Search Results (1,482)

This work proposes a systematic study of different computational schemes for fluorine Nuclear Magnetic Resonance (¹⁹F NMR) chemical shifts, with special emphasis placed on the basis set issue. This study encompasses two stages of calculation, namely, the development of the computational schemes for the geometry optimization of fluorine compounds and the NMR chemical shift calculations. In both stages, the performance of different density functional theory functionals is considered against the method of coupled-cluster singles and doubles (CCSD), with the latter representing a theoretical reference in this work. This exchange-correlation functional study is accompanied with a basis set study in both stages of calculation. Basis sets of different families, sizes, and valence-splitting levels are considered. Various locally dense basis sets (LDBSs) are proposed for the calculation of ¹⁹F NMR chemical shifts, and their performance is assessed by comparison of the calculated chemical shifts with both theoretical and experimental reference data. Overall, the pcS-3/pcS-2 LDBS scheme is recommended as the most balanced locally dense basis set scheme for fluorine chemical shift calculations. Full article

The deamidation rate is relatively high for Asn residues with Phe as the C-terminal adjacent residue in γS-crystallin, which is one of the human crystalline lens proteins. However, peptide-based experiments indicated that bulky amino acid residues on the C-terminal side impaired Asn deamination. In this study, we hypothesized that the side chain of Phe affects the Asn deamidation rate and investigated the succinimide formation process using quantum chemical calculations. The B3LYP density functional theory was used to obtain optimized geometries of energy minima and transition states, and MP2 and M06-2X calculations were used to obtain the single-point energy. Activation barriers and rate-determining step changed depending on the orientation of the Phe side chain. In pathways where an interaction occurred between the benzene ring and the amide group of the Asn residue, the activation barrier was lower than in pathways where this interaction did not occur. Since the aromatic ring is oriented toward the Asn side in experimentally determined structures of γS-crystallin, the above interaction is considered to enhance the Asn deamidation. Full article

This study theoretically investigates the potential of a polyacrylamide copolymerized with amylose, a primary component of starch, to evaluate its efficiency in removing heavy metals from industrial wastewater. This material concept seeks to combine the high adsorption capacity of polyacrylamide with the low cost and biodegradability of starch, ultimately aiming to offer an economical, efficient, and sustainable alternative for wastewater treatment. To this end, a computational model based on density functional theory (DFT) was developed, utilizing the B3LYP functional with the 6-311++G(d,p) basis set, a widely recognized combination that strikes a balance between accuracy and computational cost. The interactions between an acrylamide-amylose (AM/Amy) polymer matrix, as well as the individual polymers (AM and Amy), and the metal ions Pb, Hg, and Cd in their hexahydrated form (M·6H₂O) were analyzed. This modeling approach, where M represents any of these metals, simulates a realistic aqueous environment around the metal ion. Molecular geometries were optimized, and key parameters such as total energy, dipole moment, frontier molecular orbital (HOMO-LUMO) energy levels, and Density of States (DOS) graphs were calculated to characterize the stability and electronic reactivity of the molecules. The results indicate that this proposed copolymer, through its favorable electronic properties, exhibits a high adsorption capacity for metal ions such as Pb and Cd, positioning it as a promising material for environmental applications. Full article

We review a metric theory of gravitation that combines Newtonian gravity with Lorentz invariance. Beginning with a conformastatic metric justified by the Weak Equivalence Principle. We describe, within the Newtonian approximation, the spacetime geometry generated by a static distribution of dust matter. To extend this description to moving sources, we apply a Lorentz transformation to the static metric. This procedure yields, again within the Newtonian approximation, the metric associated with moving bodies. In doing so, we construct a gravitational framework that captures key relativistic features—such as covariance under Lorentz transformations—while remaining rooted in Newtonian dynamics. This approach offers an alternative route to describing weak-field gravitational interactions, without relying directly on Einstein’s field equations. Full article

The entanglement entropy of a random tensor network (RTN) is studied using tools from free probability theory. Random tensor networks are simple toy models that help in understanding the entanglement behavior of a boundary region in the anti-de Sitter/conformal field theory (AdS/CFT) context. These can be regarded as specific probabilistic models for tensors with particular geometry dictated by a graph (or network) structure. First, we introduce a model of RTN obtained by contracting maximally entangled states (corresponding to the edges of the graph) on the tensor product of Gaussian tensors (corresponding to the vertices of the graph). The entanglement spectrum of the resulting random state is analyzed along a given bipartition of the local Hilbert spaces. The limiting eigenvalue distribution of the reduced density operator of the RTN state is provided in the limit of large local dimension. This limiting value is described through a maximum flow optimization problem in a new graph corresponding to the geometry of the RTN and the given bipartition. In the case of series-parallel graphs, an explicit formula for the limiting eigenvalue distribution is provided using classical and free multiplicative convolutions. The physical implications of these results are discussed, allowing the analysis to move beyond the semiclassical regime without any cut assumption, specifically in terms of finite corrections to the average entanglement entropy of the RTN. Full article

