Critical Point Pc Research Articles

Experimental Study of the Effect of Wire Electrical Discharge Machining on Crack tip Opening Displacement for Compact Tension Specimens of Low Carbon Steel

Fracture mechanics approach is important for all mechanical and civil projects that might involve cracks in metallic materials the purpose of this paper is to determine a crack tip opening displacement fracture toughness experimentally, also study the effect of thickness on CTOD fracture toughness of low carbon steel and study the effect of Wire Electrical Discharge Machine (WEDM) to have a pre-crack, instead of fatigue pre-crack by using a CT specimen of low carbon steel with a thickness of (8,10, and15 mm), a width of 30mm, crack length of 15mm, and pre-crack of 1.3mm for all samples, this dimension according to ASTM-E399-13, by pulling the specimen in a 100 KN universal testing machine at a slow speed rate of 0.5 mm/min, the load applied on the specimen is generally a tension load. The crack tip plastically deforms until a critical point PC at this moment a crack is initiated. The computer-controlled universal testing machine gives the value of the load and the displacement transducer gives a crack mouth opening displacement. Critical crack tip opening displacement CTOD is found with the plastic hinge model (PHM) method. The result showed the stress intensity factor KI increases with increased loading in the elastic region and the thickness effect refers to the effect of the plastic zone at the crack tip on the stress intensity factor, In a thin specimen, a plastic zone is large at the fracture tip leads to a high-stress intensity factor at the fracture tip but in the thick specimen, on the other hand, has a small a plastic zone and a low-stress intensity factor around the crack tip. The fracture toughness is found to increase with an increase in the thickness of specimens.

Apparent Fracture Toughness of the CoB-Co2B Interface

Abstract In this study, new results for the interfacial fracture toughness of the CoB-Co2B layer formed at the surface of the ASTM F1537, Standard Specification for Wrought Cobalt-28Chromium-6Molybdenum Alloys for Surgical Implants (UNS R31537, UNS R31538, and UNS R31539), alloy were estimated. Initially, the cobalt boride layers were developed by means of the powder-pack boriding process at 1,173 K with 6 h of exposure, and 1,223 K with 8 h of exposure. The depth-sensing Vickers microindentation tests were performed using applied loads ranging between 1 and 2.3 N to generate a crack along the CoB-Co2B interface. The apparent fracture toughness (Kca) of the CoB-Co2B interface was estimated using a half-penny cracking model and considering the interfacial values of the Young’s modulus, hardness, and the critical point (Pc, ac), in which Pc was considered as a criterion of the adhesion between CoB and Co2B. To verify the influence of the cobalt boride layer thickness and the magnitude of the residual stresses developed on CoB-Co2B interface, the cracking model was extended to estimate the Kca for the boriding condition at 1,273 K with 6 h of exposure. In addition, the magnitude of the shear stresses on the CoB-Co2B interface was analyzed by the finite element method as a function of the indentation loads of 1 and 2.3 N using the boriding conditions of 1,173 K with 6 h of exposure and 1,223 K with 8 h of exposure. The results showed that the interfacial fracture toughness of the CoB-Co2B increased as a function of the CoB layer thickness, whereas the magnitude of the compressive residual stresses decreased for the thicker cobalt boride layer formed at 1,273 K with 6 h of exposure. Finally, the distribution of the maximum shear stresses located on the CoB-Co2B interface oscillated from 3.9 to 4.4 GPa according to the indentation loads.

Deconfined Critical Point in a Doped Random Quantum Heisenberg Magnet

We describe the phase diagram of electrons on a fully connected lattice with random hopping, subject to a random Heisenberg spin exchange interaction between any pair of sites and a constraint of no double occupancy. A perturbative renormalization group analysis yields a critical point with fractionalized excitations at a nonzero critical value pc of the hole doping p away from the half-filled insulator. We compute the renormalization group to two loops, but some exponents are obtained to all loop order. We argue that the critical point pc is flanked by confining phases: a disordered Fermi liquid with carrier density 1+p for p>pc and a metallic spin glass with carrier density p for p<pc. Additional evidence for the critical behavior is obtained from a large-M analysis of a model which extends the SU(2) spin symmetry to SU(M). We discuss the relationship of the vicinity of this deconfined quantum critical point to key aspects of cuprate phenomenology.6 MoreReceived 24 December 2019Revised 18 February 2020Accepted 23 March 2020DOI:https://doi.org/10.1103/PhysRevX.10.021033Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum criticalityQuantum phase transitionsPhysical SystemsCupratesTechniquesSachdev-Ye-Kitaev modelCondensed Matter, Materials & Applied Physics

