arXiv subjects

Golan Bel

Publications and source records attributed to Golan Bel.

At least 19 recordsLinked to original sources

arXiv2022

Patterns and Stability of Coupled Multi-Stable Nonlinear Oscillators

Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and stability of coupled driven-damped Helmholtz-Duffing oscillators in bi-stability regimes. We find that despite the fact that the system parameters and the driving force are identical, the stability of the two states to spatially non-uniform perturbations is very different. Moreover, the final stable states, resulting from these spatial perturbations, are not solely dictated by the wavelength of the perturbing mode and take different spatial configurations in terms of the coupled oscillator phases.

nlin.PS↗

arXiv2022

Testing the consistency of the resonant wave interaction approximation with simulated dynamics of idealized 2D internal wave fields

Nonlinear interaction and breaking of internal ocean waves are responsible for much of the interior ocean mixing, affecting ocean carbon storage and the global overturning circulation. These interactions may affect the observed Garrett-Munk wave energy spectrum, in addition to the recently explored interaction of waves with ocean eddies. According to the resonant wave interaction approximation, that is commonly used to derive the kinetic equation for the energy spectrum, the dominant interactions are between wave triads whose wavevectors satisfy $\mathbf{k}=\mathbf{p}+\mathbf{q}$, and whose frequencies satisfy $\omega_{\mathbf{k}}=|\omega_{\mathbf{p}}\pm\omega_{\mathbf{q}}|$. In order to test the validity of the resonant wave interaction approximation, we examine several analytical derivations of the theory. The assumptions underlying each derivation are tested using idealized direct 2D numerical simulations, representing near-observed energy levels of the oceanic internal wave field. We show that the slow-amplitude assumptions underlying the derivations are inconsistent with the simulated dynamics in this particular set of simulations. In addition, most of the triads satisfying the resonant conditions do not contribute significantly to nonlinear wave energy transfer in our simulations, while some interactions that are dominant in nonlinear energy transfers do not satisfy the resonance conditions. We also point to possible self-consistency issues with some derivations found in the literature.

nlin.CD↗

arXiv2020

Different anomalous diffusion regimes measured in the dynamics of tracer particles in actin networks

It was previously believed that diffusion of a tracer particle in a viscoelastic material should be of the fractional Brownian motion (fBm) type. This is due to the long-term memory in the response of such materials to mechanical perturbations. Surprisingly, the diffusion of a tracer particle in a network of a purified protein, actin, was found to conform to the continuous time random walk (CTRW) type in one study that focused on the ensemble average characteristics. Here, we analyze the dynamics of two differently sized tracer particles in actin networks of different mesh sizes. We find that the ratio of tracer particle size to the characteristic length scale of a bio-polymer network plays a crucial role in determining the type of diffusion the particle performs. We find that the tracer particle diffusion has features of fBm when the particle is large compared to the mesh size, of normal diffusion when the particle is much smaller than the mesh size, and of CTRW in between these two limits. Based on our findings, we propose and verify numerically a new model for the tracer particle's motion in all regimes. Our model suggests that diffusion in actin networks consists of fBm of the tracer particle coupled with occasional caging events with power-law-distributed escape times.

cond-mat.soft↗

arXiv2020

Identification of Anomalous Diffusion Sources by Unsupervised Learning

Fractional Brownian motion (fBm) is a ubiquitous diffusion process in which the memory effects of the stochastic transport result in the mean squared particle displacement following a power law, $\langle {Δr}^2 \rangle \sim t^α$, where the diffusion exponent $α$ characterizes whether the transport is subdiffusive, ($α<1$), diffusive ($α= 1$), or superdiffusive, ($α>1$). Due to the abundance of fBm processes in nature, significant efforts have been devoted to the identification and characterization of fBm sources in various phenomena. In practice, the identification of the fBm sources often relies on solving a complex and ill-posed inverse problem based on limited observed data. In the general case, the detected signals are formed by an unknown number of release sources, located at different locations and with different strengths, that act simultaneously. This means that the observed data is composed of mixtures of releases from an unknown number of sources, which makes the traditional inverse modeling approaches unreliable. Here, we report an unsupervised learning method, based on Nonnegative Matrix Factorization, that enables the identification of the unknown number of release sources as well the anomalous diffusion characteristics based on limited observed data and the general form of the corresponding fBm Green's function. We show that our method performs accurately for different types of sources and configurations with a predetermined number of sources with specific characteristics and introduced noise.

