Double-well Model Research Articles

Auditory noise influences human visual perception of ambiguous information: multi-modal integration during bistable perception

When the sensory system receives an ambiguous signal, human perception often switches spontaneously between two different interpretations. This phenomenon is called bistable perception, and has been considered important to understanding sensory system. In this study, we investigated the intervals of spontaneous switching, defined as reversal time τ, to examine the temporal dynamics of bistable perception. We also studied the multi-modal feature of bistable switching by applying auditory noise with the visual stimuli. Our hypothesis is that auditory noise would significantly alter the reversal time of bistable visual perception. By building a computational model, we could explain the influence of auditory noise on the reversal time. In the human psychophysical experiments, we first measured the reversal time with visual stimulus only, using two types of bistable visual movies: the racetrack [1] and the rotating 3D cylinder (Figure ​(Figure1A).1A). We observed that the reversal times are widely varied across the subjects but fairly consistent within the subject in both cases. Interestingly, we also found that the reversal time for the racetrack and the rotating cylinder were highly correlated (N = 9, R2 = 0.84, Figure ​Figure1C).1C). Next, we performed the experiment with auditory noise and visual stimuli together, and found that the reversal times are significantly altered. Importantly, when auditory noise was given, we found a systematic change such that a fast switching subjects (short τ) tend to slow down the switching while slow switching subjects (long τ) tend to speed up, so that the difference of τ between the two groups become insignificant (Figure ​(Figure1D).1D). Lastly, we designed a double-well energy model with destabilization/restabilization processes [2], and the model could well explain the observed phenomena. Figure 1 Effect of auditory noise in visual bistable perception. A. Two bistable visual movies. B. Example response and τ distribution. C. Peak of τ distribution in no noise condition. D. Peak of τ distribution with auditory noise condition. ...

Double-well dynamics of noise-driven control activation in human intermittent control: the case of stick balancing.

When facing a task of balancing a dynamic system near an unstable equilibrium, humans often adopt intermittent control strategy: Instead of continuously controlling the system, they repeatedly switch the control on and off. Paradigmatic example of such a task is stick balancing. Despite the simplicity of the task itself, the complexity of human intermittent control dynamics in stick balancing still puzzles researchers in motor control. Here we attempt to model one of the key mechanisms of human intermittent control, control activation, using as an example the task of overdamped stick balancing. In doing so, we focus on the concept of noise-driven activation, a more general alternative to the conventional threshold-driven activation. We describe control activation as a random walk in an energy potential, which changes in response to the state of the controlled system. By way of numerical simulations, we show that the developed model captures the core properties of human control activation observed previously in the experiments on overdamped stick balancing. Our results demonstrate that the double-well potential model provides tractable mathematical description of human control activation at least in the considered task and suggest that the adopted approach can potentially aid in understanding human intermittent control in more complex processes.

Investigation of electron localization in harmonic emission from asymmetric molecular ion**Project supported by the National Natural Science Foundation of China (Grant No. 11404204), the Key Project of Chinese Ministry of Education (Grant No. 211025), the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20111404120004), the Natural Science Foundation for Young Scientists of Shanxi Province, China

We theoretically investigate the electron localization around two nuclei in harmonic emission from asymmetric molecular ion. The results show that the ionization process of electron localized around one nucleus competes with its transfer process to the other nucleus. By increasing the initial vibrational level, more electrons localized around the nucleus D+ tend to transfer to the nucleus He2+ so that the ionizations of electrons localized around the nucleus He2+ increase. In this case, the difference in harmonic efficiency between HeH2+ and HeD2+ decreases while the difference in harmonic spectral structure increases. The evident minimum can be observed in the harmonic spectrum of HeH2+ compared with that in the spectral structure of HeD2+, which is due to the strong interference of multiple recombination channels originating from two nuclei. Time-dependent nuclear probability density, electron-nuclear probability density, double-well model, and time-frequency maps are presented to explain the underlying mechanisms.

Discrete exact solutions for the double-well potential model through the discrete tanh method

In this paper, we investigate discrete exact solutions for the double-well potential model by using the discrete tanh method. As a result, various discrete new solutions are obtained. They include breathers, kink, antikink and periodic waves solutions for different values of the discrete variable n. We also establish conditions for obtaining these types of solutions. The amplitude of these solutions decreases when the discrete variable n increases. The total energy is also calculated for each kind of solutions. Finally, we show, in the comparison with the continuous case, that some of our results where soliton like similar solutions are well known in the literature.

