Critical Conditions For Transition Research Articles

Coacervate Formation in Dilute Aqueous Solutions of Inorganic Molecular Clusters with Simple Divalent Countercations.

We report a complex coacervate formed by a 2.5 nm-diameter, rigid uranyl peroxide molecular cluster (Li68K12(OH)20)[UO2(O2)OH]60, U6060-) and SrCl2 salt in dilute aqueous solutions, including its location in the phase diagram, composition, rheological features, and critical conditions for phase transitions. In this coacervate, the Sr2+ cations are a major building component, and the coacervate phase covers a substantial region of the phase diagram. This coacervate demonstrates features that differ from traditional coacervates formed by oppositely charged long-chain polyelectrolytes, especially in its formation mechanism, dehydration, enhancement of mechanical strength with increasing ionic strength, and the change of salt partition preference into the coacervate and supernatant phases with ionic strength.

Probabilistic activity driven model of temporal simplicial networks and its application on higher-order dynamics.

Network modeling characterizes the underlying principles of structural properties and is of vital significance for simulating dynamical processes in real world. However, bridging structure and dynamics is always challenging due to the multiple complexities in real systems. Here, through introducing the individual's activity rate and the possibility of group interaction, we propose a probabilistic activity-driven (PAD) model that could generate temporal higher-order networks with both power-law and high-clustering characteristics, which successfully links the two most critical structural features and a basic dynamical pattern in extensive complex systems. Surprisingly, the power-law exponents and the clustering coefficients of the aggregated PAD network could be tuned in a wide range by altering a set of model parameters. We further provide an approximation algorithm to select the proper parameters that can generate networks with given structural properties, the effectiveness of which is verified by fitting various real-world networks. Finally, we construct the co-evolution framework of the PAD model and higher-order contagion dynamics and derive the critical conditions for phase transition and bistable phenomenon using theoretical and numerical methods. Results show that tendency of participating in higher-order interactions can promote the emergence of bistability but delay the outbreak under heterogeneous activity rates. Our model provides a basic tool to reproduce complex structural properties and to study the widespread higher-order dynamics, which has great potential for applications across fields.

Gravity-coupled flutter and contact of a flag near a wall

The stability and postcritical behaviour of a horizontal flag undergoing gravity-induced deformation and periodic contact with a nearby horizontal rigid wall are experimentally investigated. The results elucidate the combined effects of gravity and contact on flutter, and reveal design principles for application to triboelectric energy harvesting. By varying the free-stream velocity, flag thickness and distance between the flagpole and the wall, the dynamics of the flag are classified into quasistatic equilibrium, flutter, partial contact and saturated contact modes. Considering the significance of gravitational effects, a new dimensionless flow velocity is proposed to identify the distribution of the dynamic modes, and its definition varies according to whether the wall is placed above or below the flag. The critical conditions for transitions between the dynamic modes are determined from the balance of fluid dynamic and gravitational effects. The distance from the flagpole to the wall is found to be more critical for transitions in the lower-wall configuration than in the upper-wall configuration. The peak contact force as well as the oscillation amplitude and frequency at postequilibrium exhibits remarkably different trends depending on the location of the wall. The peak contact force imposed on the wall by the fluttering flag weakens as the distance to the wall increases in the case of an upper wall, whereas it becomes stronger in the case of a lower wall.

Critical criterion for droplet breakup in a contractive microchannel

Predicting the critical transition condition for different behaviors of droplet flowing through a micro contraction is a classic academic issue, and there is currently a lack of a simple and universally applicable prediction formula. This article aims to construct critical transition conditions for different droplet behaviors through their characteristic time. In present work, the droplet behavior, including deformation and breakup, are observed in a locally contractive microchannel by a high-speed camera. By tracing the dynamic evolution of droplet interface, it is found that the essential differences between droplet deformation and breakup is whether the minimum neck width will be less than the critical value for the appearance of the irreversible collapse. Based on this, two characteristic times are proposed to describe the deformation and breakup processes, which well explain the trend of flow pattern transition lines. Two mathematical models are established for the two characteristic times, and the critical conditions for the transformation from deformation to breakup is derived from these models. The predicted results are in good agreement with the experimental results, indicating the applicability of the proposed method in this paper.

