Two-state Theory Research Articles

Unraveling thermodynamic anomalies of water: A molecular simulation approach to probe the two-state theory with atomistic and coarse-grained water models.

Thermodynamic and dynamic anomalies of water play a crucial role in supporting life on our planet. The two-state theory attributes these anomalies to a dynamic equilibrium between locally favored tetrahedral structures (LFTSs) and disordered normal liquid structures. This theory provides a straightforward, phenomenological explanation for water's unique thermodynamic and dynamic characteristics. To validate this two-state feature, it is critical to unequivocally identify these structural motifs in a dynamically fluctuating disordered liquid. In this study, we employ a recently introduced structural parameter (θavg) that characterizes the local angular order within the first coordination shell to identify these LFTSs through molecular dynamics simulations. We employ both realistic water models with a liquid-liquid critical point (LLCP) and a coarse-grained water model without an LLCP to study water's anomalies in low-pressure regions below 2 kbar. The two-state theory consistently describes water's thermodynamic anomalies in these models, both with and without an LLCP. This suggests that the anomalies predominantly result from the two-state features rather than criticality, particularly within experimentally accessible temperature-pressure regions.

Ligand Field Sensitive Spin Acceleration in the Iron-Catalyzed [2 + 2] Cycloaddition of Unactivated Alkenes and Dienes.

Redox-active pyridine(diimine) (PDI) iron catalysts promote the reversible [2 + 2] cycloaddition of alkenes and dienes to cyclobutane derivatives that have applications ranging from fuels to chemically recyclable polymers. Metallacycles were identified as key intermediates, and spin crossover from the singlet to the triplet surface was calculated to facilitate the reductive coupling step responsible for the formation of the four-membered ring. In this work, a series of sterically and electronically differentiated PDI ligands was studied for the [2 + 2] cycloaddition of ethylene and butadiene to vinylcyclobutane. Kinetic studies revealed that the fastest and slowest turnover were observed with equally electron-deficient supporting ligands that either feature phenyl-substituted imine carbon atoms (MeBPDI) or a pyrazine core (MePZDI). While the oxidative cyclization was comparatively slow for both catalysts, the rate of reductive coupling─determined by stoichiometric 13C2H4 labeling studies─correlated with the turnover frequencies. Two-state density functional theory studies and the distinct electronic structures of related (iPrBPDI) and (iPrPZDI) iron methyl complexes revealed significantly different ligand field strengths due to either diminished ligand σ-donation (MeBPDI) or promoted metal π-backbonding (MePZDI). Spin acceleration, leading to fast reductive coupling and catalytic turnover, was promoted in the case of the weaker ligand field and depends on both the nature and position of the electron-withdrawing group. This study provides strong evidence for the role of two-state reactivity in C(sp3)-C(sp3) bond formation and insights on how ligand design either promotes or inhibits spin acceleration in earth-abundant metal catalysis.

Prediction of water anomalous properties by introducing the two-state theory in SAFT.

Water is one of the most abundant substances on earth, but it is still not entirely understood. It shows unusual behavior, and its properties present characteristic extrema unlike any other fluid. This unusual behavior has been linked to the two-state theory of water, which proposes that water forms different clusters, one with a high density and one with a low density, which may even form two distinct phases at low temperatures. Models incorporating the two-state theory manage to capture the unusual extrema of water, unlike traditional equations of state, which fail. In this work, we have derived the framework to incorporate the two-state theory of water into the Statistical-Associating-Fluid-Theory (SAFT). More specifically, we have assumed that water is an ideal solution of high density water molecules and low density water molecules that are in chemical equilibrium. Using this assumption, we have generalized the association term SAFT to allow for the simultaneous existence of the two water types, which have the same physical parameters but different association properties. We have incorporated the newly derived association term in the context of the Perturbed Chain-SAFT (PC-SAFT). The new model is referred to as PC-SAFT-Two-State (PC-SAFT-TS). Using PC-SAFT-TS, we have succeeded in predicting the characteristic extrema of water, such as its density and speed of sound maximum, etc., without loss of accuracy compared to the original PC-SAFT. This new framework is readily extended to mixtures, and PC-SAFT-TS manages to capture the solubility minimum of hydrocarbons in water in a straightforward manner.

