Search Results (173)

Functionally graded porous beams are increasingly used in lightweight engineering structures, where thermal effects and material inhomogeneity significantly influence vibration behavior. In this study, the thermoelastic free vibration of functionally graded porous Euler–Bernoulli beams with temperature-dependent material properties is investigated by considering uniform and symmetric porosity distributions, together with uniform, linear, and nonlinear temperature fields. The governing equations are derived based on classical Euler–Bernoulli beam theory and solved using the Differential Transformation Method, while the accuracy of the semi-analytical formulation is verified through a Hermite-based finite element model. The results show that increasing temperature reduces the bending stiffness due to thermal axial forces and leads to a rapid decrease in natural frequency as the critical buckling temperature is approached. Increasing porosity generally decreases the natural frequency, although a slight increase may occur in symmetric distributions because of the accompanying reduction in mass density. The present study provides a computational framework for the thermo-vibration analysis of functionally graded porous beams in lightweight structural applications. Full article

The accurate description of nonadiabatic quantum molecular dynamics represents one of the most significant challenges in modern computational chemistry, serving as a gateway to understanding complex phenomena ranging from photochemistry and electron transfer to surface scattering and biological exciton transport. A key difficulty lies in bridging high-level electronic structure theory for ground and excited states with accurate quantum dynamics theory. Although on-the-fly semiclassical approaches are increasingly viable, most quantum dynamics simulations still rely on pre-constructed potential energy surfaces, or in the nonadiabatic context, diabatic potential energy matrices (DPEMs). This perspective paper addresses the theoretical foundations, construction methodologies, and emerging frontiers of DPEMs. We examine the mathematical framework of the adiabatic-to-diabatic transformation, addressing the inherent topological challenges imposed by the geometric phase and the curl condition. We further analyze the transformative impact of machine learning, detailing how machine learning algorithms, such as permutation invariant polynomial neural networks and deep learning architectures, are reshaping the construction of global, high-dimensional DPEMs. Finally, we explore the disruptive potential of quantum computing, discussing how quantum algorithms are automating the direct simulation of nonadiabatic dynamics. In emerging quantum-centric workflows, DPEMs will continue to provide the critical bridge which enables the mapping of realistic, time-dependent molecular Hamiltonians onto quantum hardware. Full article

This paper is devoted to the introduction and systematic study of $(P,Q)$-normal operators in the context of semi-Hilbertian spaces, where P and Q are non-constant complex polynomials in one variable. This class generalizes the well-known notion of polynomially normal operators and offers a natural setting to study their structural properties in spaces endowed with a semi-inner product induced by a positive operator. We establish fundamental properties of $(P,Q)$-normal operators, including conditions for commutativity with respect to the $\mathbf{A}$-adjoint and relations to other classes of $\mathbf{A}$-operators. Several examples are provided to illustrate the theory and demonstrate how $(P,Q)$-normality extends classical concepts in operator theory. Full article

