Initial Unstable State Research Articles

SPICE Modelling-Assisted evaluation of dynamic on-resistance characterization in Schottky p-GaN HEMTs amid synchronous buck transient instabilities

This study addresses the critical gap in dynamic on-resistance characterization for GaN HEMTs within the initial unstable state in a non-isolated DC-DC converter, where the output voltage and currents fluctuate and exhibit overshoots or undershoots before stabilizing to their steady-state values, a domain within solar photovoltaic (PV) Maximum Power Point Tracking (MPPT) implementations which is crucial yet insufficiently examined. The authors present a novel multi-pulse test circuit within a synchronous buck converter configuration, complemented by SPICE simulation. This combination allows for the accurate assessment of clamping circuits' performance during transient states, significantly improving the precision of RDS(ON) measurements in unsteady phases. The approach deviates from conventional methods by merging empirical data with simulation insights to validate the efficacy of clamping circuits. The experimental results affirm the methodology's precision, with the highlighted Circuit V showcasing a marginal deviation of 2.32 % from existing benchmarks. This finding substantiates the method's dependability and practicality contributing to the GaN power electronics field. In addition, this research provides a powerful analytical tool for RDS(ON) evaluation, culminating in the design of a test PCB that synergizes with both simulated and empirical evidence, contributing future research in GaN HEMT power converter applications.

Effect of a novel generalized incidence rate function in [formula omitted] model: Stability switches and bifurcations

When a disease outbreaks in a population, the incidence rate function may increase initially with an increase of infective and then decrease due to inhibitory effects before getting saturated. For this purpose, we propose a new generalized incidence rate function and demonstrate the impact of this incidence rate function’s non-monotonic feature on the stability of endemic equilibria. In this paper, an SIR compartmental model with this new nonlinear incidence rate function and saturated treatment rate function is proposed. We obtain a disease free equilibrium which is locally stable for R0<1 and unstable otherwise. The system may have multiple endemic equilibria which can be either anti-saddle (node, focus or center) or saddle. We discover that when the incidence rate function is increasing at an anti-saddle endemic equilibrium, the endemic equilibrium may become either stable, unstable or switch stability via a parameter change. However, when the incidence rate function is non-monotonic and if the incidence rate decreases at an anti-saddle endemic equilibrium, the endemic equilibrium is always stable. Due to the limited treatment, we find forward (transcritical) and backward bifurcations. We also establish Hopf bifurcation and saddle–node bifurcation in the model system. Further, we incorporate the incubation delay in the model system. We obtain the same number of equilibria in the delay model. The disease free equilibrium is locally asymptotically stable for all delay lengths for R0<1. The endemic equilibrium switches its stability due to change in delay. Due to delay variation, the increasing incidence rate at an anti-saddle endemic equilibrium causes the multiple stability switches of the equilibrium from both stable and unstable initial states. Further, when the incidence rate decreases at the stable anti-saddle endemic equilibrium, it switches its stability once or multiple times and finally becomes unstable due to delay variation. We explicitly, show multiple stability switches of an endemic equilibrium due to existence of multiple Hopf bifurcations. When we further analyzed model system numerically, we could establish the existence of Hopf–Hopf bifurcation of codimension 2. In this case, the increase in the delay parameter causes the existence of two oscillatory solutions around the unstable endemic equilibrium. Hence, our results show that the delay system either destabilize developing the same frequency oscillations via Hopf bifurcation or two different frequency oscillations via Hopf–Hopf bifurcation of codimension 2. The existence and exhibition of these two frequency oscillations are novel and have not been explored much in epidemiological models.

Quantum dots as a probe of fundamental physics: deviation from exponential decay law

We explore a possibility of measuring deviation from the exponential decay law in pure quantum systems. The power law behavior at late times of decay time profile is predicted in quantum mechanics, and has been experimentally attempted to detect, but with failures except a claim in an open system. It is found that electron tunneling from resonance state confined in man-made atoms, quantum dots, has a good chance of detecting the deviation and testing theoretical predictions. How initial unstable state is prepared influences greatly the time profile of decay law, and this can be used to set the onset time of the power law at earlier times. Comparison with similar process of nuclear alpha decay to discover the deviation is discussed, to explain why there exists a difficulty in this case.

