Contraction Coefficient Research Articles

Development of correlation model for cavitating spray using Eulerian simulations

Modern high-pressure injection systems for heavy-duty applications are prone to cavitation, which may have a detrimental effect on the system integrity. The present study aims to develop reliable correlations for Lagrangian engineering simulations to predict the onset of cavitation. Using the extensive data generated from the high-fidelity Eulerian volume-of-fluid (VOF) simulations of a single-hole injector for a wide range of operating conditions, a proper set of discharge ( Cd) and contraction ( Ca) coefficients are determined. In particular, four significant factors characterizing nozzle geometry are considered: the K factor, inlet curvature radius, nozzle exit radius, and channel length, as well as ambient and injection pressures. The results showed that a larger K factor and inlet curvature radius yielded higher Cd and Ca values, while the exit radius and channel length had a less significant impact on the cavitation dynamics. The smaller pressure difference between the nozzle inlet and exit mitigated the cavitation formation. These trends were well described using the mathematical regression model. Furthermore, two other correlation models based on the regression learner and artificial neural network methods were also developed. Of these three models, the mathematical regression model yielded the best agreement with an external validation dataset.

Mathematical and numerical modelling of rapid transients at partially lifted sluice gates

In the present paper, we study the mathematical and numerical modelling of rapid transients at partially lifted sluice gates in the context of one-dimensional Shallow water Equations. First, improved exact solutions of the dam-break problem with partially lifted gate are presented, assuming (i) the dependence of the gate contraction coefficient on the upstream flow depth, and (ii) a viable definition of the submerged flow equation. We show that an exact dam-break solution always exists for any set of initial conditions, but there are also initial conditions for which the solution is multiple. To cope with this case, a novel disambiguation criterion based on the continuous dependence of the solution on the initial conditions is used to select the physically congruent choice amongst the alternatives. Finally, we present a one-dimensional Finite Volume numerical model for the approximate solution of the Shallow water Equations equipped with an approximate Riemann solver for the sluice gate treatment at cells interfaces. The numerical experiments show that the embedding of the steady state gate equations (equilibrium approach) into the approximate Riemann solver leads to unsatisfactory dam-break simulations, while a novel relaxed version of the gate equations (non-equilibrium approach) supplies results that are in agreement with both the novel exact solutions and the laboratory dam-break results available from the literature.

Empirical and instance‐dependent estimation of Markov chain and mixing time

AbstractWe address the problem of estimating the mixing time of a Markov chain from a single trajectory of observations. Unlike most previous works which employed Hilbert space methods to estimate spectral gaps, we opt for an approach based on contraction with respect to total variation. Specifically, we estimate the contraction coefficient introduced in Wolfer (2020), inspired from Dobrushin's. This quantity, unlike the spectral gap, controls the mixing time up to strong universal constants and remains applicable to nonreversible chains. We improve existing fully data‐dependent confidence intervals around this contraction coefficient, which are both easier to compute and thinner than spectral counterparts. Furthermore, we introduce a novel analysis beyond the worst‐case scenario by leveraging additional information about the transition matrix. This allows us to derive instance‐dependent rates for estimating the matrix with respect to the induced uniform norm, and some of its mixing properties.

On the Efficiency of the Density Functional Theory (DFT)-Based Computational Protocol for 1H and 13C Nuclear Magnetic Resonance (NMR) Chemical Shifts of Natural Products: Studying the Accuracy of the pecS-n (n = 1, 2) Basis Sets.

The basis set issue has always been one of the most important factors of accuracy in the quantum chemical calculations of NMR chemical shifts. In a previous paper, we developed new pecS-n (n = 1, 2) basis sets purposed for the calculations of the NMR chemical shifts of the nuclei of the most popular NMR-active isotopes of 1-2 row elements and successfully approbated these on the DFT calculations of chemical shifts in a limited series of small molecules. In this paper, we demonstrate the performance of the pecS-n (n = 1, 2) basis sets on the calculations of as much as 713 1H and 767 13C chemical shifts of 23 biologically active natural products with complicated stereochemical structures, carried out using the GIAO-DFT(PBE0) approach. We also proposed new alternative contraction schemes for our basis sets characterized by less contraction depth of the p-shell. New contraction coefficients have been optimized with the property-energy consistent (PEC) method. The accuracies of the pecS-n (n = 1, 2) basis sets of both the original and newly contracted forms were assessed on massive benchmark calculations of proton and carbon chemical shifts of a vast variety of natural products. It was found that less contracted pecS-n (n = 1, 2) basis sets provide no noticeable improvement in accuracy. These calculations represent the most austere test of our basis sets as applied to routine calculations of the NMR chemical shifts of real-life compounds.