physics.app-ph↗

arXiv2020

Different time scales in dynamic systems with multiple exits

Stochastic biochemical and transport processes have various final outcomes, and they can be viewed as dynamic systems with multiple exits. Many current theoretical studies, however, typically consider only a single time scale for each specific outcome, effectively corresponding to a single-exit process and assuming the independence of each exit process. But the presence of other exits influences the statistical properties and dynamics measured at any specific exit. Here, we present theoretical arguments to explicitly show the existence of different time scales, such as mean exit times and inverse exit fluxes, for dynamic processes with multiple exits. This implies that the statistics of any specific exit dynamics cannot be considered without taking into account the presence of other exits. Several illustrative examples are described in detail using analytical calculations, mean-field estimates, and kinetic Monte Carlo computer simulations. The underlying microscopic mechanisms for the existence of different time scales are discussed. The results are relevant for understanding the mechanisms of various biological, chemical, and industrial processes, including transport through channels and pores.

cond-mat.stat-mech↗

arXiv2019

Dynamics and escape of active particles in a harmonic trap

The dynamics of active particles is of interest at many levels and is the focus of theoretical and experimental research. There have been many attempts to describe the dynamics of particles affected by random active forces in terms of an effective temperature. This kind of description is tempting due to the similarities (or lack thereof) with systems in or near thermal equilibrium. However, the generality and validity of the effective temperature is not yet fully understood. Here, we studied the dynamics of trapped particles subjected to both thermal and active forces. The particles were not overdamped. Expressions for the effective temperature due to the potential and kinetic energies were derived, and they differ from each other. A third possible effective temperature can be derived from the escape time of the particle from the trap, using a Kramers-like expression for the mean escape time. We found that over a large fraction of the parameter space, the potential energy effective temperature is in agreement with the escape temperature, while the kinetic effective temperature only agrees with the former two in the overdamped limit. Moreover, we show that the specific implementation of the random active force, and not only its first two moments and the two point auto-correlation function, affects the escape time distribution.

cond-mat.stat-mech↗

arXiv2019

Improved reliability and accuracy of CMIP5 global mean surface temperature projections

Climate predictions are only meaningful if the associated uncertainty is reliably estimated. A standard practice for providing climate projections is to use an ensemble of projections. The ensemble mean serves as the projection while the ensemble spread is used to estimate the associated uncertainty. The main drawbacks of this approach are the fact that there is no guarantee that the ensemble projections adequately sample the possible future climate conditions and that the quantification of the ensemble spread relies on assumptions that are not always justified. The relation between the true uncertainties associated with projections and ensemble spreads is not fully understood. Here, we suggest using simulations and measurements of past conditions in order to study both the performance of the ensemble members and the relation between the ensemble spread and the uncertainties associated with their predictions. Using an ensemble of CMIP5 long-term climate projections that was weighted according to a sequential learning algorithm and whose spread was linked to the range of past measurements, we found considerably reduced uncertainty ranges for the projected Global Mean Surface Temperature (GMST). The results suggest that by employing advanced ensemble methods and using past information, it is possible to provide more reliable and accurate climate projections.

physics.ao-ph↗

arXiv2018

Geographic Dependence of the Solar Radiation Spectrum at Intermediate to High Frequencies

The solar radiation spectrum is important for renewable energy harvesting, as well as climate and ecological systems analysis. In addition to seasonal/annual and diurnal oscillations, the signal is composed of different frequencies ($f$) that modulate each other. This results in a continuous spectrum with a power-law dependence over the entire frequency range from 1/year up to at least 1/min. Geographical location plays an important role in determining the temporal variability of solar radiation and naturally affects its spectral power-law decay, primarily due to the latitudinal dependence of daylight duration and its seasonal variation,. Employing a model to calculate the clear sky solar radiation intensity at various global locations, we show that significant spatial variability exists, particularly versus the latitude, which we quantify via the exponent of the spectral power-law. At most locations, the spectral power-law dependence of the intermediate (1/day $< f <$ 1/hour) frequencies is different from that of the high ($f > 1/$hour) frequencies. We demonstrate the origin of this power-law dependence from simple arguments, explain its geographic dependence and discuss the implications for photovoltaic power generation and solar-driven systems, and hence the impact on grid stability.

physics.geo-ph↗

arXiv2017

Gradual Regime Shifts in Fairy Circles

Large responses of ecosystems to small changes in the conditions--regime shifts--are of great interest and importance. In spatially extended ecosystems, these shifts may be local or global. Using empirical data and mathematical modeling, we investigated the dynamics of the Namibian fairy circle ecosystem as a case study of regime shifts in a pattern-forming ecosystem. Our results provide new support, based on the dynamics of the ecosystem, for the view of fairy circles as a self-organization phenomenon driven by water-vegetation interactions. The study further suggests that fairy circle birth and death processes correspond to spatially confined transitions between alternative stable states. Cascades of such transitions, possible in various pattern-forming systems, result in gradual rather than abrupt regime shifts.

