Discontinuous Transition Research Articles

Poloxamer 407 and Hyaluronic Acid Thermosensitive Hydrogel-Encapsulated Ginsenoside Rg3 to Promote Skin Wound Healing.

Ginsenoside Rg3 has shown beneficial effects in various skin diseases. The current interest in designing and developing hydrogels for biomedical applications continues to grow, inspiring the further development of drug-loaded hydrogels for tissue repair and localized drug delivery. The aim of the present study was to develop an effective and safe hydrogel (Rg3-Gel), using ginsenoside Rg3, and we evaluated the wound-healing potential and therapeutic mechanism of Rg3-Gel. The results indicated that the optimized Rg3-Gel underwent discontinuous phase transition at low and high temperatures. Rg3-Gel also exhibited good network structures, swelling water retention capacity, sustainable release performance, and excellent biocompatibility. Subsequently, the good antibacterial and antioxidant properties of Rg3-Gel were confirmed by in vitro tests. In full-thickness skin defect wounded models, Rg3-Gel significantly accelerated the wound contraction, promoted epithelial and tissue regeneration, and promoted collagen deposition and angiogenesis. In addition, Rg3-Gel increased the expression of autophagy proteins by inhibiting the MAPK and NF-KB pathways in vivo. It simultaneously regulated host immunity by increasing the abundance of beneficial bacteria and the diversity of the wound surface flora. From these preliminary evaluations, it is possible to conclude that Rg3-Gel has excellent application potential in wound-healing drug delivery systems.

Pattern formation and phase transition in the collective dynamics of a binary mixture of polar self-propelled particles.

The collective behavior of a binary mixture of polar self-propelled particles (SPPs) with different motile properties is studied. The binary mixture consists of slow-moving SPPs (sSPPs) of fixed velocity v_{s} and fast-moving SPPs (fSPPs) of fixed velocity v_{f}. These SPPs interact via a short-range interaction irrespective of their types. They move following certain position and velocity update rules similar to the Vicsek model (VM) under the influence of an external noise η. The system is studied at different values of v_{f} keeping v_{s}=0.01 constant for a fixed density ρ=0.5. Different phase-separated collective patterns that appear in the system over a wide range of noise η are characterized. The fSPPs and the sSPPs are found to be orientationally phase synchronized at the steady state. We studied an orientational order-disorder transition varying the angular noise η and identified the critical noise η_{c} for different v_{f}. Interestingly, both the species exhibit continuous transition for v_{f}<100v_{s} and discontinuous transition for v_{f}>100v_{s}. A new set of critical exponents is determined for the continuous transitions. However, the binary model is found to be nonuniversal as the values of the critical exponents depend on the velocity. The effect of interaction radius on the system behavior is also studied.

Cooperative epidemic spreading in simplicial complex

Higher-order interaction exists widely in real-world networks and dramatically affects the system’s phase transition and critical phenomena. In the study of epidemic spreading dynamics on higher-order networks, the discontinuous phase transition and bistable physical phenomena have attracted the attention of many scholars. However, epidemics are rarely spread individually but are spread on high-order networks so that multiple epidemics interact mutually. The dynamics of promoting transmission on higher-order networks still lack research. This paper explored the cooperative spreading of two epidemics in the simplicial complex, which simultaneously includes structural and dynamical reinforcement effects. We use the Markov chain and mean-field methods to predict the outbreak size and threshold for theoretical analysis. Increase the structural or dynamical reinforcement effect, and the spreading dynamics are promoted, i.e., a more significant outbreak size and smaller threshold. When the two reinforcement effects are strong, the system will have a discontinuous phase transition and hysteresis loop, and a large initial seed size will lead to the easy outbreak of the epidemic. For the greater initial seed size, the dynamical reinforcement effect affects the outbreak size in most cases.

