Critical Geometry Research Articles

Critical 1- and 2-point spin correlations for the O(2) model in 3d bounded domains

We study the critical properties of the 3d O(2) universality class in bounded domains through Monte Carlo simulations of the clock model. We use an improved version of the latter, chosen to minimize finite-size corrections at criticality, with 8 orientations of the spins and in the presence of vacancies. The domain chosen for the simulations is the slab configuration with fixed spins at the boundaries. We obtain the universal critical magnetization profile and two-point correlations, which favorably compare with the predictions of the critical geometry approach based on the Yamabe equation. The main result is that the correlations, once the dimensionful contributions are factored out with the critical magnetization profile, are shown to depend only on the distance between the points computed using a metric found solving the corresponding fractional Yamabe equation. The quantitative comparison with the corresponding results for the Ising model at criticality is shown and discussed. Moreover, from the magnetization profiles the critical exponent η is extracted and found to be in reasonable agreement with up-to-date results.

Automatic Optimization of Gas Insulated Components Based on the Streamer Inception Criterion

Gas insulated transmission lines (GILs) are used in electrical systems mainly for power transmission and High Voltage substation interconnection. In this paper, we focus on the development of complex numerical tools for the optimization of gas insulated HVDC components by the estimation of realistic electric field distribution and the voltage holding of the designed geometry. In particular, the paper aims at describing the correct modelling approach suitable to study high voltage components in DC, considering the nonlinear behaviour characterizing the electrical conductivity of solid and gas insulators. The simulated field distribution is then adopted to estimate the voltage holding of the dielectric gas, with a convenient engineering technique, based on the streamer criterion. These two tools are integrated in an automatic optimization package developed in COMSOL® and MATLAB®, with the purpose of adjusting the critical geometry features, suffering from excessive electrical stress and possibly giving rise to electrical breakdown, in order to guide the designer towards a robust solution.

The Porosity-dependence of Bulk Modulus of Dry Porous Materials

By semi-analytical modifications to Mackenzie’s equation, a new third-order relation between bulk modulus and porosity is developed for porous materials. Compared with Mackenzie’s equation, the proposed equation takes into consideration critical porosity and real geometry represented by the assembly of hollow spheres. It has been shown that the proposed equation is in better agreement with 10 sets of published data than Mackenzie’s equation and that has an advantage in predicting the matrix bulk modulus even lack of the data of dense porous specimens. In addition, the proposed equation can describe the bulk modulus of porous materials with critical porosity well. However, Mackenzie’s equation cannot work.

Local Elasto–plastic Buckling of Isotropic Plates With Cutouts Under Tension Loading Conditions

The motivation of the presented study was the observation of the existence of local loss of stability “tension buckling” in the experimental tests of composite and metallic plates with cut-outs subjected to tension. Because of this, the numerical analyses of the aluminum plate with elliptical or circular cutouts at the center and subjected to tensile load are studied in the paper. Although the whole structure is uniformly stretched, the circumferential compressive stresses in the vicinity of the cutout edge are observed. First of all, the linear buckling analysis is carried out for different sizes of the holes. Based on these results, the size of the hole is chosen, where the circumferential stress magnitude in the vicinity of the cutout is the lowest or even comparable to the yield stress of the material. The computations are made for three different values of thickness. Finally, the nonlinear buckling analysis is carried out without and with the plasticity effects included. Generally, in the case of the circular and vertically oriented elliptical cut-out, the loss of stability in the tensed plate is always observed. However, in elastic-plastic analyses, the values of the critical parameters significantly differ from the results obtained for elastic buckling. Finally, the critical geometries for further experimental tests were defined.