Perforation of carbon fiber reinforced plastic laminates struck transversely by hemispherical-nosed projectiles

This study focuses on perforation of carbon fiber reinforced plastic (CFRP) laminates struck transversely by hemispherical-nosed projectiles. Global deformation with local rupture failures for thin laminates and localized response failures for thick laminates are two common categories of the ballistic perforation of CFRP laminates. An analytical model is proposed considering these two failure modes and their transition conditions. The ballistic limit predicted for laminates in global deformation with a local rupture failure mode is given based on the energy dissipation method, and an ultimate perforation failure criterion is derived based on the bottom surface tensile fracture of the laminate. A critical transition condition of the two failure modes is obtained by combing the localized response failure model and Von Karman’s critical impact velocity concept. Model predictions agree with the experimental and numerical results regarding ballistic limits in a wide ratio range of laminate thickness H and hemispherical-nosed projectile diameter d.

Machinability of nickel-titanium shape memory alloys under dry and chilled air cutting conditions

Nickel-titanium (NiTi) shape memory alloys (SMAs) undergo phase transformation between austenitic and martensitic phases in response to applied thermal or mechanical stress, resulting in unique properties and applications. However, machinability often becomes challenging due to property and temperature sensitivity attributes. The use of chilled air to influence machinability in macro-milling was investigated in this study. Other than that, differential scanning calorimetry (DSC) was used to determine the temperature of phase transformation. The results showed that milling with chilled air and minimal lubrication significantly improved machining performance by reducing tool wear and burr formation. Moreover, surface quality has also improved significantly. A notable discovery is that the machining process can change the critical conditions for phase transition, enabling new performance capability of tuning material hysteresis.

Nonlinear Bloch dynamics and spin-wave generation in a Bose-Hubbard ladder subject to effective magnetic field.

The two-leg magnetic ladder is the simplest and ideal model to reflect the coupling effects of lattice and magnetic field. It is of great significance to study some novel phases, topological characteristics, and chiral characteristics in condensed matter physics. In particular, the left-right leg degree of freedom can be regarded as a pseudospin, and the two-leg magnetic ladder also provides an ideal platform for the study of spin dynamics. Here the ground state, Bloch oscillations (BOs), and spin dynamics of the interacting two-leg magnetic ladder subject to an external linear force are studied by using variational approach and numerical simulation. In the absence of the external linear force, the critical condition of transition between the zero-momentum state and plane-wave state is obtained analytically, and the physical mechanism of the ground-state transition is revealed. When the external linear force presents, the occurrence of BOs excites the spin dynamics, and we reveal the chiral BOs and the accompanied spin dynamics of the system in different ground states. In particular, we further study the influence of periodically modulated linear force on BOs and spin dynamics. The frequencies of the linear force corresponding to the resonances and pseudoresonances are obtained analytically, which result in rich nonlinear dynamics. In resonances, stable and strong BOs (with larger amplitude) are observed. In pseudoresonances, because the pseudoresonance frequencies are related to the initial momentum and phase of the wave packet, a dispersion effect takes place and strong diffusion of wave packet occurs. When the frequency is nonresonant, drift and weak dispersion of wave packet occur simultaneously with the wave-packet oscillation. In all cases, the wave-packet dynamics is accompanied with periodic but anharmonic pseudospin oscillation. The BOs and spin dynamics are effectively controlled by periodically modulating the linear force.

Flame propagation regimes and critical conditions for flame acceleration and detonation transition for hydrogen-air mixtures at cryogenic temperatures

A series of more than 100 experiments with hydrogen-air mixtures have been performed at cryogenic temperatures from 90 to 130 K and ambient pressure. A wide range of hydrogen concentrations from 8 to 60%H2 in a shock tube of 5-m long and 54 mm id was tested. Flame propagation regimes were investigated for all hydrogen compositions at three different blockage ratios 0, 30% and 60% as a function of initial temperature. Piezoelectric pressure sensors and InGaAs photo-diodes have been applied to monitor the flame and shock propagation velocity of the combustion process. More than 150 experiments at ambient pressure and temperature were conducted as the reference data for cryogenic experiments. The critical expansion ratio σ∗ for an effective flame acceleration to the speed of sound was experimentally found at cryogenic temperatures. The detonability criteria for smooth and obstructed channels were used to evaluate the detonation cell sizes at cryogenic temperatures as well. The main peculiarities of cryogenic combustion with respect to the safety assessment were that the maximum combustion pressure was several times higher and the run-up-distance to detonation was two times shorter compared to ambient temperature independent of lower chemical reactivity at cryogenic conditions.

