Master equation simulations of bistable and excitable dynamics in a model of a thermochemical system

The effect of fluctuations on the dynamics of a model of a bistable thermochemical system is studied by means of the master equation. The system has three stationary states and exhibits two types of bistability: the coexistence of two stable focuses and the coexistence of a stable focus with a stable limit cycle separated by a saddle point. Stochastic effects are important when the system is close to the bifurcation, in which the stable limit cycle disappears through a homoclinic orbit. In this case the distribution of the first passage time from the stable limit cycle to the stable focus has a multipeak form. The dependence of this distribution on the number of particles is presented. Near the homoclinic orbit bifurcation, the system also exhibits excitability due to a particular shape of the basin of attraction of the stable focus.     

The SNA analysis of a minimal model for bistability in the MAPK signaling cascade model

Successive phosphorylation cascades mediated by mitogen-activated protein kinases (MAPKs) are known to act as switches initiating various cellular processes. In addition, models of the MAPK reaction network are displaying other nonlinear phenomena including bistability and periodic oscillations. Recently bistability has been explained as a consequence of interaction between single and double phosphorylation/dephosphorylation pathways in the Stage 2 subsystem of the Huang-Ferrell model of the MAPK and a core bistable model has been proposed. Here we focus on a detailed stability analysis of the steady states of this minimal model. The analysis uses methods of convex analysis and stoichiometric network theory.     

Topological ferroelectric bistability in a polarization-modulated orthogonal smectic liquid crystal

We report a bent-core liquid crystal (LC) compound exhibiting two fluid smectic phases in which two-dimensional, polar, orthorhombic layers order into three-dimensional ferroelectric states. The lower-temperature phase has a uniform polarization field which responds in an analog fashion to applied electric field. The higher-temperature phase is a new smectic state with periodic undulation of the polarization, structurally modulated layers, and a bistable response to applied electric field which originates in the periodically splay-modulated bulk of the LC rather than by surface stabilization at the cell boundaries.     

Molecular-based electronically switchable tunnel junction devices.

Solid-state tunnel junction devices were fabricated from Langmuir Blodgett molecular monolayers of a bistable [2]catenane, a bistable [2]pseudorotaxane, and a single-station [2]rotaxane. All devices exhibited a (noncapacitive) hysteretic current-voltage response that switched the device between high- and low-conductivity states, although control devices exhibited no such response. Correlations between the structure and solution-phase dynamics of the molecular and supramolecular systems, the crystallographic domain structure of the monolayer film, and the room-temperature device performance characteristics are reported.     

High hopes: can molecular electronics realise its potential?

Manipulating and controlling the self-organisation of small collections of molecules, as an alternative to investigating individual molecules, has motivated researchers bent on processing and storing information in molecular electronic devices (MEDs). Although numerous ingenious examples of single-molecule devices have provided fundamental insights into their molecular electronic properties, MEDs incorporating hundreds to thousands of molecules trapped between wires in two-dimensional arrays within crossbar architectures offer a glimmer of hope for molecular memory applications. In this critical review, we focus attention on the collective behaviour of switchable mechanically interlocked molecules (MIMs)--specifically, bistable rotaxanes and catenanes--which exhibit reset lifetimes between their ON and OFF states ranging from seconds in solution to hours in crossbar devices. When these switchable MIMs are introduced into high viscosity polymer matrices, or self-assembled as monolayers onto metal surfaces, both in the form of nanoparticles and flat electrodes, or organised as tightly packed islands of hundreds and thousands of molecules sandwiched between two electrodes, the thermodynamics which characterise their switching remain approximately constant while the kinetics associated with their reset follow an intuitively predictable trend--that is, fast when they are free in solution and sluggish when they are constrained within closely packed monolayers. The importance of seamless interactions and constant feedback between the makers, the measurers and the modellers in establishing the structure-property relationships in these integrated functioning systems cannot be stressed enough as rationalising the many different factors that impact device performance becomes more and more demanding. The choice of electrodes, as well as the self-organised superstructures of the monolayers of switchable MIMs employed in the molecular switch tunnel junctions (MSTJs) associated with the crossbars of these MEDs, have a profound influence on device operation and performance. It is now clear, after much investigation, that a distinction should be drawn between two types of switching that can be elicited from MSTJs. One affords small ON/OFF ratios and is a direct consequence of the switching in bistable MIMs that leads to a relatively small remnant molecular signature--an activated chemical process. The other leads to a very much larger signature and ON/OFF ratios resulting from physical or chemical changes in the electrodes themselves. Control experiments with various compounds, including degenerate catenanes and free dumbbells, which cannot and do not switch, are crucial in establishing the authenticity of the small ON/OFF ratios and remnant molecular signatures produced by bistable MIMs. Moreover, experiments conducted on monolayers in MSTJs of molecules designed to switch and molecules designed not to switch have been probed directly by spectroscopic and other means in support of MEDs that store information through switching collections of bistable MIMs contained in arrays of MSTJs. In the quest for the next generation of MEDs, it is likely that monolayers of bistable MIMs will be replaced by robust crystalline extended structures wherein the switchable components, derived from bistable MIMs, are organised precisely in a periodic manner.     

