Three-mode Model Research Articles

Round-robin scheduling protocol-based stabilization for discrete-time Markov jumping neural networks

This paper focuses on the stabilization problem of discrete-time Markov jumping neural networks (DMJNNs) under communication constraints between the actuators and the remote controller. To reduce the communication burden, a round-robin scheduling protocol is introduced to allocate the right to a single actuator to exclusively use the communication channel at a given time while ensuring that multiple nodes can take turns to occupy the channel for signal transmission. Two criteria for stochastic analysis of the closed-loop network model are presented based on different assumptions of the activation functions. Then, numerically tractable design methods for the required controller gains are developed. Finally, the three-mode DMJNN model is used as an example to illustrate the complementarity and effectiveness of the presented analysis results and design methods.

Optimal control of N-H photodissociation of pyridinyl.

The N-H photodissociation dynamics of the pyridinyl radical upon continuous excitation to the optically bright, first excited ππ* electronic state by an ultra-violet (UV) laser pulse has been investigated within the mathematical framework of optimal control theory. The genetic algorithm (GA) is employed as the optimization protocol. We considered a three-state and three-mode model Hamiltonian, which includes the reaction coordinate, R (a1 symmetry); the coupling coordinates (namely, out-of-plane bending coordinate of the hydrogen atom of azine group), Θ (b1 symmetry); and the wagging mode, Q9 (a2 symmetry). The three electronic states are the ground, ππ*, and πσ* states. The πσ* state crosses both the ground state and the ππ* state, and it is a repulsive state on which N-H dissociation occurs upon photoexcitation. Different vibrational wave functions along the coupling coordinates, Θ and Q9, of the ground electronic state are used as the initial condition for solving the time-dependent Schrödinger equation. The optimal UV laser pulse is designed by applying the GA, which maximizes the dissociation yield. We obtained over 95% dissociation yield through the πσ* asymptote using the optimal pulse of a time duration of ∼30 000a.u. (∼725.66fs).

Chaos signatures of current phase transition in a toroidal trap

In this work we demonstrate how the current phase transition of atomic Bose–Einstein condensates in a toroidal trap can be controlled by applying a zero-mean oscillatory driving field. Here, the current phase transition means that the long-time averaged current undergoes a transition from a zero value to a nonzero value (or the transition from a nonzero value to a zero value). We show that due to the self-trapping effect in momentum space, the oscillatory amplitude of the current can be significantly suppressed and a nearly constant directed current can be obtained preserving the initial current values, by decreasing the driving amplitude, even when the atomic interactions are relatively small. We also reveal numerically the mean-field chaos can serve as an indicator of a quantum phase transition between the vanishing current regime and nonvanishing current regime. Our results are corroborated by an effective three-mode model, which provides an excellent account of the current dynamics of the system.

High-Gain Traveling-Wave Parametric Amplifier Based on Three-Wave Mixing

We extend the theory for a Josephson-junction traveling-wave parametric amplifier (TWPA) operating in the three-wave-mixing regime and we propose a scheme for achieving high gain. The continuous three-mode model [P.K. Tien, J. Appl. Phys. 29, 1347 (1958)] is, on one hand, extended to describe a discrete chain of Josephson junctions at high frequencies close to the spectral cutoff where there is no up-conversion. On the other hand, we also develop a continuous multimode theory for the small frequency limit where the frequency dispersion is close to linear. We find that in both cases the gain is significantly reduced compared to the prediction by the continuous three-mode model as the result of increasingly strong dispersion at the high frequencies and generation of up-converted modes at the small frequencies. The developed theory is in quantitative agreement with simulations of the full solution of the dynamical equations. To recover the high gain, we propose to engineer a chain with dispersive features to form a two-band frequency spectrum and to place the pump frequency within the upper band close to the spectral cutoff. We prove that there exists a sweet spot, where the signal and the pump are phase matched, while the up-conversion is inhibited. This results in a high gain, which grows exponentially with the length of the TWPA.

