14,810 research outputs found
Short relaxation times but long transient times in both simple and complex reaction networks
When relaxation towards an equilibrium or steady state is exponential at
large times, one usually considers that the associated relaxation time ,
i.e., the inverse of that decay rate, is the longest characteristic time in the
system. However that need not be true, and in particular other times such as
the lifetime of an infinitesimal perturbation can be much longer. In the
present work we demonstrate that this paradoxical property can arise even in
quite simple systems such as a chain of reactions obeying mass action kinetics.
By mathematical analysis of simple reaction networks, we pin-point the reason
why the standard relaxation time does not provide relevant information on the
potentially long transient times of typical infinitesimal perturbations.
Overall, we consider four characteristic times and study their behavior in both
simple chains and in more complex reaction networks taken from the publicly
available database "Biomodels." In all these systems involving mass action
rates, Michaelis-Menten reversible kinetics, or phenomenological laws for
reaction rates, we find that the characteristic times corresponding to
lifetimes of tracers and of concentration perturbations can be much longer than
Ergodic Actions and Spectral Triples
In this article, we give a general construction of spectral triples from
certain Lie group actions on unital C*-algebras. If the group G is compact and
the action is ergodic, we actually obtain a real and finitely summable spectral
triple which satisfies the first order condition of Connes' axioms. This
provides a link between the "algebraic" existence of ergodic action and the
"analytic" finite summability property of the unbounded selfadjoint operator.
More generally, for compact G we carefully establish that our (symmetric)
unbounded operator is essentially selfadjoint. Our results are illustrated by a
host of examples - including noncommutative tori and quantum Heisenberg
manifolds.Comment: 18 page
All-Pay Auctions with Endogenous Rewards
This paper examines a perfectly discriminating contest (all-pay auction) with two asymmetric players. Valuations are endogenous and depend on the effort each player invests in the contest. The shape of the valuation function is common knowledge and differs between the contestants. Some key properties of R&D races, lobbying activity and sport contests are captured by this framework. Once the unique equilibrium in mixed strategies analyzed, we derive a closed form of the expected expenditure of both players. We characterize the expected expenditure by means of incomplete Beta functions. We focus on unordered valuations.All-pay auctions, contests
All-pay auctions with endogenous rewards
This paper examines a perfectly discriminating contest (all-pay auction) with two asymmetric players. Valuations are endogenous and depend on the effort each player invests in the contest. The shape of the valuation function is common knowledge and differs between the contestants. Some key properties of R&D races, lobbying activity and sport contests are captured by this framework. Once the unique equilibrium in mixed strategies analyzed, we derive a closed form of the expected expenditure of both players. We characterize the expected expenditure by the means of incomplete Beta functions. We focus on unordered valuations.all-pay auctions, contests
Surface-Wave Dispersion Retrieval Method and Synthesis Technique for Bianisotropic Metasurfaces
We propose a surface-wave dispersion retrieval method and synthesis technique
that applies to bianisotropic metasurfaces that are embedded in symmetric or
asymmetric environments. Specifically, we use general zero-thickness sheet
transition conditions to relate the propagation constants of surface-wave modes
to the bianisotropic susceptibility components of the metasurface, which can
themselves be directly related to its scattering parameters. It is then
possible to either obtain the metasurface dispersion diagram from its known
susceptibilities or, alternatively, compute the susceptibilities required to
achieve a desired surface-wave propagation. The validity of the method is
demonstrated by comparing its results to those obtained with exact dispersion
relations of well known structures such as the propagation of surface plasmons
on thin metallic films. In particular, this work reveals that it is possible to
achieve surface-wave propagation only on one side of the metasurface either by
superposition of symmetric and asymmetric modes in the case of anisotropic
metasurfaces or by completely forbidding the existence of the surface wave on
one side of the structure using bianisotropic metasurfaces
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