The cosmological constant (CC, $\Lambda$) problem stands as one of the most profound puzzles in the theory of gravity, representing a remarkable discrepancy of about 120 orders of magnitude between the observed value of dark energy and its natural expectation from quantum field theory. This paper synthesizes two innovative paradigms—holographic naturalness (HN) and pre-geometric gravity (PGG)—to propose a unified and natural resolution to the problem. The HN framework posits that the stability of the CC is not a matter of radiative corrections but rather of quantum information and entropy. The large entropy $S_{\mathrm{dS}}\sim M_{\mathrm{P}}^2/\Lambda$ of the de Sitter (dS) vacuum (with $M_{\mathrm{P}}$ being the Planck mass) acts as an entropic barrier, exponentially suppressing any quantum transitions that would otherwise destabilize the vacuum. This explains why the universe remains in a state with high entropy and relatively low CC. We then embed this principle within a pre-geometric theory of gravity, where the spacetime geometry and the Einstein–Hilbert action are not fundamental, but emerge dynamically from the spontaneous symmetry breaking of a larger gauge group, SO($1,4$)→SO($1,3$), driven by a Higgs-like field ${\varphi }^A$. In this mechanism, both $M_{\mathrm{P}}$ and $\Lambda$ are generated from more fundamental parameters. Crucially, we establish a direct correspondence between the vacuum expectation value (VEV) v of the pre-geometric Higgs field and the de Sitter entropy: $S_{\mathrm{dS}}\sim v$ (or $v^3$). Thus, the field responsible for generating spacetime itself also encodes its information content. The smallness of $\Lambda$ is therefore a direct consequence of the largeness of the entropy $S_{\mathrm{dS}}$, which is itself a manifestation of a large Higgs VEV v. The CC is stable for the same reason a large-entropy state is stable: the decay of such state is exponentially suppressed. Our study shows that new semi-classical quantum gravity effects dynamically generate particles we call “hairons”, whose mass is tied to the CC. These particles interact with Standard Model matter and can form a cold condensate. The instability of the dS space, driven by the time evolution of a quantum condensate, points at a dynamical origin for dark energy. This paper provides a comprehensive framework where the emergence of geometry, the hierarchy of scales and the quantum-information structure of spacetime are inextricably linked, thereby providing a novel and compelling path toward solving the CC problem. Full article

In this paper, we develop a geometric, structure-preserving semi-discrete formulation of Maxwell’s equations in both three- and two-dimensional settings within the framework of discrete exterior calculus. The proposed approach preserves the intrinsic geometric and topological structures of the continuous theory while providing a consistent spatial discretization. We analyze the essential properties of the proposed semi-discrete model and compare them with those of the classical Maxwell’s equations. As a representative example, the framework is applied to a combinatorial two-dimensional torus, where the semi-discrete Maxwell system reduces to a set of first-order linear ordinary differential equations. An explicit expression for the general solution of this system is also derived. Full article

We present a time-dependent nonperturbative theory of the reconstruction of attosecond beating by interference of multiphoton transitions (RABBIT) for photoelectron emission from hydrogen atoms in the transverse direction relative to the laser polarization axis. Extending our recent semiclassical strong-field approximation (SFA) model developed for parallel emission, we deduce analytical expressions for the transition amplitudes and demonstrate that the photoelectron probability distribution can be factorized into interhalf- and intrahalfcycle interference contributions, the latter modulating the intercycle pattern responsible for sideband formation. We identify the intrahalfcycle interference arising from trajectories released within the same half cycle as the mechanism governing attosecond phase delays in the perpendicular geometry. Our results reveal the suppression of even-order sidebands due to destructive interhalfcycle interference, leading to a characteristic spacing between adjacent peaks that doubles the standard spacing observed along the polarization axis. Comparisons with numerical calculations of the SFA and the ab initio solution of the time-dependent Schrödinger equation confirm the accuracy of the semiclassical description. This work provides a unified framework for understanding quantum interferences in attosecond chronoscopy, bridging the cases of parallel and perpendicular electron emission in RABBIT-like protocols. Full article

We extend the classical fractal uncertainty principle (FUP) framework in time-frequency analysis by exploring several novel directions. First, we generalize the FUP beyond the classical Gaussian window by investigating non-Gaussian windows and the corresponding generalized Fock space techniques. Second, we develop uncertainty estimates in alternative joint representations, including the continuous wavelet transform and directional representations such as shearlets. Third, we study fractal uncertainty on random and anisotropic fractal sets, providing probabilistic and geometric refinements of the FUP. Fourth, we connect these results with semiclassical and microlocal analysis, thereby elucidating the role of fractal geometry in resonance theory and pseudodifferential operators. Finally, we extend the analysis beyond Gaussian Gabor multipliers by considering non-Gaussian generating functions and irregular lattice samplings. Our results yield new operator norm estimates and spectral properties, with potential applications in signal processing, quantum mechanics, and numerical analysis. Full article