Stochastic transitions through unstable limit cycles in a model of bistable thermochemical system

The master equation approach is used to study transitions through an unstable limit cycle surrounding a stable focus in two-variable systems with three stationary states. The model considered describes a bistable thermochemical system. Two cases are studied. In the first one transitions occur from a basin of attraction of a stable limit cycle to a basin of attraction of a stable focus surrounded by an unstable limit cycle. In the second case, stochastic trajectories cross the unstable limit cycle going from a basin of attraction of a stable node to a basin of attraction of a stable focus. Distribution functions of the first passage time between these attractors are calculated and discussed for systems with various numbers of particles. The distribution functions in both cases exhibit a multi-peak character. A fine structure of single peaks is observed in the first case.     

A unified perspective on the hydrogen atom transfer and proton-coupled electron transfer mechanisms in terms of topographic features of the ground and excited potential energy surfaces as exemplified by the reaction between phenol and radicals

The relation between the hydrogen atom transfer (HAT) and proton-coupled electron transfer (PCET) mechanisms is discussed and is illustrated by multiconfigurational electronic structure calculations on the ArOH + R(*) --> ArO(*) + RH reactions. The key topographic features of the Born-Oppenheimer potential energy surfaces that determine the predominant reaction mechanism are the conical intersection seam of the two lowest states and reaction saddle points located on the shoulders of this seam. The saddle point corresponds to a crossing of two interacting valence bond states corresponding to the reactant and product bonding patterns, and the conical intersection corresponds to the noninteracting intersection of the same two diabatic states. The locations of mechanistically relevant conical intersection structures and relevant saddle point structures are presented for the reactions between phenol and the N- and O-centered radicals, (*)NH2 and (*)OOCH3. Points on the conical intersection of the ground doublet D0 and first excited doublet D1 states are found to be in close geometric and energetic proximity to the reaction saddle points. In such systems, either the HAT mechanism or both the HAT mechanism and the proton-coupled electron transfer (PCET) mechanism can take place, depending on the relative energetic accessibility of the reaction saddle points and the D0/D1 conical intersection seams. The discussion shows how the two mechanisms are related and how they blend into each other along intermediate reaction paths. The recognition that the saddle point governing the HAT mechanism is on the shoulder of the conical intersection governing the PCET mechanism is used to provide a unified view of the competition between the two mechanisms (and the blending of the two mechanisms) in terms of the prominent and connected features of the potential energy surface, namely the saddle point and the conical intersection. The character of the dual mechanism may be understood in terms of the dominant valence bond configurations of the intersecting states, which are zero-order approximations to the diabatic states.     

Pt(100)/NO+CO体系随机共振的理论研究

在远离平衡的条件下,NO在Pt(100)表面进行的催化还原反应表现出化学振荡和化学多稳态等复杂的动力学行为.利用Fink等提出的反应模型,通过计算机模拟对体系的控制参量进行周期调制和随机调制,在简单双稳区以及振荡与稳态的共存区,观察到随机共振(StochasticResonance:SR)现象.     

