1,867 research outputs found
Another analytic view about quantifying social forces
Montroll had considered a Verhulst evolution approach for introducing a
notion he called "social force", to describe a jump in some economic output
when a new technology or product outcompetes a previous one. In fact,
Montroll's adaptation of Verhulst equation is more like an economic field
description than a "social force". The empirical Verhulst logistic function and
the Gompertz double exponential law are used here in order to present an
alternative view, within a similar mechanistic physics framework. As an
example, a "social force" modifying the rate in the number of temples
constructed by a religious movement, the Antoinist community, between 1910 and
1940 in Belgium is found and quantified. Practically, two temple inauguration
regimes are seen to exist over different time spans, separated by a gap
attributed to a specific "constraint", a taxation system, but allowing for a
different, smooth, evolution rather than a jump. The impulse force duration is
also emphasized as being better taken into account within the Gompertz
framework. Moreover, a "social force" can be as here, attributed to a change in
the limited need/capacity of some population, coupled to some external field,
in either Verhulst or Gompertz equation, rather than resulting from already
existing but competing goods as imagined by Montroll.Comment: 4 figures, 29 refs., 15 pages; prepared for Advances in Complex
System
The dynamics of a low-order coupled ocean-atmosphere model
A system of five ordinary differential equations is studied which combines
the Lorenz-84 model for the atmosphere and a box model for the ocean. The
behaviour of this system is studied as a function of the coupling parameters.
For most parameter values, the dynamics of the atmosphere model is dominant.
For a range of parameter values, competing attractors exist. The Kaplan-Yorke
dimension and the correlation dimension of the chaotic attractor are
numerically calculated and compared to the values found in the uncoupled Lorenz
model. In the transition from periodic behaviour to chaos intermittency is
observed. The intermittent behaviour occurs near a Neimark-Sacker bifurcation
at which a periodic solution loses its stability. The length of the periodic
intervals is governed by the time scale of the ocean component. Thus, in this
regime the ocean model has a considerable influence on the dynamics of the
coupled system.Comment: 20 pages, 15 figures, uses AmsTex, Amssymb and epsfig package.
Submitted to the Journal of Nonlinear Scienc
Heating and thermal squeezing in parametrically-driven oscillators with added noise
In this paper we report a theoretical model based on Green functions, Floquet
theory and averaging techniques up to second order that describes the dynamics
of parametrically-driven oscillators with added thermal noise. Quantitative
estimates for heating and quadrature thermal noise squeezing near and below the
transition line of the first parametric instability zone of the oscillator are
given. Furthermore, we give an intuitive explanation as to why heating and
thermal squeezing occur. For small amplitudes of the parametric pump the
Floquet multipliers are complex conjugate of each other with a constant
magnitude. As the pump amplitude is increased past a threshold value in the
stable zone near the first parametric instability, the two Floquet multipliers
become real and have different magnitudes. This creates two different effective
dissipation rates (one smaller and the other larger than the real dissipation
rate) along the stable manifolds of the first-return Poincare map. We also show
that the statistical average of the input power due to thermal noise is
constant and independent of the pump amplitude and frequency. The combination
of these effects cause most of heating and thermal squeezing. Very good
agreement between analytical and numerical estimates of the thermal
fluctuations is achieved.Comment: Submitted to Phys. Rev. E, 29 pages, 12 figures. arXiv admin note:
substantial text overlap with arXiv:1108.484
A metaphor for adiabatic evolution to symmetry
In this paper we study a Hamiltonian system with a spatially asymmetric
potential. We are interested in the effects on the dynamics when the potential
becomes symmetric slowly in time. We focus on a highly simplified non-trivial
model problem (a metaphor) to be able to pursue explicit calculations as far as
possible. Using the techniques of averaging and adiabatic invariants, we are
able to study all bounded solutions, which reveals significant asymmetric
dynamics even when the asymmetric contributions to the potential have become
negligibly small.Comment: 27 pages, LaTeX 2e, 8 figures include
Parametric and autoparametric resonance
Parametric and autoparametric resonance play an important part in many applications while posing interesting mathematical challenges. The linear dynamics is already nontrivial whereas the nonlinear dynamics of such systems is extremely rich and largely unexplored. The role of symmetries is essential, both in the linear and in the nonlinear analysis
The validation of metaphors
In this paper we introduce models as metaphors for the description of reality We consider a number of case studies of contemporary research pollution of the NorthSea
the ow
eld of theWadden Sea
drillstring dynamics
the use of metaphors in psychoanalysis In all these cases validation of the results takes a very dierent form Also this validation is certainly not in agreement with the picture of scienti
c research projected by textbook examples
In the discussion we draw some conclusions on the use and appreciation of models and metaphors in the science
On averaging methods for partial differential equations
The analysis of weakly nonlinear partial differential equations both qualitatively and quantitatively
is emerging as an exciting eld of investigation In this report we consider specic results
related to averaging but we do not aim at completeness The sections and contain important material which is not easily accessible in the literature
Of the literature which we will not discuss in detail we should mention Formal approximation methods which have been nicely presented by Cole and Kevorkian A number of formal methods for nonlinear hyperbolic equations on unbounded domains have been analysed with respect to the question of asymptotic validity by van der Burg
Higher order resonance in two degree of freedom Hamiltonian system
This paper reviews higher order resonance in two degrees of freedom Hamilto-
nian systems. We consider a positive semi-definite Hamiltonian around the origin.
Using normal form theory, we give an estimate of the size of the domain where
interesting dynamics takes place, which is an improvement of the one previously
known. Using a geometric numerical integration approach, we investigate this in
the elastic pendulum to find additional evidence that our estimate is sharp. In an
extreme case of higher order resonance, we show that phase interaction between
the degrees of freedom occurs on a short time-scale, although there is no energy
interchange
Evolution towards symmetry
The dynamics of timedependent evolution towards symmetry in Hamiltonian systems poses a dicult problem as the analysis has to be global in phasespace For one and two degrees of freedom systems this leads to the presence of one respectively two global adiabatic invariants and also the persistence of asymmetric features over a long tim
- …