Effective Potential Function Research Articles

Stochastic resonance in a monostable system driven by time-delayed feedback

The characteristic of a monostable stochastic resonance system driven by time-delayed feedback is investigated. Under the small-delay approximation theory, the effective potential function of the system is obtained and the influence of system parameters on the shape of the potential function is also discussed. Furthermore, we consider the influence of the input signal on the system and derive the asymmetric bistable potential function. By using the adiabatic approximation theory and the two-state theory, the theoretical expressions of the steady-state probability distribution function, mean first-passage time and signal-to-noise ratio are obtained, which are three excellent metrics to measure the performance of system. Simulation results show that the parameters A, a and τ can motivate the SR phenomenon while β suppresses the SR phenomenon. At last, the numerical simulation results obtained from the original Langevin equation and the effective Langevin equation can verify whether the theoretical derivation is correct.

An ideal metal contact with monolayer Ti2CO2

Density functional theory calculations are performed to reveal the nature of the contact between metal (Au, Pd, Sc) and monolayer Ti2CO2, thereby finding an ideal metal contact for the application Ti2CO2 as nanoelectronic device. The calculations of effective potential and electron localization function for the Au, Pd and Sc top contacts with Ti2CO2 show that their effective tunnel barrier vanish to zero, and Pd-Ti2CO2 has minimum localization. Moreover, analyses of density of states and energy bands indicate that Au-, Pd-, and Sc-Ti2CO2 are purely Ohmic contacts, leading to a high electron injection efficiency, and Pd has the lowest Schottky barriers. The electron density and electron difference density are investigated, indicating that a strong electron interaction occurs between Pd and Ti2CO2. Based on these results, the device based on Ti2CO2 with Pd electrodes should have better electron injection efficiency and lower contact resistance than the one with Au or Sc electrodes.

Dynamics of living cells in a cytomorphological state space

Cells are nonequilibrium systems that exchange matter and energy with the environment to sustain their metabolic needs. The nonequilibrium nature of this system presents considerable challenges to developing a general theory describing its behavior; however, when studied at appropriate spatiotemporal scales, the behavior of ensembles of nonequilibrium systems can resemble that of a system at equilibrium. Here we apply this principle to a population of cells within a cytomorphological state space and demonstrate that cellular transition dynamics within this space can be described using equilibrium formalisms. We use this framework to map the effective energy landscape underlying the cytomorphological state space of a population of mouse embryonic fibroblasts (MEFs) and identify topographical nonuniformity in this space, indicating nonuniform occupation of cytomorphological states within an isogenic population. The introduction of exogenous apoptotic agents fundamentally altered this energy landscape, inducing formation of additional energy minima that correlated directly with changes in sensitivity to apoptosis induction. An equilibrium framework allows us to describe the behavior of an ensemble of single cells, suggesting that although cells are complex nonequilibrium systems, the application of formalisms derived from equilibrium thermodynamics can provide insight into the basis of nongenetic heterogeneities within cell populations, as well as the relationship between cytomorphological and functional heterogeneity.

Stochastic resonance in time-delayed exponential monostable system driven by weak periodic signals

Based on the exponential monostable potential, we study an exponential monostable system with time-delayed feedback driven by weak periodic signals and additive Gaussian white noises. The small delay approximation is used to deduce the steady-state probability distribution and the effective potential function is derived. The system parameters l and b, time delay τ, feedback strength β can change the shapes of the potential function. The mean first-passage time (MFPT) is calculated, which plays an extremely important role in the research of particles escape. And the signal-to-noise ratio (SNR) of the system can be obtained by using the adiabatic approximation theory. The phenomenon of stochastic resonance is investigated under different system parameters and time-delayed feedback. The amplitude of SNR can be changed by adjusting the system parameters. When the feedback strength β is positive (or negative), the time delay τ can promote (or suppress) the stochastic resonance phenomenon. The SNR versus the noise intensity D presents the stochastic resonance phenomenon. In addition, the SNR increases non-monotonically with the increasing feedback strength β and the parameter b. Also, the analysis and numerical simulation results of SNR are in good agreement with the formula simulation.

Stochastic resonance in a time polo-delayed asymmetry bistable system driven by multiplicative white noise and additive color noise

Stochastic resonance (SR) in a time polo-delayed asymmetry bistable system driven by multiplicative white noise and additive color noise is investigated in this paper. First, the effective potential function is deduced based on probability density approach theory, small delay approximation theory and colored noise approximation theory. Second, the mean first-passage time (MFPT) which plays an important role in investigating on particles escape rate is derived and we find that the effect of additive color noise is more observable than that of multiplicative white noise on MFPT. Finally, influences of different parameters on SR are studied by signal-to-noise ratio (SNR). The analytic expression of SNR is derived and three-dimensional graphs of SNR with different parameters are obtained. We conclude that time delay τ and time delay strength e can suppress SR and that asymmetric item r has a non-monotone effect on SR. The results also suggest that adjusting the additive noise intensity Q is more sensitive than that of the multiplicative noise intensity D in controlling SNR.