Use Of Mining Tailings in The Manufacture of Ecological Bricks to Encourage the Construction of Sustainable Housing

This work aimed to manufacture ecological bricks using mining tailings, by-products of mining activity, to contribute to sustainable housing development. The Peruvian technical standards E.060 and E.070 are used as a reference framework to achieve this. The study focuses on various aspects, such as mineralogical analysis, particle size distribution, plasticization, workability, and rheology. The research methodology adopted is deductive, with an applied and quantitative approach. A retrolective data collection instrument and descriptive, explanatory, correlational, and descriptive level approaches are used. The results obtained from this research reveal significant findings. It was observed that including 20% of an alkaline binder based on calcined clay improves the development of bricks in areas with severe climatic conditions. In addition, incorporating lime fibers reduces thermal conductivity and increases bricks' compressive and bending strength. Blocks containing 30% clay cork reinforce the bricks' bulk density, thermal conductivity, and strength. On the other hand, it was verified that tailings with lead-zinc sulfide, reduced by 47%, comply with the carbonization and contraction coefficient. Shale, fly ash, and cement tailings achieved a compressive strength of 26 MPa and a water absorption rate of 14.32%. The addition of steel filings by 3% improves compressive strength. Likewise, incorporating plastic waste increases the compressive strength to reach 37.5 MPa. As for geopolymers, it was observed that viscosity recovery is in a range between 65% and 82%. Finally, recycled aggregates, with a maximum nominal size of 3/8" and 1/4", meet the standard requirements, providing a compressive strength of up to 8 MPa. Finally, this study demonstrates the potential of using mining tailings and other recycled materials to manufacture ecological bricks for sustainable housing development in mining communities, offering viable solutions from an environmental and construction point of view.

Simulating hyperelastic materials with anisotropic stiffness models in a particle-based framework

We present a particle-based smoothed particle hydrodynamics (SPH) framework for simulating hyperelastic materials with anisotropic stiffness models. While most elastic simulations predominantly rely on mesh-based approaches, such as the Finite Element method, the relationship between Lamé’s first parameter and Poisson’s ratio complicates the strict enforcement of volume conservation, making it challenging to stabilize simulations for common biological tissues like fat and muscle. In this paper, we couple an implicit divergence-free SPH solver with particle-based deformation gradient computation and apply various elastic energy functions to achieve incompressible elastic simulations. The incompressibility of elastic objects and collisions between different bodies are managed by the implicit SPH algorithm. We further incorporate anisotropic energy functions, constructed from the extrapolation of Cauchy–Green invariants, to introduce anisotropic properties to the objects. By integrating activation and contraction coefficients into the energy functions, particles can simulate muscle contractions and lift heavy objects. Our method can effectively represent elastic objects with varying mechanical properties across different directions and be further employed to mimic muscle contractions. Experiments demonstrate that our approach provides realistic simulations for a wide range of animal and human body movements.

Analysis of the flow phenomenon of fluid undergoing a sudden contraction to an annular gap

The paper presents the visualization results of the sudden contraction flow field with an annular gap downstream of the contraction cross section. The contraction ratio directly influences the flow phenomena. No stationary vortices were observed upstream of the contraction cross section, and flow separation divided the flow field within the annular gap into a recirculation zone, a shear layer, and a mainstream zone. Vena-contracta point and reattachment point occurred within the flow field of the annular gap. The production of Reynolds stress varied with the contraction ratio, and the momentum exchange mainly occurred in the recirculation zone and the shear layer, while the flow state in the mainstream zone tended to become isotropic. Rapid changes in turbulent kinetic energy primarily occurred in the shear layer, and the production term of turbulent kinetic energy contributed the most. Applying computational fluid dynamics and experimental results, this study has formulated an expression for the contraction coefficient of the proposed model. The axial positions of the vena-contracta point and reattachment point have a strong correlation with the contraction ratio, which can be represented by an exponential function.