Molecular dynamics simulations and experimental study of the effects of an ionic surfactant on the wettability of low-rank coal

The surfactants sodium dodecyl benzene sulfonate, dodecyl dimethyl betaine, and dodecyl trimethyl ammonium bromide were used to study the effect of an ionic surfactant on coal wettability. A lignite-surfactant-water system was constructed using the Wender coal chemical structure model and Materials Studio molecular simulation software, and the static potential of a single molecule was determined by quantum chemical calculations. The initial and equilibrium configurations of the system, relative concentration distribution, and mean-square displacement (MSD) of water molecules were analyzed thoroughly. Additionally, the surface tension and contact angle of aqueous surfactant solutions with different mass concentrations were measured to analyze the relationship between concentration and the rate of reduction of surface tension and of contact angle. The analysis showed that when the surface static potential of the lignite molecule was larger than that of water molecules, the water molecules were easily attracted and exhibited a wetting phenomenon. The water-surfactant-coal system gradually tended from an initial unstable state to a stable state with low energy. Specifically, the hydrophilic groups in the surfactant were tilted toward the water phase and the hydrophobic chains were adsorbed on the surface of coal, which helped enhance the wettability of the coal. The relative concentration distribution range of the SDBS was 26–52 Å, which was wider than the other two surfactants. Additionally, the MSD curve showed that the diffusion coefficient of the water molecules in the water-SDBS-coal system reached a maximum value of 4.23 × 10−2, resulting in accelerated wetting of the coal body. When the SDBS mass concentration was 3%, the surface tension decreased to the minimum value (21.86 mN/m) and the minimum contact angle was 16.12°. Based on the simulation results and experimental test data, the wettability of the three surfactants to lignite was SDBS > BS-12 > DTAB. The findings of this study help to better understand the wetting mechanism of surfactants on lignite, which is conducive to the rapid screening of surfactants with strong wetting ability on lignite, expanding the use of surfactants, and is of great significance to the control and prevention of coal dust pollution.

Shaking earth: Non-linear seismic processes and the second law of thermodynamics: A case study from Canterbury (New Zealand) earthquakes

Earthquakes are non-linear phenomena that are often treated as a chaotic natural processes. We propose the use of the Second Law of Thermodynamics and entropy, H, as an indicator of the equilibrium state of a seismically active region (a seismic system). In this sense, in this paper we demonstrate the exportability of first principles (e.g., thermodynamics laws) to others scientific fields (e.g., seismology). We suggest that the relationship between increasing H and the occurrence of large earthquakes reflects the irreversible transition of a system. From this point of view, a seismic system evolves from an unstable initial state (due to external stresses) to a state of reduced stress after an earthquake. This is an irreversible transition that entails an increase in entropy. In other words, a seismic system is in a metastable situation that can be characterised by the Second Law of Thermodynamics. We investigated two seismic episodes in the Canterbury area of New Zealand: the 2010 Christchurch earthquake (M = 7.2) and the 2016 Kaikoura earthquake (M = 7.8). The results are remarkably in line with our theoretical forecasts. In other words, an earthquake, understood as an irreversible transition, must results in an increase in entropy.

Earthquakes and entropy: Characterization of occurrence of earthquakes in southern Spain and Alboran Sea.

We propose the use of entropy, H, as an indicator of the equilibrium state of a seismically active region (seismic system). The relationship between an increase in H and the occurrence of a great earthquake in a study area can be predicted by acknowledging the irreversible transition of a system. From this point of view, the seismic system evolves from an unstable initial state (due to external stresses) to another, where the stresses have dropped after the earthquake occurred. It is an irreversible transition that entails an increase in entropy. Five seismic episodes were analyzed in the south of the Iberian Peninsula, the Alboran Sea (Mediterranean Sea), and the North of Morocco: two of them of moderate-high magnitude (Al Hoceima, 2004 and 2016) and three of them of moderate-low magnitude (Adra, 1993-1994; Moron, 2007; and Torreperogil, 2012-2013). The results are remarkably in line with the theoretical forecasts; in other words: an earthquake, understood as an irreversible transition, must suppose an increase in entropy.

Nonuniqueness in a Single-Column Model for Moist Convection

Abstract We investigate a moist atmospheric column convection model by considering the atmosphere as a single vertical column of air parcels, each of which contains water vapor. The moist convective adjustment of both air and water mass in the column is considered from an (unstable) initial state to a statically stable final configuration of parcels. Two variations of an algorithm based upon swapping neighboring parcels are compared: after swapping, no parcels remain supersaturated. The results of these algorithms are compared directly with those of the adjustment algorithm of Cheng et al., which adjusts an atmospheric column to achieve the global maximum of a relevant cost functional. Two examples are considered: in the first, the algorithms adjust to similar arrangements, showing that the global maximum of the functional is the dynamically preferred state, while in the second, the algorithms adjust to significantly different states. Thus, we identify a nonuniqueness to the solution to the adjustment problem in terms of local and global cost functional maximizers. We then discuss the relevance of this nonuniqueness to numerical prediction in weather and climate models.

