Subcritical Phase Research Articles

Continuum line-of-sight percolation on Poisson–Voronoi tessellations

AbstractIn this work, we study a new model for continuum line-of-sight percolation in a random environment driven by the Poisson–Voronoi tessellation in the d-dimensional Euclidean space. The edges (one-dimensional facets, or simply 1-facets) of this tessellation are the support of a Cox point process, while the vertices (zero-dimensional facets or simply 0-facets) are the support of a Bernoulli point process. Taking the superposition Z of these two processes, two points of Z are linked by an edge if and only if they are sufficiently close and located on the same edge (1-facet) of the supporting tessellation. We study the percolation of the random graph arising from this construction and prove that a 0–1 law, a subcritical phase, and a supercritical phase exist under general assumptions. Our proofs are based on a coarse-graining argument with some notion of stabilization and asymptotic essential connectedness to investigate continuum percolation for Cox point processes. We also give numerical estimates of the critical parameters of the model in the planar case, where our model is intended to represent telecommunications networks in a random environment with obstructive conditions for signal propagation.

Conformal generation of an exotic rotationally invariant harmonic oscillator

An exotic rotationally invariant harmonic oscillator (ERIHO) is constructed by applying a non-unitary isotropic conformal bridge transformation (CBT) to a free planar particle. It is described by the isotropic harmonic oscillator Hamiltonian supplemented by a Zeeman type term with a real coupling constant $g$. The model reveals the Euclidean ($|g|<1$) and Minkowskian ($|g|>1$) phases separated by the phases $g=+1$ and $g=-1$ of the Landau problem in the symmetric gauge with opposite orientation of the magnetic field. A hidden symmetry emerges in the system at rational values of $g$. Its generators, together with the Hamiltonian and angular momentum produce non-linearly deformed $\mathfrak{u}(2)$ and $\mathfrak{gl}(2,{\mathbb R})$ algebras in the cases of $0<|g|<1$ and $\infty>|g|>1$, which transmute one into another under the inversion $g\rightarrow -1/g$. Similarly, the true, $\mathfrak{u}(2)$, and extended conformal, $\mathfrak{gl}(2,{\mathbb R})$, symmetries of the isotropic Euclidean oscillator ($g=0$) interchange their roles in the isotropic Minkowskian oscillator ($|g|=\infty$), while two copies of the $\mathfrak{gl}(2,{\mathbb R})$ algebra of analogous symmetries mutually transmute in Landau phases. We show that the ERIHO system is transformed by a peculiar unitary transformation into the anisotropic harmonic oscillator generated, in turn, by anisotropic CBT. The relationship between the ERIHO and the subcritical phases of the harmonically extended Landau problem, as well as with a plane isotropic harmonic oscillator in a uniformly rotating reference frame, is established.

Limit Theorems for the One-Dimensional Random Walk with Random Resetting to the Maximum

The first part of this paper is devoted to study a model of one-dimensional random walk with memory to the maximum position described as follows. At each step the walker resets to the rightmost visited site with probability $$r \in (0,1)$$ and moves as the simple random walk with remaining probability. Using the approach of renewal theory, we prove the laws of large numbers and the central limit theorems for the random walk. These results reprove and significantly enhance the analysis of the mean value and variance of the process established in Majumdar et al. (Phys Rev E 92:052126, 2015). In the second part, we expand the analysis to the situation where the memory of the walker decreases over time by assuming that at the step n the resetting probability is $$r_n = \min \{rn^{-a}, \tfrac{1}{2}\}$$ with r, a positive parameters. For this model, we first establish the asymptotic behavior of the mean values of $$X_n$$ -the current position and $$M_n$$ -the maximum position of the random walk. As a consequence, we observe an interesting phase transition of the ratio $${{\mathbb {E}}}[X_n]/{{\mathbb {E}}}[M_n]$$ when a varies. Precisely, it converges to 1 in the subcritical phase $$a\in (0,1)$$ , to a constant $$c\in (0,1)$$ in the critical phase $$a=1$$ , and to 0 in the supercritical phase $$a>1$$ . Finally, when $$a>1$$ , we show that the model behaves closely to the simple random walk in the sense that $$\frac{X_n}{\sqrt{n}} \overset{(d)}{\longrightarrow } {\mathcal {N}}(0,1)$$ and $$\frac{M_n}{\sqrt{n}} \overset{(d)}{\longrightarrow } \max _{0 \le t \le 1} B_t$$ , where $${\mathcal {N}}(0,1)$$ is the standard normal distribution and $$(B_t)_{t\ge 0}$$ is the standard Brownian motion.