On the delineation of the flow separation zone in open-channel confluences

In the context of a T-shaped open-channel confluence, where the tributary flow separates at the downstream junction edge and creates a separation zone in the post-confluence channel, this paper provides a critical reflection upon the terminology and the delineation methods for the separation zone and its proxies: the recirculation zone and the reverse flow zone. Following the fluid-mechanical literature on flow separation, the separation zone is delineated by a dividing surface formed by the three-dimensional (3D) streamlines separating from the downstream junction edge. Based on a dense 3D time-averaged velocity field obtained from a Large-Eddy Simulation of a lab-style confluence flow, the separation zone turns out to be open. Near the bed, the dividing surface exhibits a gap, through which mainly tributary fluid enters the separation zone, leading to a limited discharge flowing through that zone. Downstream of the section where the merging flows are the most contracted, the dividing surface does not reattach to the inner bank, prohibiting the determination of a maximum length of the separation zone. Downstream of that section, the dividing surface gradually loses its role as a skeleton for the separation zone shear layer. Due to mixing, the separation zone and the adjacent maximum velocity zone gradually dissolve and transform into the flow recovery zone, as in a wake. By means of flow visualization with 3D streamlines, revealing different types of recirculating motions, the maximum recirculation zone extent is determined. Then three simplified methods commonly used in the literature to quantify the dimensions of the separation zone or its proxies are evaluated by comparison with the 3D streamline method. By adopting various simplifying assumptions about the flow, the pseudo-streamline method, the zero-unit-discharge method and the zero-velocity method yield definite reasonable maximum lengths for the recirculation zone and the reverse flow zone. With the exception of the zero-velocity method, all simplified methods yield reasonable estimates for the maximum widths and the corresponding contraction coefficients of the separation zone proxies. Still, contrary to the simplified methods, only the 3D streamline method can provide physical insight into the flow features occurring in the separation zone or its proxies.

Self-Vibration of Liquid Crystal Elastomer Strings under Steady Illumination.

Self-vibrating systems based on active materials have been widely developed, but most of the existing self-oscillating systems are complex and difficult to control. To fulfill the requirements of different functions and applications, it is necessary to construct more self-vibrating systems that are easy to control, simple in material preparation and fast in response. This paper proposes a liquid crystal elastomer (LCE) string-mass structure capable of continuous vibration under steady illumination. Based on the linear elastic model and the dynamic LCE model, the dynamic governing equations of the LCE string-mass system are established. Through numerical calculation, two regimes of the LCE string-mass system, namely the static regime and the self-vibration regime, are obtained. In addition, the light intensity, contraction coefficient and elastic coefficient of the LCE can increase the amplitude and frequency of the self-vibration, while the damping coefficient suppresses the self-oscillation. The LCE string--mass system proposed in this paper has the advantages of simple structure, easy control and customizable size, which has a wide application prospect in the fields of energy harvesting, autonomous robots, bionic instruments and medical equipment.

Ternary Implicit Criterion for Robust Exponential Stability of Perturbed Stochastic BAM Systems

This brief presents the sufficient criterion to guarantee the robust exponential stability (RES) of perturbed stochastic nonlinear bidirectional associative memory system with derivative contraction coefficients and piecewise constant arguments (SDPNBAM system). Different from the method of solving multiple transcendental equations, the upper bounds of derivative contraction coefficients, stochastic disturbances and piecewise constant arguments are parsed by the same well-defined ternary transcendental equation and characterized by a feasible geometrical enclosed space, formulating the main ternary implicit criterion. Accordingly, the dynamical interconnection among perturbed ternary variables constrained in the same transcendental equation is formed and to moderate the SDPNBAM system to be stable ultimately. Finally, the numerical simulation shows the effectiveness of main results.

