Search results for "Statistical physics"
showing 10 items of 1402 documents
On the thermodynamic origin of metabolic scaling
2018
The origin and shape of metabolic scaling has been controversial since Kleiber found that basal metabolic rate of animals seemed to vary as a power law of their body mass with exponent 3/4, instead of 2/3, as a surface-to-volume argument predicts. The universality of exponent 3/4 -claimed in terms of the fractal properties of the nutrient network- has recently been challenged according to empirical evidence that observed a wealth of robust exponents deviating from 3/4. Here we present a conceptually simple thermodynamic framework, where the dependence of metabolic rate with body mass emerges from a trade-off between the energy dissipated as heat and the energy efficiently used by the organi…
Dynamic complexities in host-parasitoid interaction
1999
In the 1970s ecological research detected chaos and other forms of complex dynamics in simple population dynamics models, initiating a new research tradition in ecology. However, the investigations of complex population dynamics have mainly concentrated on single populations and not on higher dimensional ecological systems. Here we report a detailed study of the complicated dynamics occurring in a basic discrete-time model of host-parasitoid interaction. The complexities include (a) non-unique dynamics, meaning that several attractors coexist, (b) basins of attraction (defined as the set of the initial conditions leading to a certain type of an attractor) with fractal properties (pattern of…
The role of noise on the steady state distributions of phytoplankton populations
2016
The spatio-temporal behaviour of total chlorophyll concentration is investigated in the middle of the Tyrrhenian Sea by using a stochastic approach. The study is based on a reaction-diffusion-taxis model, which is used to analyse the dynamics of five phytoplankton groups, responsible for about 80% of the total chlorophyll a inside the euphotic zone of the water column. The analysis is performed by considering: (i) the intraspecific competition of the phytoplanktonic groups for limiting factors, i.e. light intensity and nutrient concentration, (ii) the seasonal changes of environmental variables, and (iii) the random fluctuations of the components of the velocity field and temperature. Speci…
Non-unique population dynamics: basic patterns
2000
We review the basic patterns of complex non-uniqueness in simple discrete-time population dynamics models. We begin by studying a population dynamics model of a single species with a two-stage, two-habitat life cycle. We then explore in greater detail two ecological models describing host‐macroparasite and host‐parasitoid interspecific interactions. In general, several types of attractors, e.g. point equilibria vs. chaotic, periodic vs. quasiperiodic and quasiperiodic vs. chaotic attractors, may coexist in the same mapping. This non-uniqueness also indicates that the bifurcation diagrams, or the routes to chaos, depend on initial conditions and are therefore non-unique. The basins of attrac…
Nonlinear network dynamics for interconnected micro-grids
2018
Abstract This paper deals with transient stability in interconnected micro-grids. The main challenge is to understand the impact of the connectivity of the graph and model nonlinearities on transient and steady-state behavior of the system as a whole. The contribution of this paper is three-fold. First, we provide a robust classification of transient dynamics for different intervals of the parameters for a single micro-grid. We prove that underdamped dynamics and oscillations arise when the damping coefficient is below a certain threshold which we calculate explicitly as function of the product between the inertia coefficient and the synchronization parameter. Second, for interconnected mic…
A continued fraction based approach for the Two-photon Quantum Rabi Model
2019
We study the Two Photon Quantum Rabi Model by way of its spectral functions and survival probabilities. This approach allows numerical precision with large truncation numbers, and thus exploration of the spectral collapse. We provide independent checks and calibration of the numerical results by studying an exactly solvable case and comparing the essential qualitative structure of the spectral functions. We stress that the large time limit of the survival probability provides us with an indicator of spectral collapse, and propose a technique for the detection of this signal in the current and upcoming quantum simulations of the model. E.L. acknowledges fruitful discussions with D. Braak. I.…
Dynamic coarse-graining fills the gap between atomistic simulations and experimental investigations of mechanical unfolding
2017
We present a dynamic coarse-graining technique that allows to simulate the mechanical unfolding of biomolecules or molecular complexes on experimentally relevant time scales. It is based on Markov state models (MSM), which we construct from molecular dynamics simulations using the pulling coordinate as an order parameter. We obtain a sequence of MSMs as a function of the discretized pulling coordinate, and the pulling process is modeled by switching among the MSMs according to the protocol applied to unfold the complex. This way we cover seven orders of magnitude in pulling speed. In the region of rapid pulling we additionally perform steered molecular dynamics simulations and find excellen…
Attraction in n ‐dimensional differential systems from network regulation theory
2018
On a Planar Dynamical System Arising in the Network Control Theory
2016
We study the structure of attractors in the two-dimensional dynamical system that appears in the network control theory. We provide description of the attracting set and follow changes this set suffers under the changes of positive parameters µ and Θ.
Inferring causation from time series in earth system sciences
2019
The heart of the scientific enterprise is a rational effort to understand the causes behind the phenomena we observe. In large-scale complex dynamical systems such as the Earth system, real experiments are rarely feasible. However, a rapidly increasing amount of observational and simulated data opens up the use of novel data-driven causal methods beyond the commonly adopted correlation techniques. Here, we give an overview of causal inference frameworks and identify promising generic application cases common in Earth system sciences and beyond. We discuss challenges and initiate the benchmark platform causeme.net to close the gap between method users and developers.