Stochastic resonance in Hindmarsh-Rose neural model driven by multiplicative and additive Gaussian noise

This paper investigates the occurrence of stochastic resonance in the three-dimensional Hindmarsh-Rose (HR) neural model driven by both multiplicative and additive Gaussian noise. Firstly, the three-dimensional HR neural model is transformed into the one-dimensional Langevin equation of the HR neural model using the adiabatic elimination method, and the effects of HR neural model parameters on the potential function are analyzed. Secondly the Steady-state Probability Density (SPD), the Mean First-Passage Time (MFPT), and the Signal-to-Noise Ratio (SNR) of the HR neural model are derived, based on two-state theory. Then, the effects of different parameters (a, b, c, s), noise intensity, and the signal amplitude on these metrics are analyzed through theoretical simulations, and the behavior of particles in a potential well is used to analyze how to choose the right parameters to achieve high-performance stochastic resonance. Finally, numerical simulations conducted with the fourth-order Runge–Kutta algorithm demonstrate the superiority of the HR neural model over the classical bistable stochastic resonance (CBSR) in terms of performance. The peak SNR of the HR neural model is 0.63 dB higher than that of the CBSR system. Simulation results indicate that the occurrence of stochastic resonance occur happens in HR neural model under different values of parameters. Furthermore, under certain conditions, there is a ‘suppress’ phenomenon that can be produced by changes in noise, which provides great feasibilities and practical value for engineering application.

Impact of Non-Gaussian Noise and Time Delay on Stability and Stochastic Resonance for a FitzHugh-Nagumo Neural System Subjected to a Multiplicative Periodic Signal

In this paper, we focus on the investigations on the stochastic stability and the stochastic resonance (SR) phenomena for a FitzHugh-Nagumo system with time delay induced by a multiplicative non-Gaussian colored noise and an additive Gaussian colored noise. By use of the fast descent method, the unified colored noise approximation and the two-state theory for the SR, the stationary probability density function (SPDF) and the signal-to-noise ratio (SNR) caused by different noise terms and time delay are explored. The investigation results indicate that the two noise intensities, time delay and the departure parameter from the Gaussian noise can all reduce the probability density around the two stable states and destroy the stability of the neural system; while the two noise correlation times [Formula: see text] and [Formula: see text] can both improve the probability density around both stable states and reinforce the biological stability of the neural system. As regards the SNR, it is found that the two noise intensities and the departure coefficient can all weaken the SR effect, while time delay [Formula: see text] and the correlation time [Formula: see text] of the multiplicative noise will always magnify the SR phenomenon. It is worth to mention that the correlation time [Formula: see text] of the additive noise can stimulate the SR effect, but not alter the maximum of the SNR.

Entropic stochastic resonance for a confined system driven by two constant forces and multiplicative noise

The entropic stochastic resonance (ESR) phenomenon for a confined system driven by two constant forces, by two periodic forces and multiplicative noise is studied. The Fokker-Planck equation corresponding to the confined structure is obtianed applying Fick-Jacob approximation. The transition rates from the stable states are derived under the adiabatic approximation condition. The signal-to-noise ratios (SNRs) for the fundamental and higher harmonics are derived by virtue of two-state theory. Analysis result indicates that the SNR for fundamental harmonic decreases as increasing the constant force along x-direction, while the SNR for fundamental harmonic can obtain one maxmimum value with the increment of the constant force along y-direction. Each of the SNRs for higher harmonics can get one resonance peak as increasing the two constant forces. Two peaks appear when the SNRs vary with the multiplicative noise intensity, while only one peak value takes place when the SNRs change with the additive noise strength. The influence of the boundary parameters of the confined system on the SNRs is discussed.

Influence of colored cross-correlated noise on stochastic resonance for an underdamped bistable system subjected to multiplicative and additive noises

The stochastic resonance (SR) behavior for an underdamped bistable system with colored cross-correlated noise between multiplicative and additive noise is investigated. The stationary probability density is obtained under the condition of the detailed balance. The expressions for the signal-to-noise ratios (SNRs) for two initial states is deduced by applying two-state theory under the adiabatic condition. The analysis result indicates that the SR phenomenon takes place when the SNRs vary with the coupling strength and the correlation time of the cross-correlated noise. Double SR phenomenon occurs on SNRs’ curves with the increase of the strength of the additive noise. One resonance peak exists when the SNRs change with the damping coefficient and with the intensity of the multiplicative noise.