Reversible transition from ferrofluid drop to spikes due to an approaching magnet

Remarkably, we experimentally evidenced normal field instability-driven reversible transition from ferrofluid droplet to spikes, when a sessile ferrofluid drop is exposed to a varying magnetic field gradient due to an approaching magnet, without flipping its direction of motion. We find the reversible transition is attributed to the critical magnetization of the ferrofluid and a characteristic wavelength that control normal-field instability. We extend the theory of magnetic instability by including non-uniformity in the magnetic field in all directions to predict the critical condition for transition, which is in good agreement with experiments. The spacing between spikes and spike height, and the number of spikes measured from experiments are in agreement with existing theory.

Investigation of conditions leading to critical transitions between abrasive belt wear modes for rail grinding

In abrasive belt rail grinding, understanding the abrasive belt wear mechanisms is important for improving grinding accuracy and abrasive belt service life. Taking a single ceramic grit in a stable grinding state as an example, this study investigated the critical transition conditions and recognition methods between the different wear modes. Based on the crack growth equation, the critical transition condition from abrasion to fracture was modeled by calculating the stress around the cracks hiding in the grit tip. The transition condition between fracture and pull-off was determined by comparing the external stress around the grit root and the bonding strength of the resin binder. These critical conditions were verified by single grit scratching experiments and the improved Sc wear map method.

Thermodynamic analysis and prediction on the wetting properties of pore array superhydrophobic laser-texturing surfaces

Superhydrophobic surfaces fabricated by laser irradiation on various materials have been reported recently to show excellent wetting properties. However, there are only limited works regarding the theoretical analysis and prediction of the wetting properties of different surface structures, especially the widely used pore array laser-texturing surfaces, whose fabrication process is simple and time-saving. Here we propose a two-dimensional thermodynamic structure model based on the actual pore array laser-texturing surfaces, and four wetting states are defined in our model. By minimizing the Gibbs free energy, equilibrium contact angle and contact angle hysteresis representing wetting properties are calculated, and the effects of defined parameters (intrinsic contact angle θY, pore space b, and pore depth H) on wetting properties are analyzed in detail to find out the critical transition conditions among different wetting states. Besides, actual pore array laser-texturing surfaces are fabricated for further validation, and the wetting properties in measurement are found to be in good agreement with those in prediction, indicating that our model is credible and can be used to guide the design of the pore array superhydrophobic laser-texturing surfaces.

Polarized and unpolarized phases of spin-orbit-coupled Bose-Einstein condensates in optical lattice

We investigate the phase transition of the Bose-Einstein condensates with equal-weight Rashba and Dresselhaus spin-orbit coupling trapped in one-dimensional optical lattice. Based on the variational and two-mode approximation, the critical condition for phase transition between polarized and unpolarized Bloch wave phase is obtained analytically for the first time, which explicitly reveals rich competitive relationship among spin-orbit coupling, optical lattice and atomic interactions in determining the phase transition of the system. It is shown that the change of the energy minima and the phase transition point by the optical lattice depends on the atomic interactions and spin-orbit coupling. Our results provide a theoretical evidence for deep understanding of the competition mechanism between the optical lattice and spin-orbit coupling for the ground state phase transition of spin-orbit-coupled Bose-Einstein condensates in optical lattice.

Prediction of the stratified type flow transition with the linear stability analysis in horizontal pipe

The critical transition conditions from the stratified smooth flow to the 2-D wave and K-H wave flow in a horizontal pipe are analyzed on the basis of the viscous linear stability analysis in consideration of the interfacial shear stress. By interpreting the available experimental data in water–air and water-carbon dioxide flow, it is found that the wavelength at the transition conditions is between the one specified at the neutral stability and the one at the maximum amplification factor. Based on this fact, the wavelength is then correlated with four dimensionless parameters. To further evaluate the feasibility of the correlation, the experiments on the liquid nitrogen-vaporous nitrogen horizontal flow are conducted. The calculated results agree reasonably well with the experimental data in this work and the water–air data available in the literature. Furthermore, the effects of the liquid viscosity and the surface tension on the transition condition are also briefly discussed.

