Search Results (60)

Ester-based lubricants have been widely used owing to their excellent overall performance. In this study, the quantitative structure–property relationship (QSPR) approach was combined with molecular descriptors, a genetic algorithm (GA), and an artificial neural network (ANN) to systematically predict the key properties—kinematic viscosity at 40 °C and 100 °C, viscosity index, pour point, and flash point—of 64 diester-based lubricants. Quantum chemical calculations were first performed to obtain the equilibrium geometries and electronic information of the molecules. Geometry optimizations and frequency analyses were carried out using the Gaussian 16 software at the B3LYP/6-31G (d, p) level, providing a reliable foundation for molecular descriptor computation. Subsequently, topological, geometrical, and electronic descriptors were calculated using the RDKit toolkit, and the optimal feature subsets were selected by GA and used as ANN inputs for property prediction. The results showed that the ANN models exhibited good performance in predicting viscosity and flash point, with R² values of 0.9455 and 0.8835, respectively, indicating that the ANN effectively captured the nonlinear relationships between molecular structure and physicochemical properties. In contrast, the prediction accuracy for pour point was relatively lower (R² = 0.6155), suggesting that it is influenced by complex molecular packing and crystallization behaviors at low temperatures. Overall, the study demonstrates the feasibility of integrating quantum chemical calculations with the QSPR–ANN framework for lubricant property prediction, providing a theoretical basis and data-driven tool for molecular design and performance optimization of ester-based lubricants. Full article

Quantum mechanics postulates wave–particle duality and assigns amplitudes of the form $e^{iS/\hslash }$, yet no existing formulation explains why physical observables depend only on the phase of the action. Here we show that if the quantum of action ${\hslash }_{\mathrm{geom}}$ is finite, the classical action manifold $\mathbb{R}$ becomes compact under the identification $S\equiv S+2\pi {\hslash }_{\mathrm{geom}}$, yielding a $U\left(1\right)$ action space on which only modular action is observable. Wave interference then follows as a geometric necessity: a finite action quantum forces physical amplitudes to live on a circle, while the classical limit arises when the modular spacing $2\pi {\hslash }_{\mathrm{geom}}$ becomes negligible compared with macroscopic actions. We formulate this as a compact-action theorem. Chronon Field Theory (ChFT) provides the physical origin of ${\hslash }_{\mathrm{geom}}$: its causal field ${\Phi }^{\mu }$ carries a quantized symplectic flux $\oint \omega ={\hslash }_{\mathrm{geom}}$, making Planck’s constant a geometric topological invariant rather than an imposed parameter. Within this medium, the Real–Now–Front (RNF) supplies a local reconstruction rule that reproduces the structure of the Feynman path integral, the Schrödinger evolution, the Born rule, and macroscopic definiteness as consequences of geometric compatibility rather than supplemental postulates. Phenomenologically, identifying the electron as the minimal chronon soliton—carrying the fundamental unit of symplectic flux—links its spin, charge, and stability to topological properties of the chronon field, yielding concrete experimental signatures. Thus the compact-action/RNF framework provides a unified geometric origin for quantum interference, measurement, and matter, together with falsifiable predictions of ChFT. Full article

By extending the four-dimensional semi-Riemann geometry to higher-dimensional Finsler/Hamilton geometry, the canonical quantization of the fundamental metric tensor of general relativity, i.e., an approach that tackles a geometric quantity, is derived. With this quantization, the smooth continuous Finsler structure is transformed into a quantized Hamilton structure through the kinematics of a free-falling quantum particle with a positive mass, along with the introduction of the relativistic generalized uncertainty principle (RGUP) that generalizes quantum mechanics by integrating gravity. This transformation ensures the preservation of the positive one-homogeneity of both Finsler and Hamilton structures, while the RGUP dictates modifications in the noncommutative relations due to integrating consequences of relativistic gravitational fields in quantum mechanics. The anisotropic conformal transformation of the resulting metric tensor and its inverse in higher-dimensional spaces has been determined, particularly highlighting their translations to the four-dimensional fundamental metric tensor and its inverse. It is essential to recognize the complexity involved in computing the fundamental inverse metric tensor during a conformal transformation, as it is influenced by variables like spatial coordinates and directional orientation, making it a challenging task, especially in tensorial terms. We conclude that the derivations in this study are not limited to the structure in tangent and cotangent bundles, which might include both spacetime and momentum space, but are also applicable to higher-dimensional contexts. The theoretical framework of quantization of general relativity based on quantizing its metric tensor is primarily grounded in the four-dimensional metric tensor and its inverse in pseudo-Riemannian geometry. Full article