Unstable yet static initial state: A universal method for studying Rayleigh-Taylor instability and lock exchange

An experimental method for investigating hydrodynamic instability combining light and a physical gel is proposed. Our method allows for a detailed study of hydrodynamic instabilities.

Phase transitions, inhomogeneous horizons and second-order hydrodynamics

We use holography to study the spinodal instability of a four-dimensional, strongly-coupled gauge theory with a first-order thermal phase transition. We place the theory on a cylinder in a set of homogeneous, unstable initial states. The dual gravity configurations are black branes afflicted by a Gregory-Laflamme instability. We numerically evolve Einstein’s equations to follow the instability until the system settles down to a stationary, inhomogeneous black brane. The dual gauge theory states have constant temperature but non-constant energy density. We show that the time evolution of the instability and the final states are accurately described by second-order hydrodynamics. In the static limit, the latter reduces to a single, second-order, non-linear differential equation from which the inhomogeneous final states can be derived.

Density properties of glasses of CaO(Na2O)–Al2O3(MgO)–SiO2 system, studied at pressures to 6.0 GPa, in comparison with the properties of similar melts

The density properties (relative change in the density, (d − d0)/d, initial bulk modulus, K0, and the derivative of bulk modulus with respect to pressure, К′) of silicate glasses of the CaO(Na2O)–Al2O3(MgO)–SiO2 system are compared with those of silicate melts. It is shown that К0 values obtained for the glasses using Birch–Murnaghan equation in the pressure range with the normal behavior of bulk modulus significantly lower К0 values, which were obtained for glasses using the ultrasonic or Brillouin scattering methods. This phenomenon is explained by the different state of the glasses, which were obtained by different methods. Brillouin scattering method allows obtaining the K0 value, which characterizes the initial unstable state of glass, while with the use of other method (using Birch–Murnaghan equation in the pressure range with the normal behavior of bulk modulus) we determine K0 for glass, which is in the hypothetical metastable state, close to the supercooled liquid. K0 values for glasses, which are in the hypothetical metastable state are close to К0 values for silicate melts. When (K0)glass and (K0)melt have similar values, higher compressibility of melts is determined by smaller values of the derivative of the bulk modulus, K′, compared with glasses of similar compositions. The relation between the parameters (d − d0)/d, K0, K′ and the degree of depolymerization, NBO/T, of silicate glasses and melts was found. The greater the degree of depolymerization, the less is the compressibility of glasses and melts. Simple models for the semiempirical determination of the melts density properties in the first approximation using the density properties of the corresponding glasses are proposed. The possibility of using silicate glasses as the models of deep melts was shown by example of tholeiite basalt glass and melt.

LES Investigation of the Hysteresis Regime in the Cold Model of a Rotating-Pipe Swirl Burner

We investigate numerically the hydrodynamics of regime transitions of flow in a cold replica of a non-premixed swirl burner in which hysteresis was detected when transiting from an attached long flame to a short lifted flame and vice versa (Hubner et al. Exper. Thermal and Fluid Scie. 27, 481–489 2003 Tummers et al. Comb. Flame 156(2), 447–459 2009. The unconfined highly swirling annular jet is generated by rotating the outer pipe of the annular air supply at 4000 rpm, while gas is fed through an inner annulus. The imposed rotation number N=U wall/U 0 , controlled by the flow rate, ranged from 2.8 for the stable flame to 4.9 for the unstable flame. The large-eddy simulations (LES) results for two regimes, N = 2.8 and 3.26, agree well with the available experimental data, reproducing notably different sizes and strengths of the central recirculation bubbles. Just as in the experiment, the transients were simulated by a sudden imposition of the inflow mass flux that corresponds to the target hysteretic state at an intermediate rotation number. Contrary to the experimental findings in flame, where both the stable and unstable flames were observed at the same bulk flow parameters in the hysteresis region (N = 3.26), the LES of cold flow resulted in indistinguishable time-averaged flow patterns differing from the both initial states, indicating that in the configuration considered the hysteresis is associated with flame lift-off and reattachment. The analysis of the transients dynamics showed, however, that the flow undergoes different adjustments when approaching from the stable and unstable initial states, suggesting that the hydrodynamics is indeed the precursor of hysteresis. The sudden hysteretic change of the regime observed depends on whether the thermal effects will overrule the inertia of the strong near-nozzle vortex structures.

