SCALING LAWS IN THE MACROECONOMY

2008 ◽  
Vol 11 (01) ◽  
pp. 131-138 ◽  
Author(s):  
D. DELLI GATTI ◽  
C. DI GUILMI ◽  
M. GALLEGATI ◽  
E. GAFFEO ◽  
G. GIULIONI ◽  
...  
Keyword(s):  
Statistical Physics ◽  
Scaling Laws ◽  
Multiagent System ◽  
Power Laws ◽  
Financial Fragility ◽  
Economic Profession

The practice of detecting power laws and scaling behaviors in economics and finance has gained momentum in the last few years, due to the increased use of concepts and methods first developed in statistical physics. Some disappointment has emerged in the economic profession, however, as regards the models proposed so far to theoretically explain these phenomena. In this paper we aim to address this criticism, showing that scaling behaviors can naturally emerge in a multiagent system with optimizing interacting units characterized by financial fragility.

Scaling

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Distribution Function ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Power Law ◽  
Scaling Laws ◽  
Power Laws ◽  
Distribution Functions ◽  
Temporal Process ◽  
Approximate Power

Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.

scholarly journals A new approach to business fluctuations: heterogeneous interacting agents, scaling laws and financial fragility

2005 ◽  
Vol 56 (4) ◽  
pp. 489-512 ◽  
Author(s):  
Domenico Delli Gatti ◽  
Corrado Di Guilmi ◽  
Edoardo Gaffeo ◽  
Gianfranco Giulioni ◽  
Mauro Gallegati ◽  
...  
Keyword(s):  
Scaling Laws ◽  
Financial Fragility ◽  
New Approach ◽  
Business Fluctuations ◽  
Interacting Agents ◽  
Heterogeneous Interacting Agents

Preliminary Evidence for a Theory of the Fractal City

1996 ◽  
Vol 28 (10) ◽  
pp. 1745-1762 ◽  
Author(s):  
M Batty ◽  
Y Xie
Keyword(s):  
Fractal Dimension ◽  
Urban Form ◽  
Scaling Laws ◽  
Fractal Dimensions ◽  
Power Laws ◽  
Preliminary Evidence ◽  
Residential Development ◽  
Self Similarity ◽  
Estimation Techniques ◽  
Data Source

In this paper, we argue that the geometry of urban residential development is fractal. Both the degree to which space is filled and the rate at which it is filled follow scaling laws which imply invariance of function, and self-similarity of urban form across scale. These characteristics are captured in population density functions based on inverse power laws whose parameters are fractal dimensions. First we outline the relevant elements of the theory in terms of scaling relations and then we introduce two methods for estimating fractal dimension based on varying the size of cities and the scale at which their form is detected. Exact and statistical estimation techniques are applied to each method respectively generating dimensions which measure the extent and the rate of space filling. These methods are then applied to residential development patterns in six industrial cities in the northeastern United States, with an innovative data source from the TIGER/Line files. The results support the theory of the fractal city outlined in books by Batty and Longley and Frankhauser, but with the clear conclusion that different scale and estimation techniques generate different types of fractal dimension.

INTRODUCTION

2012 ◽  
Vol 22 (04) ◽  
pp. 1202002 ◽  
Author(s):  
CHANGPIN LI ◽  
YANG QUAN CHEN ◽  
BLAS M. VINAGRE ◽  
IGOR PODLUBNY
Keyword(s):  
Fractional Calculus ◽  
Scaling Laws ◽  
Power Laws ◽  
Fractional Dynamics ◽  
Long Range Interactions ◽  
Potential Applications ◽  
Dynamics And Control ◽  
Long Memory Processes ◽  
Fractional Differential ◽  
And Control

Fractional Dynamics and Control is emerging as a new hot topic of research which draws tremendous attention and great interest. Although the fractional calculus appeared almost in the same era when the classical (or integer-order) calculus was born, it has recently been found that it can better characterize long-memory processes and materials, anomalous diffusion, long-range interactions, long-term behaviors, power laws, allometric scaling laws, and so on. Complex dynamical evolutions of these fractional differential equation models, as well as their controls, are becoming more and more important due to their potential applications in the real world. This special issue includes one review article and twenty-three regular papers, covering fundamental theories of fractional calculus, dynamics and control of fractional differential systems, and numerical calculation of fractional differential equations.