Periodic orbits in biological molecules: phase space structures and selectivity in alanine dipeptide

Small and large molecules may localize their energy in specific bonds or generally in vibrational modes for extended periods of time, an effect which may have dramatic consequences in reaction dynamics. Periodic orbits offer the means to identify phase space regions with localized motions. The author demonstrate that techniques to locate periodic orbits developed for small molecules can be applied to large molecules such as alanine dipeptide. The widely used empirical force fields are employed and principal families of periodic orbits associated with local-type motions and emanated from the lowest energy minima and saddle points are investigated. Continuation of these families at high energies unravels the stable and unstable regions of phase space as well as elementary bifurcations such as saddle nodes.     

Coherent third-order spectroscopic probes of molecular chirality

The third-order optical response of a system of coupled localized anharmonic vibrations is studied using a Green's function solution of the nonlinear exciton equations for bosonized excitons, which are treated as interacting quasiparticles. The explicit calculation of two-exciton states is avoided and the scattering of quasiparticles provides the mechanism of optical nonlinearities. To first-order in the optical wave vector we find several rotationally invariant tensor components for isotropic ensembles which are induced by chirality. The nonlocal nonlinear susceptibility tensor is calculated for infinitely large periodic structures in momentum space, where the problem size reduces to the exciton interaction radius. Applications are made to alpha and 3(10) helical infinite peptides.     

Photoaligned bistable twisted nematic liquid crystal displays

Novel, optically bistable, twisted nematic liquid crystal display configurations obtained using photoaligned and photopatterned substrates are presented. Switching by 360° between two stable twist configurations is shown. Undesired intermediate states which reduce bistability are effectively suppressed by photopatterned domains around picture elements which exhibit different azimuthal- and zenithal-aligning directions. The high degree of stability of the new, domain-stabilized bistable configurations enables the formation of nematic displays with inherent long term optical memory. Display switching at a few volts is demonstrated.     

Photoaligned bistable twisted nematic liquid crystal displays

Novel, optically bistable, twisted nematic liquid crystal display configurations obtained using photoaligned and photopatterned substrates are presented. Switching by 360° between two stable twist configurations is shown. Undesired intermediate states which reduce bistability are effectively suppressed by photopatterned domains around picture elements which exhibit different azimuthal- and zenithal-aligning directions. The high degree of stability of the new, domain-stabilized bistable configurations enables the formation of nematic displays with inherent long term optical memory. Display switching at a few volts is demonstrated.     

Finite-Temperature Dimer Method for Finding Saddle Points on Free Energy Surfaces

The dimer method and its variants have been shown to be efficient in finding saddle points on potential surfaces. In the dimer method, the most unstable direction is approximately obtained by minimizing the total potential energy of the dimer. Then, the force in this direction is reversed to move the dimer toward saddle points. When the finite-temperature effect is important for a high-dimensional system, one usually needs to describe the dynamics in a low-dimensional space of reaction coordinates. In this case, transition states are collected as saddle points on the free energy surface. The traditional dimer method cannot be directly employed to find saddle points on a free energy surface since the surface is not known a priori. Here, we develop a finite-temperature dimer method for searching saddle points on the free energy surface. In this method, a constrained rotation dynamics of the dimer system is used to sample dimer directions and an efficient average method is used to obtain a good approximation of the most unstable direction. This approximated direction is then used in reversing the force component and evolving the dimer toward saddle points. Our numerical results suggest that the new method is efficient in finding saddle points on free energy surfaces. © 2019 Wiley Periodicals, Inc.     

Isolation techniques for long‐term bistability of the bistable twisted nematic mode

Low power, storage liquid crystal displays are of interest in the foreseeable future in portable applications. The use of a bistable twisted namatic (BTN) mode in a true storage device requires long term bistability of its operating states since it is intrinsically a metastable device. Two novel isolation techniques are described and demonstrated to isolate and stabilize the operating states in a BTN device. Existing limitations are highlighted and further areas for research suggested.     

