Quasi-stationary Research Articles

Initiations of Mesoscale Convective Systems in the Middle Reaches of the Yangtze River Basin Based on FY‐4A Satellite Data: Statistical Characteristics and Environmental Conditions

AbstractBased on the brightness temperature observed by the Fengyun‐4A satellite, eight hundred mesoscale convective systems (MCSs) are identified in the middle reaches of the Yangtze River Basin during the warm seasons (April–September) of 2018–2021, and these MCSs are categorized into the quasistationary (QS) type and the outward‐moving (OM; i.e., moving beyond the source region) type. Afterward, the initiations of the MCSs are backward tracked using a hybrid method of areal overlapping and optical flow. Then, the main features of QS‐MCSs and OM‐MCSs and their respective synoptic circulations and environmental parameters are analyzed. The QS‐MCSs primarily occur in July and August and are mainly initiated in the afternoon. The OM‐MCSs mostly occur in June and July with two initiation peaks at noon and late night, respectively. The QS‐MCSs are mainly initiated in mountainous areas. In contrast, the OM‐MCSs are mainly initiated in plain areas. Compared to the OM‐MCSs, the QS‐MCSs show notable diurnal variation in intensity and develop more rapidly. Circulations of a total of 285 days (without direct influences from tropical cyclones) are objectively classified into three patterns by using the k‐means algorithm. Pattern‐I, which is closely related to low‐level jets, shows the most similar features to those of typical Mei‐yu fronts, and it acts as the most favorable circulation type for MCS initiations. Pattern‐II is dominated by northwesterlies, with a relatively stable layer in the low‐level troposphere. Pattern‐III features a dry‐adiabatic or even a superadiabatic layer that contributes to decreasing the layer stability.

Numerical study on the characteristics of the seismic response of subway shield tunnels beneath rock mountains: A case study in China

In this study, we investigated the characteristics of the seismic response of a subway shield tunnel beneath a rock mountain through the finite-element method based on a practical subway tunnel project in China. We discuss the influence of the spectral nonstationarity of seismic motion on tunnel responses. First, a set of quasistationary (QS) and fully nonstationary (FN) bedrock motions were artificially simulated. Second, the background information of the referenced project was briefly discussed, and correspondingly, several refined numerical models were established. Finally, the mutual relationship between a subway tunnel and the overlying rock mountains under QS bedrock motions was studied, and the results under the QS and FN bedrock motions were compared to clarify the effect of the spectral nonstationarity of ground motions. We found that i) an overlying rock mountain can suppress the acceleration response of an underground tunnel, and combined with the seismic motion, high confining pressure owing to the existence of an overlying mountain aggravates the radial shear-stress response and damage to the tunnel; ii) the spectral nonstationarity of input motions results in higher acceleration responses at the mountaintop and on the tunnel and causes greater radial shear stress and damage to the tunnel, even though the input PGAs and waveforms for QS and FN motions are the same. Therefore, artificial seismic motions exhibiting spectral nonstationarity may provide conservative results.

Simple quasistationary method for simulations of epidemic processes with localized states

Epidemic processes on random graphs or networks are marked by localization of activity that can trap the dynamics into a metastable state, confined to a subextensive part of the network, before visiting an absorbing configuration. Quasistationary (QS) method is a technique to deal with absorbing states for finite sizes and has played a central role in the investigation of epidemic processes on heterogeneous networks where localization is a hallmark. The standard QS method possesses high computer and algorithmic complexity for large systems besides parameters whose choice are not systematic. However, simpler approaches, such as a reflecting boundary condition (RBC), are not able to capture the localization effects as the standard QS method does. In the present work, we propose a QS method that consists of reactivating nodes proportionally to the time they were active along the preceding simulation. The method is compared with the standard QS and RBC methods for the susceptible-infected-susceptible model on complex networks, which is a prototype of a dynamic process with strong localization effects. We verify that the method performs as well the as standard QS in all investigated simulations, providing the same scaling exponents, epidemic thresholds, and localized phases, thus overcoming the limitations of other simpler approaches. We also report that the present method has significant lower computer and algorithmic complexity than the standard QS method. So, this method arises as a simpler and efficient tool to analyze localization on heterogeneous structures through QS simulations.