Hydraulic characteristics of a sluice gate over a broad-crested weir

Vertical sluice gates are commonly used to control and measure flow in irrigation and drainage networks. To reduce their size and associated maintenance and operation costs, they are sometimes installed above broad-crested weirs. To explore the effects of the installation location of the sluice gate and the sill height on the hydrodynamic characteristics of the flow passing through the sluice-gated weir, six laboratory models were tested. The 427 and 449 data points included both free- and submerged-flow conditions, respectively. Analytical relationships were developed for the contraction, head-loss, and Henry's (1950) discharge coefficients. Based on the maximization of the discharge and contraction coefficients and the minimization of the head-loss coefficient, results suggest that a gate should be installed at a distance of L/2 (where L is the sill length) from the upstream end of the weir crest, and the height of 1.25Hd (where Hd is the water depth as referenced from the weir sill elevation) is the optimal height for the weir. By conducting experiments and constructing correlations for determining the contraction and head-loss coefficients under free flow conditions, the average values of these coefficients for the laboratory models were obtained as 0.664 and 0.133, respectively. Applying the average contraction and head-loss coefficients to the developed relationship for estimating the free and submerged discharge coefficients resulted in an error of 4% and 6%, respectively. WinGate alpha 0.2 software was used to estimate the experimental free and submerged discharge coefficient of the gated weir with an average error of 5.4% and 12.7%, respectively. It was done without any consideration of the cross-section shape of the weir or the location of the gate on the weir sill. In addition, an inspection of the submergence threshold of the gated weir showed an increase in the submergence threshold when the gate was moved further downstream from the upstream end of the sill.

Light-Fueled Synchronization of Two Coupled Liquid Crystal Elastomer Self-Oscillators.

The synchronization and group behaviors of self-excited coupled oscillators are common in nature and deserve to be explored, for self-excited motions have the advantages of actively collecting energy from the environment, being autonomous, making equipment portable, and so on. Based on light-powered self-excited oscillators composed of liquid crystal elastomer (LCE) bars, the synchronization of two self-excited coupled oscillators is theoretically studied. Numerical calculations show that self-excited oscillations of the system have two synchronization modes, in-phase mode and anti-phase mode, which are mainly determined by their interaction. The time histories of various quantities are calculated to elucidate the mechanism of self-excited oscillation and synchronization. For strong interactions, the system always develops into in-phase synchronization mode, while for weak interaction, the system will evolve into anti-phase synchronization mode. Furthermore, the effects of initial conditions, contraction coefficient, light intensity, and damping coefficient on the two synchronization modes of the self-excited oscillation are investigated extensively. The initial condition generally does not affect the synchronization mode and its amplitude. The amplitude of self-oscillation always increases with increasing contraction coefficient, gravitational acceleration, and light intensity, while it decreases with the increasing damping coefficient. This work will deepen people's understanding of the synchronization behaviors of self-excited coupled oscillators, and the theoretical framework could be extended to scenarios involving large-scale synchronization of the systems with numerous interacting oscillators.

Stiffness sensing by smooth muscle cells: Continuum mechanics modeling of the acto-myosin role

Aortic smooth muscle cells (SMCs) play a vital role in maintaining homeostasis in the aorta by sensing and responding to mechanical stimuli. However, the mechanisms that underlie the ability of SMCs to sense and respond to stiffness change in their environment are still partially unclear. In this study, we focus on the role of acto-myosin contractility in stiffness sensing and introduce a novel continuum mechanics approach based on the principles of thermal strains. Each stress fiber satisfies a universal stress-strain relationship driven by a Young's modulus, a contraction coefficient scaling the fictitious thermal strain, a maximum contraction stress and a softening parameter describing the sliding effects between actin and myosin filaments. To account for the inherent variability of cellular responses, large populations of SMCs are modeled with the finite-element method, each cell having a random number and a random arrangement of stress fibers. Moreover, the level of myosin activation in each stress fiber satisfies a Weibull probability density function. Model predictions are compared to traction force measurements on different SMC lineages. It is demonstrated that the model not only predicts well the effects of substrate stiffness on cellular traction, but it can also successfully approximate the statistical variations of cellular tractions induced by intercellular variability. Finally, stresses in the nuclear envelope and in the nucleus are computed with the model, showing that the variations of cytoskeletal forces induced by substrate stiffness directly induce deformations of the nucleus which can potentially alter gene expression. The predictability of the model combined to its relative simplicity are promising assets for further investigation of stiffness sensing in 3D environments. Eventually, this could contribute to decipher the effects of mechanosensitivity impairment, which are known to be at the root of aortic aneurysms.

Energy loss and contraction coefficients-based vertical sluice gate's discharge coefficient under submerged flow using symbolic regression.