Knowledge transferring and conversion in the early stage of collaborative product design by entrepreneurial teams

PurposeThe purpose of the study is to discover a model of knowledge conversion and knowledge transferring/sharing barriers in an entrepreneurial team (ET) working with innovative users at the early and fuzzy front end (FFE) stage of collaborative product design (Co-PD) process.Design/methodology/approachThe exploratory research framework included sampling, data collection and data analysis, through sequential levels of categorizations, undertaken jointly with constant comparative analysis. The sample frame is the pool of ETs/startups from university business accelerators that carry out Co-PD at the FFE stage. The research survey is based on observations of the collaborative ETs activities, questionnaires and in-depth interviews with them. The research was conducted on individual and team levels when Co-PD process and ET activities were in progress.FindingsThis study identified specific set of concepts of knowledge conversion and transferring/sharing and their barriers that reflect specificity of Co-PD processes at the FFE stage in collaborative ETs. The discovered conversion process is represented by the socialization, externalization and internalization, three-mode knowledge conversion model. The significance of barriers and frequency of their occurrence were measured in knowledge transferring/sharing in collaborative ETs on individual and team levels.Originality/valueThis study shows novel insights into how knowledge transfers/shares and converts in the context of ET working with innovative users in Co-PD process at the FFE stage.

Dynamics of recurrent modulational instability near its separatrix in nonlinear fiber optics

Separatrix crossing stands for the continuation of the modulation instability into the strong depleted regime and is responsible for the symmetry breaking nature of the recurrence phenomenon. The near-separatrix dynamic for recurrent modulational instability is of great importance because it is closely associated with the formation of rogue breather structures. Here, we have developed the underlying phase-space structure of nonlinear modulation instability by treating the three-mode truncate model as a simple oscillator. This allowed us to reveal the high sensitivity of the switching dynamics characterized by inner or outer trajectories to the initial condition around a separatrix. Our results present a major step forward towards the complete understanding of recurrent modulational instability in a truly conservative setting and can provide a guidance to experimentally measure the involved recursive behaviors.

Unification of valley and anomalous Hall effects in a strained lattice

Two dimensional lattices are an important stage for studying many aspects of quantum physics, in particular the topological phases. The valley Hall and anomalous Hall effects are two representative topological phenomena. Here we show that they can be unified in a strained honeycomb lattice, where the hopping strengths between neighboring sites are designed by mimicking those between the Fock states in a three-mode Jaynes-Cummings model. Such a strain induces an effective magnetic field which results in quantized Landau levels. The eigenstates in the zeroth Landau level can be represented by the eigenstates of a large pseudo-spin. We find that the valley Hall current and the chiral edge current in the Haldane model correspond to the spin precession around different axes. Our study sheds light on connection between seemingly unrelated topological phases in condensed matter physics.

Coupled electrochemical-abuse-heat-transfer model to predict thermal runaway propagation and mitigation strategy for an EV battery module

Safe and reliable design of lithium-ion battery packs necessitates prevention of thermal runaway and its propagation. To characterize the propagation behaviour in a battery module, a three-mode heat transfer model coupled with electrochemical and abuse-reaction-kinetics models is developed here. The efficacy of an active thermal management system in preventing damage-cascade for a standard EV module geometry (as used in Tesla) is elucidated. The model effectively captures the temperature profile, heat generation rate, and the extent of resulting decomposition of cell-components as validated against the literature. A temperature spike is applied to a cell within a standard battery module to emulate abuse driven runaway. The propagation of damage to other cells due to the temperature-spike in the triggered cell is simulated through the model as developed. A counter-intuitive non-monotonic trend (increasing first, decreasing later) is observed for the damage-severity as a function of coolant flow rate. Through a unified analysis of cumulative heat generation and heat dissipation through coolant, a mitigation strategy for runaway propagation is obtained in terms of a generalized non-dimensional parameter, Runway Mitigation Number (RMN), which predicts runaway propagation beyond a value of ~1.8 for similar module designs.

Temperature effects on singlet fission dynamics mediated by a conical intersection.