Identifying vital nodes by Achlioptas process

The vital nodes are the ones that play an important role in the organization of network structure or the dynamical behaviors of networked systems. Previous studies usually applied the node centralities to quantify the importance of nodes. Realizing that the percolation clusters are dominated by local connections in the subcritical phase and by global connections in the supercritical phase, in this paper we propose a new method to identify the vital nodes via a competitive percolation process that is based on an Achlioptas process. Compared with the existing node centrality indices, the new method performs overall better in identifying the vital nodes that maintain network connectivity and facilitate network synchronization when considering different network structure characteristics, such as link density, degree distribution, assortativity, and clustering. We also find that our method is more tolerant of noisy data and missing data. More importantly, compared with the unique ranking list of nodes given by most centrality methods, the randomness of the percolation process expands the possibility space of the optimal solutions, which is of great significance in practical applications.

Identification of Self-Organized Critical State on Twitter Based on the Retweets’ Time Series Analysis

There is a number of studies, in which it is established that the observed flows of microposts generated by microblogging social networks (e.g., Twitter) are characterized by avalanche-like behavior. Time series of microposts depicting such streams are the time series with a power-law distribution, with 1/f noise and long memory. Despite this, there are no studies devoted to the detection and analysis of self-organized critical state, subcritical phase, and supercritical phase. The presented paper is devoted to the detection and investigation of such critical states and phases. An algorithm is proposed that allowed to detect of critical phases and critical conditions on Twitter, based on the analysis of retweets time series corresponding to the three debates of the 2016 United States Presidential Election, as the most popular debate in the history of America, collecting 84 million live views.

Critical and Ictal Phases in Simulated EEG Signals on a Small-World Network.

Healthy brain function is marked by neuronal network dynamics at or near the critical phase, which separates regimes of instability and stasis. A failure to remain at this critical point can lead to neurological disorders such as epilepsy, which is associated with pathological synchronization of neuronal oscillations. Using full Hodgkin-Huxley (HH) simulations on a Small-World Network, we are able to generate synthetic electroencephalogram (EEG) signals with intervals corresponding to seizure (ictal) or non-seizure (interictal) states that can occur based on the hyperexcitability of the artificial neurons and the strength and topology of the synaptic connections between them. These interictal simulations can be further classified into scale-free critical phases and disjoint subcritical exponential phases. By changing the HH parameters, we can model seizures due to a variety of causes, including traumatic brain injury (TBI), congenital channelopathies, and idiopathic etiologies, as well as the effects of anticonvulsant drugs. The results of this work may be used to help identify parameters from actual patient EEG or electrocorticographic (ECoG) data associated with ictogenesis, as well as generating simulated data for training machine-learning seizure prediction algorithms.

Hydrochar for Industrial Wastewater Treatment: An Overview on its Advantages and Applications

Water pollution is one of the environmental challenges facing the world society. Consequently, the pollutants both domestic and industrial wastewater are identified as an environmental threat. Hydrochar (HC) appears as a cost-effective and eco-friendly solution to this environmental threat. HC is the solid produced from the wet pyrolysis process for biomass that is rich in carbon in a sub-critical liquid phase, called the Hydro-Thermal Carbonization Process (HTC). This review aims to address the possibility of using HC as the most effective solution to the industrial wastewater. HTC has proven a greater yield than dry pyrolysis (30%-60% wt). To date, HC is listed as a promising lower-cost alternate adsorbent for removing wastewater pollutants. In Egypt for example, only few studies have been published investigating the properties of HC and its environmental applications. In this review, we will shed light on the preparation, characterization, and previous studies on the development and recent applications of HC. In addition, we will discuss the challenges to produce HC at a commercial scale. To the best of our knowledge, there is only few research studies addressing the HC production in the Middle East countries. Therefore, the door is still opened for more research on developing production techniques on HC from different biomass, and implementation in various environmental applications