Highly sensitive photonic crystal fiber sensor based on surface plasmon resonance for low refractive index detection

A photonic crystal fiber (PCF) sensor based on surface plasmon resonance with a gold film coating is designed and investigated for detecting the analytes with a low refractive index (RI). The critical geometry parameter is optimized by the finite element method to increase the sensitivity of the sensor. An open-ring structure with a 70-nm-thickness gold film coated on the inner surface is located on the left and right sides of the PCF sensor, and its angle is equal to or greater than 90 deg. The spectral and amplitude sensitivities are numerically calculated to evaluate the sensing performance of the proposed sensor. The simulation results indicate that the maximum and average sensitivities are 68,000 and 9583 nm / RIU, respectively. The resolution is a critical parameter for assessing the sensing performance of the sensor with a maximum value of 1.47 × 10 − 6 RIU. The simulation results show that the RI of analytes that the sensor can detect ranges from 1.20 to 1.31. Therefore, the sensor possesses wide application prospects in the field of biosensors.

Near-critical reflection of internal waves

Internal waves describe the (linear) response of an incompressible stably stratified fluid to small perturbations. The inclination of their group velocity with respect to the vertical is completely determined by their frequency. Therefore the reflection on a sloping boundary cannot follow Descartes' laws, and it is expected to be singular if the slope has the same inclination as the group velocity. In this paper, we prove that in this critical geometry the weakly viscous and weakly nonlinear wave equations have actually a solution which is well approximated by the sum of the incident wave packet, a reflected second harmonic and some boundary layer terms. This result confirms the prediction by Dauxois and Young, and provides precise estimates on the time of validity of this approximation.

Analysis of unsteady flow around an axial circular cylinder of critical geometry using combined synchronous measurement in magnetic suspension and balance system

The wake structure of a freestream-aligned circular cylinder and its aerodynamic characteristics were investigated using a magnetic suspension and balance system (MSBS), which can levitate a model to eliminate support interference. The objectives of the present study were to investigate the flow field around a freestream-aligned circular cylinder and to clarify its effect on the aerodynamic force and base pressure. Experiments were conducted using a 0.3-m MSBS for support-free wind tunnel tests. Six models with fineness ratios (length to diameter, L/D) of 1.0, 1.25, 1.5, 1.75, 2.0, and 2.25 were used. The freestream velocity was set to 10 and 20 m/s, which correspond to Reynolds numbers based on model diameters of $$3.3\times 10^4$$ and $$6.7\times 10^4$$ , respectively. The velocity field, aerodynamic force, and base pressure were measured for each freestream-aligned circular cylinder. Two characteristic fluctuations with frequencies of $${\text {St}} < 0.05$$ and $${\text {St}} \approx 0.13$$ were observed in a nonreattaching flow field. A low-frequency axisymmetric fluctuation related to the drag force and base pressure was observed in the axial direction. A high-frequency antisymmetric fluctuation related to the lift force was observed in the radial direction. These features are in good agreement with those of both recirculation-bubble pumping and vortex shedding observed in the wake of a disk reported in previous studies (Berger et al., J Fluids Struct 4(3):231–257, 1990; Yang et al., Phys Fluids 27(6):064101, 2015).

Design and Decomposition Analysis of Mixing Zone Structures on Flame Dynamics for a Swirl Burner

The recirculation zone and the swirl flame behavior can be influenced by the burner exit shape, and few studies have been made into this structure. Large eddy simulation was carried out on 16 cases to distinguish critical geometry factors. The time series of the heat release rate were decomposed using seasonal-trend decomposition procedure to exclude the effect of short physical time. Dynamic mode decomposition (DMD) was performed to separate flame structures. The frequency characteristics extracted from the DMD modes were compared with those from the flame transfer functions. Results show that the flame cases can be categorized into three types, all of which are controlled by a specific geometric parameter. Except one type of flame, they show nonstationary behavior by the Kwiatkowski–Phillips–Schmidt–Shin test. The frequency bands corresponding to the coherent structures are identified. The flame transfer function indicates that the flame can respond to external excitation in the frequency range 100–300 Hz. The DMD modes capture the detailed flame structures. The higher frequency bands can be interpolated as the streamwise vortices and shedding vortices. The DMD modes, which correspond to the bands of flame transfer functions, can be estimated as streamwise vortices at the edges.

