Phase Transition Phenomena Research Articles

Crystallization deformation and phase transitions of coarse-grained sulfate saline soils upon cooling

The volumetric expansion of saline soils under cooling could pose a threat to infrastructure constructed on these soils. This study examines the crystallization deformation characteristics of coarse-grained sulfate saline soils subject to stepwise cooling from 30 °C to −15 °C. Soil columns are prepared in plexiglass buckets with different fine contents, percent compaction, moisture contents, and sodium sulfate content. Cumulative heave and temperature evolution are measured when the specimens are maintained in a temperature-controlled environmental chamber (freezing in three dimensions). Upon cooling, salt and ice crystals grow in soil pores, leading to volumetric expansion. A model is proposed to describe the precipitation-induced deformation varying with temperature based on random forest (RF). The RF-based model reveals that the initial salt-to-water ratio exerts the most significant influence on the accumulated deformation, followed by moisture content, soil salinity, percent compaction, and soil gradation. The initial precipitation and freezing points (response variables) are expressed as two separate functions of soil properties (predictor variables) using the multivariate adaptive regression splines (MARS). The MARS-based models demonstrate that the precipitation points are mainly affected by the initial salt-to-water ratio and soil salinity; all factors contribute to the freezing point prediction, given the combined action of salt and ice crystallization. A threshold soil salinity of 33.33% existed in the evolution of precipitation points, while a threshold fine content of 35% and a threshold soil salinity of 39.68% were observed in freezing point predictions. The interaction mechanism of salt and ice crystallizations led to incredible difficulty capturing freezing points rather than precipitation points and predicting the sample heave. Although the evaluation metrics (RMSE, MAPE, and R2) confirm that the RF- and MARS-based models achieve the regression tasks well, more efforts are needed toward the second phase transition phenomenon and its implications for explaining thermally induced saline soil response. The findings may guide the utilization and management of land resources in saline areas.

Freiheitssatz and phase transition for the density model of random groups

Magnus’ Freiheitssatz [20] states that if a group is defined by a presentation with m generators and a single cyclically reduced relator, and this relator contains the last generating letter, then the first $$m-1$$ letters freely generate a free subgroup. We study an analogue of this theorem in the Gromov density model of random groups [14], showing a phase transition phenomenon at density $$d_r = \min \{\frac{1}{2}, 1-\log _{2m-1}(2r-1)\}$$ with $$1\le r\le m-1$$ : we prove that for a random group with m generators at density d, if $$d < d_r$$ then the first r letters freely generate a free subgroup; whereas if $$d > d_r$$ then the first r letters generate the whole group. This result partially answers a general problem proposed by Gromov in 2003 [15]: existence/nonexistence of non-free subgroups in a random group.

Girth, magnitude homology and phase transition of diagonality

This paper studies the magnitude homology of graphs focusing mainly on the relationship between its diagonality and the girth. The magnitude and magnitude homology are formulations of the Euler characteristic and the corresponding homology, respectively, for finite metric spaces, first introduced by Leinster and Hepworth–Willerton. Several authors study them restricting to graphs with path metric, and some properties which are similar to the ordinary homology theory have come to light. However, the whole picture of their behaviour is still unrevealed, and it is expected that they catch some geometric properties of graphs. In this article, we show that the girth of graphs partially determines the magnitude homology, that is, the larger girth a graph has, the more homologies near the diagonal part vanish. Furthermore, applying this result to a typical random graph, we investigate how the diagonality of graphs varies statistically as the edge density increases. In particular, we show that there exists a phase transition phenomenon for the diagonality.

Polymer-Rich Dense Phase Can Concentrate Metastable Silica Precursors and Regulate Their Mineralization.

Multistep mineralization processes are pivotal in the fabrication of functional materials and are often characterized by far from equilibrium conditions and high supersaturation. Interestingly, such 'nonclassical' mineralization pathways are widespread in biological systems, even though concentrating molecules well beyond their saturation level is incompatible with cellular homeostasis. Here, we show how polymer phase separation can facilitate bioinspired silica formation by passively concentrating the inorganic building blocks within the polymer dense phase. The high affinity of the dense phase to mobile silica precursors generates a diffusive flux against the concentration gradient, similar to dynamic equilibrium, and the resulting high supersaturation leads to precipitation of insoluble silica. Manipulating the chemistry of the dense phase allows to control the delicate interplay between polymer chemistry and silica precipitation. These results connect two phase transition phenomena, mineralization and coacervation, and offer a framework to achieve better control of mineral formation.