Rydberg atoms play a crucial role in testing atomic structure theory, quantum computing and simulation. Measurements of transition frequencies from the $2^{1,3}S$ states to Rydberg ${}^{1,3}P$ states have reached a precision of several kHz, which poses significant challenges for theoretical calculations, since the accuracy of variational energy calculations decreases rapidly with increasing principal quantum number n. Recently the complex “triple” Hylleraas basis was employed to attain the ionization energy of helium $24{}^{1}P$ state with high accuracy. Different from it, we extended the correlated B-spline basis functions (C-BSBFs) to calculate the Rydberg states of helium. The nonrelativistic energies of $1snp$${}^{1,3}P$ states up to $n=27$ achieve at least 14 significant digits using a unified basis set, thereby greatly reducing the complexity of the optimization process. Results of geometric structure parameters and cusp conditions were presented as well. Both the global operator and direct calculation methods are employed and cross-checked for contact potentials. This C-BSBF method not only obtains high-accuracy energies across all studied levels but also confirms the effectiveness of the C-BSBFs in depicting long-range and short-range correlation effects, laying a solid foundation for future high-accuracy Rydberg-state calculations with relativistic and QED corrections included in helium atom and low-Z helium-like ions. Full article

This study proposes an Index-Based Neural Network (IBNN) framework for the static analysis of truss structures, employing a Lagrangian dual optimization technique grounded in the force method. A truss is a discrete structural system composed of linear members connected to nodes. Despite their geometric simplicity, analysis of large-scale truss systems requires significant computational resources. The proposed model simplifies the input structure and enhances the scalability of the model using member and node indices as inputs instead of spatial coordinates. The IBNN framework approximates member forces and nodal displacements using separate neural networks and incorporates structural equations derived from the force method as mechanics-informed constraints within the loss function. Training was conducted using the Augmented Lagrangian Method (ALM), which improves the convergence stability and learning efficiency through a combination of penalty terms and Lagrange multipliers. The efficiency and accuracy of the framework were numerically validated using various examples, including spatial trusses, square grid-type space frames, lattice domes, and domes exhibiting radial flow characteristics. Multi-index mapping and domain decomposition techniques contribute to enhanced analysis performance, yielding superior prediction accuracy and numerical stability compared to conventional methods. Furthermore, by reflecting the structured and discrete nature of structural problems, the proposed framework demonstrates high potential for integration with next-generation neural network models such as Quantum Neural Networks (QNNs). Full article

We establish a comprehensive framework demonstrating that physical reality can be understood as a holographic encoding of underlying computational structures. Our central thesis is that different geometric realizations of the same physical system represent equivalent holographic encodings of a unique computational structure. We formalize quantum complexity as a physical observable, establish its mathematical properties, and demonstrate its correspondence with geometric descriptions. This framework naturally generalizes holographic principles beyond AdS/CFT correspondence, with direct applications to black hole physics and quantum information theory. We derive specific, quantifiable predictions with numerical estimates for experimental verification. Our results suggest that computational structure, rather than geometry, may be the more fundamental concept in physics. Full article

The optimization of independent automotive suspension systems, which is one of the main pillars of the vehicle performance and comfort, is currently going through a revolutionary change due to the development of artificial intelligence and quantum computing. This paper aims to review the multi-objective optimization of suspension parameters including camber, caster, and toe to discuss the complex design issues that arise from geometric and dynamic considerations. Some of the most common computational methodologies, which are Genetic Algorithms, Particle Swarm Optimization, and Gradient Descent, are discussed in this paper along with the new quantum computing techniques such as Gate-Based quantum computing and Quantum Annealing (QA). In addition, this review incorporates information from the practice of automotive manufacturers who have incorporated the use of artificial intelligence and quantum computing in their suspension systems. However, there are still some issues remaining, such as the computational cost, real-time flexibility, and the applicability of theoretical concepts to actual engineering structures. Some potential future research directions are introduced in this paper, such as hybrid optimization approaches, quantum techniques, and adaptive materials, which are considered as potential directions for future development. This systematic review presents a conceptual framework for researchers and engineers to follow, stressing the importance of interdisciplinarity in the development of intelligent suspension systems with performance objectives that are capable of adjusting to various road conditions. The findings of this work underscore the growing importance of complex computational techniques in modern automotive industry and highlight their potential to shape future developments based on emerging trends and industry practices. Full article