New critical exponent inequalities for percolation and the random cluster model

We apply a variation on the methods of Duminil-Copin, Raoufi, and Tassion to establish a new differential inequality applying to both Bernoulli percolation and the Fortuin-Kasteleyn random cluster model. This differential inequality has a similar form to that derived for Bernoulli percolation by Menshikov but with the important difference that it describes the distribution of the volume of a cluster rather than of its radius. We apply this differential inequality to prove the following: The critical exponent inequalities $\gamma \leq \delta-1$ and $\Delta \leq \gamma +1$ hold for percolation and the random cluster model on any transitive graph. These inequalities are new even in the context of Bernoulli percolation on $\mathbb{Z}^d$, and are saturated in mean-field for Bernoulli percolation and for the random cluster model with $q \in [1,2)$. The volume of a cluster has an exponential tail in the entire subcritical phase of the random cluster model on any transitive graph. This proof also applies to infinite-range models, where the result is new even in the Euclidean setting.

Subcritical Phase Separation and Occurrence of Deep-Seated Brines at the NW Caldera Vent Field, Brothers Volcano: Evidence from Fluid Inclusions in Hydrothermal Precipitates

The northwestern caldera wall of Brothers volcano in the southern Kermadec arc features several clusters of hydrothermal venting in a large area that extends from near the caldera floor (~1700 mbsl) almost up to the crater rim (~1300 mbsl). Abundant black smoker-type hydrothermal chimneys and exposed stockwork mineralization in this area provide an excellent archive of hydrothermal processes that form seafloor massive sulfide deposits. Using sulfate precipitates from chimneys and stockwork recently recovered by remotely operated vehicles, we conducted fluid inclusion microthermometry and Sr isotope studies to determine the role of phase separation and mixing between vent fluid and seawater. The variability in the vast majority of fluid inclusion salinities (i.e., 0.1–5.25 wt.% NaCl eq.) and entrapment temperatures of up to 346°C are indicative of phase-separated hydrothermal fluids. Large salinity variations in samples with entrapment temperatures mostly below the boiling temperature for the sample’s depth show that the majority of fluids ascending below the NW Caldera are phase separating in the subsurface and cooling, prior to discharge. In several samples, entrapment temperatures of over 343°C suggest that phase-separating fluids have at least sporadically exited the seafloor at the NW Caldera site. Isobaric-isenthalpic mixing trends between coexisting phase-separated vapors and brines with seawater are consistent with phase-separated fluids at near-seafloor pressures of ~170 bar and suggest that the vast majority of the ascending fluids continue to phase separate to within tens to hundreds of meters below seafloor prior to mixing with seawater. A small subset of the most saline fluid inclusions (up to 18.6 wt.% NaCl eq.) is unlikely formed by near-seafloor phase separation and is considered to be produced either by supercritical phase separation or by the contribution of a magmatic brine from near the magmatic-hydrothermal interface. 87Sr/86Sr values of sulfate samples range from 0.7049 (i.e., near hydrothermal end-member) to 0.7090 (i.e., near seawater) and show that the crystals grew from vapor- and brine-derived fluids in a hydrothermally dominated mixing regime. Our work provides new insights into mineral growth conditions, mixing regimes, and in particular, the extent and character of subseafloor phase separation during the formation of hydrothermal vents and their underlying stockwork in seawater-dominated, arc-related hydrothermal systems.

Subcritical phase of d-dimensional Poisson–Boolean percolation and its vacant set

We prove that the Poisson–Boolean percolation on ℝ d undergoes a sharp phase transition in any dimension under the assumption that the radius distribution has a 5d-3 finite moment (in particular we do not assume that the distribution is bounded). To the best of our knowledge, this is the first proof of sharpness for a model in dimension d≥3 that does not exhibit exponential decay of connectivity probabilities in the subcritical regime. More precisely, we prove that in the whole subcritical regime, the expected size of the cluster of the origin is finite, and furthermore we obtain bounds for the origin to be connected to distance n: when the radius distribution has a finite exponential moment, the probability decays exponentially fast in n, and when the radius distribution has heavy tails, the probability is equivalent to the probability that the origin is covered by a ball going to distance n (this result is new even in two dimensions). In the supercritical regime, it is proved that the probability of the origin being connected to infinity satisfies a mean-field lower bound. The same proof carries on to conclude that the vacant set of Poisson–Boolean percolation on ℝ d undergoes a sharp phase transition.