Reputation in Majority Rule Model leading to democratic states

We study the Majority Rule (MR) model, a sociophysics model developed to describe how a group of agents with initial different opinions can reach consensus. At each instant of time, a group is selected at random and discuss among each other. After the discussion, all members of this discussion group follow the majority opinion. The number of agents in the discussion group is not fixed and it is selected each instant of time from a Gaussian distribution. The system dynamics stops when only one opinion survive. In this work we introduced in the MR model a ‘reputation’ for each agent, a weight to be considered in the system dynamics. Our results show that the introduction of reputation leads the system to a steady state in which not every agent on the system have exactly the same status, but a majority of them sharing the same opinion. In addition, our model with the inclusion of reputation do not show the critical point usually observed. Instead we have obtained the critical point pc = 1, in contrast with the standard Majority Rule model.

Quasi‐polynomial mixing of critical two‐dimensional random cluster models

We study the Glauber dynamics for the random cluster (FK) model on the torus with parameters (p,q), for q ∈ (1,4] and p the critical point pc. The dynamics is believed to undergo a critical slowdown, with its continuous‐time mixing time transitioning from for p ≠ pc to a power‐law in n at p = pc. This was verified at p ≠ pc by Blanca and Sinclair, whereas at the critical p = pc, with the exception of the special integer points q = 2,3,4 (where the model corresponds to the Ising/Potts models) the best‐known upper bound on mixing was exponential in n. Here we prove an upper bound of at p = pc for all q ∈ (1,4], where a key ingredient is bounding the number of nested long‐range crossings at criticality.

Evaluation of ENSO simulations in CMIP5 models: A new perspective based on percolation phase transition in complex networks

In this study, the performance of CMIP5 models in simulating the El Niño-Southern Oscillation (ENSO) is evaluated by using a new metric based on percolation theory. The surface air temperatures (SATs) over the tropical Pacific Ocean are constructed as a SAT network, and the nodes within the network are linked if they are highly connected (e.g., high correlations). It has been confirmed from reanalysis datasets that the SAT network undergoes an abrupt percolation phase transition when the influences of the sea surface temperature anomalies (SSTAs) below are strong enough. However, from simulations of the CMIP5 models, most models are found incapable of capturing the observed phase transition at a proper critical point Pc. For the 15 considered models, four even miss the phase transition, indicating that the simulated SAT network is too stable to be significantly changed by the SSTA below. Only four models can be considered cautiously with some skills in simulating the observed phase transition of the SAT network. By comparing the simulated SSTA patterns with the node vulnerabilities, which is the chance of each node being isolated during a ENSO event, we find that the improperly simulated sea-air interactions are responsible for the missing of the observed percolation phase transition. Accordingly, a careful study of the sea-air couplers, as well as the atmospheric components of the CMIP5 models is suggested. Since the percolation phase transition of the SAT network is a useful phenomenon to indicate whether the ENSO impacts can be transferred remotely, it deserves more attention for future model development.

Optimal Design of Gas-Expanded Liquid Ethylene Oxide Production with Zero Carbon Dioxide Byproduct

The concept of ethylene epoxidation over methyltrioxorhenium (MTO) catalyst could save the world from global warming since the epoxidation reaction never produces carbon dioxide as byproduct. Unlike the conventional gas epoxidation reaction with oxygen, this reaction takes place in the (ethylene) gas-expanded liquid solvent phase (methanol) while the reaction oxidant is hydrogen peroxide. The reaction takes place at temperatures and pressures close to the ethylene critical point (Pc = 50.42 bar; Tc = 48.56 °F) (Gas Encyclopedia by Air Liquide, https://encyclopedia.airliquide.com/ethylene). In this paper, an optimized design and operation for MTO based ethylene oxide (EO) production processes has been developed, which has less manufacturing costs compared with the one from the current literature ( Ind. Eng. Chem. Res. 2013, 52, 18−29). The developed EO system could produce 200,000 tons of ethylene oxide per year at a purity of 99.9%. It has two reactors for ethylene epoxidation and hydrogen peroxide decomp...