The comparison of statistical features and synoptic circulations between the eastward-propagating and quasi-stationary MCSs during the warm season around the second-step terrain along the middle reaches of the Yangtze River

Mesoscale convective systems (MCSs) around the second-step terrain (106°–113°E, 28°–35°N), along the middle reaches of the Yangtze River, were detected, tracked and classified using a black body temperature (TBB) dataset during May to August 2000–2016 (except 2005). The MCSs were divided into eastward-propagating (EP) and quasi-stationary (QS) types, to compare their spatial and temporal distributions and convective intensities, and to identify the favorable synoptic conditions for the formation and evolution of EP MCSs. The results showed that both MCS types occurred most often in July. The EP MCSs were mainly initiated over the eastern regions of the study area, while the QS type mainly originated in the western regions of the study area. Both MCS types mainly formed in the afternoon, but a second peak occurred in the early morning for QS MCSs. The EP MCSs had a larger cloud area at their mature stage and a lower cloud brightness temperature, indicating more intense convection. Additionally, the longer lifetime and further eastward propagation of the EP MCSs meant that they had a great influence on the precipitation over the middle and lower reaches of the Yangtze River. Synoptic circulation analysis demonstrated that the combination of the mid-level low trough east of the Tibetan Plateau (TP), and the western pacific subtropical high (WPSH), favored the formation and eastward propagation of EP MCSs. The positive vertical relative vorticity and stronger vertical wind shear provided dynamic conditions favorable for convective organization and development. Furthermore, a stronger low level jet imported warm and moist air to the eastern edge of, and the regions east of, the second-step terrain. The substantial convergence of water vapor promoted the development and long-lived maintenance of the EP MCSs.

Superluminal moving defects in the Ising spin chain

Quantum excitations in lattice systems always propagate at a finite maximum velocity. We probe this mechanism by considering a defect travelling at a constant velocity in the quantum Ising spin chain in transverse field. Independently of the microscopic details of the defect, we characterize the expectation value of local observables at large times and large distances from the impurity, where a Local Quasi Stationary State (LQSS) emerges. The LQSS is strongly affected by the defect velocity: for superluminal defects, it exhibits a growing region where translational invariance is spontaneously restored. We also analyze the behavior of the friction force exerted by the many-body system on the moving defect, which reflects the energy required by the LQSS formation. Exact results are provided in the two limits of extremely narrow and very smooth impurity. Possible extensions to more general free-fermion models and interacting systems are discussed

Sampling methods for the quasistationary regime of epidemic processes on regular and complex networks.

A major hurdle in the simulation of the steady state of epidemic processes is that the system will unavoidably visit an absorbing, disease-free state at sufficiently long times due to the finite size of the networks where epidemics evolves. In the present work, we compare different quasistationary (QS) simulation methods where the absorbing states are suitably handled and the thermodynamical limit of the original dynamics can be achieved. We analyze the standard QS (SQS) method, where the sampling is constrained to active configurations, the reflecting boundary condition (RBC), where the dynamics returns to the pre-absorbing configuration, and hub reactivation (HR), where the most connected vertex of the network is reactivated after a visit to an absorbing state. We apply the methods to the contact process (CP) and susceptible-infected-susceptible (SIS) models on regular and scale free networks. The investigated methods yield the same epidemic threshold for both models. For CP, that undergoes a standard collective phase transition, the methods are equivalent. For SIS, whose phase transition is ruled by the hub mutual reactivation, the SQS and HR methods are able to capture localized epidemic phases while RBC is not. We also apply the autocorrelation time as a tool to characterize the phase transition and observe that this analysis provides the same finite-size scaling exponents for the critical relaxation time for the investigated methods. Finally, we verify the equivalence between RBC method and a weak external field for epidemics on networks.