The co-production of CO₂ continues to remain the bane of several hydrogen production technologies, including the steam reforming of methane and the dry reforming of methane processes. Efficient utilization of abundant greenhouse gas in the form of methane provides opportunities for the design of an innovative system that will maximize the use of such a raw material in the most environmentally friendly manner. The study of the mechanism of the pyrolysis of methane reactions over molten metals provides promise for improved hydrogen yield and methane conversion with a greater turnover frequency. Catalyst electronic properties computed via Density Functional Theory using the Quantum Espresso code provided data that were built into a database. Using Bismuth as the base metal, active transition metals including Ni, Cu, Pd, Pt, Ag, and Au of different concentrations of 5, 10, 15, and 25% were placed on 96 atoms of the base metal and relaxed to obtain the optimized geometric structures for the catalytic reaction studies. The kinetics of the individual elementary steps of the pyrolysis reaction at preset temperatures over the bi-metals were calculated using the Car-Parinello (CP) method and Nudge Elastic Band (NEB) computations. The collated data of the various pyrolysis of methane reactions over the different bi-metals was used to train machine learning models for the prediction of reaction outcome, catalytic performance, and efficient operating conditions for the pyrolysis of methane over molten metals. The turnover frequency, which is determined using the transition state energies of the fundamental reaction cycles, will be used to simulate the stability of the catalyst. Full article

The lack of dense random-access memory is one of the main obstacles to the development of digital superconducting computers. It has been suggested that AVRAM cells, based on the storage of a single Abrikosov vortex—the smallest quantized object in superconductors—can enable drastic miniaturization to the nanometer scale. In this work, we present the numerical modeling of such cells using time-dependent Ginzburg–Landau equations. The cell represents a fluxonic quantum dot containing a small superconducting island, an asymmetric notch for the vortex entrance, a guiding track, and a vortex trap. We determine the optimal geometrical parameters for operation at zero magnetic field and the conditions for controllable vortex manipulation by short current pulses. We report ultrafast vortex motion with velocities more than an order of magnitude faster than those expected for macroscopic superconductors. This phenomenon is attributed to strong interactions with the edges of a mesoscopic island, combined with the nonlinear reduction of flux-flow viscosity due to the nonequilibrium effects in the track. Our results show that such cells can be scaled down to sizes comparable to the London penetration depth, ∼100 nm, and can enable ultrafast switching on the picosecond scale with ultralow energy per operation, ∼${10}^{-19}$ J. Full article

We investigate the energy spectra and optical absorption of a 3D quantum dot–double quantum ring structure of GaAs/Al_0.3Ga_0.7As with adjustable geometrical parameters. In the effective mass approximation, we perform 3D numerical computations using as height profile a superposition of three Gaussian functions. Independent variations of height and width of the dot and of the rings and also of the dot–rings distance determine particular responses, useful in practical applications. We consider that a suitable manipulation of the geometrical parameters of this type of quantum coupling offer a variety of responses and, more important, the possibility of a fine adjusting in energy spectra and in the opportunity of choosing definite absorption domains, properties required for the improvement of the performances of optoelectronic devices. Full article

Alternative mathematical explorations in quantum computing can be of great scientific interest, especially if they come with penetrating physical insights. In this paper, we present a critical revisitation of our application of geometric (Clifford) algebras (GAs) in quantum computing as originally presented in [C. Cafaro and S. Mancini, Adv. Appl. Clifford Algebras 21, 493 (2011)]. Our focus is on testing the usefulness of geometric algebras (GAs) techniques in two quantum computing applications. First, making use of the geometric algebra of a relativistic configuration space (namely multiparticle spacetime algebra or MSTA), we offer an explicit algebraic characterization of one- and two-qubit quantum states together with a MSTA description of one- and two-qubit quantum computational gates. In this first application, we devote special attention to the concept of entanglement, focusing on entangled quantum states and two-qubit entangling quantum gates. Second, exploiting the previously mentioned MSTA characterization together with the GA depiction of the Lie algebras $\mathrm{SO}\left(3;\mathbb{R}\right)$ and $\mathrm{SU}\left(2;\mathbb{C}\right)$ depending on the rotor group ${\mathrm{Spin}}^{+}\left(3,0\right)$ formalism, we focus our attention to the concept of universality in quantum computing by reevaluating Boykin’s proof on the identification of a suitable set of universal quantum gates. At the end of our mathematical exploration, we arrive at two main conclusions. Firstly, the MSTA perspective leads to a powerful conceptual unification between quantum states and quantum operators. More specifically, the complex qubit space and the complex space of unitary operators acting on them merge in a single multivectorial real space. Secondly, the GA viewpoint on rotations based on the rotor group ${\mathrm{Spin}}^{+}\left(3,0\right)$ carries both conceptual and computational advantages compared to conventional vectorial and matricial methods. Full article