scholarly journals Scaling laws for perturbations in the ocean–atmosphere system following large CO<sub>2</sub> emissions

2015 ◽  
Vol 11 (1) ◽  
pp. 95-134
Author(s):  
N. Towles ◽  
P. Olson ◽  
A. Gnanadesikan
Keyword(s):  
Power Law ◽  
Scaling Laws ◽  
Emission Rate ◽  
Power Laws ◽  
Total Carbon ◽  
Co2 Removal ◽  
Carbon Cycle Model ◽  
Atmosphere Temperature ◽  
Ocean Carbon ◽  
System Variables

Abstract. Scaling relationships are derived for the perturbations to atmosphere and ocean variables from large transient CO2 emissions. Using the carbon cycle model LOSCAR (Zeebe et al., 2009; Zeebe, 2012b) we calculate perturbations to atmosphere temperature and total carbon, ocean temperature, total ocean carbon, pH, and alkalinity, marine sediment carbon, plus carbon-13 isotope anomalies in the ocean and atmosphere resulting from idealized CO2 emission events. The peak perturbations in the atmosphere and ocean variables are then fit to power law functions of the form γDαEbeta, where D is the event duration, E is its total carbon emission, and γ is a coefficient. Good power law fits are obtained for most system variables for E up to 50 000 PgC and D up to 100 kyr. However, these power laws deviate substantially from predictions based on simplified equilibrium considerations. For example, although all of the peak perturbations increase with emission rate E/D, we find no evidence of emission rate-only scaling α + β =0, a prediction of the long-term equilibrium between CO2 input by volcanism and CO2 removal by silicate weathering. Instead, our scaling yields α + β &amp;simeq; 1 for total ocean and atmosphere carbon and 0< α + β < 1 for most of the other system variables. The deviations in these scaling laws from equilibrium predictions are mainly due to the multitude and diversity of time scales that govern the exchange of carbon between marine sediments, the ocean, and the atmosphere.

A Dripping Faucet as a Nonextensive System

2004 ◽  
Author(s):  
T. J. P. Penna ◽  
J. C. Sartorelli
Keyword(s):  
Long Range ◽  
Statistical Physics ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Power Laws ◽  
Main Task ◽  
Nonextensive Statistical Mechanics ◽  
System A ◽  
Microscopic Interactions ◽  
Probability Densities

Here we present our attempt to characterize a time series of drop-to-drop intervals from a dripping faucet as a nonextensive system. We found a long-range anticorrelated behavior as evidence of memory in the dynamics of our system. The hypothesis of faucets dripping at the edge of chaos is reinforced by results of the linear rate of the increase of the nonextensive Tsallis statistics. We also present some similarities between dripping faucets and healthy hearts…. Many systems in Nature exhibit complex or chaotic behaviors. Chaotic behavior is characterized by short-range correlations and strong sensitivity to small changes of the initial conditions. Complex behavior is characterized by the presence of long-range power-law correlations in its dynamics. In the latter, the sensitivity to a perturbation of the initial condition is weaker than in the former. Because the probability densities are frequently described as inverse power laws, the variance and the mean often diverge. Although it is hard to predict the long-term behavior of such systems, it is still possible to get some information from them and even to find similarities between two apparently very distinct systems. Tools from statistical physics are frequently used because the main task here is to deal with diverse macroscopic phenomena and to try to explain them, starting with the microscopic interactions among many individual components. The microscopic interactions are not necessarily complicated, but the collective behavior can determine a rather intricate macroscopic description. Nonextensive statistical mechanics, since its proposal in 1988 [27], has been applied to an impressive collection of systems in which spatial or temporal longrange correlations appear. Hence, it can also become a useful tool to characterize such systems. Here, we present an attempt of using such formalism to try to understand the intriguing behavior of an apparently simple system: a dripping faucet.