Path integral molecular dynamics for exact quantum statistics of multi-electronic-state systems

An exact approach to compute physical properties for general multi-electronic-state (MES) systems in thermal equilibrium is presented. The approach is extended from our recent progress on path integral molecular dynamics (PIMD), Liu et al. [J. Chem. Phys. 145, 024103 (2016)] and Zhang et al. [J. Chem. Phys. 147, 034109 (2017)], for quantum statistical mechanics when a single potential energy surface is involved. We first define an effective potential function that is numerically favorable for MES-PIMD and then derive corresponding estimators in MES-PIMD for evaluating various physical properties. Its application to several representative one-dimensional and multi-dimensional models demonstrates that MES-PIMD in principle offers a practical tool in either of the diabatic and adiabatic representations for studying exact quantum statistics of complex/large MES systems when the Born-Oppenheimer approximation, Condon approximation, and harmonic bath approximation are broken.

Capturing RNA Folding Free Energy with Coarse-Grained Molecular Dynamics Simulations

We introduce a coarse-grained RNA model for molecular dynamics simulations, RACER (RnA CoarsE-gRained). RACER achieves accurate native structure prediction for a number of RNAs (average RMSD of 2.93 Å) and the sequence-specific variation of free energy is in excellent agreement with experimentally measured stabilities (R2 = 0.93). Using RACER, we identified hydrogen-bonding (or base pairing), base stacking, and electrostatic interactions as essential driving forces for RNA folding. Also, we found that separating pairing vs. stacking interactions allowed RACER to distinguish folded vs. unfolded states. In RACER, base pairing and stacking interactions each provide an approximate stability of 3–4 kcal/mol for an A-form helix. RACER was developed based on PDB structural statistics and experimental thermodynamic data. In contrast with previous work, RACER implements a novel effective vdW potential energy function, which led us to re-parameterize hydrogen bond and electrostatic potential energy functions. Further, RACER is validated and optimized using a simulated annealing protocol to generate potential energy vs. RMSD landscapes. Finally, RACER is tested using extensive equilibrium pulling simulations (0.86 ms total) on eleven RNA sequences (hairpins and duplexes).

Dynamical complexity and stochastic resonance in an asymmetry bistable system with time delay

The dynamical complexity and stochastic resonance (SR) of a time-delayed asymmetric bistable system are studied. Firstly, The effective potential function and steady-state probability density function are deduced based on Born-Oppenheimer approximation theory, and we find that the asymmetric item and time-delayed feedback item can both affect the curve of these two functions, especially the asymmetric item can induce phase displacement. Secondly, the mean first-passage time (MFPT) which plays an important role in research on particles escape rate is derived and we obtain an approximate asymmetric item r which can maintain a steady MFPT. Finally, the influences of different parameters on SR are researched by signal-to-noise ratio (SNR). The analytic expression of SNR is derived and three dimensional graphs and contour maps of SNR with different parameters are obtained. The results indicate that time delay τ and time delay strength e can enhance the SNR and the asymmetric item r has a non-monotone effect on SNR. Notably, adjusting time delay strength e is more sensitive than that of the time delay τ in controlling SR.

Impact of two types of time delays and cross-correlated multiplicative and additive noises on stability and stochastic resonance for a metapopulation system

In this paper, we investigate the stability and the shift between the extinction state and the stable one of a large density and the stochastic resonance (SR) for a metapopulation system subjected to two types of time delay terms, cross-correlation noises and multiplicative signal. By using the fast descent method and the method of small delay approximation, the expressions of the effective potential function and the signal-to-noise ratio (SNR) are obtained. We denote by Q the intensity of the multiplicative noise, and M the intensity of the additive noise, θ and τ the two time delay terms introduced into the metapopulation system. Our main results show some facts that time delay θ and the strength of correlation noise λ can restrain the development of the metapopulation, while the other term of time delay τ can accelerate the expansion of the population from the extinction state to the large stable one. We discover that it is possible to enhance the signal-to-noise ratio by adjusting the intensities of the multiplicative, additive noises and the time delays of the stochastic metapopulation system

Mean extinction time and stability for a metapopulation system subjected to correlated Gaussian and non-Gaussian noises

In this paper, we investigate the shift between the stable state of a large density and the extinction state, the mean extinction time for a metapopulation system induced by the associated Gaussian additive noise and non-Gaussian multiplicative noise. By applying the approximate Fokker–Planck equation, the fast descent method and the path integral approach, we obtain the expressions of the effective potential function and the mean extinction time. The numerical results show that the additive noise can damage the stability of the system, while the associated noise and the noise correlation times τ0 and τ can strengthen the stability of the population system. In the meantime, the maximum of the mean first-passage time appears in the meta-population system due to the impacts of different types of noises and their correlation time terms. It can effectively extend the extinction time of the metapopulation to enhance the strength of the correlation noise and two terms of noise correlation time. Conversely, the additive noise plays a negative role in preventing the extinction of the population. On the other side, a proper small multiplicative noise intensity can produce the positive effect on lengthening the life of the metapopulation.

