Search results for "Asymptotic"

Asymptotic behavior of positive solutions of a Dirichlet problem involving supercritical nonlinearities

2013

On some bifurcation analysis techniques for continuous systems

2016

This paper is devoted to techniques in bifurcation analysis for continuous mechanical systems, concentrating on polynomial equations and implicitly given functions. These are often encountered in problems of mechanics and especially in stability analysis. Taking a classical approach, we summarize the relevant features of the cubic polynomial equation, and present some new aspects for asymptotics and parametric representation of the solutions. This is followed by a brief look into the implicit function theorem as a tool for analyzing bifurcations. As an example from mechanics, we consider bifurcations in the transverse free vibration problem of an axially compressed beam. peerReviewed

KERNEL ESTIMATION OF THE TRANSITION DENSITY IN BIFURCATING MARKOV CHAINS

2023

We study the kernel estimator of the transition density of bifurcating Markov chains. Under some ergodic and regularity properties, we prove that this estimator is consistent and asymptotically normal. Next, in the numerical studies, we propose two data-driven methods to choose the bandwidth parameters. These methods are based on the so-called two bandwidths approach.

Models of the population playing the Rock-Paper-Scissors game

2018

We consider discrete dynamical systems coming from the models of evolution of populations playing rock - paper - scissors game . Asymptotic behaviour of trajectories of these systems is described, occurrence of the Neimark-Sacker bifurcation and nonexistence of time averages are proved.

On the qualitative analysis of the solutions of a mathematical model of social dynamics

2006

Abstract This work deals with a family of dynamical systems which were introduced in [M.L. Bertotti, M. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Math. Models Methods Appl. Sci. 7 (2004) 1061–1084], modelling the evolution of a population of interacting individuals, distinguished by their social state. The existence of certain uniform distribution equilibria is proved and the asymptotic trend is investigated.

Convergence of dynamic programming principles for the $p$-Laplacian

2018

We provide a unified strategy to show that solutions of dynamic programming principles associated to the $p$-Laplacian converge to the solution of the corresponding Dirichlet problem. Our approach includes all previously known cases for continuous and discrete dynamic programming principles, provides new results, and gives a convergence proof free of probability arguments.

Pants complex, TQFT and hyperbolic geometry

2021

We present a coarse perspective on relations of the $SU(2)$-Witten-Reshetikhin-Turaev TQFT, the Weil-Petersson geometry of the Teichm\"uller space, and volumes of hyperbolic 3-manifolds. Using data from the asymptotic expansions of the curve operators in the skein theoretic version of the $SU(2)$-TQFT, as developed by Blanchet, Habegger, Masbaum and Vogel, we define the quantum intersection number between pants decompositions of a closed surface. We show that the quantum intersection number admits two sided bounds in terms of the geometric intersection number and we use it to obtain a metric on the pants graph of surfaces. Using work of Brock we show that the pants graph equipped with this …

Asymptotic theory of resonant tunneling in quantum waveguides of variable cross-section

2008

Halkaisijaltaan muunnellun kvanttiaaltojohtimen kapenemat toimivat tehokkaina potentiaalivalleina elektronin pitkittäissuuntaiselle liikkeelle. Kaksi kapenemaa muodostaa kvanttiresonaattorin, jossa resonoiva tunnelointi voi tapahtua. Tämä tarkoittaa sitä, että elektronit, joiden energia on lähellä resonanssia, läpäisevät resonaattorin todennäköisyydellä lähellä yhtä.Sarafanov kuvailee väitöskirjassaan asymptoottisesti elektroniaallon etenemistä kvanttiaaltojohtimessa, jossa on kaksi kapenemaa. Aaltoluvun k oletetaan olevan ensimmäisen ja toisen kynnysluvun välissä, jolloin vain sisään tuleva ja poismenevä aalto voivat edetä jokaisessa aaltojohtimen päässä äärettömyydessä. Väitöskirjassa esi…

Multiplicity results for asymmetric boundary value problems with indefinite weights

2004

We prove existence and multiplicity of solutions, with prescribed nodal properties, to a boundary value problem of the formu″+f(t,u)=0,u(0)=u(T)=0. The nonlinearity is supposed to satisfy asymmetric, asymptotically linear assumptions involving indefinite weights. We first study some auxiliary half-linear, two-weighted problems for which an eigenvalue theory holds. Multiplicity is ensured by assumptions expressed in terms of weighted eigenvalues. The proof is developed in the framework of topological methods and is based on some relations between rotation numbers and weighted eigenvalues.

Asymptotic expansions and causal representations through the loop-tree duality

2022

Large-scale particle physics experiments have provided a vast amount of high-quality data during the last decades. A leading role has been played by the Large Hadron Collider where the evaluation and analysis of its second run is currently still in progress while the third run is about to start, promising ever higher precision data of particle collisions and subsequent decays. The agreement between experimental observations and theoretical predictions using the Standard Model of Particle Physics is excellent. Indeed, this is a problem since there are currently few clues for how genuine shortcomings of the model can be overcome. New physics phenomena can appear either at higher energies, whi…