Out-of-centre distortions around an octahedrally coordinated Ti4+ in BaTiO3

The prototypical ferroelectric system BaTiO3 is an oxide with a perovskite-type structure that exhibits a textbook example of multiple phase transitions associated with an out-of-centre distortion of the octahedral Ti4+ cations. This research combines the double-well potentials model and the bond valence model, to provide an explanation for the cubic–tetragonal–orthorhombic–rhombohedric phase transition sequence. It is shown that to consider the atomic displacements can only occur in the strict respect of their valence, which is calculated with the bond valence model, is sufficient to lead to the clear prediction of the whole transition sequence.

Interacting heavy fermions in a disordered optical lattice

We have theoretically studied the effect of disorder on ultracold alkaline-earth atoms governed by the Kondo lattice model in an optical lattice via simplified double-well model and hybridization mean-field theory. Disorder-induced narrowing and even complete closure of hybridization gap have been predicted and the compressibility of the system has also been investigated for metallic and Kondo insulator phases in the presence of the disordered potential. To make connection to the experimental situation, we have numerically solved the disordered Kondo lattice model with an external harmonic trap and shown both the melting of Kondo insulator plateau and an compressibility anomaly at low-density.

Tracy-Widom distribution as instanton sum of 2D IIA superstrings

We present an analytic expression of the nonperturbative free energy of a double-well supersymmetric matrix model in its double scaling limit, which corresponds to two-dimensional type IIA superstring theory on a nontrivial Ramond-Ramond background. To this end we draw upon the wisdom of random matrix theory developed by Tracy and Widom, which expresses the largest eigenvalue distribution of unitary ensembles in terms of a Painleve II transcendent. Regularity of the result at any value of the string coupling constant shows that the third-order phase transition between a supersymmetry-preserving phase and a supersymmetry-broken phase, previously found at the planar level, becomes a smooth crossover in the double scaling limit. Accordingly, the supersymmetry is always broken spontaneously as its order parameter stays nonzero for the whole region of the coupling constant. Coincidence of the result with the unitary one-matrix model suggests that one-dimensional type 0 string theories partially correspond to the type IIA superstring theory. Our formulation naturally allows for introduction of an instanton chemical potential, and reveals the presence of a novel phase transition, possibly interpreted as condensation of instantons.

Theoretical investigation on nearsightedness of finite model and molecular systems based on linear response function analysis.

We examined nearsightedness of electronic matter (NEM) of finite systems on the basis of linear response function (LRF). From the computational results of a square-well model system, the behavior of responses obviously depends on the number of electrons (N): as N increases, LRF, δρ(r)/δv(r′), decays rapidly for the distance, |r−r′|. This exemplifies that the principle suggested by Kohn and Prodan holds even for finite systems: the cause of NEM is destructive interference among electron density amplitudes. In addition, we examined double-well model systems, which have low-lying degenerate levels. In this case, there are two types of LRF: the cases of the half-filled and of full-filled in low-lying degenerate levels. The response for the former is delocalized, while that of the later is localized. These behaviors of model systems are discussed in relation to the molecular systems’ counterparts, H2, He22+, and He2 systems. We also see that NEM holds for the dissociated limit of H2, of which the mechanism is similar to that of the insulating state of solids as suggested by Kohn. We also examined LRF of alanine tripeptide system as well as butane and butadiene molecules, showing that NEM of the polypeptide system is caused by sp3 junctions at Cα atoms that prevent propagation of amplitudes of LRF, which is critically different from that of NEM for finite and infinite homogeneous systems.

SUSY double-well matrix model as 2D IIA superstring on RR background

We discuss an interpretation of a simple supersymmetric matrix model with a double-well potential as two-dimensional type IIA superstrings on a nontrivial Ramond-Ramond background. In particular, we can see direct correspondence between single trace operators in the matrix model and vertex operators in the type IIA theory by computing scattering amplitudes and comparing the results in both sides. Next, we explicitly compute nonperturbative instanton contributions in the matrix model and find that they survive in a double scaling limit realizing the type IIA superstring theory. This suggests that the supersymmetry is spontaneously broken by nonperturbative effect in the target space of the type IIA superstring theory.