Between supercritical liquids and gases – Reconciling dynamic and thermodynamic state transitions

Experimental, computational, and theoretical results have shown that the notion of a homogeneous supercritical state space has to be replaced with distinct liquid-like and gas-like regions, divided by a cross-over line. Several such cross-over lines have been proposed, such as the Frenkel line, the Fisher-Widom line, and the Widom line. We use thermodynamics arguments, molecular dynamics (MD) simulations, and experimental data to investigate the relation between these lines. This work proposes a new interpretation of the Widom line based on the curvature of the Gibbs free energy, showing that the supercritical cross-over can be evaluated as a projection of the subcritical phase transition from a liquid to an ideal gas state to supercritical conditions. We show that the cross-over across the Widom line should not be regarded as instantaneous, but instead as spreading over a finite temperature interval. The thermodynamic character of the Widom line becomes negligible at reduced pressures p/pcr > 3 and disappears completely at higher pressures p/pcr > 10. We find evidence that measured transitions attributed to the Widom line do in fact match the Frenkel line better. In this way, we suggest a consistent view of the supercritical state space and resolve apparent contradictions.

Gradient supercritical fluid chromatography coupled to mass spectrometry with a gradient flow of make-up solvent for enantioseparation of cathinones

In the past two decades, supercritical fluid chromatography has evolved from a niche application to a comprehensive technology and a fully-fledged alternative to conventional high-performance liquid chromatography.In this study, we have focused on chiral separation of synthetic cathinones in gradient supercritical fluid chromatography coupled to mass spectrometry using an inverse gradient of a make-up solvent. Synthetic cathinones possess an amphetamine-like effect and, therefore, are frequently being offered on the Internet as a replacement for illicit drugs. Cathinones are chiral compounds, however, they are usually marketed and used as racemic mixtures. Since the effect of individual enantiomers can significantly vary, there is a need for the development of enantioseparation methods enabling to study the biological effects of individual enantiomers. Since cathinones are basic molecules, they are easily protonated (positively charged) under weakly acidic mobile phase conditions, which is a typical feature of supercritical mobile phases with an alcohol as an organic modifier. The positively charged species represent ideal analytes for ion exchangers, such as chiral zwitterion ion exchangers Chiralpak ZWIX (+) and Chiralpak ZWIX (−), which possess a positively and negatively charged unit in the molecular structure of the selectors. The presence of the positive charge in the selector's structure, functioning as a counter-ion for the positively charged analytes, significantly reduces the required amount of a buffer, which is plausible for hyphenation of such a separation system with mass spectrometry. For mass spectrometry hyphenated to supercritical fluid chromatography, the use of a make-up solvent is required to avoid analyte precipitation when using a low concentration of an organic co-solvent (modifier) in the super-/subcritical mobile phase. Hereby, we introduce a unique approach, which is based on the gradient introduction of the make-up to the post-column effluent. Using this approach, it is possible to keep constant the overall amount of the organic solvent (modifier and make-up) introduced into the mass spectrometer when using a gradient of the organic modifier. We show that the developed gradient elution method facilitates the chiral separation of all employed analytes, while the mobile-phase gradient compensation by the inverse make-up gradient enables their detection with high signal intensities.