A Simple Method for Determining the Critical Point of the Soil Water Retention Curve

Core Ideas A fixed tangent line method was developed to estimate the critical point of the soil water retention curve as an alternative to the commonly used flexible tangent line method. The critical points of the soil water retention curve from the proposed method and the flexible tangent line method were compared. Particle‐size distribution and specific surface area had significant effects on the critical point of the soil water retention curve. The transition point between capillary water and adsorbed water, which is the critical point Pc [defined by the critical matric potential (ψc) and the critical water content (θc)] of the soil water retention curve (SWRC), demarcates the energy and water content region where flow is dominated by capillarity or liquid film flow. Accurate estimation of Pc is crucial for modeling water movement in the vadose zone. By modeling the dry‐end (matric potential &lt; –104.2 cm H2O) and wet‐end (matric potential &gt; –104.2 cm H2O) sections of the SWRC using the models of Campbell and Shiozawa, and of van Genuchten, a fixed tangent line method was developed to estimate Pc as an alternative to the commonly used flexible tangent line method. The relationships between Pc, and particle‐size distribution and specific surface area (SSA) were analyzed. For 27 soils with various textures, the mean RMSE of water content from the fixed tangent line method was 0.007 g g–1, which was slightly better than that of the flexible tangent line method. With increasing clay content or SSA, ψc was more negative initially but became less negative at clay contents above ∼30%. Increasing the silt contents resulted in more negative ψc values, whereas soils with higher sand content had less negative ψc values. The magnitude of θc increased linearly with SSA and clay content. Our findings suggest that Pc estimated from the fixed tangent line method could represent the actual values and clarify the effect of particle‐size distribution and SSA on Pc.

Targeted attack on networks coupled by connectivity and dependency links

Coupled systems used to increase capacity were shown beneficial as long as it does not open pathways to cascades. Previous studies on the robustness of coupled networks except for interdependent networks are almost the cases of random attack. Many challenges remain exist in targeted-attack problem of coupled networks. Since nodes within coupled networks show different functions for each network, this paper both analytically and numerically analyzed the robustness of coupled networks under three types of targeted attacking strategies, including attacking on nodes by considering internal and external degree, internal degree only, and external degree only. For coupled network with both interdependent and interconnected links, all degree distributions of intra- and inter-connectivity links are Poissonian, we find the system undergoes from second to first order phase transition as coupling strength q increases. The fraction of nodes in the giant component P∞ at stable state, the critical phase transition threshold pc (first order threshold pcI and second order threshold pcII), and the critical point (pc,qc) separating the first and second order phase transitions are analytically obtained for three types of attacking strategies with attacking probability parameter α=0,1. We also find the system becomes more vulnerable as the average degree of intra-links k̄ or inter-links K̄ decreases. Therefore, the minimum average degrees k̄min and K̄min to maintain the system stable are obtained for the case of α=0,1. Moreover, we discussed three typical cases of coupled networks, interdependent networks (K̄=0), interacting networks (q=0) and bipartite network (k=0, q=0), the analytical expressions of P∞, pc and (pc,qc) (only for interdependent) are given respectively. Besides, we study the equivalence relations between interdependent networks and coupled networks with connectivity and dependency links for the same pc. The results imply that we can adjust the parameters q, k̄ and K̄ to make the two systems have the same robustness. Moreover, the results imply that one should not only protect nodes with high degree of intra-links or inter-links, but also defend nodes, the sum of whose degree of intra-links and inter-links is big, can avoid the system becoming vulnerable.

