588,200 research outputs found
Periodic orbits close to elliptic tori and applications to the three-body problem
We prove, under suitable non-resonance and non-degeneracy ``twist''
conditions, a Birkhoff-Lewis type result showing the existence of infinitely
many periodic solutions, with larger and larger minimal period, accumulating
onto elliptic invariant tori (of Hamiltonian systems). We prove the
applicability of this result to the spatial planetary three-body problem in the
small eccentricity-inclination regime. Furthermore, we find other periodic
orbits under some restrictions on the period and the masses of the ``planets''.
The proofs are based on averaging theory, KAM theory and variational methods.
(Supported by M.U.R.S.T. Variational Methods and Nonlinear Differential
Equations.
Nonlinear stage of Benjamin-Feir instability in forced/damped deep water waves
We study a three-wave truncation of a recently proposed damped/forced
high-order nonlinear Schr\"odinger equation for deep-water gravity waves under
the effect of wind and viscosity. The evolution of the norm (wave-action) and
spectral mean of the full model are well captured by the reduced dynamics.
Three regimes are found for the wind-viscosity balance: we classify them
according to the attractor in the phase-plane of the truncated system and to
the shift of the spectral mean. A downshift can coexist with both net forcing
and damping, i.e., attraction to period-1 or period-2 solutions. Upshift is
associated with stronger winds, i.e., to a net forcing where the attractor is
always a period-1 solution. The applicability of our classification to
experiments in long wave-tanks is verified.Comment: 8 pages, 4 figure
A STOCHASTIC SIMULATION-BASED HYBRID INTERVAL FUZZY PROGRAMMING APPROACH FOR OPTIMIZING THE TREATMENT OF RECOVERED OILY WATER
In this paper, a stochastic simulation-based hybrid interval fuzzy programming (SHIFP) approach
is developed to aid the decision-making process by solving fuzzy linear optimization problems.
Fuzzy set theory, probability theory, and interval analysis are integrated to take into account the
effect of imprecise information, subjective judgment, and variable environmental conditions. A
case study related to oily water treatment during offshore oil spill clean-up operations is conducted
to demonstrate the applicability of the proposed approach. The results suggest that producing a
random sequence of triangular fuzzy numbers in a given interval is equivalent to a normal
distribution when using the centroid defuzzification method. It also shows that the defuzzified
optimal solutions follow the normal distribution and range from 3,000-3,700 tons, given the
budget constraint (CAD 110,000-150,000). The normality seems to be able to propagate
throughout the optimization process, yet this interesting finding deserves more in-depth study
and needs more rigorous mathematical proof to validate its applicability and feasibility. In
addition, the optimal decision variables can be categorized into several groups with different
probability such that decision makers can wisely allocate limited resources with higher
confidence in a short period of time. This study is expected to advise the industries and
authorities on how to distribute resources and maximize the treatment efficiency of oily
water in a short period of time, particularly in the context of harsh environments
The evolutionary stage of an RRs star SX Phe
The evolutionary stage for a short period variable SX Phe was investigated. It was assumed that SX Phe is a mixed star with low metal abundance in which the material was mixed after the star evolved off the main sequence, and is in the second hydrogen burning stage. The validity of this hypothesis was examined by constructing two evolutionary sequences with (X,Z,M/solar mass) = (0.5,0.004,0.75) and (0.5,0.001,0.70) in the hydrogen burning phase and computed the pulsation period. Agreement between theoretical results and observational data was sufficient to conclude that the mixed model is actually adequate for SX Phe. The applicability of this model to other RRs stars is briefly discussed
- …