Pair approximation for the q -voter models with quenched disorder on networks

Using two models of opinion dynamics, the q-voter model with independence and the q-voter model with anticonformity, we discuss how the change of disorder from annealed to quenched affects phase transitions on networks. To derive phase diagrams on networks, we develop the pair approximation for the quenched versions of the models. This formalism can be also applied to other quenched dynamics of similar kind. The results indicate that such a change of disorder eliminates all discontinuous phase transitions and broadens ordered phases. We show that although the annealed and quenched types of disorder lead to the same result in the q-voter model with anticonformity at the mean-field level, they do lead to distinct phase diagrams on networks. These phase diagrams shift towards each other as the average node degree of a network increases, and eventually, they coincide in the mean-field limit. In contrast, for the q-voter model with independence, the phase diagrams move towards the same direction regardless of the disorder type, and they do not coincide even in the mean-field limit. To validate our results, we carry out Monte Carlo simulations on random regular graphs and Barabási-Albert networks. Although the pair approximation may incorrectly predict the type of phase transitions for the annealed models, we have not observed such errors for their quenched counterparts.

Offline motion libraries and online MPC for advanced mobility skills

We describe an optimization-based framework to perform complex locomotion skills for robots with legs and wheels. The generation of complex motions over a long-time horizon often requires offline computation due to current computing constraints and is mostly accomplished through trajectory optimization (TO). In contrast, model predictive control (MPC) focuses on the online computation of trajectories, robust even in the presence of uncertainty, albeit mostly over shorter time horizons and is prone to generating nonoptimal solutions over the horizon of the task’s goals. Our article’s contributions overcome this trade-off by combining offline motion libraries and online MPC, uniting a complex, long-time horizon plan with reactive, short-time horizon solutions. We start from offline trajectories that can be, for example, generated by TO or sampling-based methods. Also, multiple offline trajectories can be composed out of a motion library into a single maneuver. We then use these offline trajectories as the cost for the online MPC, allowing us to smoothly blend between multiple composed motions even in the presence of discontinuous transitions. The MPC optimizes from the measured state, resulting in feedback control, which robustifies the task’s execution by reacting to disturbances and looking ahead at the offline trajectory. With our contribution, motion designers can choose their favorite method to iterate over behavior designs offline without tuning robot experiments, enabling them to author new behaviors rapidly. Our experiments demonstrate complex and dynamic motions on our traditional quadrupedal robot ANYmal and its roller-walking version. Moreover, the article’s findings contribute to evaluating five planning algorithms.

Superfluid transition temperature and fluctuation theory of spin-orbit- and Rabi-coupled fermions with tunable interactions

We obtain the superfluid transition temperature of equal Rashba-Dresselhaus spin-orbit- and Rabi-coupled Fermi superfluids, from the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) regimes in three dimensions for tunable $s$-wave interactions. In the presence of Rabi coupling, we find that spin-orbit coupling enhances (reduces) the critical temperature in the BEC (BCS) limit. For fixed interactions, we show that spin-orbit coupling can convert a first-order (discontinuous) phase transition into a second-order (continuous) phase transition, as a function of Rabi coupling. We derive the Ginzburg-Landau free energy to sixth power in the superfluid order parameter to describe both continuous and discontinuous phase transitions as a function of spin-orbit and Rabi couplings. Lastly, we develop a time-dependent Ginzburg-Landau fluctuation theory for an arbitrary mixture of Rashba and Dresselhaus spin-orbit couplings at any interaction strength.