Light-Front Perturbation Without Spurious Singularities

A new form of the light front Feynman propagators is proposed. It contains no energy denominators. Instead the dependence on the longitudinal subinterval \(x^2_L = 2 x^{+} x^{-}\) is explicit and a new formalism for doing the perturbative calculations is invented. These novel propagators are implemented for the one-loop effective potential and various 1-loop 2-point functions for a massive scalar field. The consistency with results for the standard covariant Feynman diagrams is obtained and no spurious singularities are encountered at all. Some remarks on the calculations with fermion and gauge fields in QED and QCD are added.

Including Tunneling in Non-Born-Oppenheimer Simulations.

For electronically nonadiabatic processes in all but the simplest systems, the most practical multidimensional simulation method is a semiclassical approximation in which a trajectory or the center of a wave packet follows a classical path governed by an effective potential energy function. Here, we show how such simulations can be made more realistic by including tunneling by the army ants tunneling method. We illustrate the theory by calculations with model potential energy surfaces; one model study is in the adiabatic limit, and the other one has nonadiabatic transitions between two electronic states during the tunneling event. The army ants tunneling algorithm is used to efficiently sample tunneling events in the trajectories in both cases. This work makes it possible to simulate complex nonadiabatic chemical processes by efficiently including the important quantum effect of tunneling.

Prediction of transport properties of CO2-N2 binary mixtures via the inversion of reduced-viscosity collision integrals

In the present study, the main purpose is to extract information about the effective intermolecular potential energy function for binary mixture of nitrogen and carbon dioxide by the usage of a direct inversion of the experimentally reduced viscosity and second virial coefficient data and then to reproduce the dilute gas transport properties from the inverted potential energy. The Lennard-Jones (12, 6) potential energy function has been employed as the initial potential model required by the inversion method. The MSV potential obtained in this way is in reasonable agreement with the independently known Co2-N2 potential energy function. Using the inverted pair potential energies, the Chapman-Enskog scheme is employed to calculate transport properties of CO2-N2 in a wide composition and temperature range. The close agreement between the predicted values and the literature results of transport properties demonstrate the predictive power of the inversion scheme.

Vibrational resonance in a Duffing system with fractional-order external and intrinsic dampings driven by the two-frequency signals

The phenomenon of vibrational resonance (VR) in a Duffing system with both fractional-order external damping and fractional-order intrinsic damping driven by the two-frequency periodic signals is investigated. It is observed that the resonance amplitude Q can be optimized by an appropriate choice of the amplitude of the high-frequency signal. The obtained relationship between VR and the fractional-orders shows that both fractional-order external damping and fractional-order intrinsic damping can induce changes of the shapes of the effective potential function and then lead to more abundant resonance behaviors than in the traditional dynamic systems.

Vevacious: a tool for finding the global minima of one-loop effective potentials with many scalars

Several extensions of the Standard Model of particle physics contain additional scalars implying a more complex scalar potential compared to that of the Standard Model. In general these potentials allow for charge and/or color breaking minima besides the desired one with correctly broken SU(2)_L times U(1)_Y . Even if one assumes that a metastable local minimum is realized, one has to ensure that its lifetime exceeds that of our universe. We introduce a new program called Vevacious which takes a generic expression for a one-loop effective potential energy function and finds all the tree-level extrema, which are then used as the starting points for gradient-based minimization of the one-loop effective potential. The tunneling time from a given input vacuum to the deepest minimum, if different from the input vacuum, can be calculated. The parameter points are given as files in the SLHA format (though is not restricted to supersymmetric models), and new model files can be easily generated automatically by the Mathematica package SARAH. This code uses HOM4PS2 to find all the minima of the tree-level potential, PyMinuit to follow gradients to the minima of the one-loop potential, and CosmoTransitions to calculate tunneling times.