Finite-temperature dynamics of singlet fission in crystalline rubrene is investigated by utilizing the Dirac-Frenkel time-dependent variational method in combination with multiple Davydov D2 trial states. To probe temperature effects on the singlet fission process mediated by a conical intersection, the variational method is extended to include number state propagation with thermally averaged Boltzmann distribution as initialization. This allows us to simulate two-dimensional electronic spectroscopic signals of two-mode and three-mode models of crystalline rubrene in the temperature range from 0 K to 300 K. It is demonstrated that an elevated temperature facilitates excitonic population transfer and accelerates the singlet fission process. In addition, increasing temperature leads to dramatic changes in two-dimensional spectra, thanks to temperature-dependent electronic dephasing and to an increased number of system eigenstates amenable to spectroscopic probing.

The Analysis of Multivariate Longitudinal Data: An Instructive Application of the Longitudinal Three-Mode Model

Structural equation modeling is a common technique to assess change in longitudinal designs. However, these models can become of unmanageable size with many measurement occasions. One solution is the imposition of Kronecker product restrictions to model the multivariate longitudinal structure of the data. The resulting longitudinal three-mode models (L3MMs) are very parsimonious and have attractive interpretation. This paper provides an instructive description of L3MMs. The models are applied to health-related quality of life (HRQL) data obtained from 682 patients with painful bone metastasis, with eight measurements at 13 occasions; before and every week after treatment with radiotherapy. We explain (1) how the imposition of Kronecker product restrictions can be used to model the multivariate longitudinal structure of the data, (2) how to interpret the Kronecker product restrictions and the resulting L3MM parameters, and (3) how to test substantive hypotheses in L3MMs. In addition, we discuss the challenges for the evaluation of (differences in) fit of these complex and parsimonious models. The L3MM restrictions lead to parsimonious models and provide insight in the change patterns of relationships between variables in addition to the general patterns of change. The L3MM thus provides a convenient model for multivariate longitudinal data, as it not only facilitates the analysis of complex longitudinal data but also the substantive interpretation of the dynamics of change.

Parametric resonance of a Bose-Einstein condensate in a ring trap with periodically driven interactions

We study the instability of a ring Bose-Einstein condensate under a periodic modulation of inter-atomic interactions. The condensate exhibits temporal and spatial patterns induced by the parametric resonance, which can be characterized by Bogoliubov quasi-particle excitations in the Floquet basis. As the ring geometry significantly limits the number of excitable Bogoliubov modes, we are able to capture the non-linear dynamics of the condensate using a three-mode model. We further demonstrate the robustness of the temporal and spatial patterns against disorder, which are attributed to the mode-locking mechanism under the ring geometry. Our results can be observed in cold atomic systems and are also relevant to physical systems described by the non-linear Schrodinger's equation.

Two-State, Three-Mode Parametrization of the Force Field of a Retinal Chromophore Model.

In recent years, the potential energy surfaces of the penta-2,4-dieniminium cation have been investigated using several electronic structure methods. The resulting pool of geometrical, electronic, and energy data provides a suitable basis for the construction of a topographically correct analytical model of the molecule force field and, therefore, for a better understanding of this class of molecules, which includes the chromophore of visual pigments. In the present contribution, we report the construction of such a model for regions of the force field that drive the photochemical and thermal isomerization of the central double bound of the cation. While previous models included only two modes, it is here shown that the proposed three-mode model and corresponding set of parameters are able to reproduce the complex topographical and electronic structure features seen in electronically correlated data obtained at the XMCQDPT2//CASSCF/6-31G* level of theory.