Methane storage in nano-pores: Molecular dynamics simulation and density functional theory

Anticipated changes in the complex reservoir production business model increase the demand for reliable methods of the total reservoir storage and capacity estimation for tight formations. The task is complicated by the fact that at nano-scale phase transition and adsorption phenomena are system size dependent. Therefore, fluid phase behavior in nano-pores is sufficiently different from those in the bulk. As the result, understanding of hydrocarbon content behavior in nano-pores at different pressures is of high demand, because such knowledge is crucial for development of an optimum production plan.In the current study, we present a detailed investigation of neat methane distribution in a system of slit nano-pores formed by graphene sheets. The fluid in slit pores is considered to be in thermodynamic equilibrium with the fluid in the larger matrix pore (bulk), thus the concentration of methane in pores is governed by the pressure in the connected bulk volume. The pressure and temperature ranges considered are chosen to represent typical reservoir conditions.The main goal of this study is to suggest a method that (1) is simple enough to be routinely applied for the practical purposes within the industry, and (2) takes into account all major phenomena, which govern fluid behavior in nano-scale pores. To match both criteria, we started with precise molecular dynamics (MD) simulations (fully atomistic and coarse grained) and then utilized the obtained data to calibrate parameters for classical density functional theory approach (c-DFT). In such a way, we managed to adjust computationally cheap and robust c-DFT method to produce the same results as atomically precise MD simulation. Finally, we summarized some results in a simple analytical formula, which describes methane adsorption on flat surfaces.The developed approach enables improved gas in-place estimation, especially in tight formations, which can be extremely valuable for both production design and economics evaluation.

The classification of disordered phases of mixed spin (2,1/2) Ising model and the chaoticity of the corresponding dynamical system

We study an Ising model having the mixed spins {±1/2} and {±2,±1,0} on Cayley tree of second-order. We construct the Gibbs measures corresponding to the model and classify the disordered phases associated to the Gibbs measures. Using the compatibility condition, we obtain the system of functional equations associated with the model. Contrary to the Ising model with two different neighbor interactions, we prove that for the given model, the phase transition phenomenon occurs in both the antiferromagnetic and antiferromagnetic regions. Stability analysis of the dynamic system associated with the model is performed at the obtained fixed point. By calculating the Lyapunov exponent numerically, we show that the corresponding dynamical system exhibits the chaotic behavior in some regions. We identify regions where the disordered phases are extreme by means of a tree-indexed Markov chain. We satisfy the Kesten–Stigum condition for non-extremality of the disordered phase according to the fixed point.

Observer-based Periodic Event-triggered Boundary Control of the One-phase Stefan Problem

The Stefan problem models the phenomenon of phase transition between a liquid and a solid as the time evolution of the temperature profile of a liquid-solid material and its moving interface. This paper provides a novel observer-based periodic event-triggered boundary control (PETBC) strategy for the one-phase Stefan problem using the position and velocity measurements of the moving interface. We propose a method to convert a specific class of continuous-time dynamic event-triggers that require continuous monitoring to periodic event-triggers that only require periodic evaluation. We achieve this result by finding an upper bound on the underlying continuous-time event-trigger between two successive periodic evaluations. We provide an explicit criterion for choosing a sampling period for periodically evaluating the event-trigger. The control input is updated only at events indicated by the periodic event-trigger and is applied in a zero-order hold fashion between two events. We establish the closed-loop system well-posedness along with certain model validity conditions under the proposed PETBC. Further, we prove that the exponential convergence to the setpoint under continuous-time event-triggered boundary control (CETBC) is preserved under the proposed PETBC. We provide simulation results to validate the theoretical developments.

