Search results for "dynamical system"
showing 10 items of 523 documents
Robust regulation with an H<inf>&#x221E;</inf> constrain for linear two-time scale systems
2010
In this paper, the problem of robust multi-objective control design with an H ∞ constrain is studied for a class of linear two-time scale systems. The design is based on a new modelling approach under the assumption of norm-boundedness of the fast dynamics. In this method, a portion of the fast dynamics is treated as a norm-bounded perturbation in the design by its maximum possible gain. In this view, the problem of robust multi-objective control design is performed only for the certain dynamics of the two-time scale system, whose order is less than that of the original system. One illustrative example is used to demonstrate the validity of the proposed approach.
Random attractors for stochastic lattice systems with non-Lipschitz nonlinearity
2011
In this article, we study the asymptotic behaviour of solutions of a first-order stochastic lattice dynamical system with an additive noise. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions so that uniqueness of the Cauchy problem fails to be true. Using the theory of multi-valued random dynamical systems, we prove the existence of a random compact global attractor.
Dynamical analysis of anisotropic inflation
2016
Inflaton coupling to a vector field via the $f^2(\phi)F_{\mu\nu}F^{\mu\nu}$ term is used in several contexts in the literature, such as to generate primordial magnetic fields, to produce statistically anisotropic curvature perturbation, to support anisotropic inflation and to circumvent the $\eta$-problem. Here, I perform dynamical analysis of such a system allowing for most general Bianchi I initial conditions. I also confirm the stability of attractor equilibrium points in phase-space directions that had not been investigated before.
A measurement of the \(\tau\) leptonic branching fractions
1995
Abstract: A sample of 25000 Z(0) --> tau(-)tau(+) events collected by the DELPHI experiment at LEP in 1991 and 1992 is used to measure the leptonic branching fractions of the tau lepton. The results are B(tau --> e nu) = (17.51+/-0.39)% and B(tau --> mu nu) = (17.02+/-0.31)%. The ratio of the muon and electron couplings to the weak charged current is measured to be g(mu)/g(e) = 1.000+/-0.013, satisfying e-mu universality. The average leptonic branching fraction corrected to the value for a massless lepton, assuming e-mu universality, is found to be B(tau --> l nu) = (17.50+/-0.25)%.
Power Corrections to Event Shapes with Mass-Dependent Operators
2013
We introduce an operator depending on the "transverse velocity'' r that describes the effect of hadron masses on the leading 1/Q power correction to event-shape observables. Here, Q is the scale of the hard collision. This work builds on earlier studies of mass effects by Salam and Wicke [J. High Energy Phys. 05 (2001) 061] and of operators by Lee and Sterman [Phys. Rev. D 75, 014022 (2007)]. Despite the fact that different event shapes have different hadron mass dependence, we provide a simple method to identify universality classes of event shapes whose power corrections depend on a common nonperturbative parameter. We also develop an operator basis to show that at a fixed value of Q, the…
Test of lepton flavour universality in K+→ℓ+ν decays
2011
Abstract A precision test of lepton flavour universality has been performed by measuring the ratio R K of kaon leptonic decay rates K + → e + ν and K + → μ + ν in a sample of 59 813 reconstructed K + → e + ν candidates with ( 8.71 ± 0.24 ) % background contamination. The result R K = ( 2.487 ± 0.013 ) × 10 − 5 is in agreement with the Standard Model expectation.
Measurement of the B0→D*−π+π−π+ branching fraction
2016
Using a sample of (470.9 +- 2.8) x 10^6 BB-bar pairs, we measure the decay branching fraction B(B^0 -> D^*- pi^+ pi^- pi^+) = (7.26 +- 0.11 +- 0.31) x 10^-3, where the first uncertainty is statistical and the second is systematic. Our measurement will be helpful in studies of lepton universality by measuring B(B^0 -> D^*- tau^+ nu_tau) using tau^+ -> pi^+ pi^- pi^+ nu-bar_tau decays, normalized to B(B^0 -> D^*- pi^+ pi^- pi^+.
β-Decay Half-Lives of 110 Neutron-Rich Nuclei across theN=82Shell Gap: Implications for the Mechanism and Universality of the AstrophysicalrProcess
2015
The $\ensuremath{\beta}$-decay half-lives of 110 neutron-rich isotopes of the elements from $_{37}\mathrm{Rb}$ to $_{50}\mathrm{Sn}$ were measured at the Radioactive Isotope Beam Factory. The 40 new half-lives follow robust systematics and highlight the persistence of shell effects. The new data have direct implications for $r$-process calculations and reinforce the notion that the second ($A\ensuremath{\approx}130$) and the rare-earth-element ($A\ensuremath{\approx}160$) abundance peaks may result from the freeze-out of an $(n,\ensuremath{\gamma})\ensuremath{\rightleftarrows}(\ensuremath{\gamma},n)$ equilibrium. In such an equilibrium, the new half-lives are important factors determining t…
Euler integral as a source of chaos in the three–body problem
2022
In this paper we address, from a purely numerical point of view, the question, raised in [20, 21], and partly considered in [22, 9, 3], whether a certain function, referred to as "Euler Integral", is a quasi-integral along the trajectories of the three-body problem. Differently from our previous investigations, here we focus on the region of the "unperturbed separatrix", which turns to be complicated by a collision singularity. Concretely, we reduce the Hamiltonian to two degrees of freedom and, after fixing some energy level, we discuss in detail the resulting three-dimensional phase space around an elliptic and an hyperbolic periodic orbit. After measuring the strength of variation of the…
Semipredictable dynamical systems
2015
A new class of deterministic dynamical systems, termed semipredictable dynamical systems, is presented. The spatiotemporal evolution of these systems have both predictable and unpredictable traits, as found in natural complex systems. We prove a general result: The dynamics of any deterministic nonlinear cellular automaton (CA) with $p$ possible dynamical states can be decomposed at each instant of time in a superposition of $N$ layers involving $p_{0}$, $p_{1}$,... $p_{N-1}$ dynamical states each, where the $p_{k\in \mathbb{N}}$, $k \in [0, N-1]$ are divisors of $p$. If the divisors coincide with the prime factors of $p$ this decomposition is unique. Conversely, we also prove that $N$ CA w…