1,755 research outputs found
An exactly solvable nonlinear model: Constructive effects of correlations between Gaussian noises
A system with two correlated Gaussian white noises is analysed. This system
can describe both stochastic localization and long tails in the stationary
distribution. Correlations between the noises can lead to a nonmonotonic
behaviour of the variance as function of the intensity of one of the noises and
to a stochastic resonance. A method for improving the transmission of external
periodic signal by tuning parameters of the system discussed in this paper is
proposed
Reintroducing Intergenerational Equilibrium: Key Concepts behind the New Polish Pension System
Poland adopted a new pension system in 1999. This new pension system allows Poland to reduce pension expenditure (as a percent of GDP), instead of increasing it – as is projected for the majority of other OECD countries. This paper presents the conceptual background of the new system design. The new system’s long-term objective is to ensure intergenerational equilibrium irrespective of the demographic situation. This requires stabilisation of the share of GDP allocated to the entire retired generation. Traditional pension systems aim, instead, at stabilisation of the share of GDP per retiree. The change in demographic structure observed over the past for a couple of decades and this historic attempt to stabilise the share of GDP per retiree led to severe fiscal problems and negative externalities for growth, as observed in numerous countries. Many countries have tried to reform their pension systems in different ways to try to resolve the issue of these ever-increasing costs. Although the Polish reform uses a number of techniques applied elsewhere, its design differs from the typical approaches – and the lessons and results are promising for all OECD countries. This paper presents the theoretical and practical application of this alternative approach and as such, the key features of the new Polish pension system design.pensions, equilibrium, GDP, pension debt servicing, income allocation, generations
A model for effective interactions in binary colloidal systems of soft particles
While the density functional theory with integral equations techniques are
very efficient tools in numerical analysis of complex fluids, an analytical
insight into the phenomenon of effective interactions is still limited. In this
paper we propose a theory of binary systems which results in a relatively
simple analytical expression combining arbitrary microscopic potentials into
the effective interaction. The derivation is based on translating many particle
Hamiltonian including particle-depletant and depletant-depletant interactions
into the occupation field language. Such transformation turns the partition
function into multiple Gaussian integrals, regardless of what microscopic
potentials are chosen. In result, we calculate the effective Hamiltonian and
discuss when our formula is a dominant contribution to the effective
interactions. Our theory allows us to analytically reproduce several important
characteristics of systems under scrutiny. In particular, we analyze the
effective attraction as a demixing factor in the binary systems of Gaussian
particles, effective interactions in the binary mixtures of Yukawa particles
and the system of particles consisting of both repulsive core and
attractive/repulsive Yukawa interaction tail, for which we reproduce the
'attraction-through-repulsion' and 'repulsion-through-attraction' effects.Comment: Second version of article, after major revision due to the comments
from reviewers. Includes overhauled introductory section, new, more compact
derivation and more elaborate examples than previousl
Thermodynamically consistent Langevin dynamics with spatially correlated noise predicts frictionless regime and transient attraction effect
While the origin of temporal correlations in Langevin dynamics have been
thoroughly researched, the understanding of Spatially Correlated Noise (SCN) is
rather incomplete. In particular, very little is known about the relation
between friction and SCN. In this article, we derive the formal formula for the
spatial correlation function in the particle-bath interactions. This expression
shows that SCN is the inherent component of binary mixtures, originating from
the effective (entropic) interactions. Further, employing this spatial
correlation function, we postulate the thermodynamically consistent Langevin
equation driven by SCN and the adequate Fluctuation-Dissipation Relation. The
thermodynamical consistency is achieved by introducing the spatially variant
friction coefficient, which can be also derived analytically. This coefficient
exhibits a number of intriguing properties, e.g. the singular behavior for
certain interaction types. Eventually, we apply this new theory to the system
of two charged particles in the presence of counter-ions. Such particles
interact via the screened-charge Yukawa potential and the inclusion of SCN
leads to the emergence of the anomalous frictionless regime. In this regime the
particles can experience active propulsion leading to the transient attraction
effect. This effect suggests a non-equilibrium mechanism facilitating the
molecular binding of the like-charged particles.Comment: expanded and revised version resubmitted to Phys. Rev.
Non-Gaussian polymers described by alpha-stable chain statistics: model, applications and effective interactions in binary mixtures
The Gaussian chain model is the classical description of a polymeric chain,
which provides the analytical results regarding end-to-end distance, the
distribution of segments around the mass center of a chain, coarse grained
interactions between two chains and effective interactions in binary mixtures.
This hierarchy of results can be calculated thanks to the alpha stability of
the Gaussian distribution. In this paper we show that it is possible to
generalize the model of Gaussian chain to the entire class of alpha stable
distributions, obtaining the analogous hierarchy of results expressed by the
analytical closed-form formulas in the Fourier space. This allows us to
establish the alpha-stable chain model. We begin with reviewing the
applications of Levy flights in the context of polymer sciences, which include:
chains with heavy-tailed distributions of persistence length, polymers adsorbed
to the surface and the chains driven by a noise with power-law spatial
correlations. Further, we derive the distribution of segments around the mass
center of the alpha-stable chain and the coarse-grained interaction potential
between two chains is constructed. These results are employed to discuss the
model of binary mixture consisting of the alpha-stable chains. On what follows,
we establish the spinodal decomposition condition generalized to the particles
described by the shape of alpha-stable distributions. This condition is finally
applied to analyze the on-surface phase separation of adsorbed polymers, which
are known to be described with heavy tailed statistics.Comment: Complete version prepared for submission to Phys. Rev.
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