Universal V-shaped temperature-pressure phase diagram in the iron-based superconductorsKFe2As2,RbFe2As2, andCsFe2As2

We report a sudden reversal in the pressure dependence of Tc in the iron-based superconductor RbFe2As2, at a critical pressure Pc = 11 kbar. Combined with our prior results on KFe2As2 and CsFe2As2, we find a universal V-shaped phase diagram for Tc vs P in these fully hole-doped 122 materials, when measured relative to the critical point (Pc, Tc). From measurements of the upper critical field Hc2(T) under pressure in KFe2As2 and RbFe2As2, we observe the same two-fold jump in (1/Tc)(-dHc2/dT) across Pc, compelling evidence for a sudden change in the structure of the superconducting gap. We argue that this change is due to a transition from one pairing state to another, with different symmetries on either side of Pc. We discuss a possible link between scattering and pairing, and a scenario where a d-wave state favored by high-Q scattering at low pressure changes to a state with s+- symmetry favored by low-Q scattering at high pressure.

A kinetic model and scaling properties of non-equilibrium clustering of self-propelled particles

We demonstrate that the clustering statistics and the corresponding phase transition to non-equilibrium clustering found in many experiments and simulation studies with self-propelled particles (SPPs) with alignment can be obtained by a simple kinetic model. The key elements of this approach are the scaling of the cluster cross-section with cluster size—described by an exponent α—and the scaling of the cluster perimeter with cluster size—described by an exponent β. The analysis of the kinetic approach reveals that the SPPs exhibit two phases: (i) an individual phase, where the cluster size distribution (CSD) is dominated by an exponential tail that defines a characteristic cluster size, and (ii) a collective phase characterized by the presence of a non-monotonic CSD with a local maximum at large cluster sizes. Through a finite-size study of the kinetic model, we show that the critical point Pc that separates the two phases scales with the system size N as Pc∝N−ξ, while the CSD p(m), at the critical point Pc, is always a power law such that p(m)∝m−γ, where m is the cluster size. Our analysis shows that the critical exponents ξ and γ are a function of α and β, and even provides the relationship between them. Furthermore, the kinetic approach suggests that in the thermodynamic limit, a genuine clustering phase transition, in two and three dimensions, requires that α = β. Interestingly, the critical exponent γ is found to be in the range 0.8 < γ < 1.5 in line with the observations from experiments and simulations.

The impact of connection density on scale-free distribution in random networks

Preferential attachment is considered as a fundamental mechanism that contributes to the scale-free characteristics of random networks, which include growth and non-growth networks. There exist some situations of non-growth random networks, particularly for very sparse or dense networks, where preferential attachments cannot consequentially result in true scale-free features, but only in scale-free-like appearances. This phenomenon implies that, a close relationship exists between the connection density p and the scaling. In this study, we propose a self-organized model with constant network size to study the phenomenon. We show analytically and numerically that there exists a certain critical point pc. Only when p=pc, the random network evolves into steady scale-free state. Otherwise, the network exhibits a steady scale-free-like state. The closer the p approximates pc, the closer the scale-free-like distribution approximates the true scale-free distribution. Our results show that, in random network lack of growth, a preferential scheme does not necessarily lead to a scale-free state, and a formation of scale-free is a consequence of two mechanisms: (i) a preferential scheme and (ii) appropriate connection density.

The geometry of percolation fronts in two-dimensional lattices with spatially varying densities

Percolation theory is usually applied to lattices with a uniform probability p that a site is occupied or that a bond is closed. The more general case, where p is a function of the position x, has received less attention. Previous studies with long-range spatial variations in p(x) have only investigated cases where p has a finite, non-zero gradient at the critical point pc. Here we extend the theory to two-dimensional cases in which the gradient can change from zero to infinity. We present scaling laws for the width and length of the hull (i.e. the boundary of the spanning cluster). We show that the scaling exponents for the width and the length depend on the shape of p(x), but they always have a constant ratio 4/3 so that the hull's fractal dimension D = 7/4 is invariant. On this basis, we derive and verify numerically an asymptotic expression for the probability h(x) that a site at a given distance x from pc is on the hull.

基盤岩上に形成される周期的ステップ地形

In rivers located in mountain areas, a series of steps are often observed to be formed on bedrock. This is called cyclic steps formed by bedrock incision. This study proposes a simplified model for describing the erosion process by abrasion due to bedload, and obtain an equilibrium step shape migrating upstream without changing its shape. It is found that there are three important parameters: the threshold velocity Ut for bedload, the availability function at the Froude critical point pc, and the average slope. Once these three parameters are given, the wavelength L, the erosion rate averaged over one step length En, and the water and bed surface profiles are determined. It is found that qualitative features of steps observed in experiments are well described by the analysis.