Semi-obstructed splitting behaviors of droplet in an asymmetric microfluidic T-junction

Asymmetric droplet splitting is a common method to obtain micro-droplets of different sizes. The study of droplet asymmetric splitting behaviors is of great significance to the fields of biomedicine, energy, chemical industry and food engineering. In this paper, the control flow is introduced into a branch of the T-shaped microchannel to control the pressure distribution in the channel and precisely control the size of the daughter droplets. The method is simple to operate and is a preferred method for asymmetric microfluidic splitting. Existing studies have analyzed droplet splitting modes, critical conditions for flow pattern transitions, and splitting dynamics, but the theoretical prediction of droplet asymmetric splitting behaviors needs to be strengthened. Moreover, compared with tunnel splitting and obstructed splitting, which are more abundantly studied, neither semi-obstructed splitting as an intermediate state of tunnel splitting nor obstructed splitting is analyzed sufficiently. Therefore, a microfluidic T-junction chip is designed and fabricated, with which asymmetrical splitting behaviors of droplets with a tunnel in a microfluidic T-junction are investigated experimentally. The influence of flow rate regulation on the droplet splitting ratio is studied. And a theoretical model is also established to predict the splitting ratio. The results are concluded as follows: 1) the process of asymmetrical droplet splitting is divided into three stages i.e. early squeezing, late squeezing and rapid pinch-off stage. In the early stage of squeezing, the radius of curvature of the droplet neck is sizable, and the additional pressure of interfacial tension is minor. Compared with the additional pressure that hinders neck contraction, the upstream continuous phase driving force is dominant, and the width of the neck changes linearly with time; in the process of late squeezing, the upstream pressure driving effect is still greater than the hindering effect of the additional tension, and the neck width changes exponentially with time; However, in the rapid pinch-off stage, the interfacial tension pointing to the center of the cross section of droplet neck dominates the pinch-off stage. Then, the droplet neck shrinks sharply. 2) Adjusting the flow rate of the branch channel can effectively control the asymmetric splitting ratio of the droplets, and under the current semi-obstructed asymmetric splitting of the droplets, the regulation effect is less affected by the size of the mother droplet, but more affected by the capillary number. 3) The prediction model of droplet splitting ratio based on the pressure drop model can effectively predict the droplet splitting ratio.

Critical behavior of interfacial t-ZrO2 and other oxide features of zirconium alloy reaching critical transition condition

Transition of zirconium alloys during uniform corrosion is not expected but inevitable, since it accelerates the degradation of corrosion property. Up to now, proposed transition mechanisms have not clearly illustrated the critical behavior of interfacial t-ZrO2 and other oxide features under the critical transition condition. Therefore, study on the under-transition sample was carried out. Microscopically, the monoclinic stress increases after transition, strongly supporting the occurrence of transformation from t-ZrO2 to m-ZrO2. A sudden stress decrease in t-ZrO2 occurs in pre-transition region of the under-transition sample. This decrease might be attributed to formation of permeable paths which induce consumption of interfacial oxygen vacancies. This critical behavior possibly destabilizes the grown t-ZrO2 grains. And the post-transition regions will propagate after t-ZrO2 transformation. The transition region in the oxide consists of lateral cracks propagated transgranularly and large numbers of interconnected pores, both of which may originate from t-ZrO2 transformation. Current works suggest that three critical behaviors of t-ZrO2 induce oxide fracture and corrosion transition. The growth nature and evolution mechanism of t-ZrO2 are further illustrated. Even though t-ZrO2 layer similarly evolve as the ZrO suboxide layer, the unstable nature of t-ZrO2 indicates that it is severely affected by grain size, stress value and chemical composition.

Experimental study of bubble dynamics and flow transition recognition in a fluidized bed with wet particles

This paper studies the bubble dynamics and flow transition behavior in wet particle systems. Non-coherent algorithm was used to quantitatively calculate the bubble diameters in a three-dimensional fluidized bed system loaded with wet particles, obtaining the bubble dynamics under the action of liquid. The results indicate that the incoherent analysis can detect the formation of even tiny bubbles in the fluidized bed. The kurtosis and skewness of the pressure fluctuation signal was used to obtain the critical transition conditions of the flow pattern from turbulent to laminar. Through the decay index of the incoherent spectrum, the operating conditions of the Levy-Kolmogorov flow pattern to the Kolmogorov flow region were determined. From the comparison of the liquid bridge and the drag forces, the competitive mechanism of different forces acting on the particles that conformed the bed was analyzed, reflecting the change of the apparent minimum fluidization velocity of wet particles.

Dynamics and phase transitions in biased ladder systems with magnetic flux

The ground states and the dynamics of a biased two-leg flux ladder in the presence of a gravitational field are discussed. In the absence of the gravitational field, the ground states and the critical condition of phase transition are obtained analytically. We identify the Meissner phase, Vortex phase, and interestingly, two new Plane Wave phases, that break both Z2 and time-reversal symmetry, characterized by the imbalance particle density distribution, asymmetry double well energy band structure in Plane Wave I (PWI) phase and asymmetry single well energy band structure in Plane Wave II (PWII) phase, respectively. In the presence of a longitudinal dc gravitational field, rich chiral Bloch oscillation and Landau-Zener tunneling are predicted theoretically and confirmed numerically. The characteristics of the chiral Bloch oscillation can distinguish the novel phases intuitively. Our work gives an interesting way to discuss the quantum phase transitions in a dynamical way.