Activity, diffusion, and correlations in a two-dimensional conserved stochastic sandpile

We perform large-scale simulations of a two-dimensional restricted height conserved stochastic sandpile, focusing on particle diffusion and mobility, and spatial correlations. Quasistationary (QS) simulations yield the critical particle density to high precision [pc = 0.7112687(2)], and show that the diffusion constant scales in the same manner as the activity density, as found previously in the one-dimensional case. Short-time scaling is characterized by subdiffusive behavior (mean-square displacement ∼ tγ with γ < 1), which is easily understood as a consequence of the initial decay of activity, ρ(t) ∼ t−δ, with γ = 1 − δ. We verify that at criticality, the activity-activity correlation function , as expected at an absorbing-state phase transition. Our results for critical exponents are consistent with, and somewhat more precise than, predictions derived from the Langevin equation for stochastic sandpiles in two dimensions.

Prediction of Multipactor Breakdown for Multicarrier Applications: The Quasi-Stationary Method

A new prediction algorithm for multipactor breakdown determination in multicarrier signals is presented. This new algorithm assumes a quasi-stationary (QS) model based on the nonstationary theory for single-carrier signals. It determines the worst case, i.e., the combination of signal phases that yields the lowest breakdown level per carrier, using multipactor electron growth models. It considers the secondary emission yield properties of the material and the time-varying value of the multicarrier signal envelope.

Quasistationary simulations of the contact process on quenched networks

We present high-accuracy quasistationary (QS) simulations of the contact process in quenched networks, built using the configuration model with both structural and natural cutoffs. The critical behavior is analyzed in the framework of the anomalous finite-size scaling which was recently shown to hold for the contact process on annealed networks. It turns out that the quenched topology does not qualitatively change the critical behavior, leading only (as expected) to a shift of the transition point. The anomalous finite-size scaling holds with exactly the same exponents of the annealed case, so we can conclude that heterogeneous mean-field theory works for the contact process on quenched networks, at odds with previous claims. Interestingly, topological correlations induced by the presence of the natural cutoff do not alter the picture.

Quasistationary analysis of the contact process on annealed scale-free networks

We present an analysis of the quasistationary (QS) state of the contact process (CP) on annealed scale-free networks using a mapping of the CP dynamics in a one-step process and analyzing numerically and analytically the corresponding master equation. The relevant QS quantities determined via the master equation exhibit an excellent agreement with direct QS stochastic simulations of the CP. The high accuracy of the resulting data allows a probe of the strong corrections to scaling present in both the critical and supercritical regions, corrections that mask the correct finite-size scaling obtained analytically by applying an exact heterogeneous mean-field approach. Our results represent a promising starting point for a deeper understanding of the contact process and absorbing phase transitions on real (quenched) complex networks.

Conserved directed percolation: exact quasistationary distribution of small systems andMonte Carlo simulations

We study symmetric sleepy random walkers, a model exhibiting an absorbing-state phasetransition in the conserved directed percolation (CDP) universality class. Unlike mostexamples of this class studied previously, this model possesses a continuously variablecontrol parameter, facilitating analysis of critical properties. We study the model using twocomplementary approaches: analysis of the numerically exact quasistationary (QS)probability distribution on rings of up to 22 sites, and Monte Carlo simulationof systems of up to 32 000 sites. The resulting estimates for critical exponentsβ, , and z, and themoment ratio m211 = ⟨ρ2⟩/⟨ρ⟩2 (ρ is the activity density), based on finite-size scaling at the critical point, are in agreementwith previous results for the CDP universality class. We find, however, that theapproach to the QS regime is characterized by a value of the dynamic exponentz different than that found in the QS regime.

