Geometric Transition Research Articles

Exploring percolation phase transition in the three-dimensional Ising model with machine learning

Abstract The percolation study offers valuable insights into the characteristics of phase transition, shedding light on the underlying mechanisms that govern the formation of global connectivity within the system. We explore the percolation phase transition in the 3D cubic Ising model by employing two machine learning techniques. Our results demonstrate the capability of machine learning methods in distinguishing different phases during the percolation transition. Through the finite-size scaling analysis on the output of the neural networks, the percolation temperature and a correlation length exponent in the geometrical percolation transition are extracted and compared to those in the thermal magnetization phase transition within the 3D Ising model. These findings provide a valuable way essential for enhancing our understanding of the property of the QCD critical point, which belongs to the same universality class as the 3D Ising model.Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

Isotropic ↔ anisotropic surface geometry transitions induced by adsorbed surfactants at water/vapor interfaces.

Adsorbates at a water/vapor interface change the surface geometry through altered surface tension, yet detailed theoretical studies are relatively sparse, and many applications focus on ensemble average characteristics. Here, we demonstrate that different interpretations of surface geometry emerge when considering the distributions of surface curvature and orientation as a function of adsorbed surfactant concentration and sterics. At low surface densities, the tributyl phosphate (TBP) sorbed water/vapor surface has an increased presence of ridges that are defined by principal curvatures κ1 and κ2 of opposite signs yet close in magnitude. As the TBP surface density increases, the difference in principal curvatures slowly increases. There is a distinct transition of the surface geometry, where the ridge-like features become much more pronounced, having sides whose orientation is normal to a flat interfacial plane. Thus, as the TBP surfactant is added to the surface, the surface curvatures become anisotropic in terms of the difference in magnitude of κ1 and κ2. We label this an isotropic → anisotropic geometric transition. Comparing the surface geometry as a function of the carbon tail length of the alkyl phosphate surfactant reveals that smaller surfactants also anisotropically enhance surface curvatures and that adsorbed alkyl tails to the surface stabilize and increase the symmetry of surface waves along the two principal curvature axes. We label this an anisotropic → isotropic geometric transition. These results reflect the opportunity to incorporate more realistic distributions of surface geometry within the collective understanding of statistical theories of surfaces, including capillary wave theory.

Uhlmann quench and geometric dynamic quantum phase transition of mixed states

Uhlmann quench and geometric dynamic quantum phase transition of mixed states

Nonlinear to geometric focusing transition: beam self-cleaning and self-focusing critical power

We propose an easy but effective approach to find a transition numerical aperture between the regimes of laser pulse filamentation with nonlinear focusing and with geometric focusing predominance. The suggested method based on the beam profile measurements allows correction of the data provided by spectra measurements. Using a simple semi-analytical model, we study the dependence of the transition numerical aperture on the pulse power and medium nonlinearity. The analysis shows that in condensed media the transition from the nonlinear to geometric focusing regime occurs at much tighter focusing than in air. Moreover, if the medium nonlinear refractive index is high enough, only the nonlinear focusing regime is observed even at numerical apertures close to one, which allows symmetric plasma channel formation.

Free energy and metastable states in the square-lattice $J_1$-$J_2$ Ising model

Free energy as a function of polarization is calculated for the square-lattice J_1J1-J_2J2 Ising model for J_2 < |J_1|/2J2<|J1|/2 using the random local field approximation (RLFA) and Monte Carlo (MC) simulations. Within RLFA, it reveals a metastable state with zero polarization in the ordered phase. In addition, the Landau free energy calculated within RLFA indicates a geometric slab-droplet phase transition at low temperature, which cannot be predicted by the mean field approximation. In turn, restricted free energy calculations for finite-size samples, exact and using MC simulations, reveal metastable states with a wide range of polarization values, but with only two domains. Taking into account the dependence of the restricted free energy on the nearest-neighbor correlations allows us to identify several more metastable states. The calculations also reveal additional slab-droplet transitions at J_2 > |J_1|/4J2>|J1|/4. These findings enrich our knowledge of the J_1J1-J_2J2 Ising model and the RLFA as a useful theoretical tool to study phase transitions in spin systems.

