient on the concentration.

Thermal analysis of the system benzene-stannic bromide

1. A study was made of the fusion diagram of the system benzene-stannic bromide. A simple eutectic was established at −9.9° and 34.1 moles percent of stannic bromide. 2. The heat of mixing of the components at the eutectic composition and temperature was estimated and found to be 256 ± 125 cal per mole of mixture. 3. It was shown that structural concepts which explain the interaction of benzene and carbon tetrahalides are applicable also to binary systems of benzene and stannic halides. 4. It was shown that stannic bromide undergoes a polymorphous transformation at 15.3° The heat of transformation was determined and found to be 304± 15 cal/mole.