Modeling Wind Turbines in the Simulation of Power System Dynamics

Modeling Wind Turbines in the Simulation of Power System DynamicsThis paper deals with the modeling of variable speed wind turbines for stability studies. Using the space-phasor representation and the fundamental relationships governing the operation of the machine quasi stationary model, suitable control algorithms for the simulation of the doubly-fed induction machine (DFIM) as well as the permanent magnet synchronous machine (PMSM) operating on an interconnected system are developed. The control schemes include the pitch-angle/speed control and the decoupled control of the real and reactive power outputs. As an additional modeling option, the generic model for variable speed machine has been introduced. The models were then implemented on a representative test network, and simulations have been carried out to observe the response of the control system to typical abnormal situations such as three phase grid faults to compare the accuracy of the generic models with the detailed quasi-stationary (QSS) models.

Performance analysis of a Poisson–Pareto queue over the full range of system parameters

There have been many queuing analyses for a single server queue fed by an M/G/~ traffic process, in which G is a Pareto distribution, that focus on certain limiting conditions. In this paper we enhance the so-called Quasi-Stationary (QS) approximation - a queuing analysis introduced previously that provides an algorithm for computation of an accurate approximation for the stationary queue distribution, applicable to the entire range of system parameters. By numerical evaluation of the QS approximation and the asymptotic approximations (large buffer, many sources, and heavy traffic) over an extremely wide range of parameter values we are able to graphically display consistency of the QS approximation with all the asymptotic results. We demonstrate that the accuracy of the asymptotic approximations is satisfactory only in limited regions of the system parameter space.

Absorbing-state phase transitions: Exact solutions of small systems

I derive precise results for absorbing-state phase transitions using exact (numerically determined) quasistationary (QS) probability distributions for small systems. Analysis of the contact process on rings of 23 or fewer sites yields critical properties (control parameter, order-parameter ratios, and critical exponents z and betanu_(perpendicular)) with an accuracy of 0.06% or better; precise results are also obtained for the pair contact process. The QS distribution yields insights on the statistical entropy of these models. Preliminary application to a model in the stochastic sandpile class is also described.

Analysis of thermally stimulated luminescence and conductivity without quasi-equilibrium approximation

Thermally stimulated luminescence (TSL) and conductivity (TSC) are considered using the classical insulator model that assumes one kind of active trap, one kind of inactive deep trap and one kind of recombination centre. Kinetic equations describing the model are solved numerically without and with the use of quasi-equilibrium (QE) approximation. The QE state is characterized by the parameter qI = (dnc/dt)/Ie, where dnc/dt is the rate of change of free electron density, and Ie is the TSL intensity. The QE state parameter qI, the relative recombination probability γ = Ie/(Ie + It) (It is the trapping intensity) and a new parameter called a quasi-stationary (QS) state parameter q* = qIγ = (dnc/dt)/(Ie + It) are used for the analysis of the TSL and TSC. The QE and QS states are determined by conditions |qI| ≪ 1 and, respectively, |q*| ≪ 1. The TSL and TSC curves and the temperature dependences of qI, q*, γ the recombination lifetime and the occupancies of active traps and recombination centres are numerically calculated for five sets of kinetic parameters and different heating rates. These calculation results show that (1) the upper limit of the heating rate for the presence of the QS state appears at a higher heating rate than that for the QE state when the retrapping process is present, and (2) the TSL (TSC) curves in the QS state have properties similar to those for the TSL (TSC) curves in the QE state. Approximate formulae for calculation of the parameters qI and q* in the initial range of the TSL and TSC curves are derived and used in the heating-rate methods, proposed in this work, for determination of those parameters from the calculated TSL curves.

Exploring the Thermodynamic Limit of Hamiltonian Models: Convergence to the Vlasov Equation

We here discuss the emergence of quasistationary states (QSS), a universal feature of systems with long-range interactions. With reference to the Hamiltonian mean-field model, numerical simulations are performed based on both the original N-body setting and the continuum Vlasov model which is supposed to hold in the thermodynamic limit. A detailed comparison unambiguously demonstrates that the Vlasov-wave system provides the correct framework to address the study of QSS. Further, analytical calculations based on Lynden-Bell's theory of violent relaxation are shown to result in accurate predictions. Finally, in specific regions of parameters space, Vlasov numerical solutions are shown to be affected by small scale fluctuations, a finding that points to the need for novel schemes able to account for particle correlations.