ROLE OF GEOMETRICAL ART IN THE MORPHOLOGICAL DEVELOPMENT OF MUGHAL TOMBS

Art and architecture are said to be interconnected from a long time. Mughal time period has been said to have the maximum art and art influence in its era. The architecture of that time is termed to be marvellous and spectacular. Art is considered something that is unique and a form of self-expression. The aim of this paper is to investigate the geometry used in morphological development of Mughal monuments and in their transitions. Live case study is done to explore the different elements, their geometry, artworks, and materials in Mughal monuments (Humayun’s Tomb and Itimad-Ud-Daulah tomb). The geometrical transitions in different elements of the tomb buildings studied and their interrelationship is then found. Findings shows that these transformations contributed in the development of overall morphological definition of Mughal tomb structures. It can be seen that Mughal era art and architecture made use of geometry in their morphological development. Also, different materials and art forms were used in different architectural elements of tomb buildings.

Preliminary Failure Analyses of Loaded Hot Water Bottles

Hot water bottles are widely utilised for their therapeutic advantages, such as relieving muscle tension and imparting warmth. However, the increasing frequency and potential risks associated with bursting or failure necessitate a detailed examination of the contributing factors as their failure is not fully understood in a scientific manner. With the apparent lack of analysis of hot water bottles in the literature, this study employs, for the first time, a dual methodology involving finite-element (FE) analysis conducted in ABAQUS and experimental validation to systematically investigate the underlying mechanisms leading to failure incidents. Through FE modelling and analysis, the stress and strain distribution within typical hot water bottles is modelled under compression loading conditions, facilitating the identification of vulnerable areas prone to failure. Experimental validation encompasses uniaxial loading compression tests on distinct specimens, generating load–displacement curves that elucidate material responses to compressive forces and highlight variations in load-bearing capacities. The study explores diverse failure modes, attributing them to stress concentration at geometric transitions and contact regions. Stress–strain curves contribute valuable insights into material characteristics, with ultimate stress values as crucial indicators of resistance to deformation and rupture. The FE analysis simulation results visualise deformation patterns and stress concentration zones. The findings illustrate that the highest stress concentration areas exist in the internal boundary of hot water bottles near the neck and cap region. This is experimentally confirmed through the bursting failures of four samples, with three failures occurring in this specific region. The findings support the guidance that users should avoid sleeping with a hot water bottle as it may fail under compression if they lay on top of it. Meanwhile, this result guides manufacturers to strengthen the weak areas of hot water bottles around the nicks and edges. This study significantly enhances our understanding of hot water bottle mechanics, thereby guiding design practice to improve overall performance and user safety. In summary, hot water bottles are commonly used but have not been investigated scientifically regarding external loading conditions and their related failure, as the current study has achieved. Identifying the weak points through experiment and simulation directs manufacturers towards required improvements in particular regions, such as the bottleneck and edge reinforcement during the design and manufacturing phases.

Correction to Nickel‐Based Single‐Molecule Catalysts with Synergistic Geometric Transition and Magnetic Field‐Assisted Spin Selection Outperform RuO2 for Oxygen Evolution

Correction to Nickel‐Based Single‐Molecule Catalysts with Synergistic Geometric Transition and Magnetic Field‐Assisted Spin Selection Outperform RuO₂ for Oxygen Evolution

Geometry over algebras

We study geometric structures arising from Hermitian forms on linear spaces over real algebras beyond the division ones. Our focus is on the dual numbers, the split-complex numbers, and the split-quaternions. The corresponding geometric structures are employed to describe the spaces of oriented geodesics in the hyperbolic plane, the Euclidean plane, and the round 2-sphere. We also introduce a simple and natural geometric transition between these spaces. Finally, we present a projective model for the hyperbolic bidisc, that is, the Riemannian product of two hyperbolic discs.