Energy uncertainty of the final state of a decay process

We derive the expression for the energy uncertainty of the final state of a decay of an unstable quantum state prepared at the initial time $t=0$. This expression is function of the time $t$ at which a measurement is performed to determine if the state has decayed and, if yes, in which one of the infinitely many possible final states. For large times the energy spread is, as expected, given by the decay width $\Gamma$ of the initial unstable state. However, if the measurement of the final state is performed at a time $t$ comparable to (or smaller than) the mean lifetime of the state $1/\Gamma$, then the uncertainty on the energy of the final state is much larger than the decay width $\Gamma$. Namely, for short times an uncertainty of the type $1/t$ dominates, while at large times the usual spread $\Gamma$ is recovered. Then, we turn to a generic two-body decay process and describe the energy uncertainty of each one of the two outgoing particles. We apply these formulas to the two-body decays of the neutral and charged pions and to the spontaneous emission process of an excited atom. As a last step, we study a case in which the non-exponential decay is realized ad show that for short times eventual asymmetric terms are enhanced in the spectrum.

Accuracy and response-time distributions for decision-making: linear perfect integrators versus nonlinear attractor-based neural circuits

Animals choose actions based on imperfect, ambiguous data. “Noise” inherent in neural processing adds further variability to this already-noisy input signal. Mathematical analysis has suggested that the optimal apparatus (in terms of the speed/accuracy trade-off) for reaching decisions about such noisy inputs is perfect accumulation of the inputs by a temporal integrator. Thus, most highly cited models of neural circuitry underlying decision-making have been instantiations of a perfect integrator. Here, in accordance with a growing mathematical and empirical literature, we describe circumstances in which perfect integration is rendered suboptimal. In particular we highlight the impact of three biological constraints: (1) significant noise arising within the decision-making circuitry itself; (2) bounding of integration by maximal neural firing rates; and (3) time limitations on making a decision. Under conditions (1) and (2), an attractor system with stable attractor states can easily best an integrator when accuracy is more important than speed. Moreover, under conditions in which such stable attractor networks do not best the perfect integrator, a system with unstable initial states can do so if readout of the system’s final state is imperfect. Ubiquitously, an attractor system with a nonselective time-dependent input current is both more accurate and more robust to imprecise tuning of parameters than an integrator with such input. Given that neural responses that switch stochastically between discrete states can “masquerade” as integration in single-neuron and trial-averaged data, our results suggest that such networks should be considered as plausible alternatives to the integrator model.

Detection of weak signals through nonlinear relaxation times for a Brownian particle in an electromagnetic field

The detection of weak signals through nonlinear relaxation times for a Brownian particle in an electromagnetic field is studied in the dynamical relaxation of the unstable state, characterized by a two-dimensional bistable potential. The detection process depends on a dimensionless quantity referred to as the receiver output, calculated as a function of the nonlinear relaxation time and being a characteristic time scale of our system. The latter characterizes the complete dynamical relaxation of the Brownian particle as it relaxes from the initial unstable state of the bistable potential to its corresponding steady state. The one-dimensional problem is also studied to complement the description.

Long-time behavior of many-particle quantum decay

While exponential decay is ubiquitous in Nature, deviations at both short and long times are dictated by quantum mechanics. Non-exponential decay is known to arise due to the possibility of reconstructing the initial state from the decaying products. We discuss the quantum decay dynamics by tunneling of a many-particle system, characterizing the long-time non-exponential behavior of the non-escape and survival probabilities. The effects of contact interactions and quantum statistics are described. It is found that whereas for non-interacting bosons the long-time decay follows a power-law with an exponent linear in the number of particles $\N$, the exponent becomes quadratic in $\N$ in the fermionic case. The same results apply to strongly interacting many-body systems related by the generalized Bose-Fermi duality. The faster fermionic decay can be traced back to the effective hard-core interactions between particles, which are as well the decaying products, and exhibit spatial anti-bunching which hinders the reconstruction of the initial unstable state. The results are illustrated with a paradigmatic model of quantum decay from a trap allowing leaks by tunneling, whose dynamics is described exactly by means of an expansion in resonant states.