nlin.PS↗

arXiv2017

Localized states qualitatively change the response of ecosystems to varying conditions and local disturbances

The response of dynamical systems to varying conditions and disturbances is a fundamental aspect of their analysis. In spatially extended systems, particularly in pattern-forming systems, there are many possible responses, including critical transitions, gradual transitions and locally confined responses. Here, we use the context of vegetation dynamics in drylands in order to study the response of pattern-forming ecosystems to oscillating precipitation and local disturbances. We focus on two precipitation ranges, a bistability range of bare soil with a patterned vegetation state, and a bistability range of uniform vegetation with a patterned vegetation state. In these ranges, there are many different stable states, which allow for both abrupt and gradual transitions between the system states to occur. We find that large amplitude oscillations of the precipitation rate can lead to a collapse of the vegetation in one range, while in the other range, they result in the convergence to a patterned state with a preferred wavelength. In addition, we show that a series of local disturbances results in the collapse of the vegetation in one range, while it drives the system toward fluctuations around a finite average biomass in the other range. Moreover, it is shown that under certain conditions, local disturbances can actually increase the overall vegetation density. These significant differences in the system response are attributed to the existence of localized states in one of the bistability ranges.

nlin.PS↗

arXiv2017

Quantifying the uncertainties in an ensemble of decadal climate predictions

Meaningful climate predictions must be accompanied by their corresponding range of uncertainty. Quantifying the uncertainties is non-trivial, and different methods have been suggested and used in the past. Here, we propose a method that does not rely on any assumptions regarding the distribution of the ensemble member predictions. The method is tested using the CMIP5 1981-2010 decadal predictions and is shown to perform better than two other methods considered here. The improved estimate of the uncertainties is of great importance for both practical use and for better assessing the significance of the effects seen in theoretical studies.

physics.ao-ph↗

arXiv2016

Effects of quenched disorder on critical transitions in pattern-forming systems

Critical transitions are of great interest to scientists in many fields. Most knowledge about these transitions comes from systems exhibiting the multistability of spatially uniform states. In spatially extended and, particularly, in pattern-forming systems, there are many possible scenarios for transitions between alternative states. Quenched disorder may affect the dynamics, bifurcation diagrams and critical transitions in nonlinear systems. However, only a few studies have explored the effects of quenched disorder on pattern-forming systems, either experimentally or by using theoretical models. Here, we use a fundamental model describing pattern formation, the Swift-Hohenberg model and a well-explored mathematical model describing the dynamics of vegetation in drylands to study the effects of quenched disorder on critical transitions in pattern-forming systems. We find that the disorder affects the patterns formed by introducing an interplay between the imposed pattern and the self-organized one. We show that, in both systems considered here, the disorder significantly increases the durability of the patterned state and makes the transition between the patterned state and the uniform state more gradual. In addition, the disorder induces hysteresis in the response of the system to changes in the bifurcation parameter well before the critical transition occurs. We also show that the cross-correlation between the disordered parameter and the dynamical variable can serve as an early indicator for an imminent critical transition.

nlin.PS↗

arXiv2015

Decadal climate predictions using sequential learning algorithms

Ensembles of climate models are commonly used to improve climate predictions and assess the uncertainties associated with them. Weighting the models according to their performances holds the promise of further improving their predictions. Here, we use an ensemble of decadal climate predictions to demonstrate the ability of sequential learning algorithms (SLAs) to reduce the forecast errors and reduce the uncertainties. Three different SLAs are considered, and their performances are compared with those of an equally weighted ensemble, a linear regression and the climatology. Predictions of four different variables--the surface temperature, the zonal and meridional wind, and pressure--are considered. The spatial distributions of the performances are presented, and the statistical significance of the improvements achieved by the SLAs is tested. Based on the performances of the SLAs, we propose one to be highly suitable for the improvement of decadal climate predictions.

physics.ao-ph↗

arXiv2015

The Contribution of Internal and Model Variabilities to the Uncertainty in CMIP5 Decadal Climate Predictions