The notion of twist fields has played a fundamental role in many-body physics. It is used to construct the so-called disorder parameter for the study of phase transitions in the classical Ising model of statistical mechanics, it is involved in the Jordan–Wigner transformation in quantum chains and bosonisation in quantum field theory, and it is related to measures of entanglement in many-body quantum systems. I provide a pedagogical introduction to the notion of twist field and the concepts at its roots, and review some of its applications, focussing on the 1 + 1 dimension. This includes locality and extensivity, internal symmetries, semi-locality, the standard exponential form and HEGT fields, path-integral defects and Riemann surfaces, topological invariance, and twist families. Additional topics touched upon include renormalisation and form factors in relativistic quantum field theory, tau functions of integrable PDEs, thermodynamic and hydrodynamic principles, and branch-point twist fields for entanglement entropy. One-dimensional quantum systems such as chains (e.g., quantum Heisenberg model) and field theory (e.g., quantum sine-Gordon model) are the main focus, but I also explain how the notion applies to equilibrium statistical mechanics (e.g., classical Ising lattice model), and how some aspects can be adapted to one-dimensional classical dynamical systems (e.g., classical Toda chain). Full article

Prefabricated H-section steel composite wall columns (PHSWCs) are crucial for advancing modular steel construction, yet their elastic buckling performance lacks a universally accurate predictive model due to the complex interplay between section interaction and semi-rigid bolted connections. To address this, a comprehensive theoretical framework for elastic buckling analysis is developed in this study. The model integrates Euler–Bernoulli beam theory for the H-sections, a three-dimensional spring system to represent the stiffness of bolted connections, and the Green strain tensor to account for geometric nonlinearity. Validation against ABAQUS (2020) and ANSYS (2021 R1) shows high accuracy (average errors: 1.0% and 1.2%, respectively). Furthermore, a unified formula for the normalized slenderness ratio is derived via stepwise regression, which elegantly degenerates to the classical Euler solution under limiting conditions. The main conclusion is that this framework enables rapid and precise buckling analysis, reducing parametric study time by 95% compared to detailed finite element modeling. It establishes a bolt density coefficient threshold of η = 0.5 that separates composite from independent section behavior, with an optimal design range of η = 0.2 to 0.25, thereby offering a robust theoretical basis for PHSWC design. Full article

We investigate Snyder spacetime and its generalizations, including Yang and Snyder–de Sitter spaces, which constitute manifestly Lorentz-invariant noncommutative geometries. This work initiates a systematic study of gauge theory on such spaces in the semi-classical regime, formulated as Poisson gauge theory. As a first step, we construct the symplectic realizations of the relevant noncommutative spaces, a prerequisite for defining Poisson gauge transformations and field strengths. We present a general method for representing the Snyder algebra and its extensions in terms of canonical phase-space variables, enabling both the reproduction of known representations and the derivation of novel ones. These canonical constructions are employed to obtain explicit symplectic realizations for the Snyder–de Sitter space and to construct the deformed partial derivative which differentiates the underlying Poisson structure. Furthermore, we analyze the motion of freely falling particles in these backgrounds and comment on the geometry of the associated spaces. Full article

Bilayer transition metal dichalcogenides (TMDs) are promising materials for next-generation field-effect transistors (FETs) due to their atomically thin structure and favorable transport properties. In this study, we employ density functional theory (DFT) to compute the electronic band structures and phonon dispersions of bilayer WS₂, WSe₂, and MoS₂, and the electron-phonon scattering rates using the EPW (electron-phonon Wannier) method. Carrier transport is then investigated within a semiclassical full-band Monte Carlo framework, explicitly including intrinsic electron-phonon scattering, dielectric screening, scattering with hybrid plasmon–phonon interface excitations (IPPs), and scattering with ionized impurities. Freestanding bilayers exhibit the highest mobilities, with hole mobilities reaching 2300 cm²/V·s in WS₂ and 1300 cm²/V·s in WSe₂. Using hBN as the top gate dielectric preserves or slightly enhances mobility, whereas HfO₂ significantly reduces transport due to stronger IPP and remote phonon scattering. Device-level simulations of double-gate FETs indicate that series resistance strongly limits performance, with optimized WSe₂ pFETs achieving ON currents of 820 A/m, and a 10% enhancement when hBN replaces HfO₂. These results show the direct impact of first-principles electronic structure and scattering physics on device-level transport, underscoring the importance of material properties and the dielectric environment in bilayer TMDs. Full article

