arXiv subjects

Peter Ditlevsen

Publications and source records attributed to Peter Ditlevsen.

10 recordsLinked to original sources

arXiv2026

Cold Extremes during Dansgaard-Oeschger Oscillations

This paper studies the statistics of extreme cold air surface temperatures in a climate that experiences abrupt changes. We employ a CCSM4 simulation of Last Glacial Maximum conditions that exhibits rapid switching between stadial and interstadial states as data. Non-stationary linear Generalized Extreme Value (GEV) distributions are fitted to find the regions that show the most prominent changes and associate them with physical processes. The results are then compared with a non-linear model, which gives a more detailed picture of how the parameters change as a function of the AMOC strength. While different regions of the world show different extremal behaviours, many regions show an approximately linear relationship between the parameters of the GEV distributions and the strength of the AMOC within the stadial and interstadial states, with some non-linear oscillation or jump where the transition between them takes place. Physical processes such as the expansion and retreat of the sea ice and the relative changes in the strength of the currents are shown to impact the magnitude and variability of the extremes, with significant changes observed in the three parameters of the GEV. They also create teleconnections that are compared whenever possible with various proxies for the temperature of the air and the water. We show how mapping the parameters of the GEV distributions into the AMOC strength gives a way to compare results between different climate models and different climate states. Comparisons, however, need to pay heed to the dynamical characteristics of the state and the location to be meaningful.

physics.ao-ph↗

arXiv2026

Early Warning Signals Can Vanish or Amplify: Dimensionality in Complex Systems

Early warning signals (EWS), such as increasing variance and autocorrelation, are widely used to anticipate critical transitions associated with saddle-node bifurcations. However, real-world systems are often high-dimensional and multiscale, potentially altering the classical behavior of EWS. Here, we investigate how dimensionality, inertia, and red noise influence the detectability of EWS prior to tipping points. We show that when observations are not aligned with the critical direction, stable dynamics in orthogonal directions can mask EWS until very near the bifurcation. We further demonstrate that second-order dynamics with damping modify the autocorrelation structure and may either enhance or reduce signatures of critical slowing down. Finally, we study how colored noise influences EWS. Our results show that the presence and strength of EWS are not universal properties of tipping systems but depend critically on system geometry and stochastic forcing, implying that the absence of detectable EWS does not necessarily rule out an approaching critical transition.

math.DS↗

arXiv2025

Chaotic variability in a model of coupled ice streams

Regions of fast-flowing ice in ice sheets, known as ice streams, have been theorized to be able to exhibit build-up/surge oscillatory variability due to thermomechanical coupling at the base of the ice. A simple model of three coupled ice streams is constructed to replicate the spatial configuration of a single ice stream being bisected into two termini. The model is constructed to mimic existing branching ice streams in northern Greenland. This model is shown to exhibit both steady-flow and build-up/surge oscillations. Further, the variability can be chaotic due to the nonlinear coupling of three incommensurate frequencies. This provides a mode of chaotic internal variability for ice sheets that contain these types of ice streams.

nlin.CD↗

arXiv2023

Escape by jumps and diffusion by {\alpha}-stable noise across the barrier in a double well potential

Many physical and chemical phenomena are governed by stochastic escape across potential barriers. The escape time depends on the structure of the noise and the shape of the potential barrier. By applying $\alpha$-stable noise from the $\alpha=2$ Gaussian noise limit to the $\alpha<2$ jump processes, we find a continuous transition of the mean escape time from the usual dependence on the height of the barrier for Gaussian noise to a dependence solely on the width of the barrier for $\alpha$-stable noise. We consider the exit problem of a process driven by $\alpha$-stable noise in a double well potential. We study individually the influences of the width and the height of the potential barrier in the escape time and we show through scalings that the asymptotic laws are described by a universal curve independent of both parameters. When the dependence in the stability parameter is considered, we see that there are two different diffusive regimes in which diffusion is described either by Kramer's time or by the corresponding asymptotic law for $\alpha$-stable noise. We determine the regions of the noise parameter space in which each regime prevails, and exploit this result to construct an anomalous example in which a double well potential exhibit a different diffusion regime in each well for a wide range of parameters.

cond-mat.stat-mech↗

arXiv2021

Quantification and interpretation of the climate variability record

The spectral view of variability is a compelling and adaptable tool for understanding variability of the climate. In Mitchell (1976) seminal paper, it was used to express, on one graph with log scales, a very wide range of climate variations from millions of years to days. The spectral approach is particularly useful for suggesting causal links between forcing variability and climate response variability. However, a substantial degree of variability is intrinsic and the Earth system may respond to external forcing in a complex manner. There has been an enormous amount of work on understanding climate variability over the last decades. Hence in this paper, we address the question: Can we (after 40 years) update the Mitchell (1976) diagram and provide it with a better interpretation? By reviewing both the extended observations available for such a diagram and new methodological developments in the study of the interaction between internal and forced variability over a wide range of timescales, we give a positive answer to this question. In addition, we review alternative approaches to the spectral decomposition and pose some challenges for a more detailed quantification of climate variability.

physics.ao-ph↗

arXiv2019

Refined central limit theorem and infinite density tail of the Lorentz gas from Levy walk