Design and experiment of nonlinear absorber for equal-peak and de-nonlinearity

This paper generalizes and modifies the Equal-peak method for the design of nonlinear vibration absorber for use in the vibration suppression of nonlinear primary vibration system. For a vibration system with nonlinearity, the most relevant bandwidth is the resonance band, in which the undesirable nonlinear vibration phenomenon occurs because of the dramatically amplified of vibration amplitude. To generalize the Equal-peak method for a complex nonlinear primary system under force/base excitations, we utilize the nonlinear perturbation method and bifurcation theory to investigate the vibration performances and critical conditions for dynamical transition. In addition to the Equal-peak property, another novel advantage, called De-nonlinearity (introduced by coupling nonlinearity), is revealed for vibration control in addition to the known effect of nonlinearity on vibration suppression. It is discovered that by applying the nonlinear vibration absorber with appropriate design on the NL primary system, the Equal-peak property can be accurately realized, and unexpected nonlinear vibration performances can be effectively eliminated. A relevant experimental prototype is carried out to illustrate the Equal-peak and De-nonlinearity properties, which is composed of a primary vibration system with complex nonlinearity and a designed tunable nonlinear vibration absorber. The proposed modified design method for Equal-peak and De-nonlinearity properties has huge potential application in the vibration suppression for low-frequency and strong nonlinearity fields such as ships, aircrafts and ocean platform.

Subsurface damages beneath fracture pits of reaction-bonded silicon carbide after ultra-precision grinding

This paper investigated the structural defects beneath the fracture area of 6H-SiC in reaction-bonded silicon carbide (RB-SiC) ceramics after ultra-precision grinding. The nano-indentation technique was used to evaluate the evolution of deformation behavior and find the critical transition condition among elastic, plastic and fracture. It was found that beneath the fracture pits, dislocations accompanied with micro-cracks (lateral and median) were the two types of subsurface damage. However, no amorphous phase was detected. In addition, a two-beam analysis confirmed that the dislocations were activated on basal 〈a〉 and dissociated into the Shockley partial dislocations in 6H-SiC particle. The following indentation experiments revealed that the existence dislocations in the ground subsurface should be occurred earlier than cleavage. These dislocations were the predominant yielding mechanism in 6H-SiC, which initiated at a shear stress of about 23.4–28.4 Gpa through a pop-in event on load–displacement curve. Afterwards, cracks emerged when the maximum tensile stress beneath the indenter increased to 31.6 GPa. It was identified that cracks could be activated under the intersection effect of non-uniform high density dislocations. Meanwhile, the blocking effect on sliding motion of dislocations caused by cross propagating dislocations, phase boundary and sintering agents play an important role in the evolution of fracture during grinding process. At last, the deformation behavior was further elaborated to discuss the slippage on the basal plane determined by Schmid factor and structure characteristic of 6H-SiC.

Flow of a power-law fluid across a rotating cylinder in a confinement

In the present work, the flow of a power-law fluid across a confined rotating cylinder has been investigated numerically over a wide ranges of conditions as follows: Reynolds number (10−3≤Re≤40), power-law index (0.3 ≤ n ≤ 1), blockage ratio (0.2 ≤ β ≤ 0.99) that quantifies the degree of confinement and asymmetry ratio (10−3≤γ≤1) that describes the position of the cylinder from the bottom wall of the channel. The angular velocity of the cylinder is set equal to the average velocity at the inlet of the bulk flow so that the two Reynolds numbers are equal. The flow field is visualized in terms of streamlines, and the resulting hydrodynamic forces and torque acting on the rotating cylinder are computed for a range of values of the aforementioned influencing parameters. The critical conditions for transition from the steady flow to a periodic time-dependent regime have been identified. In general, the moderate degree of cylinder confinement stabilizes the flow. At high Reynolds numbers, the stabilizing effect is outweighed by the shear-thinning behaviour of the fluid and the degree of symmetry and the flow field transits from the steady to time-dependent one at certain values of the Reynolds number. The transition is delayed as the cylinder approaches one of the channel wall. For the highly confined symmetric case such as β≥0.8,γ=1, lubrication analysis is shown to be applicable. Under these conditions, the analytical results obtained from the lubrication analysis in the narrow gap are very close to the numerical results.