Correlation functions of huge operators in AdS3/CFT2: domes, doors and book pages

We describe solutions of asymptotically AdS3 Einstein gravity that are sourced by the insertion of operators in the boundary CFT2, whose dimension scales with the central charge of the theory. Previously, we found that the geometry corresponding to a black hole two-point function is simply related to an infinite covering of the Euclidean BTZ black hole [1]. However, here we find that the geometry sourced by the presence of a third black hole operator turns out to be a Euclidean wormhole with two asymptotic boundaries. We construct this new geometry as a quotient of empty AdS3 realized by domes and doors. The doors give access to the infinite covers that are needed to describe the insertion of the operators, while the domes describe the fundamental domains of the quotient on each cover. In particular, despite the standard fact that the Fefferman-Graham expansion is single-sided, the extended bulk geometry contains a wormhole that connects two asymptotic boundaries. We observe that the two-sided wormhole can be made single-sided by cutting off the wormhole and gluing on a “Lorentzian cap”. In this way, the geometry gives the holographic description of a three-point function, up to phases. By rewriting the metric in terms of a Liouville field, we compute the on-shell action and find that the result matches with the Heavy-Heavy-Heavy three-point function predicted by the modular bootstrap. Finally, we describe the geometric transition between doors and defects, that is, when one or more dual operators describe a conical defect insertion, rather than a black hole insertion.

Geometric resolution of the Schwarzschild horizon

We provide the first example of a geometric transition that resolves the Schwarzschild black hole into a smooth microstructure in eleven-dimensional supergravity on a seven-torus. The geometry is indistinguishable from a Schwarzschild black hole dressed with a scalar field in four dimensions, referred to as a Schwarzschild scalarwall. In eleven dimensions, the scalar field arises as moduli of the torus. The resolution occurs at an infinitesimal scale above the horizon, set by the size of the internal torus, where it transitions to a smooth bubbling spacetime supported by M2-brane flux. Published by the American Physical Society 2024

Research on Adaptive Cycle Engine Mode Transition Control Method

Mode transition is an important dynamic process of an adaptive cycle engine (ACE). In order to obtain a smooth mode transition process, the closed-loop controller is designed based on the strong robust augmented linear quadric regulator (ALQR) method, and with the objective of minimizing the thrust fluctuation in the process of mode transition, an open-loop geometrical mechanism control schedules optimization method based on Bézier curves is proposed, so that the closed-loop control and the open-loop control can work in coordination. The simulation results at the subsonic cruise operating point and supersonic cruise operating point show that based on the optimized open-loop geometrical mechanism control schedules and the designed closed-loop ALQR control system, the ACE achieves fast and smooth geometrical mechanisms and engine output transition during the mode transition process with a maximum thrust fluctuation of 2.58%, which is much smaller than that of the traditional linear variation geometric mechanisms with a maximum 4.64% thrust fluctuation, which verifies the effectiveness of the proposed control method.

Twisted Fibrations in M/F-theory

In this work we investigate 5-dimensional theories obtained from M-theory on genus one fibered threefolds which exhibit twisted algebras in their fibers. We provide a base-independent algebraic description of the threefolds and compute light 5D BPS states charged under finite sub-algebras of the twisted algebras. We further construct the Jacobian fibrations that are associated to 6-dimensional F-theory lifts, where the twisted algebra is absent. These 6/5-dimensional theories are compared via twisted circle reductions of F-theory to M-theory. In the 5-dimensional theories we discuss several geometric transitions that connect twisted with untwisted fibrations. We present detailed discussions of {mathfrak{e}}_6^{(2)} , {mathfrak{so}}_8^{(3)} and {mathfrak{su}}_3^{(2)} twisted fibers and provide several explicit example threefolds via toric constructions. Finally, limits are considered in which gravity is decoupled, including Little String Theories for which we match 2-group symmetries across twisted T-dual theories.

Theoretical study of CDW phases for bulk NbX2 (X = S and Se).