Incipient Bearing Fault Diagnosis Based on the Two-State Theory for Stochastic Resonance Systems

The principle of stochastic resonance (SR) has been intensively used in designing algorithms for incipient bearing fault diagnosis based on stochastic simulation. In order to directly apply the semi-analytic result to the laboratory designs, an incipient bearing fault diagnosis algorithm based on the method of moments for stochastic resonant systems was proposed, with its real-time monitoring efficiency being assured by an available table of the involving stationary moments. Nevertheless, since the noise that buried the fault signal can only be estimated after sampling, calculation of such stationary moments might be an inconvenience. To fix this inconvenience, a brand-new fault diagnosis algorithm is designed in this paper based on the two-state theory for a biased underdamped bistable stochastic resonant system. The capability and the efficiency of the algorithm in identifying the characteristic frequency of the hidden fault signal are confirmed with the experimental data sets. This investigation actually opens a new way for improving the existing SR-based diagnosis algorithms.

Multiple insights call for revision of modern thermodynamic models to account for structural fluctuations in water.

Modern thermodynamic models incorporate the concept of association (hydrogen bonding) and they can describe very satisfactorily many properties of water containing mixtures. They have not been successful in representing water's anomalous properties and this work provides a possible explanation. We have analyzed and interpreted recent experimental data, molecular simulation results, and two-state theory approaches and compared against the predictions from thermodynamic models. We show that the dominance of the tetrahedral structure implemented in modern thermodynamic models may be the reason for their failure for describing water systems. While this study does not prove the two-state theories for water, it indicates that a high level of tetrahedral structure of water is not in agreement with water's anomalous properties when used in thermodynamic models.

Unsaturated piecewise bistable stochastic resonance with three kinds of asymmetries and time-delayed feedback

The performance of an unsaturated piecewise bistable stochastic resonance (UPBSR) with three kinds of asymmetries and time-delayed feedback is investigated. Firstly, by introducing an asymmetric factor into UPBSR potential, three kinds of asymmetries are constructed, i.e., well-depth asymmetry (WDA), well-width asymmetry (WWA), and both well-depth and well-width asymmetry (BDWA). Then, by using two-state theory and small delay approximation, the output signal-to-noise ratio (SNR) is derived to analyze the behavior of SR. Enhancement ability and noise immunity are adopted as SR evaluation index. Moreover, as an intermediate result in the calculation of the SNR, the mean first passage time (MFPT), is often used to discuss the transient properties of nonlinear systems. Finally, for SNR analysis, the results show that asymmetric SR outperforms symmetric SR when the asymmetric factor is in the appropriate range, and the WDA dominates the three cases. In addition, the effect of feedback intensity on SR depends heavily on the asymmetric cases, it plays the opposite role in different asymmetric cases. In contrast, the effect of time delay is independent on the asymmetric cases, which always exhibits an improvement of SR noise immunity. As for MFPT analysis, the small γ and β are conducive to the transition of the particles between potential wells, while τ almost has no effect on the transition of particles.

Charge transfer state characterization and voltage losses of organic solar cells

A correct determination of voltage losses is crucial for the development of organic solar cells (OSCs) with improved performance. This requires an in-depth understanding of the properties of interfacial charge transfer (CT) states, which not only set the upper limit for the open-circuit voltage of a system, but also govern radiative and non-radiative recombination processes. Over the last decade, different approaches have emerged to classify voltage losses in OSCs that rely on a generic detailed balance approach or additionally include CT state parameters that are specific to OSCs. In the latter case, a correct determination of CT state properties is paramount. In this work, we summarize the different frameworks used today to calculate voltage losses and provide an in-depth discussion of the currently most important models used to characterize CT state properties from absorption and emission data of organic thin films and solar cells. We also address practical concerns during the data recording, analysis, and fitting process. Departing from the classical two-state Marcus theory approach, we discuss the importance of quantized molecular vibrations and energetic hybridization effects in organic donor-acceptor systems with the goal to providing the reader with a detailed understanding of when each model is most appropriate.

Stochastic Resonance of Asymmetric Joint Potential System and Its Application in Weak Signal Detection

In order to improve the weak signal processing capability of stochastic resonance (SR), a new asymmetric SR system with nonlinear jointed potential function is proposed in this paper. Firstly, the new joint potential stochastic resonance (JPSR) system is built by combined gaussian potential function and asymmetric bistable potential function. Secondly, the analytical expression of signal-to-noise ratio (SNR) is derived based on two-state theory and adiabatic approximation theory. Meanwhile, the influence of system parameters on SNR is discussed theoretically. Thirdly, by particle swarm optimization algorithm, the JPSR system is applied to detect actual bearing fault signals. Finally, according to numerial simulation, the results show that the proposed system can detect weak signal characteristics more effectively.