Lee-Yang zeros in the Rydberg atoms

Lee-Yang (LY) zeros play a fundamental role in the formulation of statistical physics in terms of (grand) partition functions, and assume theoretical significance for the phenomenon of phase transitions. In this paper, motivated by recent progress in cold Rydberg atom experiments, we explore the LY zeros in classical Rydberg blockade models. We find that the distribution of zeros of partition functions for these models in one dimension (1d) can be obtained analytically. We prove that all the LY zeros are real and negative for such models with arbitrary blockade radii. Therefore, no phase transitions happen in 1d classical Rydberg chains. We investigate how the zeros redistribute as one interpolates between different blockade radii. We also discuss possible experimental measurements of these zeros.

Tuning the structure and transport properties of complex plasmas using electric field

In this work, we explored the effects of uniaxial (M z ) and biaxial (M xy ) ac electric fields on the structure and transport properties of complex (dusty) plasmas (CDPs) using molecular dynamics simulations. Structures are analyzed using two diagnostic methods, one is lattice correlation function ψ(τ) and the second is radial distribution function g(r) under the influence of M z and M xy , respectively. The Green–Kubo (G-K) method has been used to compute the shear viscosity (η xy ) in the M xy ac electric field. The diffusive behavior of dust particles is investigated using G-K and Einstein methods in M z . In the limits of the varying electric field, these properties of CDPs are accounted for an appropriate range of plasma Coulomb coupling (Γ) and constant Debye screening strength (κ = 0.50) parameters with different system sizes. The simulation outcomes of ψ(τ) and g(r) indicate that the phase transition phenomena occur in CDPs with the variations of M z , M xy and Γ. The η xy and diffusion coefficients significantly increase with increasing parallel electric fields. The subdiffusion motion for short-time behavior and superdiffusion motion for long-time behavior is observed in the presence of moderate to strong electric field strengths. It is revealed that the phase transition and changes in the transports properties of CDPs significantly depend on the strength of the external electric field and plasma parameter (Γ). Novel regimes are observed where CDPs quickly respond to the external electric field. Simulation results are outstanding in the combined effects of Yukawa and anisotropic wake potential on CDPs structural and transport properties. Simulation results demonstrate that the CDPs have electrorheological characteristics. Due to these unique properties, electrorheological CDPs may be used as a platform to study the electrorheological aspects of soft matter. There is a possibility that CDPs will be used as electrorheological material in the near future.

Phase transition for the SOS model under inhomogeneous external field on a Cayley tree

ABSTRACT In this paper, we study the phase transition phenomenon for the three-state solid-on-solid (SOS) model on a Cayley tree under a non-uniform external field.

'Phase transitions' in bacteria - From structural transitions in free living bacteria to phenotypic transitions in bacteria within biofilms.

Phase transitions are common in inanimate systems and have been studied extensively in natural sciences. Less explored are the rich transitions that take place at the micro- and nano-scales in biological systems. In conventional phase transitions, large-scale properties of the media change discontinuously in response to continuous changes in external conditions. Such changes play a significant role in the dynamic behaviours of organisms. In this review, we focus on some transitions in both free-living and biofilms of bacteria. Particular attention is paid to the transitions in the flagellar motors and filaments of free-living bacteria, in cellular gene expression during the biofilm growth, in the biofilm morphology transitions during biofilm expansion, and in the cell motion pattern transitions during the biofilm formation. We analyse the dynamic characteristics and biophysical mechanisms of these phase transition phenomena and point out the parallels between these transitions and conventional phase transitions. We also discuss the applications of some theoretical and numerical methods, established for conventional phase transitions in inanimate systems, in bacterial biofilms.

The behaviors of bubble migration and pressure build-up during a dynamic shut-in procedure in deep-water drilling

A dynamic shut-in procedure is commonly adopted after a kick incident in order to build up the wellbore pressure, obtain reservoir information, and thereby handle the gas kick. In deep-water scenarios, the hydrate growth behaviors have a significant effect on gas migration and interphase mass transfer, which has not been quantitatively analyzed during the well shut-in process. In this study, a comprehensive mechanistic model of wellbore dynamics is developed considering gas migration and phase transitions. The simulation results show that the wellbore pressure field can be built up in different trends during different well shut-in periods, governed by gas seepage from the reservoir and gas migration along the wellbore, respectively. Masking the migration of free gas, the phase transition phenomena have a significant influence on the wellbore dynamics and bottomhole pressure. This work adds further insights into quantitatively characterizing the hydrate growth behaviors and interphase mass transfer rules of gas bubbles during a dynamic well shut-in procedure.

