Force Noise Research Articles

Observed Decadal North Atlantic Tripole SST Variability. Part I: Weather Noise Forcing and Coupled Response

Abstract The mechanisms responsible for the decadal variability of the tripole mode of North Atlantic SST during the latter half of the twentieth century are diagnosed using a new technique. The SST and associated ocean variability are reconstructed by forcing an interactive ensemble coupled GCM by the surface fluxes resulting from weather noise. The weather noise surface fluxes are obtained from the NCEP–NCAR reanalysis by removing the simulated atmospheric feedback to the observed SST evolution. Simulations are performed to reconstruct and estimate the contributions of the local weather noise heat flux and wind stress to the observed evolution of the tripole pattern. The results indicate that the North Atlantic tripole pattern is forced primarily by the local weather noise surface heat flux. The roles of several types of ocean circulation variability, including gyres forced by the wind stress weather noise, the wind stress feedback to the SST, and the meridional overturning circulation, are also examined. Conclusions from this approach are expected to be model dependent. Further analysis, in the context of a simple model, of the mechanisms producing the tripole variability is presented in Part II.

Energetics of stochastic resonance

In this paper, we discuss the motion of a Brownian particle in a double-well potential driven by a periodic force in terms of energies delivered by the periodic and the noise forces and energy dissipated into the viscous environment. It is shown that, while the power delivered by the periodic force to the Brownian particle is controlled by the strength of the noise, the power delivered by the noise itself is independent of the amplitude and frequency of the periodic force. The implications of this result for the mechanism of stochastic resonance in an equilibrium system is that it is not energy from the noise force which enhances a small periodic force, but rather an increase of energy delivered by the periodic force, regulated by the strength of the noise. We further re-evaluate the frequency dependence of stochastic resonance in terms of energetic terms including efficiency.

Path probability for a Brownian motion

This work reports on numerical simulations of Brownian motion in the non-dissipative limit. The objective was to prove the existence of path probability and to compute probability values for some sample paths. By simulating a large number of particles moving from point to point under Gaussian noise and conservative forces, we numerically determine that the path probability decreases exponentially with increasing Lagrangian action of the paths.

Asymmetric stochastic localization in geometry controlled kinetics

We consider the motion of Brownian particles confined in a two-dimensional symmetric bilobal enclosure with uneven cross section. Varying cross section of the confinement results in an effective entropic potential in reduced dimension. By employing two external noise forces, one additive and another multiplicative along x direction, we demonstrate that a correlation between them causes a symmetry breaking of entropic stability, i.e., a difference in relative stability of two lobes. This leads to an asymmetric localization of population in the stationary state. A two-state model is proposed to explain the asymmetric localization of population due to entropic diffusion.

Abatement of Thermal Noise due to Internal Damping in 2D Oscillators with Rapidly Rotating Test Masses

Mechanical oscillators can be sensitive to very small forces. Low frequency effects are up-converted to higher frequency by rotating the oscillator. We show that for 2-dimensional oscillators rotating at frequency much higher than the signal the thermal noise force due to internal losses and competing with it is abated as the square root of the rotation frequency. We also show that rotation at frequency much higher than the natural one is possible if the oscillator has 2 degrees of freedom, and describe how this property applies also to torsion balances. In addition, in the 2D oscillator the signal is up-converted above resonance without being attenuated as in the 1D case, thus relaxing requirements on the read out. This work indicates that proof masses weakly coupled in 2D and rapidly rotating can play a major role in very small force physics experiments.

All Titanium Microelectrode Array for Field Potential Measurements from Neurons and Cardiomyocytes—A Feasibility Study

In this paper, we describe our all-titanium microelectrode array (tMEA) fabrication process and show that uncoated titanium microelectrodes are fully applicable to measuring field potentials (FPs) from neurons and cardiomyocytes. Many novel research questions require custom designed microelectrode configurations different from the few commercially available ones. As several different configurations may be needed especially in a prototyping phase, considerable time and cost savings in MEA fabrication can be achieved by omitting the additional low impedance microelectrode coating, usually made of titanium nitride (TiN) or platinum black, and have a simplified and easily processable MEA structure instead. Noise, impedance, and atomic force microscopy (AFM) characterization were performed to our uncoated titanium microelectrodes and commercial TiN coated microelectrodes and were supplemented by FP measurements from neurons and cardiomyocytes on both platforms. Despite the increased noise levels compared to commercial MEAs our tMEAs produced good FP measurements from neurons and cardiomyocytes. Thus, tMEAs offer a cost effective platform to develop custom designed electrode configurations and more complex monitoring environments.

