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

A Theory of Optimum Tariff Under Revenue Constraint.

This paper analyzes the revenue-constrained optimum tariff problem. When a fixed level of tax revenue has to be collected only from tariffs, an efficient resource allocation can not be achieved by any tariff structure. Thus we need to find the optimum tariff structure as the second best resource allocation.TAXATION ; TRADE ; ECONOMIC THEORY

Growth suppression of antibiotic-resistant Salmonella typhimurium DT104 by a non-DT104 strain in vitro

Growth suppression of antibiotic-resistant Salmonella typhimurium DT104 by a non-DT104 strain was investigated in vitro. Chromosomal mutants of eight antibiotic-resistant DT104 strains were generated by sub-culturing on desoxycholate hydrogen sulfide lactose agar containing 25 µg/ml of nalidixic acid. Low counts of each of these mutants (designated as “minority cultures”) were inoculated into 24-h cultures of a non-DT104 S. typhimurium strain (designated as “majority culture”) to test the ability of the majority culture to suppress the multiplication of the minority culture. Multiplication of small numbers of the antibiotic-resistant DT104 strains was significantly (P < 0.05) prevented when the DT104s were added to 24-h brain heart infusion cultures of the non-DT104 strain. This observation has practical implications for the control of the menacing antibiotic-resistant Salmonella typhimurium DT104

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

Energy Centroids of Spin II States by Random Two-body Interactions

In this paper we study the behavior of energy centroids (denoted as $\bar{E_I}$) of spin $I$ states in the presence of random two-body interactions, for systems ranging from very simple systems (e.g. single-$j$ shell for very small $j$) to very complicated systems (e.g., many-$j$ shells with different parities and with isospin degree of freedom). Regularities of $\bar{E_I}$'s discussed in terms of the so-called geometric chaoticity (or quasi-randomness of two-body coefficients of fractional parentage) in earlier works are found to hold even for very simple systems in which one cannot assume the geometric chaoticity. It is shown that the inclusion of isospin and parity does not "break" the regularities of $\bar{E_I}$'s.Comment: four figures. to appear in Physical Review

Magneto-hydrodynamic Simulations of a Jet Drilling an HI Cloud: Shock Induced Formation of Molecular Clouds and Jet Breakup

The formation mechanism of the jet-aligned CO clouds found by NANTEN CO observations is studied by magnetohydrodynamical (MHD) simulations taking into account the cooling of the interstellar medium. Motivated by the association of the CO clouds with the enhancement of HI gas density, we carried out MHD simulations of the propagation of a supersonic jet injected into the dense HI gas. We found that the HI gas compressed by the bow shock ahead of the jet is cooled down by growth of the cooling instability triggered by the density enhancement. As a result, cold dense sheath is formed around the interface between the jet and the HI gas. The radial speed of the cold, dense gas in the sheath is a few km/s almost independent of the jet speed. Molecular clouds can be formed in this region. Since the dense sheath wrapping the jet reflects waves generated in the cocoon, the jet is strongly perturbed by the vortices of the warm gas in the cocoon, which breaks up the jet and forms a secondary shock in the HI-cavity drilled by the jet. The particle acceleration at the shock can be the origin of radio and X-ray filaments observed near the eastern edge of W50 nebula surrounding the galactic jet source SS433.Comment: 30 pages, 16 figure