Photoinduced phase transitions in nanogel particles for reversible CO2 capture

Solar energy has been utilized to strip CO2 for saving the CO2 capture energy consumption. However, a large temperature swing is necessary for higher regeneration efficiency, which also will result in a serious materials degradation. Herein, we report a photo triggered phase transition strategy for reversible capture CO2 using amine containing nanogel particles-based solvents with a small temperature swing. The composite absorbents were prepared by combing N-[3-(dimethylamino)propyl]methacrylamide containing nanogel particles with polydopamine. The phenomenon of photoinduced phase transition was observed in both nanogel particles-based solvents and the composite absorbents. Although the nanogel particles can release most of CO2 undergo a light irradiation, the composite absorbents present a more faster desorption rate than the former, which can be explained by an enhanced light absorbability and photothermal conversion efficiency of the latter. An average CO2 regeneration efficiency can reach up to 92.45% in five CO2 uptake and release cycles, indicating that the photo triggered phase transition can be used to develop energy efficient CO2 capture technology.

An insight into simultaneous phase transition phenomena and melt-rheology of low-density polyethylene/ethylene–vinyl acetate copolymer/expanded graphite nanocomposites through continuous extrusion foaming process

In the present article, the influences of expanded graphites (EGs) with small, medium, and large aspect ratios (SEG, MEG, and LEG, respectively) on the foamability of low-density polyethylene (LDPE)/ethylene–vinyl acetate copolymer (EVA) blend obtained from continuous extrusion foaming process were studied. The addition of EGs to the PE/EVA blend resulted in foams with smaller cells and higher cell densities. Among the different nanofillers used, EG with larger aspect ratio caused the formation of PE/EVA foams with higher void fraction, smaller cell size and larger cell density. EG nanoplatelets assisted bubble nucleation and acted as an impermeable barrier against the gas removal from the melt, where LEG behaved more successfully due to having a larger surface area with the melt. During the bubble nucleation and growth stages, PE/EVA liquid–liquid and solid–liquid phase separations took place concurrently. The presence of EG nanofillers influenced the PE/EVA phase separation and increased the mutual solubility of the polymeric constituents in each other. Besides, EG nanolayers enhanced the viscoelastic properties of PE/EVA melt, and thus prevented cell wall rupture and gas release from the melt.

Tricritical phenomena in holographic chiral phase transitions

We study critical phenomena at a tricritical point associated with a chiral phase transition which emerges in the D3/D7 model in the presence of a finite baryon number density and an external magnetic field. We numerically determine critical exponents related to the thermodynamic quantities and correlation functions. We find that the values of the critical exponents agree with the mean-field values. The scaling relations between the critical exponents are satisfied, implying that the scaling hypothesis for the free energy and the correlation functions hold. Our results indicate that the critical phenomena at the tricritical point in the D3/D7 model are well described by the conventional Landau theory.

Phase transition in the majority rule model with the nonconformist agents

Independence and anticonformity are two types of social behaviors known in social psychology literature and the most studied parameters in the opinion dynamics model. These parameters are responsible for continuous (second-order) and discontinuous (first-order) phase transition phenomena. Here, we investigate the majority rule model in which the agents adopt independence and anticonformity behaviors. We define the model on several types of graphs: complete graph, two-dimensional (2D) square lattice, and one-dimensional (1D) chain. By defining p as a probability of independence (or anticonformity), we observe the model on the complete graph undergoes a continuous phase transition where the critical points are pc≈0.334 (pc≈0.667) for the model with independent (anticonformist) agents. On the 2D square lattice, the model also undergoes a continuous phase transition with critical points at pc≈0.0608 (pc≈0.4035) for the model with independent (anticonformist) agents. On the 1D chain, there is no phase transition either with independence or anticonformity. Furthermore, with the aid of finite-size scaling analysis, we obtain the same sets of critical exponents for both models involving independent and anticonformist agents on the complete graph. Therefore they are identical to the mean-field Ising model. However, in the case of the 2D square lattice, the models with independent and anticonformist agents have different sets of critical exponents and are not identical to the 2D Ising model. Our work implies that the existence of independence behavior in a society makes it more challenging to achieve consensus compared to the same society with anticonformists.