Investigation of the initial phases of nanosecond discharges in liquid water

In this work, we examine initial phases of micro-discharges produced in deionised water by high-voltage (HV) pulses of nanosecond duration. We apply opto-electrical diagnostics with extremely high temporal (down to 30 ps) as well as spatial (down to 1 μm) resolution. Frozen interferometric and shadowgraph images show three distinct events. The first, the subcritical (no-discharge) event, is characterised by periodic perturbations of the index of refraction which depart from the anode surface and are pulled away at the speed of sound as an expanding envelope defined by the shape of the anode tip. One-dimensional hydrodynamic modelling of the subcritical phase under conditions mimicking curvatures of real anode tips reveals basic characteristics of perturbations caused by dynamic balance between the hydrostatic and electrostrictive pressures consistent with experimental observations. The second, the dark or non-luminous discharge event, is characterised by the onset of a few isolated very tiny tree-like structures growing from the anode tip. Depending on the HV amplitude, the initial structures occur with a delay of ∼2–3 ns after onset of the HV pulse and subsequently expand with average velocity of ∼1 × 105–2 × 105 m s−1, creating very dense bush-like structures made of thin hair-like filaments in a few nanoseconds. The third, the luminous discharge event, follows (nearly simultaneously) the dark discharge event and unveils much simpler tree-like morphology determined by the extension of non-luminous bush-like structures. Characteristic dimensions of observed events range from about 1 μm (typical diameter of non-luminous filaments) to tens of micrometres (characteristic diameters of luminous filaments). Furthermore, we address a possible role of microbubbles developing in the anode region due to the periodic HV pulses and verify that the UV-vis-NIR spectrometric signatures of the luminous phase notably change when replacing non-degassed deionised water with degassed.

Impregnation of mesoporous silica with poor aqueous soluble molecule using pressurized carbon dioxide: Is the solubility in the supercritical and subcritical phase a critical parameter?

Recently, mesoporous silica (MS) has been used as a material able to maintain amorphous state of active compounds and therefore, enhance the oral bioavailability of BCSII drugs. Among impregnation methods of MS, techniques using supercritical carbon dioxide (Sc-CO2) are promising tools. Solubility of compounds in Sc-CO2 is reported as one of the most critical parameters, which usually limits its use in drug formulation. Indeed, most of compounds have poor solubility in Sc-CO2. The aim of this work is to compare different MS and to study alternative processes using pressurized CO2 for insoluble molecule in Sc-CO2. By using high pressure reactor, DSC, HPLC and in vitro dissolution tests, the crystallinity and dissolution profiles of MS with different pore size (6.6 nm, 25.0 nm and 2.5 nm) impregnated with fenofibrate (FF) under Sc-CO2 were compared to select the most appropriate carrier. Then, the selected MS has been impregnated under supercritical, subcritical and atmospheric conditions. We have shown that the MS pore size of 6.6 nm provides the higher amorphous drug loading capacity as well as the faster and higher drug dissolution. In addition, FF-MS formulations produced with pressurized CO2 as fusion medium, both in subcritical and supercritical conditions; give similar crystallinity and dissolution results compared to those produced with supercritical fluids as solvent. Through this study, we show new possibilities of using CO2 for insoluble compounds in this fluid.

Multiplicative chaos and the characteristic polynomial of the CUE: The 𝐿¹-phase

In this article we prove that suitable positive powers of the absolute value of the characteristic polynomial of a Haar distributed random unitary matrix converge in law, as the size of the matrix tends to infinity, to a Gaussian multiplicative chaos measure once correctly normalized. We prove this in the whole L 1 L^1 - or subcritical phase of the chaos measure.

A tidal-influenced hydrothermal system temporarily cooled by a tropical storm

The Lutao hydrothermal field is an intertidal arc-volcanic system located offshore southeast Taiwan, hosting a Zhudanqu (ZDQ) vent and a Huwaichi (HWC) spring with strongly contrasting fluid chemistry. Low Mg, moderately enriched Cl, and H+ with respect to seawater indicate that the ZDQ endmember was derived from the brine phase that was formed during low-degree subcritical phase separation. In contrast, the endmember for the HWC vent fluids is related to the vapor phase. Temperature and pressure of the phase separation were estimated as ~150 °C and ~7 bar, respectively. The water/rock ratio was roughly calculated as about 2.The Lutao hydrothermal system was slightly affected by semi-diurnal tides, by some combination of tidal loading and tidal currents. The time delay between tides and the response of the hydrothermal system was about 3 h. While freshwater was almost absent in the HWC vent fluids at normal conditions, the typhoon “Fung-wong” on Sep 21st, 2014, led to intrusions of freshwater into the vent fluids with a percentage of ~16%. Both the ZDQ and the HWC endmember compositions showed some changes after the typhoon event, suggesting a cooling of the reaction zone. After the typhoon passed by, the hydrothermal system began to recover, evidenced by increasing percentages of the HWC endmember and decreasing freshwater contributions. The flux of the HWC endmember was estimated as 460–560 L h−1 based on these observations. This study, for the first time, reports a shallow-depth tidal-influenced hydrothermal system that was temporarily cooled by a tropical storm.