Periodic and random perturbation of catalytic oxidation of CO

When a controllable input is modulated by noise and signal, the response of a nonlinear system may exhibit a synchronized effect, which is referred to as stochastic resonance(SR). With the help of noise, the detection of weak signal may become possible and its signal-to-noise ratio can be increased. A model to describe catalytic oxidation of CO on single crystal was adopted, and its stability was studied by linear analysis method. Through computer simulation, the responses under periodic and random perturbation were analyzed. Stochastic resonance behavior was found in a narrow bistable region, or near the oscillatory region. The results shows more characteristics than those of 1-dimensional system does.     

Isolation techniques for long-term bistability of the bistable twisted nematic mode

Low power, storage liquid crystal displays are of interest in the foreseeable future in portable applications. The use of a bistable twisted namatic (BTN) mode in a true storage device requires long term bistability of its operating states since it is intrinsically a metastable device. Two novel isolation techniques are described and demonstrated to isolate and stabilize the operating states in a BTN device. Existing limitations are highlighted and further areas for research suggested.     

Intrinsic optical bistability of thin films of linear molecular aggregates: the one-exciton approximation

We perform a theoretical study of the nonlinear optical response of an ultrathin film consisting of oriented linear aggregates. A single aggregate is described by a Frenkel exciton Hamiltonian with uncorrelated on-site disorder. The exciton wave functions and energies are found exactly by numerically diagonalizing the Hamiltonian. The principal restriction we impose is that only the optical transitions between the ground state and optically dominant states of the one-exciton manifold are considered, whereas transitions to other states, including those of higher exciton manifolds, are neglected. The optical dynamics of the system is treated within the framework of truncated optical Maxwell-Bloch equations, in which the electric polarization is calculated by using a joint distribution of the transition frequency and the transition dipole moment of the optically dominant states. This function contains all the statistical information about these two quantities that govern the optical response and is obtained numerically by sampling many disorder realizations. We derive a steady-state equation that establishes a relationship between the output and input intensities of the electric field and show that within a certain range of the parameter space this equation exhibits a three-valued solution for the output field. A time-domain analysis is employed to investigate the stability of different branches of the three-valued solutions and to get insight into switching times. We discuss the possibility to experimentally verify the bistable behavior.     

Multipeak distributions of first passage times in bistable dynamics in a model of a thermochemical system.

A master equation is used to study transitions between the stable limit cycle and stable focus in the two-variable bistable system. The distribution function of the mean first passage time between these attractors and the relative dispersion of the mean first return time from the stable focus to itself as a function of the intensity of fluctuations are calculated and discussed. A coherence resonance is observed for the return time from the focus to itself.     

Transition rate prefactors for systems of many degrees of freedom

When a minimum on the potential energy surface is surrounded by multiple saddle points with similar energy barriers, the transition pathways with greater prefactors are more important than those that have similar energy barriers but smaller prefactors. In this paper, we present a theoretical formulation for the prefactors, computing the probabilities for transition paths from a minimum to its surrounding saddle points. We apply this formulation to a system of 2 degrees of freedom and a system of 14 degrees of freedom. The first is Brownian motion in a two-dimensional potential whose global anharmonicities play a dominant role in determining the transition rates. The second is a Lennard-Jones (LJ) cluster of seven particles in two dimensions. Low lying transition states of the LJ cluster, which can be reached directly from a minimum without passing through another minimum, are identified without any presumption of their characteristics nor of the product states they lead to. The probabilities are computed for paths going from an equilibrium ensemble of states near a given minimum to the surrounding transition states. These probabilities are directly related to the prefactors in the rate formula. This determination of the rate prefactors includes all anharmonicities, near or far from transition states, which are pertinent in the very sophisticated energy landscape of LJ clusters and in many other complex systems.     

Multiphonon decay of excited states of rare earth ions in crystals

Although the relaxation of excited electronic states through radiationless multiphonon processes has been well established by experiment, there are several serious problems concerning the current theoretical model in which the electron-phonon interaction is treated as a small perturbation, and the multiphonon transitions are attributed to high order expansion terms of perturbation theory. Here, we approach the problem in the framework of the adiabatic approximation. The rate of the multiphonon process is expressed in the form of the linear response time correlation function which is then evaluated by means of the saddle point approximation. The resulting expression predicts an approximately exponential dependence of the rate on the transition gap and a temperature dependence that agrees quantitatively with experiment.