Noise-induced enhancement of stability in a metastable system with damping

The mean first passage time of a Brownian particle from an initial unstable state in a metastable system with damping is investigated. The system is analyzed in the low to high damping regime, and the role played by the damping parameter is studied. We observe the noise enhanced stability effect for all the initial unstable states under study and for all values of the damping parameter γ investigated. The curves show a behavior of the mean first passage time vs γ very close to that observed for an overdamped particle in the presence of colored noise as a function of the correlation time.

Evolution of cluster size-distributions in nucleation-growth and spinodal decomposition processes in a regular solution

Nucleation-growth and spinodal decomposition processes are two of the basic mechanisms first-order phase transitions – like condensation and boiling, segregation or crystallization and melting – may proceed. Their adequate theoretical description is essential in order to understand the basis mechanisms of self-structuring of matter at nano-scale dimensions. The basic features of evolution of cluster size-distributions are discussed in detail both for meta-stable (nucleation) and unstable (spinodal decomposition) initial states for a simple model of a binary mixture. The results are obtained by the numerical solution of a set of kinetic equations where the thermodynamics of cluster formation is formulated based on the generalized Gibbs' method. It is shown, that nucleation will not proceed, in general (especially in meta-stable initial states near to the spinodal curve), via the saddle point but in trajectories of evolution by-passing the saddle point. For systems in unstable initial states, spinodal decomposition can proceed similarly to nucleation forming clusters evolving to the new phase via the ridge of the thermodynamic potential hyper-surface.

Detection of weak and large electric fields through the transient dynamics of a Brownian particle in an electromagnetic field

In this work we present a mechanism to detect the presence of an external electric field of either weak or large amplitude by means of the decay process from an unstable state, described by a bistable potential, of an electrically charged Brownian particle embedded in a uniform electromagnetic field. Since the detection process takes place around the initial unstable state of the bistable potential, our theoretical description is given in the linear approximation of the aforementioned potential. The decay process is characterized through the statistics of the passage time distribution calculated by means of two theoretical approaches relying on the overdamped Langevin equation: one is the quasideterministic approach valid for large times and used for the detection of weak signals, whereas the other one is the rotational approach, valid for intermediate times and adequate for the detection of large electric-field amplitudes.

Pulsating Instability of a Bose-Einstein Condensate in an Optical Lattice

We find numerically that in the limit of weak atom-atom interactions a Bose-Einstein condensate in an optical lattice may develop a pulsating dynamical instability in which the atoms nearly periodically form a peak in the occupation numbers of the lattice sites, and then return to the unstable initial state. Multiple peaks behaving similarly are also found. Simple arguments show that the pulsating instability is a remnant of integrability, and give a handle on the relevant physical scales.

Description of self‐reported fluid intake and its effects on body weight, symptoms, quality of life and physical capacity in patients with stable chronic heart failure

To describe the self-reported fluid intake and its effects on body weight, signs and symptoms of heart failure, quality of life, physical capacity and thirst, in patients with stabilised chronic heart failure. Patients with chronic heart failure are often recommended a fluid restriction of 1.5 l/day but there is no evidence in the literature for this recommendation and little is known about the fluid intake consequences. Crossover study. Chronic heart failure patients, clinically stabilised after an unstable state, were randomised to a 32-week cross-over study assessing the clinical importance of fluid prescription. In a secondary analysis of 63 patients, efficacy variables were analysed in relation to the self-reported median fluid intake of 19 ml/kg body weight/day. The mean fluid intake was 16 ml/kg/day in the below-median group and 24 ml/kg/day in the above-median group. No between-group differences were found in change in body weight, signs and symptoms, diuretic use, quality of life or physical capacity. However, the above-median group significantly decreased sense of thirst and difficulties to adhere to the fluid prescription compared with the below-median group. In clinically stabilised chronic heart failure patients on optimal pharmacological treatment, a larger fluid intake was associated with decreasing thirst without any measurable negative effects on signs and symptoms of heart failure, diuretic use or physical capacity. Thus, a more liberal fluid intake may be advisable in chronic heart failure patients who have been stabilised after an initial unstable clinical state. Nurses involved in the care for patients with heart failure known how troublesome thirst can be and how difficult it can be to follow a restricted fluid intake. This study indicates that it is possible to reassess and recommend a less strict fluid intake in stabilised patients with chronic heart failure.