Melting upon Coalescence of Solid Nanoparticles

The large surface-to-volume ratio of nanoparticles is understood to be the source of many interesting phenomena. The melting temperature of nanoparticles is shown to dramatically reduce compared to bulk material. Yet, at temperatures below this reduced melting point, a liquid-like atomic arrangement on the surface of nanoparticles is still anticipated to influence its properties. To understand such surface effects, here, we study the coalescence of Au nanoparticles of various sizes using molecular dynamics simulations. Analysis of the potential energy and Lindemann index distribution across the nanoparticles reveals that high-energy, high-mobility surface atoms can enable the coalescence of nanoparticles at temperatures much lower than their corresponding melting point. The smaller the nanoparticles, the larger the difference between their melting and coalescence temperatures. For small enough particles and/or elevated enough temperatures, we found that the coalescence leads to a melting transition of the two nominally solid nanoparticles, here discussed in relation to the heat released due to the surface reduction upon the coalescence and the size dependence of latent heat. Such discontinuous melting transitions can lead to abrupt changes in the properties of nanoparticles, important for their applications at intermediate temperatures.

Quantum contact process on scale-free networks

The quantum contact process (QCP), a combination of the quantum coherent and classical incoherent processes, exhibits a quantum absorbing phase transition (QAPT). Most studies of the QCP have focused on the case in which active states are induced by the s-excited state of Rydberg atoms. Thus, quantum coherence is induced by short-range interactions. In this case, a QAPT in one dimension is second-order. However, when active states are induced by the d-excited state, long-range interactions must be considered. In this case, even in one dimension, a discontinuous transition occurs. Thus, the type of QAPT depends on interaction range. Here, we aim to investigate how the QAPT depends on embedded structure and thus consider the QCP model on scale-free (SF) networks, in which the degree distribution follows a power law Pd(k) ~ k−λ and the mean distance between two nodes depends on system size N logarithmically. Thus, we can find how the QAPT depends on interaction range and the heterogeneity of the number of connections simultaneously. We find analytically that various types of QAPTs emerge depending on the degree exponent λ. Finally, we compare the properties of the PT of the QCP with those of its classical counterparts.

Information propagation influenced by individual fashion-passion trend on multi-layer weighted network

In recent years, prior research on information propagation has considered individual relationships on social network as binary but ignored individual intimacy heterogeneity. Furthermore, individuals like to concurrently use multiple social networks and meanwhile show different passions for information acceptance, called individual fashion-passion trend (IFPT) characteristics. Therefore, we first construct a multi-layer weighted social network to catch individual intimacy heterogeneity, and then build an adoption threshold model with tent-like probability function to explore the IFPT characteristics. Next a partition theory based on edge-weight and IFPT threshold is utilized to quantify and analyze individual information propagation mechanism. The simulated results and theoretical analyses exhibit crossover phenomena of phase transition. When individual has a strong IFPT, the increasing style of the final adoption size shows a second-order continuous phase transition. While individual has a weak IFPT, the increasing style of the final adoption size exhibits a first-order discontinuous phase transition. More excitingly, fixing the value of the information propagation unit probability, a maximum final adoption size can be obtained at an optimal IFPT value. Moreover, weight distribution heterogeneity accelerates information propagation and the change of phase transition style from the second-order continuous phase transition to first-order discontinuous phase transition. Finally, our theoretical analyses coincide with the simulated results.

Suppression of discontinuous phase transitions by particle diffusion.

We investigate the phase transitions of the q-state Brownian Potts model in two dimensions (2D) comprising Potts spins that diffuse like Brownian particles and interact ferromagnetically with other spins within a fixed distance. With extensive Monte Carlo simulations we find a continuous phase transition from a paramagnetic to a ferromagnetic phase even for q>4. This is in sharp contrast to the existence of a discontinuous phase transition in the equilibrium q-state Potts model in 2D with q>4. We present detailed numerical evidence for a continuous phase transition and argue that diffusion generated dynamical positional disorder suppresses phase coexistence leading to a continuous transition.