Effect of heat accumulation on the single track formation during laser metal deposition and development of a framework for analyzing new process strategies

Laser metal deposition (LMD) is getting more attention as a 3D printing technique recently. Compared to the cladding application, the process of building 3D structures is more challenging to control when it comes to complex structures. Changing heat transfer mechanisms over the building height and at critical part geometries can lead to instabilities during the process. This paper studies the effect of the surface temperature on single track geometry formation during the LMD process. The geometrical characteristic of the track formation is a key factor that needs to be controlled and monitored in any deposition process for a stable build job. To quantify the effect of the surface temperature on the track geometry, a stepwise preheated substrate from 25 to 500 °C is used, and the track height, width, and degree of dilution are evaluated. This experiment mimics the varying temperature of the prebuilt layers that occur during additive manufacturing of freeform structures with many layers. Understanding the influence of the surface temperature over the layer geometry gives an idea of build geometry variation due to the accumulated heat input along the build direction. This helps in defining process strategies and process parameters for the laser metal deposition of components with increased accuracy and reproducibility. Advanced process strategies that are essential for a successful build job need to be incorporated into a data preparation tool for robot code generation. Commercial software packages are available for regular additive path planning using industrial robots. However, when several process strategies and process parameters need to be adapted and varied along the build direction, one is pushed to the limits of the software capabilities. Therefore, an automated data preprocessing toolbox based on MATLAB has been developed for the implementation of process strategies through user-definable rules and algorithms. This eliminates manual robot code preparation and correction. Implementation and the level of automation of this process preparation toolbox have also been discussed in this paper.

Performance Assessment of Crash Barriers used in Road Safety: A Case Study of Malekhu Kurintar Section of the Prithvi Highway

Hill roads in Nepal are comprised of critical geometry and limited roadway clearances. It causes high number of runoff roadway type of accidents with single vehicle. These accidents often carry huge number of fatalities and severe injuries. Installation of crash barriers is the most effective way of preventing such accidents along hill roads. However, the existing practice of construction of crash barriers does not show the satisfactory results. Therefore, this research aimed at the evaluation of typical crash barriers constructed along the valley side of highway. Analysis of the road accident of Malekhu-Kurintar section of Prithvi Highway record shows that this section has relatively higher accident rate and most of the accidents are runoff roadway type. Further, these accidents are mainly caused due to either the absence or the failure of the crash barriers along the valley side of the highway. On the basis of field records, kinetic energy absorbed by the crash barriers and their deflections was investigated by application of computer based analysis tool ABAQUS V6.10. It has given satisfactory results on the deflection of W-beam and plum concrete barriers due to the impact of vehicle moving in various range of speed.

Study, analysis, and characterization of ultra-precision diamond tools for single-point diamond turning

In multiple applications of advanced instrumentation, single-point diamond turning (SPDT) is a popular and effective process to generate novel surfaces with nanometric surface roughness and sub-micron surface irregularities, albeit at a high cost. In SPDT, precision diamond tooling contributes significantly to the process cost escalation. Hence, for SPDT, it is vital to have an optimal precision diamond tool deployment. In this article, details of comprehensive precision diamond tool selection and tool characterization are discussed. Three makes of selected ultra-precision diamond (UPD) tools and standard diamond tools (of a global make), designated as CFT, are considered for this study. In this tool bench-marking exercise, the fabrication of Cu–Be alloy predesigned precision components (PDPCs) of a critical geometry is selected. UPD and CFT tools are deployed to fabricate (under similar machining-metrology conditions) the PDPCs. These diamond tools are evaluated in terms of the quality parameters (variation in radius of curvature, form error, and surface roughness) of the workpieces. Further, to explore the progressive wear of these tools, multiple machining cycles are conducted on these workpieces, and their quality parameters are analyzed. Thus, the precision diamond tools of three makes are benchmarked against the CFT tool. Based on the final outcome of this analysis, suitable recommendations are provided to precision diamond tool manufacturers to improve their product in terms of performance and optimized costs to meet the ever-growing tooling demands of the SPDT community.