Critical points for spread-out self-avoiding walk, percolation and the contact process above the upper critical dimensions

We consider self-avoiding walk and percolation in ℤd, oriented percolation in ℤd×ℤ+, and the contact process in ℤd, with pD(·) being the coupling function whose range is proportional to L. For percolation, for example, each bond is independently occupied with probability pD(y−x). The above models are known to exhibit a phase transition when the parameter p varies around a model-dependent critical point pc. We investigate the value of pc when d>6 for percolation and d>4 for the other models, and L≫1. We prove in a unified way that pc=1+C(D)+O(L−2d), where the universal term 1 is the mean-field critical value, and the model-dependent term C(D)=O(L−d) is written explicitly in terms of the random walk transition probability D. We also use this result to prove that pc=1+cL−d+O(L−d−1), where c is a model-dependent constant. Our proof is based on the lace expansion for each of these models.

Thermodynamic and Transport Properties of CeMg2Cu9under Pressure

We report the transport and thermodynamic properties under hydrostatic pressure in the antiferromagnetic Kondo compound CeMg2Cu9 with a two-dimensional arrangement of Ce atoms. Magnetic specific heat Cmag(T) shows a Schottky-type anomaly around 30 K originating from the crystal electric field (CEF) splitting of the 4f state with the first excited level at \Delta_{1}/kB = 58 K and the second excited level at \Delta_{2}/kB = 136 K from the ground state. Electric resistivity shows a two-peaks structure due to the Kondo effect on each CEF level around T_{1}^{max} = 3 K and T_{2}^{max} = 40 K. These peaks merge around 1.9 GPa with compression. With increasing pressure, Neel temperature TN initially increases and then change to decrease. TN finally disappears at the quantum critical point Pc = 2.4 GPa.

Thermal Properties of a Ferromagnetic Superconductor UGe2

Thermal properties of a ferromagnetic superconductor UGe2 were investigated by the heat capacity measurements. The bulk nature of the superconductivity was confimied by the observation of a peak in the heat capacity at the superconducting transition temperature TSC, From the pressure dependence of the linear heat capacity coefficient γ, it is suggested that the low energy magnetic excitation near the critical point Pc*, where T* becomes OK, might play an important role on the superconductivity. The pressure dependence of the superconducting peak and the temperature dependence of CIT above TSC suggest that the order parameter of the superconducting state might be different between the phases below and above PC*.

Effect of temperature and salinity on the oxygen consumption of laboratory produced Penaeus vannamei postlarvae

The routine rate of oxygen consumption by Penaeus vannamei postlarvae (mean weight = 0.15 g) was determined at four temperatures and five salinities. The time course of oxygen depletion in the chambers was independent of the dissolved oxygen (DO) level down to 1.3 mg/1. Oxygen consumption during normoxic conditions increased with temperature and ranged from 0.0060 mg/g/min at 25 ppt and 20°C, to 0.0183 mg/g/min at 35 ppt and 32°C. Salinity had only a marginal effect on consumption. At high salinities, there was an increase in the metabolic demand, probably caused by an apparent loss in the capacity to maintain the osmotic and ionic balances as temperature increased. A critical point (Pc), where oxygen consumption by the shrimp changes from being independent of DO level to being dependent, was found. Pc was correlated to temperature. Below Pc, oxygen consumption was reduced to approximately 34% of the normal rate.

Critical behavior of percolation and Markov fields on branching planes

For an independent percolation model on , where is a homogeneous tree and is a one-dimensional lattice, it is shown, by verifying that the triangle condition is satisfied, that the percolation probability θ (p) is a continuous function of p at the critical point p c, and the critical exponents , γ, δ, and Δ exist and take their mean-field values. Some analogous results for Markov fields on are also obtained.

Critical behavior of percolation and Markov fields on branching planes

For an independent percolation model on , where is a homogeneous tree and is a one-dimensional lattice, it is shown, by verifying that the triangle condition is satisfied, that the percolation probability θ (p) is a continuous function of p at the critical point pc, and the critical exponents , γ, δ, and Δ exist and take their mean-field values. Some analogous results for Markov fields on are also obtained.