In most two-dimensional transition metal chalcogenides, the superconducting phase coexists with the charge density wave (CDW) phase. There exists at least one case, i.e. bulk 2H-NbS2, that does not conform to this picture. Scientists have shown great interest in trying to experimentally find the CDW phase of bulk NbS2 since 1975. Is there any theoretically more stable thermodynamic state than its higher-temperature metal phase, especially in the case of charge injection? Theoretically more stable CDW bulk configurations (TC for 2H-NbS2 and TTs for 2H-NbSe2) with partial pseudo energy gaps were predicted through the harmonic phonon softening theory and first-principles calculations. The ratios of larger to smaller pseudo gaps around K-H segment in the Brillouin zone for CDW phases are basically equal to those of superconductivity phases for bulk 2H-NbX2 (X = S and Se). The CDW phase should coexist with its superconductor state below the critical temperature rather than the metal phase for bulk 2H-NbS2. The presence of CDW phase should be more easily observed experimentally when the injected charge reaches 0.5e/Nb18S36 for bulk 2H-NbS2. Our calculations of density of state (DOS) indicated that, during Nb atoms contracting to form the CDW phases with symmetry breaking in the in-plane direction, dominant conductive carriers are always of p-type for bulk 2H-NbS2 while the alternation of carrier type from p-type to n-type occurs for bulk 2H-NbSe2. The Fermi level continuously drops and then the M-L segment of the out-of-plane energy band emerges from the Fermi surface, which corresponds to the reversal of p-n type sign. Lifshitz transition of pocket-vanishing types occurs in the out-of-plane direction without symmetry breaking during the geometrical structural phase transition for bulk 2H-NbSe2. Our calculations have theoretically addressed the long-standing coexistence issue of CDW and superconducting phases.

Bending theory of composite pressure vessels: A closed-form analytical approach

Composite pressure vessels are strategic for the present and future of the aerospace, transportation, and energy industries. These shell structures are utilized to store and transport liquids and gases and are principally composed of a cylindrical shell and two elliptical heads. The current rules for the structural design of composite pressure vessels make use of the membrane theory that excludes the bending of the structure. Nevertheless, the cylindrical shell and the elliptical heads present different curvature radii. These changes generate a localized bending deformation that determines an increase in the stress state as an effect of a local bending moment and shear force distributions that arise in the geometric transition zone. The stresses related to the bending effects die out rapidly, moving away from the junction plane, but they are sensibly higher than the membrane stress and, therefore, cannot be neglected in the mechanical assessment. Here, a closed-form analytical solution for the bending theory of composite shells is proposed. It can assist in the design of composite pressure vessels and drive the design towards reliable configurations for structural integrity. Using the Donnell–Mustari–Vlasov theory for thin-walled composite shells, the governing fourth-order differential equation is deduced and solved to obtain the displacements and stresses acting in the junction. The analytical results are successfully compared with those of reference finite element models for validation; their accuracy is proved considering different thicknesses, lay-ups, and flattening factors of the vessel

Slug flow parameters applied to dynamic riser analysis

Slug flow is a typical pattern in the petroleum production system. Its main feature is intermittency. This feature influences the riser dynamic behavior due to the coupling of its geometric configuration and time and space variation of internal fluid parameters. Although the studies that illustrate slug flow intermittency and dynamic riser behaviors have been growing recently, this discussion still needs to be expanded. Most slug models proposed in the literature are simplified and do not adequately capture the intermittency to a proper riser dynamic influence determination. Previous models neglected at least one of the following slug flow mechanisms: random features, bubble shape, liquid slug aeration, wake, and pipeline inclination effects. This paper aims to cover all these phenomena and present a model that provides realistic slug flow data for any riser analysis program. The dynamic riser analysis is not the scope of this paper. This article used a new slug tracking model that captures the intermittency to study the influence of the internal flow over the dynamic riser behavior. The model considers the liquid slug hold-up and its change over the pipe, the oil and gas thermodynamic properties, and the geometrical transition from typically horizontal plane interfaces to vertical concentric bubble shapes. The slug tracking model tests use three gas and liquid ratios (0.55, 0.7, and 0.82) with a 2.05 m/s constant mixture velocity. The maximum relative pressure deviation was 24.1. Time and space analysis of the slug flow parameters demonstrates the slug tracking capacity to reproduce the intermittency of the bubble and liquid slug lengths, void fractions, velocities, and pressures. This intermittence is essential to describe the internal slug flow influence on the structure behavior.

