A new kind of Lax-Oleinik type operator with parameters for time-periodic positive definite Lagrangian systems

In this paper we introduce a new kind of Lax-Oleinik type operator with parameters associated with positive definite Lagrangian systems for both the time-periodic case and the time-independent case. On one hand, the new family of Lax-Oleinik type operators with an arbitrary $u\in C(M,\mathbb{R}^1)$ as initial condition converges to a backward weak KAM solution in the time-periodic case, while it was shown by Fathi and Mather that there is no such convergence of the Lax-Oleinik semigroup. On the other hand, the new family of Lax-Oleinik type operators with an arbitrary $u\in C(M,\mathbb{R}^1)$ as initial condition converges to a backward weak KAM solution faster than the Lax-Oleinik semigroup in the time-independent case.Comment: We give a new definition of Lax-Oleinik type operator; add some reference

Weak KAM for commuting Hamiltonians

For two commuting Tonelli Hamiltonians, we recover the commutation of the Lax-Oleinik semi-groups, a result of Barles and Tourin ([BT01]), using a direct geometrical method (Stoke's theorem). We also obtain a "generalization" of a theorem of Maderna ([Mad02]). More precisely, we prove that if the phase space is the cotangent of a compact manifold then the weak KAM solutions (or viscosity solutions of the critical stationary Hamilton-Jacobi equation) for G and for H are the same. As a corrolary we obtain the equality of the Aubry sets, of the Peierls barrier and of flat parts of Mather's $\alpha$ functions. This is also related to works of Sorrentino ([Sor09]) and Bernard ([Ber07b]).Comment: 23 pages, accepted for publication in NonLinearity (january 29th 2010). Minor corrections, fifth part added on Mather's $\alpha$ function (or effective Hamiltonian

Arnold diffusion in the dynamics of a 4-machine power system undergoing a large fault

We focus on the seemingly complicated dynamics of a four-machine power system which is undergoing a sudden fault. Adopting a Hamiltonian (energy) formulation, we consider the system as an interconnection of (one degree of freedom) subsystems. Under certain configuration (a star network) and parameter values we establish the presence of Arnold diffusion which entails periodic, almost periodic, and complicated nonperiodic dyanmics all simultaneously present; and erratic transfer of energies between the subsystems. In section 1 we introduce the transient stability problem in a mathematical setting and explain what our results mean in the power systems context. Section 2 provides insights into Arnold diffusion and summarizes its mathematical formulation as in [8], [1]. Section 3 gives conditions for which Arnold diffusion arises on certain energy levels of the swing equations. These conditions are verified analytically in the case when all but one subsystem (machine) undergo relatively small oscillations

Workplace Stressors and Coping Strategies Among Public Hospital Nurses in Medan, Indonesia

Background: Nursing is considered as a stressful job when compared with other jobs. Prolonged stress without effective coping strategies affects not only nurses\u27 occupational life but also their nursing competencies. Medan is the biggest city in Sumatera Island of Indonesia. Two tertiary public hospital nurses in this city hold the responsibility in providing excellent care to their patients. Objective: To investigate the relationships between the nurse\u27s workplace stressors and the coping strategies used. Method: The descriptive correlational study was conducted to examine the relationships between workplace stressors and the coping strategies used in nurses of two public hospitals in Medan. The sample size of 126 nurses was drawn from selected in-patient units. Data were collected by using self-report questionnaires and focus group interview. The majority of subjects experienced low workplace stressors, where death/dying was the most commonly reported workplace stressor followed by workload. Religion was the most commonly used coping strategy. Result: Significant correlations were found between subscales of workplace stressors and coping strategies. Most of subjects used emotion-focused and dysfunctional coping strategies rather than problem-focused coping strategies. Conclusion: The nurse administrators in the hospitals need to advocate their in order to use problem-focused coping strategies more frequent than emotion-focused and dysfunctional coping strategies when dealing with workplace stressors

Particle dynamics inside shocks in Hamilton-Jacobi equations

Characteristics of a Hamilton-Jacobi equation can be seen as action minimizing trajectories of fluid particles. For nonsmooth "viscosity" solutions, which give rise to discontinuous velocity fields, this description is usually pursued only up to the moment when trajectories hit a shock and cease to minimize the Lagrangian action. In this paper we show that for any convex Hamiltonian there exists a uniquely defined canonical global nonsmooth coalescing flow that extends particle trajectories and determines dynamics inside the shocks. We also provide a variational description of the corresponding effective velocity field inside shocks, and discuss relation to the "dissipative anomaly" in the limit of vanishing viscosity.Comment: 15 pages, no figures; to appear in Philos. Trans. R. Soc. series

Periodic orbits of period 3 in the disc

Let f be an orientation preserving homeomorphism of the disc D2 which possesses a periodic point of period 3. Then either f is isotopic, relative the periodic orbit, to a homeomorphism g which is conjugate to a rotation by 2 pi /3 or 4 pi /3, or f has a periodic point of least period n for each n in N*.Comment: 7 page

Analysis of Droplet Train/Moving Substrate Interactions in Ink-Jetting Processes

Ink-jetting technology has been applied to several processes in solid free-form fabrication (SFF) wherein droplets impinge onto a substrate to deposit the build material. Droplet impact behaviour on a surface has been the interest of many researchers; however, few studies have been undertaken to investigate the interaction of droplets with the moving substrate. This paper reports the impact behaviour of the droplets jetted at different frequencies onto a substrate moving over a range of velocities. The phenomena associated with the interaction were classified into three main regimes.Mechanical Engineerin