We present novel proofs of the Riemann hypothesis by extending the standard complex Riemann zeta function into a quaternionic algebraic framework. Utilizing λ-regularization, we construct a symmetrized form that ensures analytic continuation and restores critical-line reflection symmetry, a key structural property of the Riemann ξ(s) function. This formulation reveals that all nontrivial zeros of the zeta function must lie along the critical line Re(s) = 1/2, offering a constructive and algebraic resolution to this fundamental conjecture. Our method is built on convexity and symmetrical principles that generalize naturally to higher-dimensional hypercomplex spaces. We also explore the broader implications of this framework in quantum statistical physics. In particular, the λ-regularized quaternionic zeta function governs thermodynamic properties and phase transitions in Bose–Einstein condensates. This quaternionic extension of the zeta function encodes oscillatory behavior and introduces critical hypersurfaces that serve as higher-dimensional analogues of the classical critical line. By linking the spectral features of the zeta function to measurable physical phenomena, our work uncovers a profound connection between analytic number theory, hypercomplex geometry, and quantum field theory, suggesting a unified structure underlying prime distributions and quantum coherence. Full article

This study introduces a new metric structure called the Graphical Fuzzy Cone Metric Space (GFCMS) and explores its essential properties in detail. We examine its topological aspects in detail and introduce the notion of Hausdorff distance within this setting—an advancement not previously explored in any graphical structure. Furthermore, a fixed-point result is proven within the framework of GFCMS, accompanied by examples that demonstrate the applicability of the theoretical results. As a significant application, we construct fractals within GFCMS, marking the first instance of fractal generation in a graphical structure. This pioneering work opens new avenues for research in graph theory, fuzzy metric spaces, topology, and fractal geometry, with promising implications for diverse scientific and computational domains. Full article

Time-domain (TD) diffuse reflectance can be modeled using diffusion theory (DT) to non-invasively estimate optical transport coefficients of biological media, which serve as markers of tissue physiology. We employ an optimized N-layer DT solver in cylindrical geometry to reconstruct optical coefficients of bilayered media from TD reflectance generated via Monte Carlo (MC) simulations. Optical properties for 384 bilayered tissue models representing human head or limb tissues were obtained from the literature at three near-infrared wavelengths. MC data were fit using the layered DT model to simultaneously recover transport coefficients in both layers. Bottom-layer absorption was recovered with errors under 0.02 cm⁻¹, and top-layer scattering was retrieved within 3 cm⁻¹ of input values. In contrast, recovered bottom-layer scattering had mean errors exceeding 50%. Total hemoglobin concentration and oxygen saturation were reconstructed for the bottom layer to within 10 μM and 5%, respectively. Extracted transport coefficients were significantly more accurate when obtained using layered DT compared to the conventional, semi-infinite DT model. Our results suggest using improved theoretical modeling to analyze TD reflectance analysis significantly improves recovery of deep-layer absorption. Full article

Inversion with respect to a unit sphere is a powerful tool when dealing with many problems in Mathematics. This inversion preserves harmonicity in ${\mathbb{R}}^2,$ but it does not in ${\mathbb{R}}^n,$ for $n>2.$ Lord Kelvin overcame this problem by defining a new (at the time) inversion, the so-called Kelvin’s inversion (or transformation). This inversion has many good properties, making it extremely useful in each case where the geometry of the original problem raises issues. But by using Kelvin’s inversion, these issues are transformed into easier ones, due to a simpler geometry. In this review paper, we study Kelvin’s inversion, deploying its basic properties. Moreover, we present some applications, where its use enables scientists to solve difficult problems in scattering, electrostaticity, thermoelasticity, potential theory and bioengineering. Full article

Roof water inrush accidents in coal mine driving roadways occur frequently in China, accounting for a high proportion of major coal mine water hazard accidents and causing serious losses. Aiming at the lack of research on the mechanism of roof water inrush in driving roadways and the difficulty of predicting water inrush accidents, this paper constructs a local damage criterion for coal–rock mass and a seepage–fracture coupling model based on peridynamics (PD) bond theory. It identifies three zones of water-conducting channels in roadway surrounding rock, the water fracture zone, the driving fracture zone, and the water-resisting zone, revealing that the damage degree of the water-resisting zone dominates the transformation mechanism between delayed and instantaneous water inrush. A discriminant function for the effectiveness of water-conducting channels is established, and a single-index prediction and evaluation system based on damage critical values is proposed. A “geometry damage” dual-control water inrush prediction model within the PD framework is constructed, along with a non-local action mechanism model and quantitative prediction method for water inrush. Case studies verify the threshold for delayed water inrush and criteria for instantaneous water inrush. The research results provide theoretical tools for roadway water exploration design and water hazard prevention and control. Full article