Accurate calculation of discharge is a critical taskin terms of environmental and operational regulations. In the current study, a new approach for determining vertical sluice gates' flow discharge with a minor bias is proposed. Energy-momentum equations are used to characterize the physical expression of the phenomena intended for generation of the coefficient of discharge. The coefficient of discharge is then expressed according to coefficients of energy loss and contraction. Following that, the coefficient of discharge, coefficient of contraction, and coefficient of energy loss are calculated using an optimization approach. Then, dimensional analysis is conducted and regression equations for quantifying the coefficient of energy loss is produced using symbolic regression method. The derived contraction coefficient and energy loss coefficient formulas are accordingly utilized to compute the coefficient of discharge in the vertical sluice gate and also to determine flow discharge. For computing discharge, five different scenarios are considered. The developed approaches' performance is examined against selected benchmarks from the literature. The results show that the symbolic regression method can compute discharge more accurate than its alternatives.

Laboratory investigation of solid wastes combined with tunnel slag in cement stabilized base of asphalt pavement

To coordinate the disposal and resource utilization of bulk solid waste iron ore tailings sand (IOTS) and hazardous solid waste phosphogypsum (PG), this paper has carried out the research of using the two and the tunnel slag in the pavement base, including unconfined compressive strength, splitting strength, compressive resilience modulus, frost resistance, temperature shrinkage, and dry shrinkage tests. According to the characteristics of phosphogypsum (PG), the water stability, delayed compaction, and leaching of toxic substances were studied, and the mechanism was analyzed by SEM and XRD. It is concluded that tunnel slag and IOTS are great filling materials; The inclusion of PG inhibited the hydration of cement, which results in the reduction of unconfined compressive strength and splitting strength in the early stage, and the higher mean coefficient of thermal contraction; When the content of PG did not exceed 6%, the frost resistance, water stability, and drying shrinkage coefficient performed well, and the delayed forming strength had almost no loss, providing support for the continuous construction technology of the road base and the inhibition of reflective cracks. Applying a large number of solid wastes to road engineering can not only efficiently handle various waste buildup problems but also produce a new form of road materials with important social, economic, and environmental benefits.

Adaptive basis sets for practical quantum computing

AbstractElectronic structure calculations on small systems such as H2, H2O, LiH, and BeH2 with chemical accuracy are still a challenge for the current generation of noisy intermediate‐scale quantum (NISQ) devices. One of the reasons is that due to the device limitations, only minimal basis sets are commonly applied in quantum chemical calculations, which allows one to keep the number of qubits employed in the calculations at a minimum. However, the use of minimal basis sets leads to very large errors in the computed molecular energies as well as potential energy surface shapes. One way to increase the accuracy of electronic structure calculations is through the development of small basis sets better suited for quantum computing. In this work, we show that the use of adaptive basis sets, in which exponents and contraction coefficients depend on molecular structure, provides an easy way to dramatically improve the accuracy of quantum chemical calculations without the need to increase the basis set size and thus the number of qubits utilized in quantum circuits. As a proof of principle, we optimize an adaptive minimal basis set for quantum computing calculations on an H2 molecule, in which exponents and contraction coefficients depend on the HH distance, and apply it to the generation of H2 potential energy surface on IBM‐Q quantum devices. The adaptive minimal basis set reaches the accuracy of the double‐zeta basis sets, thus allowing one to perform double‐zeta quality calculations on quantum devices without the need to utilize twice as many qubits in simulations. This approach can be extended to other molecular systems and larger basis sets in a straightforward manner.

Characterization of styrene-butadiene-styrene (SBS)-modified asphalt binders using the bending beam rheometer and the asphalt binder cracking device

The addition of styrene butadiene styrene (SBS) to asphalt binders has led to enhanced performance in pavements across the entire range of working temperatures. SBS-modified binders have also proven to be more difficult to characterize in terms of their rheological properties. Low-temperature properties of asphalt binders are typically evaluated using the bending beam rheometer (BBR), which was developed to measure creep stiffness. Recent refinements to the BBR analysis have led to the development of Δ Tc which is meant to provide more insight into the relaxation properties of the binder. The Asphalt Binder Cracking Device (ABCD) was developed to improve on this characterization by also taking into consideration the failure strength and coefficient of thermal contraction. Previous research has shown that the ABCD provides more valuable insight into the effect of SBS on the low-temperature properties of asphalt binders. This paper will evaluate the ability of these two low-temperature tests to characterize the performance of five different asphalt binders with increasing concentrations of SBS. It was found that the evaluation of the materials using Δ Tc was inconsistent with binder type and generally indicated that SBS reduced cracking resistance, while the ABCD critical temperature and the proposed Δ Tf parameter generally showed an improved correlation with SBS concentration.