Strength and salt/pH dependent-sorption capacity modulation of N-(alkyl)acrylamide-based semi-IPN hybrid gels reinforced with silica nanoparticles

A simple methodology was described for design of anionically modified thermosensitive organic-inorganic hybrid gels using silica nanoparticle-mediated semi-interpenetrating polymer networks. A thermosensitive copolymer poly(N-isopropylacrylamide-co-methacrylic acid), P(NIPA-MA), with linear polyacrylamide (LPA) chains was synthesized by conducting free radical polymerization under warm and cold conditions using NIPA and MA in the presence of SiO2 nanoparticles. Simple mixing of aqueous monomer solution with linear LPA chains and silica suspensions led to the formation of ionic thermosensitive hybrid gels. The effect of changes in solution environment on the swelling and elastic properties was investigated. Sodium salts of CH3COO−, NO3−, and SCN− were employed to understand specific ion effects and to gain an insight into the influence of kosmotrope and chaotrope solutes on swelling and elasticity at various ionic strength and temperature. The identity of counterion had a strong influence on swelling and compression modulus and was found to follow the reverse order of classical Hofmeister series (HS). The phase transition temperature decreased with increasing salt concentration, and transition changed from discontiuous to continuous. At low salt concentrations, the gels showed discontinuous phase transition at 50 °C, while transition temperature shifts towards 35–45 °C with increasing salt concentration. Dilution of the solution to 10−3 M resulted in a 2.0-fold reduction in compressive modulus of hybrid gels in NaAc solutions while a 3.0-fold reduction in NaSCN solutions. Compression modulus increased with shrinkage of hybrids due to increasing salt concentration. The effect of pH change of swelling medium on the swelling, phase transition profile and elasticity was evaluated. The continuity of pH-dependent swelling curve depended on swelling temperature. pH-triggered oscillation kinetics have been investigated to understand whether they can be used as a pH oscillator since the phase transition pH is close to 5.7. The swelling of NP-loaded hybrids followed a Fickian type diffusion. NP-loaded semi-IPN hybrid gels with typical feature of anionic structure were applied for adsorption of cationic dye methyl violet (MV). Different adsorption isotherm models were investigated to describe interfacial adsorption of MV which was strongly dependent on composition of hybrids. Langmuir isotherm model was found to be most appropriate to describe adsorption process. The superior properties imparted to the present system prepared with anionic modification, semi-IPN structure and NP-loading make semi-IPN hybrid gels suitable candidates for controlled release systems and for adsorbents of cationic dyes.

Influence of radial fuel staging on combustion instabilities and exhaust emissions from lean-premixed multi-element hydrogen/methane/air flames

The utilization of hydrogen-blended hydrocarbon fuels, or even completely carbon-free fuels like pure hydrogen and ammonia, will be indispensable in the effort to reduce anthropogenic carbon dioxide emissions from heavy-duty land-based gas turbines. In order to make this energy transition, however, low emissions, low dynamics fuel-flexible gas turbine combustion systems will be required. To address some of the key technological obstacles in the development of such systems, we explore a prototype multi-element injector assembly devised to prevent flashback in extremely fast premixed hydrogen flames, paying particular attention to the impact of radial dual-fuel staging on the generation of self-induced instabilities and the formation of nitrogen oxides and carbon monoxide. In conjunction with phase-averaged OH*/CH* chemiluminescence and OH PLIF flame imaging, we carry out extensive measurements over the full range of 0 to 100% H2/CH4 fuel staging conditions, including even/uneven blends of H2/CH4 fuels between inner and outer nozzle groups, partial/complete fuel split cases, and pure H2 or CH4 fuel for all constituent flames, under a constant thermal power condition of 78 kW. Our measurements demonstrate that whereas carbon monoxide concentrations are largely unaffected by the radial fuel staging conditions except under high and pure hydrogen percentage conditions, there exists a strong correlation between total nitrogen oxides emissions and overall adiabatic flame temperature. Integrated analyses of isocontour instability maps reveal that near XH2,g = 0.50 a discontinuous mode transition takes place, where the intermediate-amplitude lower frequency oscillations associated with relatively low hydrogen concentration conditions give way to stronger, higher frequency instabilities under high hydrogen content conditions. While even-blend (non-staging) conditions are characterized by coherent oscillations of the constituent flames, the responses of clustered flames to radial fuel staging conditions are eccentric and complex, manifested as large-scale asynchronous modulations between inner- and outer-stage heterogeneous reaction zones. This observation suggests that in a multi-element injector environment spatiotemporal incoherence driven by inhomogeneous heat release can be used to neutralize self-excited pressure oscillations, by disrupting pressure-heat release coupling processes.