The ghost of stochastic resonance: an introductory review

Nonlinear systems driven by noise and periodic forces with more than one frequency exhibit the phenomenon of Ghost Stochastic Resonance (GSR) found in a wide and disparate variety of fields ranging from biology to geophysics. The common novel feature is the emergence of a ‘ghost’ frequency in the system's output which is absent in the input. As reviewed here, the uncovering of this phenomenon helped to understand a range of problems, from the perception of pitch in complex sounds or visual stimuli, to the explanation of climate cycles. Recent theoretical efforts show that a simple mechanism with two ingredients are at work in all these observations. The first one is the linear interference between the periodic inputs and the second a nonlinear detection of the largest constructive interferences, involving a noisy threshold. These notes are dedicated to review the main aspects of this phenomenon, as well as its different manifestations described on a bewildering variety of systems ranging from neurons, semiconductor lasers, electronic circuits to models of glacial climate cycles.

Stochastic variability of oceanic flows above topography anomalies

[1] We describe a stochastic variability mechanism which is genuinely internal to the ocean, i.e., not due to fluctuations in atmospheric forcing. The key ingredient is the existence of closed contours of bottom topography surrounded by a stirring region of enhanced eddy activity. This configuration leads to the formation of a robust but highly variable vortex above the topography anomaly. The vortex dynamics integrates the white noise forcing of oceanic eddies into a red noise signal for the large scale volume transport of the vortex. The strong interannual fluctuations of the transport of the Zapiola anticyclone (∼100 Sv) in the Argentine basin are argued to be partly due to such eddy-driven stochastic variability, on the basis of a 310 years long simulation of a comprehensive global ocean model run driven by a repeated-year forcing.

Spiral waves in excitable media due to noise and periodic forcing

We investigate the jointly driven effects of external periodic forcing and Gaussian white noise on meandering spiral waves in excitable media with FitzHugh–Nagumo local dynamics. Interesting phenomena resulted from various forcing periods are found, for example, piece-wise line drift, intermittent straight-line drift and so on. We also observe new type of breakup of spiral wave between entrainment bands with 1:1 and 2:1. It is believed that the occurrence of the new type is relevant to the appearance of local bidirectional propagation window. There exist optimized noise intensities which can induce the broadest entrainments and Arnold tongues. Such a phenomenon is referred to as stochastic resonance. It is also observed that the noise makes significant effects on the spiral wave with straight-line drift. Via the tip Fourier spectrum, the varying of tip motion with external periods on the resonance band is interpreted.

Parametrically Amplified $Z$-Axis Lorentz Force Magnetometer

This paper describes a microelectromechanical systems (MEMS) Lorentz force navigation magnetometer whose fabrication is fully compatible with existing foundry processes used to manufacture MEMS inertial sensors. Operating at 1 atm, the magnetometer is shown to have a Brownian-noise-limited field resolution of 87 nT/√Hz and a corresponding angular resolution of 0.7°/√Hz. To achieve Brownian-noise-limited performance at 1 atm, parametric amplification was performed which amplifies the Lorentz force 40% more than the Brownian noise force and increases the field sensitivity of the device up to 82.5 folds. Here, the parametric signal is also used to perform electromechanical amplitude modulation to mitigate capacitive feedthrough of the drive signal to the sensing electronics.

Capillary waves of compressible fluids

The interplay of thermal noise and molecular forces is responsible for surprisingfeatures of liquids on sub-micrometer lengths—in particular at interfaces. Notonly does the surface tension depend on the size of an applied distortion andnanoscopic thin liquid films dewet faster than would be expected from hydrodynamics,but also the dispersion relation of capillary waves differ at the nanoscale fromthe familiar macroscopic behavior. Starting with the stochastic Navier–Stokesequation we study the coupling of capillary waves to acoustic surface waves which ispossible in compressible fluids. We find propagating ‘acoustic–capillary waves’ atnanometer wavelengths where in incompressible fluids capillary waves are overdamped.