BSSE-corrected consistent Gaussian basis sets of triple-zeta valence quality of the lanthanides La-Lu for solid-state calculations.

Consistent basis sets of triple-zeta valence quality for the elements La-Lu were derived for periodic quantum-chemical solid-state calculations. They are an extension of the pob-TZVP-rev2 [D. Vilela Oliveira, et al., J. Comput. Chem. 2019, 40(27), 2364-2376], [J. Laun and T. Bredow, J. Comput. Chem. 2021, 42(15), 1064-1072], [J. Laun and T. Bredow, J. Comput. Chem. 2022, 43(12), 839-846] basis sets and are based on the fully relativistic effective core potentials of the Stuttgart/Cologne group and on the def2-TZVP valence basis of the Ahlrichs group. The basis sets are constructed to minimize the basis set superposition error in crystalline systems. The contraction scheme, orbital exponents, and contraction coefficients were optimized in order to ensure robust and stable self-consistent-field convergence for a set of compounds and metals. For the applied PW1PW hybrid functional, the average deviations of the calculated lattice constants from experimental references are smaller with pob-TZV-rev2 than with standard basis sets available from the CRYSTAL basis set database. After augmentation with single diffuse s- and p-functions, reference plane-wave band structures of metals can be accurately reproduced.

Flow under vertical sluice gates: Flow stability at large gate opening and disambiguation of partial dam-break multiple solutions

The present paper deals with two open issues concerning the free orifice flow under vertical sluice gates, namely, the flow stability at large gate openings and the disambiguation of multiple solutions in the case of partial dam-break. The study of these problems, which are mutually connected, is based on ad hoc laboratory experiments and numerical simulations with a computational fluid dynamics model tracking the free surface with the two-phase volume of fluid method. A series of quasi-steady states is used to assess the threshold of relative gate openings that determines the passage from orifice flow to non-interacting flow; in addition, a set of dam-break experiments with partial gate opening (i.e., lower than the initial upstream water level) is performed to find reliable criteria to disambiguate multiple exact solutions supplied by the one-dimensional shallow water theory. It is found that the dependence of contraction and discharge coefficients on the relative gate opening has a dramatic impact on the stability of orifice flow at large gate openings.

New efficient pecS-n (n = 1, 2) basis sets for quantum chemical calculations of 31P NMR chemical shifts.

The basis sets that are used in the quantum chemical calculations of 31P NMR chemical shifts have always been one of the most important factors of accuracy. Regardless of what high-quality approach is employed, using basis sets of insufficient flexibility in the important angular regions may give poor results and lead to misassignments of the signals in the 31P NMR spectra. In this work, it was found that the existing nonrelativistic basis sets for phosphorus atom of double- and triple-ζ quality, specialized for the 31P NMR chemical shifts calculations, are essentially undersaturated in the d-angular space that occurred to play a significant role in the overall accuracy of these calculations. This problem has been thoroughly investigated, and new pecS-n (n = 1, 2) basis sets for phosphorus chemical shifts calculations were proposed. The exponents and contraction coefficients for the pecS-n basis sets were generated with the property-energy consistent method that has been introduced in our earlier paper, and has been proven useful in the creation of efficient property-oriented basis sets. New basis sets were optimized using the GIAO-DFT method with the B97-2 functional. Extensive benchmark calculations showed that the pecS-1 and pecS-2 basis sets provide very good accuracy, characterized by the corrected mean absolute percentage errors against the experiment of about 7.03 and 4.42 ppm, respectively. In particular, the accuracy of 31P NMR chemical shifts calculations achieved with the pecS-2 basis set is one of the most favorable accuracies for today. We believe that our new pecS-n (n = 1, 2) basis sets for phosphorus atom will prove useful in modern large-scale quantum chemical calculations of 31P NMR chemical shifts.