Spectral and formal stability criteria of spatially inhomogeneous stationary solutions to the Vlasov equation for the Hamiltonian mean-field model

Stability of spatially inhomogeneous solutions to the Vlasov equation is investigated for the Hamiltonian mean-field model to provide the spectral stability criterion and the formal stability criterion in the form of necessary and sufficient conditions. These criteria determine stability of spatially inhomogeneous solutions whose stability has not been decided correctly by using a less refined formal stability criterion. It is shown that some of such solutions can be found in a family of stationary solutions to the Vlasov equation, which is parametrized with macroscopic quantities and has a two-phase coexistence region in the parameter space.Comment: 17 pages, 4 figures, text modified, section VE added, references added, Accepted for publication in Phys. Rev.

Nonlinear response for external field and perturbation in the Vlasov system

A nonlinear response theory is provided by use of the transient linearization method in the spatially one-dimensional Vlasov systems. The theory inclusively gives responses to external fields and to perturbations for initial stationary states, and is applicable even to the critical point of a second order phase transition. We apply the theory to the Hamiltonian mean-field model, a toy model of a ferromagnetic body, and investigate the critical exponent associated with the response to the external field at the critical point in particular. The obtained critical exponent is nonclassical value 3/2, while the classical value is 3. However, interestingly, one scaling relation holds with another nonclassical critical exponent of susceptibility in the isolated Vlasov systems. Validity of the theory is numerically confirmed by directly simulating temporal evolutions of the Vlasov equation.Comment: 15 pages, 8 figures, accepted for publication in Phys. Rev. E, Lemma 2 is correcte

Landau like theory for universality of critical exponents in quasistatioary states of isolated mean-field systems

An external force dynamically drives an isolated mean-field Hamiltonian system to a long-lasting quasistationary state, whose lifetime increases with population of the system. For second order phase transitions in quasistationary states, two non-classical critical exponents have been reported individually by using a linear and a nonlinear response theories in a toy model. We provide a simple way to compute the critical exponents all at once, which is an analog of the Landau theory. The present theory extends universality class of the non-classical exponents to spatially periodic one-dimensional systems, and shows that the exponents satisfy a classical scaling relation inevitably by using a key scaling of momentum.Comment: 7 page

Non-mean-field Critical Exponent in a Mean-field Model : Dynamics versus Statistical Mechanics

The mean-field theory tells that the classical critical exponent of susceptibility is the twice of that of magnetization. However, the linear response theory based on the Vlasov equation, which is naturally introduced by the mean-field nature, makes the former exponent half of the latter for families of quasistationary states having second order phase transitions in the Hamiltonian mean-field model and its variances. We clarify that this strange exponent is due to existence of Casimir invariants which trap the system in a quasistationary state for a time scale diverging with the system size. The theoretical prediction is numerically confirmed by $N$-body simulations for the equilibrium states and a family of quasistationary states.Comment: 6 pages, 3 figure

Dynamical pattern formations in two dimensional fluid and Landau pole bifurcation

A phenomenological theory is proposed to analyze the asymptotic dynamics of perturbed inviscid Kolmogorov shear flows in two dimensions. The phase diagram provided by the theory is in qualitative agreement with numerical observations, which include three phases depending on the aspect ratio of the domain and the size of the perturbation: a steady shear flow, a stationary dipole, and four traveling vortices. The theory is based on a precise study of the inviscid damping of the linearized equation and on an analysis of nonlinear effects. In particular, we show that the dominant Landau pole controlling the inviscid damping undergoes a bifurcation, which has important consequences on the asymptotic fate of the perturbation.Comment: 9 pages, 7 figure

Exploring Learning Problems of Filipino Nurse Candidates Working in Japan: Based on the Results of a Practice National Board Examination of Japan Given in English

This article investigates the status of the education and training of Filipino nurse candidates who have been working in Japan under the Japan-Philippine Economic Partnership Agreement (JPEPA). A survey was conducted among Filipino nurse candidates, using a practice examination based on the English version of Japan’s National Board Examination for Registered Nurses in 2009. Categorized by area, the mean correct answer rate for nursing-related questions ranged between 61% and 73%; the rate for questions concerning basic knowledge of body functions and diseases ranged between 55% and 57%. There was a large gap in terms of the results of the examination between those who had previously seen the exam questions and those who had never seen them. While 57.1% of those who had previously seen the questions satisfied the acceptance criteria, only 23.7%of those who had never viewed the test satisfied it. Based on these results, the factors which serve as obstacles that Filipino nurse candidates encounter in passing the national examination include not only difficulties in acquiring Japanese proficiency but also differences between Japan and the Philippines in respect to the nursing education curriculum and basic nursing policies

Exploring Learning Problems of Filipino Nurse Candidates Working in Japan: Based on the Results of a Practice National Board Examination of Japan Given in English

This article investigates the status of the education and training of Filipino nurse candidates who have been working in Japan under the Japan-Philippine Economic Partnership Agreement (JPEPA). A survey was conducted among Filipino nurse candidates, using a practice examination based on the English version of Japan’s National Board Examination for Registered Nurses in 2009. Categorized by area, the mean correct answer rate for nursing-related questions ranged between 61% and 73%; the rate for questions concerning basic knowledge of body functions and diseases ranged between 55% and 57%. There was a large gap in terms of the results of the examination between those who had previously seen the exam questions and those who had never seen them. While 57.1% of those who had previously seen the questions satisfied the acceptance criteria, only 23.7%of those who had never viewed the test satisfied it. Based on these results, the factors which serve as obstacles that Filipino nurse candidates encounter in passing the national examination include not only difficulties in acquiring Japanese proficiency but also differences between Japan and the Philippines in respect to the nursing education curriculum and basic nursing policies

Full particle orbit effects in regular and stochastic magnetic fields

We present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present the particle orbits can be stochastic even though the magnetic field line orbits are not stochastic. The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the $q$-profile implies the existence of magnetic ITBs which correspond to shearless flux surfaces located in the vicinity of the $q$-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations due to separatrix reconnection. We show that a similar but more complex scenario appears in the case of particle orbits that depends in a non-trivial way on the energy and pitch angle of the particles.Comment: 25 pages, accepted for publication in Phys. Plasma