Quasi Stationary Distributions and Fleming-Viot Processes in Countable Spaces

We consider an irreducible pure jump Markov process with rates $Q=(q(x,y))$ on $\Lambda\cup\{0\}$ with $\Lambda$ countable and $0$ an absorbing state. A {\em quasi stationary distribution \rm} (QSD) is a probability measure $\nu$ on $\Lambda$ that satisfies: starting with $\nu$, the conditional distribution at time $t$, given that at time $t$ the process has not been absorbed, is still $\nu$. That is, $\nu(x) = \nu P_t(x)/(\sum_{y\in\Lambda}\nu P_t(y))$, with $P_t$ the transition probabilities for the process with rates $Q$. A Fleming-Viot (FV) process is a system of $N$ particles moving in $\Lambda$. Each particle moves independently with rates $Q$ until it hits the absorbing state $0$; but then instantaneously chooses one of the $N-1$ particles remaining in $\Lambda$ and jumps to its position. Between absorptions each particle moves with rates $Q$ independently. Under the condition $\alpha:=\sum_{x\in\Lambda}\inf Q(\cdot,x) > \sup Q(\cdot,0):=C$ we prove existence of QSD for $Q$; uniqueness has been proven by Jacka and Roberts. When $\alpha>0$ the FV process is ergodic for each $N$. Under $\alpha>C$ the mean normalized densities of the FV unique stationary measure converge to the QSD of $Q$, as $N \to \infty$; in this limit the variances vanish.

Lynden-Bell and Tsallis distributions for the HMF model

Systems with long-range interactions can reach a Quasi Stationary State (QSS) as a result of a violent collisionless relaxation. If the system mixes well (ergodicity), the QSS can be predicted by the statistical theory of Lynden-Bell (1967) based on the Vlasov equation. When the initial distribution takes only two values, the Lynden-Bell distribution is similar to the Fermi-Dirac statistics. Such distributions have recently been observed in direct numerical simulations of the HMF model (Antoniazzi et al. 2006). In this paper, we determine the caloric curve corresponding to the Lynden-Bell statistics in relation with the HMF model and analyze the dynamical and thermodynamical stability of spatially homogeneous solutions by using two general criteria previously introduced in the literature. We express the critical energy and the critical temperature as a function of a degeneracy parameter fixed by the initial condition. Below these critical values, the homogeneous Lynden-Bell distribution is not a maximum entropy state but an unstable saddle point. We apply these results to the situation considered by Antoniazzi et al. For a given energy, we find a critical initial magnetization above which the homogeneous Lynden-Bell distribution ceases to be a maximum entropy state, contrary to the claim of these authors. For an energy U=0.69, this transition occurs above an initial magnetization M_{x}=0.897. In that case, the system should reach an inhomogeneous Lynden-Bell distribution (most mixed) or an incompletely mixed state (possibly fitted by a Tsallis distribution). Thus, our theoretical study proves that the dynamics is different for small and large initial magnetizations, in agreement with numerical results of Pluchino et al. (2004). This new dynamical phase transition may reconcile the two communities.

Topological aspects of a long-range model

The mean field XY Hamiltonian, a suitable model for studying long-range interactions in extended systems, presents, amongst other interesting features, slow relaxation and formation of quasi-stationary (QS) states. It is now known that, along these QS trajectories, the system visits critical points (maxima) of the potential energy function, characterized by a large number of directions with marginal stability. This observation may provide an interpretation for the slow relaxation dynamics and the trapping in such trajectories. In this paper we present further results and discussion on topological aspects of the model.

How to simulate the quasistationary state

For a large class of processes with an absorbing state, statistical properties of the surviving sample attain time-independent values in the quasistationary (QS) regime. We propose a practical simulation method for studying quasistationary properties, based on the equation of motion governing the QS distribution. In applications to the contact process, the method is shown to reproduce exact results (for the process on a complete graph) and known scaling behavior to high precision. At the critical point, our method is about an order of magnitude more efficient than conventional simulation.