We consider point particle that collides with a periodic array of hard-core elastic scatterers where the length of the free flights is unbounded (the infinite-horizon Lorentz gas, LG). The Bleher central limit theorem (CLT) states that the distribution of the particle displacement divided by $\sqrt{t\ln t}$ is Gaussian in the limit of infinite time $t$. However it was stressed recently that the slow convergence makes this result unobservable. Using a L\'{e}vy walk model (LW) of the LG, it was proposed that the use of a rescaled Lambert function instead of $\sqrt{t\ln t}$ provides a fast convergent, observable CLT, which was confirmed by the LG simulations. We demonstrate here that this result can simplified to a mixed CLT where the scaling factor combines normal and anomalous diffusions. For narrow infinite corridors the particle for long time obeys the usual normal diffusion, which explains the previous numerical observations. In the opposite limit of small scatterers the Bleher CLT gives a good guiding. In the intermediate cases the mixed CLT applies. The Gaussian peak determines moments of order smaller than two. In contrast, the CLT gives only half the coordinate dispersion. The missing half of the dispersion and also moments of order higher than two are described by the distribution's tail (the infinite density) which we derive here. The tail is supported along the infinite corridors and formed by anomalously long flights whose duration is comparable with the whole time of observation. The moments' calculation from the tail is confirmed by direct calculation of the fourth moment from the statistics of the backward recurrence time defined as time that elapsed since the last collision. This completes the solution of the LW model allowing full comparison with the LG.

cond-mat.stat-mech↗

arXiv2019

Partial invariants, large-scale dynamo action, and the inverse transfer of magnetic helicity

The existence of partially conserved enstrophy-like quantities is conjectured to cause inverse energy transfers to develop embedded in magnetohydrodynamical (MHD) turbulence, in analogy to the influence of enstrophy in two-dimensional nonconducting turbulence. By decomposing the velocity and magnetic fields in spectral space onto helical modes, we identify subsets of three-wave (triad) interactions conserving two new enstrophy-like quantities which can be mapped to triad interactions recently identified with facilitating large-scale $\alpha$-type dynamo action and the inverse transfer of magnetic helicity. Due to their dependence on interaction scale locality, the invariants suggest that the inverse transfer of magnetic helicity might be facilitated by both local- and nonlocal-scale interactions, and is a process more local than the $\alpha$-dynamo. We test the predicted embedded (partial) energy fluxes by constructing a shell model (reduced wave-space model) of the minimal set of triad interactions (MTI) required to conserve the ideal MHD invariants. Numerically simulated MTIs demonstrate that, for a range of forcing configurations, the partial invariants are, with some exceptions, indeed useful for understanding the embedded contributions to the total spectral energy flux. Furthermore, we demonstrate that strictly inverse energy transfers may develop if enstrophy-like conserving interactions are favoured, a mechanism recently attributed to the energy cascade reversals found in nonconducting three-dimensional turbulence subject to strong rotation or confinement. The presented results have implications for the understanding of the physical mechanisms behind large-scale dynamo action and the inverse transfer of magnetic helicity, processes thought to be central to large-scale magnetic structure formation.

physics.flu-dyn↗

arXiv2019

Bifurcation of critical sets and relaxation oscillations in singular fast-slow systems

Fast-slow dynamical systems have subsystems that evolve on vastly different timescales, and bifurcations in such systems can arise due to changes in any or all subsystems. We classify bifurcations of the critical set (the equilibria of the fast subsystem) and associated fast dynamics, parametrized by the slow variables. Using a distinguished parameter approach we are able to classify bifurcations for one fast and one slow variable. Some of these bifurcations are associated with the critical set losing manifold structure. We also conjecture a list of generic bifurcations of the critical set for one fast and two slow variables. We further consider how the bifurcations of the critical set can be associated with generic bifurcations of attracting relaxation oscillations under an appropriate singular notion of equivalence.

math.DS↗

arXiv2017

Inhomogeneous preferential concentration of inertial particles in turbulent channel flow

Turbophoresis leading to preferential concentration of inertial particles in regions of low turbulent diffusivity is a unique feature of inhomogeneous turbulent flows, such as free shear flows or wall-bounded flows. In this work, the theory for clustering of weakly inertial particles in homogeneous turbulence is extended to the inhomogeneous case of a turbulent channel flow. The inhomogeneity contributes to the cluster formation in addition to clustering in homogeneous turbulence. A space-dependent rate for the creation of inhomogeneous particle concentration is derived in terms of local statistics of turbulence. We provide the formula for the pair-correlation function of concentration that factorizes in product of time and space-dependent average concentrations and time-independent factor of clustering that obeys a power-law in the distance between the points. This power-law characterizes inhomogeneous multifractality of the particle distribution. A unique demonstration and quantification of the combined effects of turbophoresis and fractal clustering in a direct numerical simulation of particle motion in a turbulent channel flow is performed according to the presented theory. The strongest contribution to clustering coming from the inhomogeneity of the flow occurs in the transitional region between viscous sublayer and the buffer layer. Further the ratio of homogeneous and inhomogeneous term depends on the wall distance. The inhomogeneous terms may significantly increase the preferential concentration of inertial particles, thus the overall degree of clustering in inhomogeneous turbulence is potentially stronger compared to particles with the same inertia in purely homogeneous turbulence.

physics.flu-dyn↗

arXiv2016

Three types of nonlinear resonances

We analyse different types of nonlinear resonances in a weakly damped Duffing oscillator using bifurcation theory techniques. In addition to (i) odd subharmonic resonances found on the primary branch of symmetric periodic solutions with the forcing frequency and (ii) even subharmonic resonances due to symmetry-broken periodic solutions that bifurcate off the primary branch and also oscillate at the forcing frequency, we uncover (iii) novel resonance type due to isolas of periodic solutions that are not connected to the primary branch. These occur between odd and even resonances, oscillate at a fraction of the forcing frequency, and give rise to a complicated resonance `curve' with disconnected elements and high degree of multistability. We use bifurcation continuation to compute resonance tongues in the plane of the forcing frequency vs. the forcing amplitude for different but fixed values of the damping rate. In this way, we demonstrate that identified here isolated resonances explain the intriguing structure of "patchy tongues" observed for week damping and link it to a seemingly unrelated phenomenon of "bifurcation superstructure" described for moderate damping.

math.DS↗