Quantum critical scaling and holographic bound for transport coefficients near Lifshitz points

The transport behavior of strongly anisotropic systems is significantly richer compared to isotropic ones. The most dramatic spatial anisotropy at a critical point occurs at a Lifshitz transition, found in systems with merging Dirac or Weyl point or near the superconductor-insulator quantum phase transition. Previous work found that in these systems a famous conjecture on the existence of a lower bound for the ratio of a shear viscosity to entropy is violated, and proposed a generalization of this bound for anisotropic systems near charge neutrality involving the electric conductivities. The present study uses scaling arguments and the gauge-gravity duality to confirm the previous analysis of universal bounds in anisotropic Dirac systems. We investigate the strongly-coupled phase of quantum Lifshitz systems in a gravitational Einstein-Maxwell-dilaton model with a linear massless scalar which breaks translations in the boundary dual field theory and sources the anisotropy. The holographic computation demonstrates that some elements of the viscosity tensor can be related to the ratio of the electric conductivities through a simple geometric ratio of elements of the bulk metric evaluated at the horizon, and thus obey a generalized bound, while others violate it. From the IR critical geometry, we express the charge diffusion constants in terms of the square butterfly velocities. The proportionality factor turns out to be direction-independent, linear in the inverse temperature, and related to the critical exponents which parametrize the anisotropic scaling of the dual field theory.

Design of multistage forging processes by numerical simulation and experimental verification

The Variety of components with different shapes & Sizes with different materials can be formed using Multi stage hot forging processes. In previous times, forging process in multi stage was designed on basis of experience gained in the previous forging practices. Nowadays, many software packages based on FE (finite elements) and FV (finite volumes) method are developed. This enables creation of forging process in more effective and accurate condition. The paper insight is given in the design of multi stage hot forging process for a critical geometry of Socket Forging in a multi-step forging process. The main criterion is to minimize the number of forging stages, proper filling and stressing of the dies by analysing the contact pressure. The Theoretical derivation & Numerical Simulation results are verified with practical, industrial environment.

Building Block Synthesis of Self-Supported Three-Dimensional Compliant Elements for Metallic Additive Manufacturing

Abstract Compliant mechanisms gain motion through the elastic deformation of the monolithic flexible elements. The geometric design freedom of metallic additive manufacturing enables the fabrication of complex and three-dimensional (3D) compliant elements within mechanisms previously too complicated to produce. However, the design of metallic additive manufactured mechanisms faces various challenges of manufacturing restrictions, such as avoiding critical overhanging geometries and minimizing the amount of support structure, which has been reported in a few cases. This paper presents a synthesis approach for translational compliant elements, involving building blocks based on leaf-type springs and covering building orientations between 0 deg and 90 deg. In particular, this range is approached by the synthesis of self-supported 3D building blocks with orientations of 0 deg, 45 deg and 90 deg. The compliant elements are built based on linear and circular plane curves and compared numerically according to their mechanical performance to create preferable building blocks. The applicability of the presented procedure and the manufacturability of the compliant mechanisms are proven by printing individual 3D building blocks and their serial aggregation with laser-based powder bed fusion. Consequently, several prototypes are demonstrated, including a bistable switch mechanism and a large displaceable rotational spring joint. In addition, a small-scale highly maneuverable segment of a surgical instrument with a grasping mechanism at the distal end is proposed.