The multiscale coarse-graining method. VIII. Multiresolution hierarchical basis functions and basis function selection in the construction of coarse-grained force fields

The multiscale coarse-graining (MS-CG) method is a method for determining the effective potential energy function for a coarse-grained (CG) model of a molecular system using data obtained from molecular dynamics simulation of the corresponding atomically detailed model. The coarse-grained potential obtained using the MS-CG method is a variational approximation for the exact many-body potential of mean force for the coarse-grained sites. Here we propose a new numerical algorithm with noise suppression capabilities and enhanced numerical stability for the solution of the MS-CG variational problem. The new method, which is a variant of the elastic net method [Friedman et al., Ann. Appl. Stat. 1, 302 (2007)], allows us to construct a large basis set, and for each value of a so-called "penalty parameter" the method automatically chooses a subset of the basis that is most important for representing the MS-CG potential. The size of the subset increases as the penalty parameter is decreased. The appropriate value to choose for the penalty parameter is the one that gives a basis set that is large enough to fit the data in the simulation data set without fitting the noise. This procedure provides regularization to mitigate potential numerical problems in the associated linear least squares calculation, and it provides a way to avoid fitting statistical error. We also develop new basis functions that are similar to multiresolution Haar functions and that have the differentiability properties that are appropriate for representing CG potentials. We demonstrate the feasibility of the combined use of the elastic net method and the multiresolution basis functions by performing a variational calculation of the CG potential for a relatively simple system. We develop a method to choose the appropriate value of the penalty parameter to give the optimal basis set. The combined effect of the new basis functions and the regularization provided by the elastic net method opens the possibility of using very large basis sets for complicated CG systems with many interaction potentials without encountering numerical problems in the variational calculation.

A portable intermolecular potential for molecular dynamics studies of NMA–NMA and NMA–H2O aggregates

A recently formulated intermolecular potential has been adapted to describe the interaction of the N-methylacetamide (NMA) dimer and of the NMA-H(2)O adduct. The pure electrostatic component of the intermolecular potential functional representation is as usual expressed in terms of a set of punctual charges distributed over the molecular frames, consistently with the permanent molecular dipole values. In contrast, the remainder of the intermolecular potential is expressed in terms of Improved Lennard Jones effective pair potential functions, referred to multiple interaction centers (or sites) placed on the N-methylacetamide molecule and to a single interaction center placed on the water molecule. The characteristic of this pair potential relies on a mix of transferable and non-transferable descriptions of the parameters. The first set of parameters has a structural connotation bearing a site-site interaction nature and exploiting the molecular polarizability decomposability. The second one, depending on the particles clustering and charge distribution and transfer, bears a delocalized and ambient bulk nature. This choice has been tested against ab initio calculations and molecular dynamics simulations. The results show that the model potential is appropriate for describing the energetic of the various stable configurations of NMA-NMA and NMA-H(2)O weakly interacting aggregates, including the formation of hydrogen bonds.

Stochastic resonance in a bistable system subject to multi-time-delayed feedback and aperiodic signal

We discuss in detail the effects of the multi-time-delayed feedback driven by an aperiodic signal on the output of a stochastic resonance (SR) system. The effective potential function and dynamical probability density function (PDF) are derived. To measure the performance of the SR system in the presence of a binary random signal, the bit error rate (BER) defined by the dynamical PDF is employed, as is commonly used in digital communications. We find that the delay time, strength of the feedback, and number of time-delayed terms can change the effective potential function and the effective amplitude of the signal, and then affect the BER of the SR system. The numerical simulations strongly support the theoretical results. The goal of this investigation is to explore the effects of the multi-time-delayed feedback on SR and give a guidance to nonlinear systems in the application of information processing.

A Generalized Formulation of Ion−π Electron Interactions: Role of the Nonelectrostatic Component and Probe of the Potential Parameter Transferability

The intermolecular potentials for hexafluorobenzene (HFBz) and 1,3,5-trifluorobenzene (TFBz) interacting with alkali (M(+); M = Li, Na, K, Rb, Cs) and halogen (X(-); X = F, Cl, Br, I) ions are provided as a combination of electrostatic and nonelectrostatic terms. The ion-HFBz and ion-TFBz electrostatic components are formulated as a sum of Coulombic potentials associated with the interactions between the ion charge and point charges on the molecular frame, whose distributions are consistent with the permanent quadrupole moment of HFBz and TFBz, respectively. The corresponding nonelectrostatic components are represented as a sum of effective potential functions, each one having a specific physical meaning, related to ion-molecular bond pair interactions. In the present paper, we test the transferability of the ion-bond potential parameters. Moreover, the powerfulness of the model is analyzed by comparing predicted binding energies and equilibrium geometries for the family of M(+)-HFBz, X(-)-HFBz, M(+)-TFBz, and X(-)-TFBz systems with available ab initio results.

Stabilization of Kapitza oscillator by symmetric periodical forces

With the application of Kapitza method of averaging for an arbitrary periodic force, the oscillator is stabilized by minimizing its effective potential energy function. The aim is to lower the frequency and amplitude of fast oscillation as compared to external harmonic/periodic kicking pulses, which is achieved by introducing special symmetric periodical kicking pulses.