Quantum logic is a well-structured theory, which has recently received some attention because of its fundamental relation to quantum computing. However, the complex foundation of quantum logic borrowing concepts from different branches of mathematics as well as its peculiar settings have made it a non-trivial task to devise suitable applications. This article aims to propose for the first time an approach using quantum logic in image processing for shape classification. We show how to make use of the principal component analysis to realize quantum logical propositions. In this way, we are able to assign a concrete meaning to the rather abstract quantum logical concepts, and we are able to compute a probability measure from the principal components. For shape classification, we consider encrypting given point clouds of different objects by making use of specific distance histograms. This enables us to initiate the principal component analysis. Through experiments, we explore the possibility of distinguishing between different geometrical objects and discuss the results in terms of quantum logical interpretation. Full article

Quantum simulation qubit models of electronic Hamiltonians rely on specific transformations in order to take into account the fermionic permutation properties of electrons. These transformations (principally the Jordan–Wigner transformation (JWT) and the Bravyi–Kitaev transformation) correspond in a quantum circuit to the introduction of a supplementary circuit level. In order to include the fermionic properties in a more straightforward way in quantum computations, we propose to use methods issued from Geometric Algebra (GA), which, due to its commutation properties, are well adapted for fermionic systems. First, we apply the Witt basis method in GA to reformulate the JWT in this framework and use this formulation to express various quantum gates. We then rewrite the general one and two-electron Hamiltonian and use it for building a quantum simulation circuit for the Hydrogen molecule. Finally, the quantum Ising Hamiltonian, widely used in quantum simulation, is reformulated in this framework. Full article

The common geometrical (symplectic) structures of classical mechanics, quantum mechanics, and classical thermodynamics are unveiled with three pictures. These cardinal theories, mainly at the non-relativistic approximation, are the cornerstones for studying chemical dynamics and chemical kinetics. Working in extended phase spaces, we show that the physical states of integrable dynamical systems are depicted by Lagrangian submanifolds embedded in phase space. Observable quantities are calculated by properly transforming the extended phase space onto a reduced space, and trajectories are integrated by solving Hamilton’s equations of motion. After defining a Riemannian metric, we can also estimate the length between two states. Local constants of motion are investigated by integrating Jacobi fields and solving the variational linear equations. Diagonalizing the symplectic fundamental matrix, eigenvalues equal to one reveal the number of constants of motion. For conservative systems, geometrical quantum mechanics has proved that solving the Schrödinger equation in extended Hilbert space, which incorporates the quantum phase, is equivalent to solving Hamilton’s equations in the projective Hilbert space. In classical thermodynamics, we take entropy and energy as canonical variables to construct the extended phase space and to represent the Lagrangian submanifold. Hamilton’s and variational equations are written and solved in the same fashion as in classical mechanics. Solvers based on high-order finite differences for numerically solving Hamilton’s, variational, and Schrödinger equations are described. Employing the Hénon–Heiles two-dimensional nonlinear model, representative results for time-dependent, quantum, and dissipative macroscopic systems are shown to illustrate concepts and methods. High-order finite-difference algorithms, despite their accuracy in low-dimensional systems, require substantial computer resources when they are applied to systems with many degrees of freedom, such as polyatomic molecules. We discuss recent research progress in employing Hamiltonian neural networks for solving Hamilton’s equations. It turns out that Hamiltonian geometry, shared with all physical theories, yields the necessary and sufficient conditions for the mutual assistance of humans and machines in deep-learning processes. Full article

Determining the oxidation potential (OP) of lithium-ion battery (LIB) electrolytes using theoretical methods will significantly speed up and simplify the process of creating a new generation high-voltage battery. The algorithm for calculating OP should be not only accurate but also fast. Our work proposes theoretical principles for evaluating the OP of LIB electrolytes by considering LiDFOB solutions with different salt concentrations in EC/DMC solvent mixtures. The advantage of the new algorithm compared to previous versions of the theoretical determination of the oxidation potential of electrolyte solutions used in lithium-ion batteries for calculations of statistically significant complexes, the structure of which was determined by the molecular dynamics method. This approach significantly reduces the number of atomic–molecular systems whose geometric parameters need to be optimized using quantum chemical methods. Due to this, it is possible to increase the speed of calculations and reduce the power requirements of the computer performing the calculations. The theoretical calculations included a set of approaches based on the methods of classical molecular mechanics and quantum chemistry. To select statistically significant complexes that can make a significant contribution to the stability of the electrochemical system, a thorough analysis of molecular dynamics simulation trajectories was performed. Their geometric parameters (including oxidized forms) were optimized by QM methods. As a result, oxidation potentials were assessed, and their dependence on salt concentration was described. Here, we once again emphasize that it is difficult to obtain, by calculation methods, the absolute OP values that would be equal (or close) to the OP values estimated by experimental methods. Nevertheless, a trend can be identified. The results of theoretical calculations are in full agreement with the experimental ones. Full article