Decadal climate predictions, which are initialized with observed conditions, are characterized by two main sources of uncertainties--internal and model variabilities. Using an ensemble of climate model simulations from the CMIP5 decadal experiments, we quantified the total uncertainty associated with these predictions and the relative importance of each source. Annual and monthly averages of the surface temperature and wind components were considered. We show that different definitions of the anomaly results in different conclusions regarding the variance of the ensemble members. However, some features of the uncertainty are common to all the measures we considered. We found that over decadal time scales, there is no considerable increase in the uncertainty with time. The model variability is more sensitive to the annual cycle than the internal variability. This, in turn, results in a maximal uncertainty during the winter in the northern hemisphere. The uncertainty of the surface temperature prediction is dominated by the model variability, whereas the uncertainty of the wind components is determined by both sources. Analysis of the spatial distribution of the uncertainty reveals that the surface temperature has higher variability over land and in high latitudes, whereas the surface zonal wind has higher variability over the ocean. The relative importance of the internal and model variabilities depends on the averaging period, the definition of the anomaly, and the location. These findings suggest that several methods should be combined in order to assess future climate prediction uncertainties and that weighting schemes of the ensemble members may reduce the uncertainties.

physics.ao-ph↗

arXiv2013

Regime shifts in models of dryland vegetation

Drylands are pattern-forming systems showing self-organized vegetation patchiness, multiplicity of stable states and fronts separating domains of alternative stable states. Pattern dynamics, induced by droughts or disturbances, can result in desertification shifts from patterned vegetation to bare soil. Pattern-formation theory suggests various scenarios for such dynamics; an abrupt global shift involving a fast collapse to bare soil, a gradual global shift involving the expansion and coalescence of bare-soil domains, and an incipient shift to a hybrid state consisting of stationary bare-soil domains in an otherwise periodic pattern. Using models of dryland vegetation we address the question which of these scenarios can be realized. We found that the models can be split into two groups: models that exhibit multiplicity of periodic-pattern and bare-soil states, and models that exhibit, in addition, multiplicity of hybrid states. Furthermore, in all models we could not identify parameter regimes in which bare-soil domains expand into vegetated domains. The significance of these findings is that while models belonging to the first group can only exhibit abrupt shifts, model belonging to the second group can also exhibit gradual and incipient shifts. A discussion of open problems concludes the paper.

nlin.PS↗

arXiv2013

A pattern-forming instability co-driven by distinct mechanisms increases pattern diversity

We use the context of dryland vegetation to study a general problem of complex pattern forming systems - multiple pattern-forming instabilities that are driven by distinct mechanisms but share the same spectral properties. We find that the co-occurrence of such instabilities results in the growth of a single mode rather than two interacting modes. The interplay between the two mechanisms, which promote or counteract each other, compensates for the simpler dynamics of a single mode by inducing higher pattern diversity. Possible implications to biodiversity of ecosystems are discussed.

nlin.PS↗

arXiv2013

The effects of psammophilous plants on sand dune dynamics

Psammophilous plants are special plants that flourish in sand moving environments. There are two main mechanisms by which the wind affects these plants: (i) sand drift exposes roots and covers branches--the exposed roots turn into new plants and the covered branches turn into new roots; both mechanisms result in an enhanced growth rate of the psammophilous plant cover of the dunes; (ii) strong winds, often associated with sand movement, tear branches and seed them in nearby locations, resulting in new plants and an enhanced growth rate of the psammophilous plant cover of the dunes. Despite their important role in dune dynamics, to our knowledge, psammophilous plants have never been incorporated into mathematical models of sand dunes. Here, we attempt to model the effects of these plants on sand dune dynamics. We construct a set of three ordinary differential equations for the fractions of surface cover of regular vegetation, biogenic soil crust and psammophilous plants. The latter reach their optimal growth under (i) specific sand drift or (ii) specific wind power. We show that psammophilous plants enrich the sand dune dynamics. Depending on the climatological conditions, it is possible to obtain one, two, or three steady dune states. The activity of the dunes can be associated with the surface cover--bare dunes are active, and dunes with significant cover of vegetation, biogenic soil crust, or psammophilous plants are fixed. Our model shows that under suitable precipitation rates and wind power, the dynamics of the different cover types is in accordance with the common view that dunes are initially stabilized by psammophilous plants that reduce sand activity, thus enhancing the growth of regular vegetation that eventually dominates the cover of the dunes and determines their activity.

physics.bio-ph↗

arXiv2013

The relation between the statistics of open ocean currents and the temporal correlations of the wind

We study the statistics of wind-driven open ocean currents. Using the Ekman layer model for the integrated currents, we investigate, analytically and numerically, the relation between the wind distribution and its temporal correlations and the statistics of the open ocean currents. We find that temporally long-range correlated wind results in currents whose statistics is proportional to the wind-stress statistics. On the other hand, short-range correlated wind leads to Gaussian distributions of the current components, regardless of the stationary distribution of the winds, and therefore, to a Rayleigh distribution of the current amplitude if the wind stress is isotropic. An interesting result is the existence of an optimum in the amplitude of the ocean currents as a function of the correlation time of the wind stress. The results were validated using an oceanic general circulation model.

physics.ao-ph↗