Nickel‐Based Single‐Molecule Catalysts with Synergistic Geometric Transition and Magnetic Field‐Assisted Spin Selection Outperform RuO2 for Oxygen Evolution (Adv. Energy Mater. 42/2023)

Nickel‐Based Single‐Molecule Catalysts with Synergistic Geometric Transition and Magnetic Field‐Assisted Spin Selection Outperform RuO₂ for Oxygen Evolution (Adv. Energy Mater. 42/2023)

Deciphering the influence of shape on vortex-induced vibrations: Insight from diamond and equilateral triangle cylinder simulations

In this study, we present a comprehensive numerical investigation on the impact of geometric shapes on vortex-induced vibrations (VIV). We deploy the OpenFOAM computational fluid dynamics toolbox to simulate undamped transverse flow-induced vibrations in diamond and equilateral triangular cylinders, operating at a Reynolds number of 100 in a uniform flow. Both cylinders possess an identical mass ratio of 10 and operate within a reduced velocity range of 1–13. Our findings reveal a substantial shift in VIV branching behavior when transitioning from a diamond to a triangular geometry, with both cylinders exhibiting solely VIV responses. Intriguingly, the triangular cylinder does not exhibit a lock-out feature. Furthermore, the triangular cylinder showcases rich dynamical behavior, the occurrence of beating. Coinciding with this geometric transition is a surge in fluid forces and heightened flow asymmetry. While the diamond cylinder predominantly exhibits the P + S mode of vortex shedding, the triangular cylinder displays an unconventional 2P vortex arrangement, contributing to the observed asymmetry. As the geometry transitions from diamond to triangular, we note a phase alignment between the lift and transverse displacement. Remarkably, the triangular cylinder exhibits a higher energy conversion efficiency than its diamond counterpart. This research underscores the significant influence of geometry on vortex-induced vibrations, providing pivotal insight for optimizing the design and performance of structures subjected to fluid flows.

Nickel‐Based Single‐Molecule Catalysts with Synergistic Geometric Transition and Magnetic Field‐Assisted Spin Selection Outperform RuO2 for Oxygen Evolution

AbstractOvercoming slow kinetics and high overpotential in electrocatalytic oxygen evolution reaction (OER) requires innovative catalysts and approaches that transcend the scaling relationship between binding energies for intermediates and catalyst surfaces. Inorganic complexes provide unique, customizable geometries, which can help enhance their efficiencies. However, they are unstable and susceptible to chemical reaction under extreme pH conditions. Immobilizing complexes on substrates creates single‐molecule catalysts (SMCs) with functional similarities to single‐atom catalysts (SACs). Here, an efficient SMC, composed of dichloro(1,3‐bis(diphenylphosphino)propane) nickel [NiCl2dppp] anchored to a graphene acid (GA), is presented. This SMC surpasses ruthenium‐based OER benchmarks, exhibiting an ultra‐low onset and overpotential at 10 mAcm−2 when exposed to a static magnetic field. Comprehensive experimental and theoretical analyses imply that an interfacial charge transfer from the Ni center in NiCl2dppp to GA enhances the OER activity. Spectroscopic investigations reveal an in situ geometrical transformation of the complex and the formation of a paramagnetic Ni center, which under a magnetic field, enables spin‐selective electron transfer, resulting in enhanced OER performance. The results highlight the significance of in situ geometric transformations in SMCs and underline the potential of an external magnetic field to enhance OER performance at a single‐molecule level.

Single and two-cells shape analysis from energy functionals for three-dimensional vertex models.

Vertex models have been extensively used for simulating the evolution of multicellular systems, and have given rise to important global properties concerning their macroscopic rheology or jamming transitions. These models are based on the definition of an energy functional, which fully determines the cellular response and conclusions. While two-dimensional vertex models have been widely employed, three-dimensional models are far more scarce, mainly due to the large amount of configurations that they may adopt and the complex geometrical transitions they undergo. We here investigate the shape of single and two-cells configurations as a function of the energy terms, and we study the dependence of the final shape on the model parameters: namely the exponent of the term penalising cell-cell adhesion and surface contractility. In single cell analysis, we deduce analytically the radius and limit values of the contractility for linear and quadratic surface energy terms, in 2D and 3D. In two-cells systems, symmetrical and asymmetrical, we deduce the evolution of the aspect ratio and the relative radius. While in functionals with linear surface terms yield the same aspect ratio in 2D and 3D, the configurations when using quadratic surface terms are distinct. We relate our results with well-known solutions from capillarity theory, and verify our analytical findings with a three-dimensional vertex model.