Building upon the geological cycle theory, this study proposes fault cycles as a critical component of tectonic cyclicity in petroliferous basins. Focusing on reservoir-controlling faults in the southwestern Qaidam Basin, we systematically analyze fault architectures and identify three distinct fault activation episodes: the Lulehe Formation (LLH Fm.), the upper part of the Xiaganchaigou Formation (UXG Fm.), and the Shizigou Formation (SZG Fm.). Three types of fault cycle models are established. These fault cycles correlate with the evolution of regional tectonic stress fields, corresponding to the Cenozoic transition from extensional to compressional stress regimes in the basin. Mechanistic analysis reveals the hierarchical control of fault cycles in hydrocarbon systems: the early cycle governs the proto-basin geometry and low-amplitude structural trap development; the middle cycle affects the source rock distribution; and the late cycle controls trap finalization and hydrocarbon migration. This study proposes a fault cycle-controlled accumulation model, providing a dynamic perspective that shifts from conventional static fault concepts to reveal fault activity periodicity and its critical multi-phase control over hydrocarbon migration and accumulation, essential for exploration in multi-episodic fault provinces. Full article

This research developed a complex physical and mathematical model of the flat rolling theory problem. This model takes into account the influence of many parameters affecting the roll’s gripping capacity and the overall stability of the entire rolling process. It is important to emphasize that the method of the argument of functions of a complex variable does not rely on simplifying assumptions commonly associated with: the linearized theory of plasticity; or the decoupled solution of stress and strain fields. Furthermore, it does not utilize the rigid-plastic material model. Within this method, solutions are developed based on the complete formulation of the system of equations in terms of stresses and strains, incorporating constitutive relations, thermal effects, and boundary conditions that define a well-posed problem in the theory of plasticity. The presented applied problem is closed in nature, yet it accounts for the effects of mechanical loading and satisfies the system of equation. For this purpose, such factors as roll geometry, physical and mechanical properties of the rolled metal (including its fluidity, hardness, plasticity, and structure heterogeneity), rolling speed, metal temperature, roll lubrication, and many other parameters that can influence the process have been taken into account. Based on the developed mathematical model, a new, previously undescribed force factor significantly affecting the capture of metal by rolls and the stability of the rolling process was identified and investigated in detail. This factor is associated with force stretching of metal in the lagging zone—the area behind the rolls, where the metal has already left the deformation zone, but continues to experience residual stress. It was shown that this stretching, depending on the process parameters, can both contribute to the rolling stability and, on the contrary, destabilize it, causing oscillations and non-uniformity of deformation. The qualitative indicators of transient regime stability have been determined for various values of the parameter α. Specifically, for α = 0.077, the ratio f/α ranges from 1.10 to 1.95; for α = 0.129, the ratio f/α ranges from 1.19 to 1.95; and for α = 0.168, the ratio f/α ranges from 1.28 to 1.95. Full article

In this work, we undertake a comprehensive study of the functional measure of gravitational path integrals within a general framework involving non-trivial configuration spaces. As in Riemannian geometry, the integration over non-trival configuration spaces requires a metric. We examine the interplay between the functional measure and the dynamics of spacetime for general configuration-space metrics. The functional measure gives an exact contribution to the effective action at the one-loop level. We discuss the implications and phenomenological consequences of this correction, shedding light on the role of the functional measure in quantum gravity theories. In particular, we describe a mechanism in which the graviton acquires a mass from the functional measure without violating the diffeomorphism symmetry nor including Stückelberg fields. Since gauge invariance is not violated, the number of degrees of freedom goes as in general relativity. For the same reason, Boulware–Deser ghosts and the vDVZ discontinuity do not show up. The graviton thus becomes massive at the quantum level while avoiding the usual issues of massive gravity. Full article

This paper investigates an integrable spin system known as the Myrzakulov-XIII (M-XIII) equation through geometric and gauge-theoretic methods. The M-XIII equation, which describes dispersionless dynamics with curvature-induced interactions, is shown to admit a geometric interpretation via curve flows in three-dimensional space. We establish its gauge equivalence with the complex coupled dispersionless (CCD) system and construct the corresponding Lax pair. Using the Sym–Tafel formula, we derive exact soliton surfaces associated with the integrable evolution of curves and surfaces. A key focus is placed on the role of geometric and gauge symmetry in the integrability structure and solution construction. The main contributions of this work include: (i) a commutative diagram illustrating the connections between the M-XIII, CCD, and surface deformation models; (ii) the derivation of new exact solutions for a fractional extension of the M-XIII equation using the Kudryashov method; and (iii) the classification of these solutions into trigonometric, hyperbolic, and exponential types. These findings deepen the interplay between symmetry, geometry, and soliton theory in nonlinear spin systems. Full article

Biological processes often involve the attachment and detachment of extended molecules to substrates. Here, the classical dimer model is used to investigate these geometric effects on the free energy, which governs both the equilibrium state and the reaction dynamics. We present a simplified version of Fisher’s derivation of the partition function of a two-dimensional dimer model at filling factor $\nu =1$, which takes into account the blocking of two adjacent sites by each dimer. Physical consequences of the dimer geometry on the entropy that are not reflected in simpler theories are identified. Specifically, for dimers adsorbing on the DNA double helix, the dimer geometry gives a persistently nonzero entropy and there is a significant charge inversion as the force binding the particles to the lattice increases relative to the thermal energy, which is not true of the simple lattice gas model for the dimers, in which all the sites are independent. Full article