Ergodicity of stochastic 2D Navier–Stokes equation with Lévy noise

In this paper we deal with the 2D Navier–Stokes equation perturbed by a Lévy noise force whose white noise part is non-degenerate and that the intensity measure of Poisson measure is σ-finite. Existence and uniqueness of invariant measure for this equation is obtained, two main properties of the Markov semigroup associated with this equation are proved. In other words, strong Feller property and irreducibility hold in the same space.

Analytic approximations of statistical quantities and response of noisy oscillators

Nonlinear oscillators have been utilized in many contexts because they encompass a large class of phenomena. For a reduced phase oscillator model with weak noise forcing that is necessarily multiplicative, we provide analytic formulas for the stationary statistical quantities of the random period. This is an important quantity which we term ‘response’ (i.e., the spike times, instantaneous frequency in neuroscience, the cycle time in chemical reactions, etc.) that is often analytically intractable in noisy oscillator systems. The analytic formulas are accurate in the weak noise limit so that one does not have to numerically solve a time-varying Fokker–Planck equation. The steady-state and dynamic responses are also analyzed with deterministic forcing. A second order analytic formula is derived for the steady-state response, whereas the dynamic response with time-varying forcing is more complicated. We focus on the specific case where the forcing is sinusoidal and accurately capture the frequency response with an analytic approximation that is obtained with a rescaling of the equation. By utilizing various techniques in the weak noise regime, this work leads to a better understanding of how the random period of nonlinear oscillators are affected by multiplicative noise and external forcing. Comparisons of the asymptotic formulas with a full oscillator system confirm the qualitative accurateness of the theory.

Enhanced force sensitivity and noise squeezing in an electromechanical resonator coupled to a nanotransistor

A nanofield-effect transistor (nano-FET) is coupled to a massive piezoelectricity based electromechanical resonator integrated with a parametric amplifier. The mechanical parametric amplifier can enhance the resonator’s displacement and the resulting electrical signal is further amplified by the nano-FET. This hybrid amplification scheme yields an increase in the mechanical displacement signal by 70 dB resulting in a force sensitivity of 200 aN Hz−1/2 at 3 K. The mechanical parametric amplifier can also squeeze the displacement noise in one oscillation phase by 5 dB enabling a factor of 4 reduction in the thermomechanical noise force level.

Stochastic stability of a viscoelastic column axially loaded by a white noise force

This paper deals with the analysis of stability of a hinged-hinged viscoelastic column subjected to a non-zero mean stochastic axial force. The randomly variable part of this is described by a stationary Gaussian white noise process. The viscosity affects the curvature of the column, for which the classic Euler–Bernoulli's model is adopted. The viscosity is described by the linear Kelvin–Voigt's model. A dynamic stability analysis is performed. Normal modes are introduced in the integro-differential equation of motion so that uncoupled modal equations are retrieved. With reference to the first mode, by using an additional state variable, three Itô’s ODE are obtained, from which the differential equations ruling the response statistical moment evolution are written by means of Itô’s differential rule. The zero solution, that is undeformed straight column, corresponds to zero moments. If the column is perturbed, it is stable when the response moments tend to zero. A necessary and sufficient condition of stability in the moments of order r is that the matrix A r of the coefficients of the ODE system ruling them has negative real eigenvalues and complex eigenvalues with negative real parts. Because of the linearity of the system the stability of the first two moments is the strongest condition of stability. If the mean axial force μ P or the white noise intensity w P are increased, there exist critical values μ Pcr , w P c r for which almost an eigenvalue is positive. The critical mean axial force is found to be inversely proportional to the parameter φ ∞ , which measures the amount of viscous deformation. The search for the critical values of w P is made numerically, and several graphs are presented for a representative column.