On the solvability of the generalized hyperbolic double-well models

We present exact solutions for the Schrödinger equation with the hyperbolic double-well potential \documentclass[12pt]{minimal}\begin{document}$V_{q}^p(x)=-V_0{\sinh ^p(\alpha x)}/{\cosh ^{q}(\alpha x)}$\end{document}Vqp(x)=−V0sinhp(αx)/coshq(αx). We show that the model preserves a finite dimensional polynomial space for some p and q. Thus using the Bethe ansatz method, we obtain closed form expressions for the spectrum and wavefunction, as well as the allowed parameter for the class \documentclass[12pt]{minimal}\begin{document}$V^p_6(x)$\end{document}V6p(x), which is contrary to a report in a recent article [C. A. Downing, J. Math. Phys. 54, 072101 (2013)]. We also discuss the hidden sl2 algebraic structure of the class.

Supersymmetric double-well matrix model as two-dimensional type IIA superstring on RR background

In the previous paper, the authors pointed out correspondence of a supersymmetric double-well matrix model with two-dimensional type IIA superstring theory on a nontrivial Ramond-Ramond background from the viewpoint of symmetries and spectrum. In this paper we further investigate the correspondence from dynamical aspects by comparing scattering amplitudes in the matrix model and those in the type IIA theory. In the latter, cocycle factors are introduced to vertex operators in order to reproduce correct transformation laws and target-space statistics. By a perturbative treatment of the Ramond-Ramond background as insertions of the corresponding vertex operators, various IIA amplitudes are explicitly computed including quantitatively precise numerical factors. We show that several kinds of amplitudes in both sides indeed have exactly the same dependence on parameters of the theory. Moreover, we have a number of relations among coefficients which connect quantities in the type IIA theory and those in the matrix model. Consistency of the relations convinces us of the validity of the correspondence.

Dynamic stochastic resonance-based grayscale logo extraction in hybrid SVD-DCT domain

This paper presents a novel dynamic stochastic resonance (DSR)-based technique for robust extraction of a grayscale logo from a tampered watermarked image. The watermark embedding is done on the singular values (SV) of the discrete cosine transform (DCT) coefficients of the cover image. DSR is then strategically applied during the logo extraction process where the SV of DCT coefficients are tuned following a double-well potential model by utilizing the noise introduced during attacks. The resilience of this technique has been tested in the presence of various noises, geometrical distortions, enhancement, compression, filtering and watermarking attacks. The proposed DSR-based technique for logo extraction gives noteworthy robustness without any significant trade-off in perceptual transparency of the watermarked image. A maximization approach has been adopted for the selection of bistable double-well parameters to establish noise-enhanced resonance. When compared with existing watermark extraction techniques based in SVD, DCT, SVD-DCT domains, as well as with their combination with DSR, the results suggest that remarkable improvement of robustness is achieved by using DSR on singular values of DCT.

Single-polaron properties for double-well electron-phonon coupling

We show that in crystals where light ions are symmetrically intercalated between heavy ions, the electron-phonon coupling for carriers located at the light sites cannot be described by a Holstein model. We introduce the double-well electron-phonon coupling model to describe the most interesting parameter regime in such systems and study it in the single-carrier limit using the momentum average approximation. For sufficiently strong coupling, a small polaron with a robust phonon cloud appears at low energies. While some of its properties are similar to those of a Holstein polaron, we highlight some crucial differences. These prove that the physics of the double-well electron-phonon coupling model cannot be reproduced with a linear Holstein model.

Physical Limits on Directional Mechanosensing of Amoeboid Crawling Cells

One of the remarkable things about many eukaryotic cells is how effective they are at sensing minute levels of mechanical stimulation, while living in a constantly changing biomechanical environment. In particular, many eukaryotic cells are able to perform directional mechanosensing by directly measuring minute spatial differences in the mechanical stress on their membrane. Using vegetative unpolarized Dictyostelium discoideum amoebae, we report the extremely high directional mechanosensitivity of those cells with mechanostimulus of the order of 0.1 Pa. Based on those experimental evidences, we develop a model to explore the limits of a single mechanosensitive channel activation using a two-state double-well model for the gating mechanism. We then focus on the physical limits of directional mechanosensing by a single cell having multiple mechanosensors and subjected to a shear flow inducing a nonuniform membrane tension similar to what is taking place at the cellular level in our experiment. Our theoretical model demonstrates that the accuracy in sensing the mechanostimulus direction not only increases with cell size and exposure to signal, but also grows for cells with a near-critical membrane prestress. Finally, the existence of a nonlinear threshold effect, fundamentally limiting the cell's ability to effectively perform directional mechanosensing at low signal-to-noise ratio, is reaveled and discussed.