Order of Magnitude Scaling: A Systematic Approach to Approximation and Asymptotic Scaling of Equations in Engineering

2012 ◽  
Vol 80 (1) ◽  
Author(s):  
Patricio F. Mendez ◽  
Thomas W. Eagar
Keyword(s):  
Scaling Laws ◽  
Solid Mechanics ◽  
Maximum Velocity ◽  
Power Laws ◽  
Maximum Temperature ◽  
Coupled Equations ◽  
Magnitude Scaling ◽  
Algebra Approach ◽  
Order Of Magnitude ◽  
Characteristic Values

This work introduces the “order of magnitude scaling” (OMS) technique, which permits for the first time a simple computer implementation of the scaling (or “ordering”) procedure extensively used in engineering. The methodology presented aims at overcoming the limitations of the current scaling approach, in which dominant terms are manually selected and tested for consistency. The manual approach cannot explore all combinations of potential dominant terms in problems represented by many coupled differential equations, thus requiring much judgment and experience and occasionally being unreliable. The research presented here introduces a linear algebra approach that enables unassisted exhaustive searches for scaling laws and checks for their self-consistency. The approach introduced is valid even if the governing equations are nonlinear, and is applicable to continuum mechanics problems in areas such as transport phenomena, dynamics, and solid mechanics. The outcome of OMS is a set of power laws that estimates the characteristic values of the unknowns in a problem (e.g., maximum velocity or maximum temperature variation). The significance of this contribution is that it extends the range of applicability of scaling techniques to large systems of coupled equations and brings objectivity to the selection of small terms, leading to simplifications. The methodology proposed is demonstrated using a linear oscillator and thermocapillary flows in welding.

SCALING LAWS IN NUMERICAL INSTABILITIES INDUCED BY FIXED-STEP INTEGRATION OF DYNAMICAL SYSTEMS

2001 ◽  
Vol 11 (12) ◽  
pp. 3145-3152 ◽  
Author(s):  
ALICIA SERFATY DE MARKUS
Keyword(s):  
Dynamical Systems ◽  
Scaling Laws ◽  
Nonlinear Dynamical Systems ◽  
Power Laws ◽  
Integration Step ◽  
Step Size ◽  
Nonlinear Dynamical ◽  
Numerical Instabilities ◽  
Simple Scaling ◽  
Physical Importance

In the conventional integration of a continuous dynamical system, the interaction between the model and fixed-step algorithms may produce important numerical effects over the resulting discrete representation. Our results indicate that there are remarkably simple scaling laws connecting the relevant parameters of the system to that value of integration step capable of overflowing the calculations. Moreover, we have identified a new type of chaotic numerical instability, which appears as the step size approaches some critical value. This effect is accurately described by means of nonanalytical power laws characteristic of phase transition phenomena. Finally, it is shown that simple nonlocal replacements in the discrete constructions significantly reduce or eliminate some of these numerical instabilities. These discretization effects were tested in several nonlinear dynamical systems of physical importance.

Scaling laws for drag of a compliant body in an incompressible viscous flow

2008 ◽  
Vol 607 ◽  
pp. 387-400 ◽  
Author(s):  
LUODING ZHU
Keyword(s):  
Viscous Flow ◽  
Scaling Laws ◽  
Scaling Law ◽  
Soap Film ◽  
Power Laws ◽  
Reynolds Numbers ◽  
Flow Speed ◽  
Immersed Boundary ◽  
Incompressible Viscous Flow ◽  
High Reynolds

Motivated by an important discovery on the drag scaling law (the 4/3 power law) of a flexible fibre in a flowing soap film by Alben et al. (Nature vol. 420, 2002, p.479) at high Reynolds numbers (2000<Re<40000), we investigate drag scaling laws at moderate Re for a compliant fibre tethered at the midpoint and submerged in an incompressible viscous flow using the immersed boundary (IB) method. Our work shows that the scaling of drag with respect to oncoming flow speed varies with Re, and the exponents of the power laws decrease monotonically from approximately 2 towards 4/3 as Re increases from 10 to 800.

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