Relaxation, chaos, and thermalization in a three-mode model of a Bose–Einstein condensate

We study the complex quantum dynamics of a system of many interacting atoms in an elongated anharmonic trap. The system is initially in a Bose–Einstein condensed state, well described by Thomas–Fermi profile in the elongated direction and the ground state in the transverse directions. After a sudden quench to a coherent superposition of the ground and lowest energy transverse modes, quantum dynamics starts. We describe this process employing a three-mode many-body model. The experimental realization of this system displays decaying oscillations of the atomic density distribution. While a mean-field description predicts perpetual oscillations of the atomic density distribution, our quantum many-body model exhibits a decay of the oscillations for sufficiently strong atomic interactions. We associate this decay with the fragmentation of the condensate during the evolution. The decay and fragmentation are also linked with the approach of the many-body model to the chaotic regime. The approach to chaos lifts degeneracies and increases the complexity of the eigenstates, enabling the relaxation to equilibrium and the onset of thermalization. We verify that the damping time and quantum signatures of chaos show similar dependences on the interaction strength and on the number of atoms.

Effect of Asymmetric Mode on CO2 State-to-State Vibrational-Chemical Kinetics.

Coupled state-to-state vibrational-chemical kinetics, gas dynamics, and heat transfer in the five-component mixture of dissociated CO2 are studied using the complete three-mode kinetic model and the reduced scheme involving mainly the vibrational states of the asymmetric mode. The emphasis is on the effect of asymmetric vibrations on the rate of dissociation, fluid dynamic variables, and heat flux. It is shown that intermode vibrational energy transitions between CO and CO2 asymmetric mode may considerably decrease the rate of dissociation; the presence of CO in the mixture quickly depletes high vibrational states and thus inhibits dissociation at low temperatures. The reduced model overpredicts populations of highly located states of the asymmetric mode, especially when intermode VV transitions are neglected; therefore, using the simplified model in flows with dominating dissociation may yield overestimated dissociation rate. In the hypersonic flow along the stagnation line, the influence of asymmetric vibrations on the fluid dynamics and heat transfer is weak; the main role belongs to chemical reactions and VT transitions in the bending mode. In this case, the computationally efficient simplified model can be used to predict macroscopic variables and heat flux without significant loss of accuracy.

The origin of absorptive features in the two-dimensional electronic spectra of rhodopsin.

In rhodopsin, the absorption of a photon causes the isomerization of the 11-cis isomer of the retinal chromophore to its all-trans isomer. This isomerization is known to occur through a conical intersection (CI) and the internal conversion through the CI is known to be vibrationally coherent. Recently measured two-dimensional electronic spectra (2DES) showed dramatic absorptive spectral features at early waiting times associated with the transition through the CI. The common two-state two-mode model Hamiltonian was unable to elucidate the origin of these features. To rationalize the source of these features, we employ a three-state three-mode model Hamiltonian where the hydrogen out-of plane (HOOP) mode and a higher-lying electronic state are included. The 2DES of the retinal chromophore in rhodopsin are calculated and compared with the experiment. Our analysis shows that the source of the observed features in the measured 2DES is the excited state absorption to a higher-lying electronic state and not the HOOP mode.

Quantum phase transition in an effective three-mode model of interacting bosons.

In this work we study an effective three-mode model describing interacting bosons. These bosons can be considered as exciton-polaritons in a semiconductor microcavity at the magic angle. This model exhibits quantum phase transition (QPT) when the parameters of the corresponding Hamiltonian are continuously varied. The properties of the Hamiltonian spectrum (e.g., the distance between two adjacent energy levels) and the phase space structure of the thermodynamic limit of the model are used to indicate QPT. The relation between spectral properties of the Hamiltonian and the corresponding classical frame of the thermodynamic limit of the model is established as indicative of QPT. The average number of bosons in a specific mode and the entanglement properties of the ground state as functions of the parameters are used to characterize the order of the transition and also to construct a phase diagram. Finally, we verify our results for experimental data obtained for a setting of exciton-polaritons in a semiconductor microcavity.