The AdS𝜃2/CFT1 correspondence and noncommutative geometry II: Noncommutative quantum black holes

In this paper, we present the construction of noncommutative [Formula: see text] black hole and its four-dimensional Yang–Mills IKKT-type matrix model which includes two competing Myers term one responsible for the condensation of pure [Formula: see text] and the other one responsible for the condensation of the dilaton field. It is argued that the phase diagram of this matrix model features three phases: (1) a gravitational phase ([Formula: see text] black hole), (2) a geometric phase ([Formula: see text] background) and (3) a Yang–Mills phase. The Hawking process is therefore seen as an exotic line of discontinuous transitions between the gravitational and geometrical phases. Alternatively, a noncommutative nonlinear sigma model describing the transition of the dilaton field between the gravitational and geometrical phases is also constructed.

Robustness of noisy quantum networks

Quantum networks allow us to harness networked quantum technologies and to develop a quantum internet. But how robust is a quantum network when its links and nodes start failing? We show that quantum complex networks based on typical noisy quantum-repeater nodes are prone to discontinuous phase transitions with respect to the random loss of operating links and nodes, abruptly compromising the connectivity of the network, and thus significantly limiting the reach of its operation. Furthermore, we determine the critical quantum-repeater efficiency necessary to avoid this catastrophic loss of connectivity as a function of the network topology, the network size, and the distribution of entanglement in the network. From all the network topologies tested, a scale-free network topology shows the best promise for a robust large-scale quantum internet.

First passage in the presence of stochastic resetting and a potential barrier.

Diffusion and first passage in the presence of stochastic resetting and potential bias have been of recent interest. We study a few models, systematically progressing in their complexity, to understand the usefulness of resetting. In the parameter space of the models, there are multiple continuous and discontinuous transitions where the advantage of resetting vanishes. We show these results analytically exactly for a tent potential, and numerically accurately for a quartic potential relevant to a magnetic system at low temperatures. We find that the spatial asymmetry of the potential across the barrier, and the number of absorbing boundaries, play a crucial role in determining the type of transition.

Percolation of interdependent networks with limited knowledge.

Real-world networks are often not isolated and the interdependence between different networks in a complex system is as important as the topological connectivity within individual networks. We develop a theoretical framework to study the robustness of interdependent networks under attacks with limited knowledge. A node may be attacked if it is the most connected node among a given number of potential victims. This number is referred to as the attacker's knowledge level, which joins the two ends, namely, the random failure with zero knowledge and the intentional attack with full knowledge of the network. We introduce percolation models with attacks over one layer and two layers as well as mixed site-bond percolation. Along with the discontinuous phase transition, we show the existence of a critical knowledge level, which indicates a transition of network robustness under the competition between connectivity and interdependence. It is unraveled that interdependent networks can be extremely fragile to the extent that a random failure on two layers would be more deleterious than a targeted attack with full knowledge over one layer. Moreover, we find that a balanced distribution of attack knowledge on both layers tends to be most destructive if the total knowledge is a conserved quantity.