Biased Random Walk Conditioned on Survival Among Bernoulli Obstacles: Subcritical Phase

We consider a discrete time biased random walk conditioned to avoid Bernoulli obstacles on ${\mathbb Z}^d$ ($d\geq 2$) up to time $N$. This model is known to undergo a phase transition: for a large bias, the walk is ballistic whereas for a small bias, it is sub-ballistic. We prove that in the sub-ballistic phase, the random walk is contained in a ball of radius $O(N^{1/(d+2)})$, which is the same scale as for the unbiased case. As an intermediate step, we also prove large deviation principles for the endpoint distribution for the unbiased random walk at scales between $N^{1/(d+2)}$ and $o(N^{d/(d+2)})$. These results improve and complement earlier work by Sznitman [Ann. Sci. Ecole Norm. Sup. (4), 28(3):345--370, 371--390, 1995].

Devil’s staircases in a thermoacoustic system with sinusoidal excitations

The influences of sinusoidal excitations on a Rijke tube system through the introduction of nonlinear dynamics are investigated in detail. The system is governed by one-dimensional partial differential equations, which are addressed by means of the Galerkin procedure and analysed from the viewpoint of nonlinear dynamics. The results show a rich variety of behaviours in the system, including subcritical bifurcation, hysteresis and phase locking. In certain parameter ranges, the solution switches between periodic and quasi-periodic. These ranges mainly depend on the intensity of the heat source in the tube. The phase-locking intervals that correspond to periodic solutions compose a devil’s staircase, whose Lebesgue measure increases as the amplitude of the excitation increases.

Process simulation of impurity impacts on CO2 fluids flowing in pipelines

Captured carbon dioxide flowing in pipelines is impure. The impurities contained in the carbon dioxide fluid impact on the properties of the fluid. The impact of each impurity has not been adequately studied and fully understood. In this study, binary mixtures containing carbon dioxide and one impurity, at the maximum permitted concentration, flowing in pipelines are studied to understand their impact on pipeline performance. A hypothetical 70 km uninsulated pipeline is assumed and simulated using Aspen HYSYS (v.10) and gPROMS (v.5.1.1). The mass flow rate is 2,200,600 kg/h; the internal and external diameters are 0.711 m and 0.785 m. 15 MPa and 9 MPa were assumed as inlet and minimum pressures and 33 °C as the inlet temperature, to ensure that the fluid remain in the dense (subcritical or supercritical) phase. Each binary fluid is studied at the maximum allowable concentration and deviations from pure carbon dioxide at the same conditions is determined. These deviations were graded to rank the impurities in order of the degree of impact on each parameter. All impurities had at least one negative impact on carbon dioxide fluid flow. Nitrogen with the highest concentration (10-mol %) had the worst impact on pressure loss (in horizontal pipeline), density, and critical pressure. Hydrogen sulphide (with 1.5-mol %) had the least impact, hardly changing the thermodynamic properties of pure carbon dioxide.

Phase Transition to Large Scale Coherent Structures in Two-Dimensional Active Matter Turbulence.

The collective motion of microswimmers in suspensions induce patterns of vortices on scales that are much larger than the characteristic size of a microswimmer, attaining a state called bacterial turbulence. Hydrodynamic turbulence acts on even larger scales and is dominated by inertial transport of energy. Using an established modification of the Navier-Stokes equation that accounts for the small-scale forcing of hydrodynamic flow by microswimmers, we study the properties of a dense suspension of microswimmers in two dimensions, where the conservation of enstrophy can drive an inverse cascade through which energy is accumulated on the largest scales. We find that the dynamical and statistical properties of the flow show a sharp transition to the formation of vortices at the largest length scale. The results show that 2D bacterial and hydrodynamic turbulence are separated by a subcritical phase transition.