Interfacial pattern selection in defiance of linear growth

In this study, we revisit Rayleigh’s visionary hypothesis (Rayleigh, Proc. R. Soc. Lond., vol. 29, 1879a, pp. 71–97), that patterns resulting from interfacial instabilities are dominated by the fastest-growing linear mode, as we study nonlinear pattern selection in the context of a linear growth (dispersion) curve that has two peaks of equal height. Such a system is obtained in a physical situation consisting of two liquid layers suspended from a heated ceiling, and exposed to a passive gas. Both interfaces are then susceptible to thermocapillary and Rayleigh–Taylor instabilities, which lead to rupture/pinch off via a subcritical bifurcation. The corresponding mathematical model consists of long-wavelength evolution equations which are amenable to extensive numerical exploration. We find that, despite having equal linear growth rates, either one of the peak-modes can completely dominate the other as a result of nonlinear interactions. Importantly, the dominant peak continues to dictate the pattern even when its growth rate is made slightly smaller, thereby providing a definite counter-example to Rayleigh’s conjecture. Although quite complex, the qualitative features of the peak-mode interaction are successfully captured by a low-order three-mode ordinary differential equation model based on truncated Galerkin projection. Far from being governed by simple linear theory, the final pattern is sensitive even to the phase difference between peak-mode perturbations. For sufficiently long domains, this phase effect is shown to result in the emergence of coexisting patterns, wherein each peak-mode dominates in a different region of the domain.

A comprehensive wireless sensor network reliability metric for critical Internet of Things applications

Evaluating the reliability of a wireless sensor network (WSN) deployment is a highly important task especially when the WSN is used for a critical Internet of Things (IoT) application. In this paper, we introduce a novel comprehensive reliability metric to evaluate the reliability of WSN deployments over their intended mission time. Unlike the existing studies on the topic, the proposed metric takes into account that sensor nodes (SNs) are multi-component systems that are subject to different component failures, namely, sensor, transceiver, processor, and battery failures. Consequently, SNs are modeled as three-mode (on, relay, and off) systems instead of the simplistic two-mode (on and off) model adopted in the existing studies. To calculate the proposed reliability metric in a computationally efficient manner, we develop a search algorithm which generates the complete path set of the given WSN deployment. Extensive experimental results demonstrate the use of the proposed metric in evaluating the reliability of several WSN deployments under different operating conditions. Results also demonstrate the computational efficiency of the developed search algorithm used for calculating the proposed metric and the significant effect of using the proposed three-mode SN model on the accuracy of the evaluated reliability.

Evaluation of multiple-imputation procedures for three-mode component models

ABSTRACTThree-mode analysis is a generalization of principal component analysis to three-mode data. While two-mode data consist of cases that are measured on several variables, three-mode data consist of cases that are measured on several variables at several occasions. As any other statistical technique, the results of three-mode analysis may be influenced by missing data. Three-mode software packages generally use the expectation–maximization (EM) algorithm for dealing with missing data. However, there are situations in which the EM algorithm is expected to break down. Alternatively, multiple imputation may be used for dealing with missing data. In this study we investigated the influence of eight different multiple-imputation methods on the results of three-mode analysis, more specifically, a Tucker2 analysis, and compared the results with those of the EM algorithm. Results of the simulations show that multilevel imputation with the mode with the most levels nested within cases and the mode with the least levels represented as variables gives the best results for a Tucker2 analysis. Thus, this may be a good alternative for the EM algorithm in handling missing data in a Tucker2 analysis.

Local and global nonlinear dynamics of thermomechanically coupled composite plates in passive thermal regime

Unified 2D continuum formulation of the nonlinear dynamic problem for a von Karman shear indeformable symmetric cross-ply composite plate in a thermomechanical environment is presented, along with the ensuing reduction procedure ending up to a three-mode discretized model with unknown transverse displacement and membrane/bending temperatures. Systematic numerical analyses in the case of thermal dynamics passively entrained by the solely active mechanical excitations allow to unveil the main features of the nonlinear response, while highlighting fundamental aspects associated with the thermomechanical coupling. Local and global dynamics of a single-layer orthotropic plate are investigated under varying in-plane/transverse excitations or thermal property of the material. Comparison with the response provided by partially coupled models and the uncoupled mechanical oscillator enables to identify situations in which thermomechanical coupling affects the nonlinear response even in the solely passive thermal setting and to frame the relevant effects within known literature results.