Effects of measures on phase transitions in two cooperative susceptible-infectious-recovered dynamics

In recent studies, it has been shown that a cooperative interaction in a co-infection spread can lead to a discontinuous transition at a decreased threshold. Here, we investigate the effects of immunization with a rate proportional to the extent of the infection on phase transitions of a cooperative co-infection. We use the mean-field approximation to illustrate how measures that remove a portion of the susceptible compartment, like vaccination, with high enough rates can change discontinuous transitions in two coupled susceptible-infectious-recovered dynamics into continuous ones while increasing the threshold of transitions. First, we introduce vaccination with a fixed rate into a symmetric spread of two diseases and investigate the numerical results. Second, we set the rate of measures proportional to the size of the infectious compartment and scrutinize the dynamics. We solve the equationsnumerically and analytically and probe the transitions for a wide range of parameters. We also determine transition points from the analytical solutions. Third, we adopt a heterogeneous mean-field approach to include heterogeneity and asymmetry in the dynamics and see if the results corresponding to homogeneous symmetric case stand.

Cascading-Failures Effect on Heterogeneous Internet of Things Systems under Targeted Selective Attack

With the rapid development of the Internet of Things (IoT), the physical system and the network space are further deeply integrated, forming a larger-scale IoT heterogeneous fusion system. The attack mode considered in the security mechanism research of traditional large-scale complex systems is relatively simple; only simple attack types such as random attacks on physical systems or network systems are considered. In addition, existing attack modalities such as selectivity, locality, and distribution cannot fully consider the characteristics of security threats in the IoT system. In this paper, for large-scale heterogeneous IoT system scenarios, attackers can attack network systems or physical systems through cyberspace. We conduct situational awareness analysis on important traffic nodes or backbone nodes and study the cascading failures of two interdependent heterogeneous space systems. In view of the existence of such targeted attack threats in large-scale IoT heterogeneous systems, we focus on security assessment and risk prediction issues. First, this paper analyzes and models different IoT heterogeneous systems. Then using the penetration theory, we analyze the cascading failure process step by step and obtain the critical threshold for system collapse failure. Finally, we further verify the correctness of the theoretical values through simulation to effectively analyze and illustrate the reliability of the parameters affecting the system risk. The experimental results show that the large-scale IoT heterogeneous system presents a first-order discontinuous transition value near the critical threshold and the power-law index of the SF network has little effect on the system security.

The fate of shear-oscillated amorphous solids.

The behavior of shear-oscillated amorphous materials is studied using a coarse-grained model. Samples are prepared at different degrees of annealing and then subjected to athermal and quasi-static oscillatory deformations at various fixed amplitudes. The steady-state reached after several oscillations is fully determined by the initial preparation and the oscillation amplitude, as seen from stroboscopic stress and energy measurements. Under small oscillations, poorly annealed materials display shear-annealing, while ultra-stabilized materials are insensitive to them. Yet, beyond a critical oscillation amplitude, both kinds of materials display a discontinuous transition to the same mixed state composed of a fluid shear-band embedded in a marginal solid. Quantitative relations between uniform shear and the steady-state reached with this protocol are established. The transient regime characterizing the growth and the motion of the shear band is also studied.

Hidden transition in multiplex networks

Weak multiplex percolation generalizes percolation to multi-layer networks, represented as networks with a common set of nodes linked by multiple types (colors) of edges. We report a novel discontinuous phase transition in this problem. This anomalous transition occurs in networks of three or more layers without unconnected nodes, P(0),=,0. Above a critical value of a control parameter, the removal of a tiny fraction Delta of nodes or edges triggers a failure cascade which ends either with the total collapse of the network, or a return to stability with the system essentially intact. The discontinuity is not accompanied by any singularity of the giant component, in contrast to the discontinuous hybrid transition which usually appears in such problems. The control parameter is the fraction of nodes in each layer with a single connection, Pi ,=,P(1). We obtain asymptotic expressions for the collapse time and relaxation time, above and below the critical point Pi _c, respectively. In the limit Delta rightarrow 0 the total collapse for Pi ,>,Pi _text {c} takes a time T propto 1/(Pi -Pi _text {c}), while there is an exponential relaxation below Pi _text {c} with a relaxation time tau propto 1/[Pi _text {c}-Pi ].