Stochastic resonance in asymmetric bistable coupled network systems driven by Gaussian colored noise

In this work studied is the synergistic effect of asymmetric bistable coupled network systems under the action of Gaussian colored noise and periodic signal. The system is a network model consisting of a large number of oscillators. The interaction and change between individuals produce complex nonlinear behavior patterns. For further research, firstly, the original N-dimensional system is reduced and approximated by using the mean field theory, the unified colored noise approximation theory and the equivalent nonlinearization method. Secondly, the Langevin equation of simplified model is obtained through the slaving principle by using the two-state model theory to derive the theoretical expression of signal-to-noise ratio. It is found that the system produces the phenomenon of scale stochastic resonance. Finally, the effects of Gaussian color noise parameters, system parameters and periodic signal parameters on the stochastic resonance behavior of asymmetric coupled network systems are discussed. The results show that the increase of Gaussian colored noise correlation time and noise intensity can promote the scale stochastic resonance phenomenon; selecting appropriate coupling coefficient can achieve the optimal stochastic resonance effect. And the stochastic resonance phenomenon of the system driven by the Gaussian colored noise and the Gaussian white noise, respectively, are analyzed and compared with each other. Research result shows that Gaussian colored noise is more conducive to enhancing stochastic resonance phenomenon.

Phenomenon of double entropic stochastic resonance with recycled noise

The double entropic stochastic resonance (DSR) phenomenon for a Brown particle moving in a confined geometry driven by a time-dependent force in the declining direction subject to additive master noise and recycled noise is investigated in this paper. Under the adiabatic approximation condition, based on two-state theory and linear response theory, the expression for the system linear response (LR) is derived. Stochastic resonance (SR) and periodic SR behavior is observed when the LR changes with the feedback coefficient and with the time-delay of the recycled noise. DSR phenomenon appears when the LR varies with the constant component and with the fluctuation noise intensity of the force in the declining direction. Tradition SR occurs on the curve of the LR when the LR varies with the intensity of the master noise. The non-monotonous effect of the parameters of the confined structure on the LR is discussed.

Energetic and entropic vibrational resonance

The influence of an energetic bistable potential on the entropic vibrational resonance (EVR) is investigated. We demonstrate the existence of vibrational resonance modulated by the high-frequency signal with energetic and entropic barriers, which is termed energetic and entropic vibrational resonance (EEVR). We use different methods, including the numerical simulation of Langevin equation, the numerical solution of Fokker-Planck equation, and the analytical expressions of two-state approximation theory, to obtain the spectral amplification factor which can be used to quantify EEVR. In addition, there are two mechanisms, the dynamical phase transition of the stable states and the matching between the escape rate and low-frequency signal on time-scale in the EEVR, which are caused by the modulation of the high-frequency signal. Finally, an auxiliary quantity called the mean entropic Poisson intensity is proposed to describe the constraint effects of the uneven boundaries on the Brownian motion. The above research provides some theoretical reference for the detection of weak signals, and the manipulation of motions of an overdamped Brownian particles, under uneven boundary constraints in small-scale stochastic systems.

Stochastic resonance induced weak signal enhancement over controllable potential-well asymmetry

A dynamical model submerged in two colored multiplicative and additive noises by colored cross-correlation is established to elaborate controllable asymmetric potential-well with depth-asymmetry and width-asymmetry. We deduce the approximate signal-to-noise ratio (SNR) as widely adopted indicator for quantifying stochastic resonance (SR) behavior in accordance with the two-state theory, where the largest SNR peaks are almost attained in the asymmetry case. Moreover, the non-monotonic resonance curves excited by the incremental multiplicative colored noise intensity show the typical SR phenomenon and the SNR peaks decline as the additive colored noise intensity increases, the SR behavior induced by multiplicative colored noise is different from that induced by varying additive one. Noteworthy, the self-correlation time of alternative noises are more effective for controlling SR than cross-correlation time of noises. More interestingly, the output SNR demonstrates double resonance peaks by varying the cross-correlation intensity from negative to positive, however, the two local optimal cross-correlation intensities are almost maintained constant as the increasing of additive noise intensity. Even the large asymmetric well-depth is always beneficial to the improvement of SNR in comparison with well-width asymmetry at the same situation, which is due to the much more energy harvesting from the noises.