Brownian motors: Joint effect of non-Gaussian noise and time asymmetric forcing

Previous works have shown that time asymmetric forcing on the one hand, as well as non-Gaussian noises on the other, can separately enhance the efficiency and current of a Brownian motor. Here, we study the result of subjecting a Brownian motor to both effects simultaneously. Our results have been compared with those obtained for the Gaussian white noise regime in the adiabatic limit. We find that, although the inclusion of the time asymmetry parameter increases the efficiency value up to a certain extent, for the present case this increase is much less appreciable than in the white noise case. We also present a comparative study of the transport coherence in the context of colored noise. Though the efficiency in some cases becomes higher for the non-Gaussian case, the Péclet number is always higher in the Gaussian colored noise case than in the white noise as well as non-Gaussian colored noise cases.

Noise-Induced Instability in the ENSO Recharge Oscillator

Abstract The conceptual El Niño–Southern Oscillation (ENSO) recharge oscillator model is used to study the linear stability of ENSO under state-dependent noise forcing. The analytical framework developed by Jin et al. is extended to more fully study noise-induced instability of ENSO. It is shown that in addition to the noise-induced positive contribution to the growth rate of the ensemble mean (first moment) evolution of the ENSO cycle, there is also a noise-induced instability for the ensemble spread (second moment). These growth rates continue to increase as the strength of the multiplicative noise increases. In both the analytical solution and the numerical model, the criticality threshold for instability of the second moment occurs at a lower value of the parameter that measures multiplicative forcing than the threshold for the first moment. The noise-induced instability not only enhances ENSO activity but also results in a large ensemble spread and thus may reduce the effectiveness of ENSO prediction. As in the additive noise forcing case, the low-frequency variability in the forcing is the important part for forcing El Niño events and the high-frequency forcing alone cannot effectively excite ENSO.

Movement Directionality in Collective Migration of Germ Layer Progenitors

Collective cell migration, the simultaneous movement of multiple cells that are connected by cell-cell adhesion, is ubiquitous in development, tissue repair, and tumor metastasis [1, 2]. It has been hypothesized that the directionality of cell movement during collective migration emerges as a collective property [3, 4]. Here we determine how movement directionality is established in collective mesendoderm migration during zebrafish gastrulation. By interfering with two key features of collective migration, (1) having neighboring cells and (2) adhering to them, we show that individual mesendoderm cells are capable of normal directed migration when moving as single cells but require cell-cell adhesion to participate in coordinated and directed migration when moving as part of a group. We conclude that movement directionality is not a de novo collective property of mesendoderm cells but rather a property of single mesendoderm cells that requires cell-cell adhesion during collective migration.

Dynamical Aspects of Mean Field Plane Rotators and the Kuramoto Model

The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc... We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N oscillators, each driven by an independent Brownian motion with a constant drift, that is each oscillator has its own frequency, which, in general, changes from one oscillator to another (these frequencies are usually taken to be random and they may be viewed as a quenched disorder). The interactions between oscillators are of long range type (mean field). We review some results on the Kuramoto model from a statistical mechanics standpoint: we give in particular necessary and sufficient conditions for reversibility and we point out a formal analogy, in the N to infinity limit, with local mean field models with conservative dynamics (an analogy that is exploited to identify in particular a Lyapunov functional in the reversible set-up). We then focus on the reversible Kuramoto model with sinusoidal interactions in the N to infinity limit and analyze the stability of the non-trivial stationary profiles arising when the interaction parameter K is larger than its critical value K_c. We provide an analysis of the linear operator describing the time evolution in a neighborhood of the synchronized profile: we exhibit a Hilbert space in which this operator has a self-adjoint extension and we establish, as our main result, a spectral gap inequality for every K>K_c.

Rich dynamics in a predator–prey model with both noise and periodic force

A spatial version of the predator–prey model with Holling III functional response, which includes some important factors such as external periodic forces, noise, and diffusion processes is investigated. For the model only with diffusion, it exhibits spiral waves in the two-dimensional space. However, combined with noise, it has the feature of chaotic patterns. Moreover, the oscillations become more obvious when the noise intensity is increased. Furthermore, the spatially extended system with external periodic forces and noise exhibits a resonant pattern and frequency-locking phenomena. These results may help us to understand the effects arising from the undeniable susceptibility to random fluctuations in the real ecosystems.