A data set on Stark broadening parameters defining the Lorentzian line profile (spectral line widths and shifts) for 31 multiplets of four-times-charged nitrogen ion (N V), with lines broadened by impacts with electrons (e), protons (p), He II ions, $\alpha$ particles (He III), and B III, B IV, B V, and B VI ions, is given. The above-mentioned data have been calculated within the frame of the semiclassical perturbation theory, for temperatures from 50,000 K to 1,000,000 K, and densities of perturbers from 10¹⁵ cm⁻³ up to 10²¹ cm⁻³. These data are, first of all, of interest for diagnostics and modeling of laser-driven plasma in experiments and investigations of proton–boron fusion, especially when the target is boron nitride (BN). Data on Stark broadening by collisions with e, p, He II ions, and $\alpha$ particles are useful for the investigation of stellar plasma, in particular for white dwarf atmospheres and subphotospheric layer modeling. Full article

The principles of least effort and the illusion of control may influence the decision-making process. It is challenging for a decision-maker to maintain complete independence when assessing the membership and non-membership degrees of indicators. However, existing neutrosophic sets and q-rung orthopair fuzzy sets assume full independence of such information. In view of this, this paper proposes a new neutrosophic set, namely the q-type semi-dependent neutrosophic set (QTSDNS), based on the classical neutrosophic set, whose membership and non-membership degrees are interrelated. QTSDNS is a generalized form of classical semi-dependent fuzzy sets, such as the intuitionistic neutrosophic set. It contains a regulatory parameter, which allows for decision-makers to flexibly adjust the model. Furthermore, a multi-attribute group decision-making (MAGDM) algorithm is proposed by integrating QTSDNS with evidence theory to solve the supplier selection problem. The algorithm first utilizes QTSDNS to represent the preference information of experts, then employs the q-TSDNWAA (or q-TSDNWGA) operator to aggregate the evaluation information of individual experts. Following the analysis of the mathematical relationship between QTSDNS and evidence theory, evidence theory is used to aggregate the evidence from each expert to obtain the group trust interval. Then, the best supplier is determined using interval number ranking methods. Finally, a numerical example is provided to demonstrate the feasibility of the proposed method. Full article

The Lorentz-breaking theory not only modifies the geometric structure of curved spacetime but also significantly alters the quantum dynamics of bosonic and fermionic fields in black hole spacetime, leading to observable physical effects on Hawking temperature and Bekenstein–Hawking entropy. This study establishes the first systematic theoretical framework for entropy modifications of charged accelerating Anti-de Sitter black holes, incorporating gauge-invariant corrections derived from Lorentz-violating quantum field equations in curved spacetime. The obtained analytical expression coherently integrates semi-classical approximations with higher-order quantum perturbative contributions. Furthermore, the methodologies employed and the resultant conclusions are subjected to rigorous analysis, establishing their physical significance for advancing fundamental investigations into black hole entropy. Full article

This article investigates fundamental inequalities within a golden-like statistical manifold (GLSM) equipped with a semi-symmetric metric connection (SSMC). We explore key geometric and analytical properties, including curvature relations and inequalities analogous to those in classical information geometry. The interplay between the golden-like structure and the SSMC yields new insights into the underlying differential geometric framework. Our results extend known inequalities in the statistical manifold (SM), providing a foundation for further studies in optimization and divergence theory within this generalized framework. Full article