Phenomenon of stochastic resonance for an underdamped monostable system with multiplicative and additive noise

The stochastic resonance (SR) phenomenon for an underdamped monostable system with multiplicative and additive noise is investigated. The expression for the stationary probability density is obtained under the condition of the detailed balance and weak noise. The signal-to-noise ratio (SNR) for the monostable system is derived based on two-state theory. The result shows that the SR phenomenon can be observed when the SNR varies with the intensities of the multiplicative and additive white noise, as well as varies with the amplitude of the additive dichotomous noise. One resonance peak can be found when the SNR changes with the damping coefficient and with other system parameters.

NBO/NRT Two-State Theory of Bond-Shift Spectral Excitation.

We show that natural bond orbital (NBO) and natural resonance theory (NRT) analysis methods provide both optimized Lewis-structural bonding descriptors for ground-state electronic properties as well as suitable building blocks for idealized “diabatic” two-state models of the associated spectroscopic excitations. Specifically, in the framework of single-determinant Hartree-Fock or density functional methods for a resonance-stabilized molecule or supramolecular complex, we employ NBO/NRT descriptors of the ground-state determinant to develop a qualitative picture of the associated charge-transfer excitation that dominates the valence region of the electronic spectrum. We illustrate the procedure for the elementary bond shifts of SN2-type halide exchange reaction as well as the more complex bond shifts in a series of conjugated cyanine dyes. In each case, we show how NBO-based descriptors of resonance-type 3-center, 4-electron (3c/4e) interactions provide simple estimates of spectroscopic excitation energy, bond orders, and other vibronic details of the excited-state PES that anticipate important features of the full multi-configuration description. The deep 3c/4e connections to measurable spectral properties also provide evidence for NBO-based estimates of ground-state donor-acceptor stabilization energies (sometimes criticized as “too large” compared to alternative analysis methods) that are also found to be of proper magnitude to provide useful estimates of excitation energies and structure-dependent spectral shifts.

A Mechanically Intelligent Crawling Robot Driven by Shape Memory Alloy and Compliant Bistable Mechanism

Abstract Mechanical components in a robotic system were used to provide body structure and mechanism to achieve physical motions following the commands from electronic controller. This kind of robotic system utilizes complex hardware and firmware for sensing and planning. To reduce computational cost and increase reliability for a robotic system, employing mechanical components to fully or partially take over control tasks is a promising way, which is also referred to as “mechanical intelligence” (MI). This paper proposes a shape memory alloy driven robot capable of using a reciprocating motion to crawl over a surface without any use of electronic controller. A mechanical logic switch is designed to determine the activation timing for a pair of antagonistic shape memory alloy (SMA) actuators. Meanwhile, a compliant pre-strain bistable mechanism is introduced to cooperate with the SMA actuators achieving reliable reciprocating motion between the two stable positions. The SMA actuator is modeled base on a static two-state theory while the bistable mechanism is described by combining a pseudo-rigid-body model (PRBM) with a Bi-beam constraint model (Bi-BCM). Following this, the design parameters of the bistable mechanism and SMA actuators are determined according to theoretical simulations. Finally, a robotic prototype is fabricated using anisotropic friction on its feet to convert the reciprocating motion of the actuator to uni-directional locomotion of the robot body over a surface. Experiments are carried out to validate the presented design concept and the modeling methods.

Asymmetric second-order stochastic resonance weak fault feature extraction method

To solve the problem that the weak fault signal is difficult to extract under strong background noise, an asymmetric second-order stochastic resonance method is proposed. By adjusting the damping factor and the asymmetry, weak signals, noise, and potential wells are matched to each other to achieve the best stochastic resonance state so that weak fault characteristics can be effectively extracted in strong background noise. Under adiabatic approximation, the effects of damping coefficient, noise intensity, and asymmetry on the output signal-to-noise ratio are discussed based on the two-state model theory. Under the same parameters, the output signal-to-noise ratio of the asymmetric second-order stochastic resonance system is better than that of the underdamped second-order stochastic resonance system. The bearing fault and field engineering experimental results are provided to justify the comparative advantage of the proposed method over the underdamped second-order stochastic resonance method.