Nondipole effects in laser-assisted electron scattering

Laser-assisted electron scattering is often described using the electric dipole approximation for the interaction between the electron and the assisting electromagnetic field. Within the dipole approximation, theory predicts a vanishing scattering cross section for processes involving exchange of photons in critical geometries, where the electron momentum transfer vector is perpendicular to the linear polarisation of the external field. In a nonrelativistic spin-free treatment, we consider modifications of the scattering cross section by nondipole contributions to the first order in 1/c in the interaction between the laser field and the electron using the nondipole strong-field-approximation Hamiltonian (Jensen et al 2020 Phys. Rev. A 101 043408). The approach allows for an analytical solution for the wave function of a free electron in the laser field with a nondipole contribution. This wave function leads to an analytical formula for the laser-assisted scattering cross section including nondipole effects. The nondipole corrections depend on the propagation direction of the field relative to the electron momentum transfer vector. The approach gives a finite cross section in scattering geometries, where the dipole approach predicts a vanishing cross section. The theory is illustrated by application to scattering geometries similar to those considered in experiments where large deviations between experimental data and predictions based on the dipole approximation have been reported. In these scattering geometries, the nondipole strong-field-approximation approach suggests an increase in the cross section by orders of magnitude compared to results obtained within the dipole approximation.

Theoretical study of cyclohexadiene/hexatriene photochemical interconversion using spin-Flip time-Dependent density functional theory

The photochemical interconversion between 1,3-cyclohexadiene (CHD) and all-cis-hexatriene (cZc-HT) is reinvestigated using spin-flip time-dependent density functional theory in combination with various hybrid functionals, BHHLYP functional showing the best performance. The critical geometries of the ground, S, and the first two excited-state, S and S, potential energy surfaces, such as, various minima, transition state, minimum-energy crossing points between S/S and S/S show an excellent agreement with those obtained by multireference wave function methods. Our results show how a low-cost method based on DFT can successfully describe and characterise the most important geometries on the potential energy surfaces along the ring-opening/closure reaction coordinate involved in the CHD to cZc-HT photoconversion.

An experimental model for pressure drop evaluation in a stenosed coronary artery

Non-invasive measurement of pressure drop has great clinical significance for the treatment of coronary artery diseases. The objective of this study is to develop a relationship that can estimate pressure drop in a stenosed coronary artery model as a function of different parameters such as blood viscosity, artery length and diameter, flow rate and flow profile, and shape and degrees of stenosis. Experimental pressure measurements from a wide range of degrees of stenosis and critical simplified geometries of stenosis along with different unsteady flow profiles are employed to evaluate the pressure drop equation. To calculate the blockage term of the pressure drop, several experimental cases are investigated, and the results show that the blockage factor is strongly dependent on the shape and degree of stenosis. Furthermore, different unsteady flow profiles are applied to calculate the pulsatile pressure drop term, and it is found that the pulsatility parameter is not a function of the flow profile or the shape of the stenosis. However, it is only a function of the degree of stenosis. To test the validity of the developed equation, pressure drops through stenosed coronary artery models with the real physiological flow profile of the left and right coronary arteries were predicted and compared with the experimental measurements. The proposed equation is able to determine the pressure drop inside a stenosed coronary artery non-invasively using the measurement of the flow profile inside the artery as well as the images of the stenosed coronary artery obtained based on the non-invasive methods.

Raft foundations design charts: development and applications

Presented in this paper design charts for estimating effective depth of raft slabs on elastic foundation are developed in compliance with punching shear design procedures provided by Russian Design Code (SP) for reinforced concrete. Codes’ formulas are generalized to include only independent parameters omitting unnecessary calculations of critical section geometry. Proposed approach considers raft slab effective depth as a function of cross section sizes of vertical members (walls, columns) only. In the conclusion reasonable range of raft slab thickness to column sizes ratios have been established for numerical tests and experiments included in fundamental studies of moderately thick plates and raft slabs resting on elastic foundations.