Evolution of the Molecular and Supramolecular Structures of PLA during the Thermally Supported Hydrolytic Degradation of Wet Spinning Fibers

Fibers formed by the wet spinning method from commercially available polylactide (PLA) variants with different d-lactide isomer contents were exposed to thermally supported hydrolytic degradation in environments with different pH values. This paper focuses on the evolution of the supramolecular structure of PLA during the accelerated degradation progress of real fabricated materials. The disorder-to-order phase transition phenomenon was investigated using wide-angle X-ray diffraction (WAXD). Additionally, differential scanning calorimetry (DSC) was applied to determine the supramolecular changes and resulting thermal properties of the polymer. The obtained results clearly show the formation of irreversible changes in the structure of the polymer, which could be an indication of the formation of microplastics (microcrystallites), as further verified by Fourier transform infrared (FTIR) spectroscopy. Transformations at the molecular and supramolecular levels depend slightly on the pH of the environment if the process is performed at temperatures near the cold crystallization point. Rapid structural transformations lead to irreversible changes and unknown thermal properties of the polymer. Instead, these changes depend on the content of the d-lactide isomer in the PLA structure. The article shows a new extended experimental overview of the degradation of real PLA objects and creates a field for further theoretical analysis.

Linear Regression and Its Inference on Noisy Network-Linked Data

AbstractLinear regression on network-linked observations has been an essential tool in modelling the relationship between response and covariates with additional network structures. Previous methods either lack inference tools or rely on restrictive assumptions on social effects and usually assume that networks are observed without errors. This paper proposes a regression model with non-parametric network effects. The model does not assume that the relational data or network structure is exactly observed and can be provably robust to network perturbations. Asymptotic inference framework is established under a general requirement of the network observational errors, and the robustness of this method is studied in the specific setting when the errors come from random network models. We discover a phase-transition phenomenon of the inference validity concerning the network density when no prior knowledge of the network model is available while also showing a significant improvement achieved by knowing the network model. Simulation studies are conducted to verify these theoretical results and demonstrate the advantage of the proposed method over existing work in terms of accuracy and computational efficiency under different data-generating models. The method is then applied to middle school students' network data to study the effectiveness of educational workshops in reducing school conflicts.

Solvent-induced crystallization and phase-transition phenomena in syndiotactic polystyrene and its relatives

The studies of time-dependent structural changes in the solvent-induced crystallization and phase transition phenomena have been reviewed by focusing mainly on syndiotactic polystyrene (SPS) and its relatives having the functional groups on the phenyl rings. The time-resolved measurement of X-ray diffraction and vibrational spectra has revealed the structural evolution process in the solvent-induced crystallization of SPS, which depends on the type (polarity, bulkiness, etc.) of the solvent molecules. The heating of the SPS-solvent complexes causes the complicated phase transitions from theδform (complex) to theγform and to theα(orβ) form. The introduction of such a polar functional group as OCH3or halogen units on the phenyl rings enhances the interactions between the SPS and the solvent, the strength of which depends on the substitution position of the OCH3units on the phenyl ring. For example, the ortho- or para-substitution dissolves the sample quite easily at room temperature, while the meta-substitution makes it possible to create the solvent complexes. The discussion has been made for the structural relation before and after the formation of the solvent-complexes.

Finite-size effect of a weakly interacting Bose gas at zero-temperature

We investigate the quantum fluctuation of a weakly interacting Bose gas confined between two parallel plates at zero temperature within two-loop approximation of the Cornwall-Jackiw-Tomboulis (CJT) effective action approach. The finite-size and boundary condition (BC) effects in the excitation atomic density, energy density, chemical potential, and sound speed are determined, including the prediction of a first-order phase transition phenomenon.