Control of electron localization to isolate and enhance molecular harmonic plateau in asymmetric HeH2+ system

Abstract High-order harmonic generation from the asymmetric molecular ion HeH2+ exposed to intense laser fields was investigated by quantum wave packet calculations in which the initial wave packet of HeH2+ was prepared in the first excited 2 p σ state. The calculated molecular harmonic plateau at low frequencies was effectively isolated and enhanced by adjusting the carrier-envelope phase (CEP) of the laser field. Furthermore, double-well model, time-dependent electronic density, electronic state population, and time-frequency analyses were presented to explain the underlying mechanism of the efficient isolated molecular plateau. By taking advantage of the CEP effect to control the electronic dynamics, this isolated molecular plateau can be used to generate high-intensity single attosecond pulses.

SUSY breaking by nonperturbative dynamics in a matrix model for 2D type IIA superstrings

We explicitly compute nonperturbative effects in a supersymmetric double-well matrix model corresponding to two-dimensional type IIA superstring theory on a nontrivial Ramond–Ramond background. We analytically determine the full one-instanton contribution to the free energy and one-point function, including all perturbative fluctuations around the one-instanton background. The leading order two-instanton contribution is determined as well. We see that supersymmetry is spontaneously broken by instantons, and that the breaking persists after taking a double scaling limit which realizes the type IIA theory from the matrix model. The result implies that spontaneous supersymmetry breaking occurs by nonperturbative dynamics in the target space of the IIA theory. Furthermore, we numerically determine the full nonperturbative effects by recursive evaluation of orthogonal polynomials. The free energy of the matrix model appears well-defined and finite even in the strongly coupled limit of the corresponding type IIA theory. The result might suggest a weakly coupled theory appearing as an S-dual to the two-dimensional type IIA superstring theory.

Physical limits on cellular directional mechanosensing

Many eukaryotic cells are able to perform directional mechanosensing by directly measuring minute spatial differences in the mechanical stress on their membranes. Here, we explore the limits of a single mechanosensitive channel activation using a two-state double-well model for the gating mechanism. We then focus on the physical limits of directional mechanosensing by a single cell having multiple mechanosensors and subjected to a shear flow inducing a nonuniform membrane tension. Our results demonstrate that the accuracy in sensing the mechanostimulus direction not only increases with cell size and exposure to a signal, but also grows for cells with a near-critical membrane prestress. Finally, the existence of a nonlinear threshold effect, fundamentally limiting the cell's ability to effectively perform directional mechanosensing at a low signal-to-noise ratio, is uncovered.

Focusing in multiwell potentials: Applications to ion channels

We investigate nonequilibrium stationary distributions induced by stochastic dichotomous noise in double-well and multiwell models of ion channel gating kinetics. The channel kinetics is analyzed using both overdamped Langevin equations and master equations. With the Langevin equation approach we show a nontrivial focusing effect due to the external stochastic noise, namely, the concentration of the probability distribution in one of the two wells of a double-well system or in one or more of the wells of the multiwell model. In the multiwell system, focusing in the outer wells is shown to be achievable under physiological conditions, while focusing in the central wells has proved possible so far only at very low temperatures. We also discuss the strength of the focusing effect and obtain the conditions necessary for maximal focusing to appear. These conditions cannot be predicted by a simple master equation approach.

Ground States of Ultracold Spin-1 Atoms in a Deep Double-Well Optical Superlattice in a Weak Magnetic Field

The ground states of the ultracold spin-1 atoms trapped in a deep one-dimensional double-well optical superlattice in a weak magnetic field are obtained. It is shown that the ground-state diagrams of the reduced double-well model are remarkably different for the antiferromagnetic and ferromagnetic condensates. The transition between the singlet state and nematic state is observed for the antiferromagnetic interaction atoms, which can be realized by modulating the tunneling parameter or the quadratic Zeeman energy. An experiment to distinguish the different spin states is suggested.

Finite mixture model applied in the analysis of a turbulent bistable flow on two parallel circular cylinders

This paper presents a study of the bistable phenomenon which occurs in the turbulent flow impinging on circular cylinders placed side-by-side. Time series of axial and transversal velocity obtained with the constant temperature hot wire anemometry technique in an aerodynamic channel are used as input data in a finite mixture model, to classify the observed data according to a family of probability density functions. Wavelet transforms are applied to analyze the unsteady turbulent signals. Results of flow visualization show that the flow is predominantly two-dimensional. A double-well energy model is suggested to describe the behavior of the bistable phenomenon in this case.