Umicore gains Hazari pre-catalysts

The Jiangnan Orogen, located between the Yangtze and Cathaysia Blocks in southern China, hosts significant gold and antimony resources. Long-standing controversies over the number and precise timing of gold, gold-antimony and antimony mineralization event(s), and the genesis of these deposits, limit the understanding and exploration of this giant gold and antimony system. Together with geological evidence, a critical review of the published geochronological data of these deposits suggest that there were two gold events in the Triassic (~235 Ma) and Early Cretaceous (~142–130 Ma), two gold-antimony events in the Early Devonian (~402 Ma) and Late Triassic-Middle Jurassic (~224–163 Ma: possibly equivalent to the two gold events), and one antimony event in the Early Cretaceous (~130 Ma). There are other possible gold events in the Neoproterozoic or at an even older age, and Ordovician to Early Devonian, which are constrained only by limited geological evidence and a few non-robust isotopic ages. The regional distribution of the gold, gold-antimony and antimony districts, and deposits therein, reveal a first-order control on the mineralization by crustal scale faults which acted as ore-forming fluid pathways connected to deep fluid and metal source areas. Second- and third-order faults that are situated along the jogs of the first-order faults, especially fault corridors defined by NNE-NE-trending second-order faults and third-order NW to E-W-trending discontinuous oblique faults, provided favorable locations for Pre-Cretaceous gold-(antimony) mineralization. In addition, NE-trending open anticlines, linked to deep crustal levels by first-order faults, host significant antimony and minor gold mineralization, and the curvilinear Fanjingshan detachment Fault hosts some gold and antimony deposits. Locally, at deposit to orebody-scales, pre-ore barren quartz veins and magmatic dikes were the loci for mineralization in some gold-antimony deposits. The structural geometry of the pre-Cretaceous gold and gold-antimony deposits suggests an Early Devonian orogenic gold-antimony mineralization event during a transpressional tectonic regime related to coeval intracontinental orogeny between the Yangtze and Cathaysian Blocks. In contrast, Triassic orogenic gold and Triassic-Middle Jurassic orogenic gold-antimony events are interpreted to relate to distal effects of the collision between the North and South China blocks. The structurally-contrasting major Early Cretaceous epizonal antimony mineralization event, together with contemporaneous hydrothermal gold mineralization, is interpreted to have been controlled by normal faults and pre-ore open folds in an extensional tectonic regime related to the distal effects of rollback of the paleo-Pacific Plate after ~135 Ma. For future geoscience-based exploration in the Orogen, documentation and interpretation of critical structural geometries of gold, gold-antimony and antimony deposits is a vital step towards successful target generation.

Effect of advance drainage on tunnel face stability using Limit Analysis and numerical simulations

Positive pore water pressures ahead of tunnels constructed under the water table influence the stability of the tunnel face, and they may considerably affect the safety of tunneling operations. Advance drainage is often necessary, since traditional support measures may be insufficient to provide the required face support pressures. This work presents an Upper Bound Solution, in the framework of Limit Analysis, to assess the stability of a tunnel face considering the influence of advance drainage boreholes in two different arrangements, upper and lower. Results of the proposed Limit Analysis approach are compared with the results of a numerical model in FLAC3D for a tunnel with a D=10m diameter, demonstrating that the critical pressures and failure geometries computed with the analytical solution correctly reproduce the FLAC3D results when the height of the water table above the tunnel crown is lower than 5 tunnel diameters. Similarly, our results are compared with the results of a similar face stability analysis conducted with a Limit Equilibrium mechanism, suggesting that the Limit Analysis approach gives lower collapse pressure values, with relative differences of up to 30% (mainly depending on the water level and on the drainage configuration), and with results that generally agree better with the numerical simulation results. Finally, the influence of the borehole layout at the tunnel face is analyzed considering different water table positions. Results confirm that the water level has a significant influence on face stability (both on critical pressure values and on failure geometries), that the advance drainage considered significantly reduces the support pressure required for stability, and that the advance drainage configuration can also affect the shape of the critical failure mechanism.