The problem of two fixed centers: bifurcation diagram for positive energies

We give a comprehensive analysis of the Euler-Jacobi problem of motion in the field of two fixed centers with arbitrary relative strength and for positive values of the energy. These systems represent nontrivial examples of integrable dynamics and are analysed from the point of view of the energy-momentum mapping from the phase space to the space of the integration constants. In this setting, we describe the structure of the scattering trajectories in phase space and derive an explicit description of the bifurcation diagram, i.e., the set of critical value of the energy-momentum map.

Linear amplification of marginally neutral baroclinic waves

Baroclinic wave development is investigated for unstable parallel shear flows in the limit of vanishing normal-mode growth rate. This development is described in terms of the propagation and interaction mechanisms of two coherent structures, called counter-propagating Rossby waves (CRWs). It is shown that, in this limit of vanishing normal-mode growth rate, arbitrary initial conditions produce sustained linear amplification of the marginally neutral normal mode (mNM). This linear excitation of the mNM is subsequently interpreted in terms of a resonance phenomenon. Moreover, while the mathematical character of the normal-mode problem changes abruptly as the bifurcation point in the dispersion diagram is encountered and crossed, it is shown that from an initial-value viewpoint, this transition is smooth. Consequently, the resonance interpretation remains relevant (albeit for a finite time) for wavenumbers slightly different from the ones defining cut-off points. The results are further applied to a two-layer version of the classic Eady model in which the upper rigid lid has been replaced by a simple stratosphere.

Monte Carlo phase diagram for diblock copolymer melts

A partial phase diagram is constructed for diblock copolymer melts using lattice-based Monte Carlo simulations. This is done by locating the order-disorder transition (ODT) with the aid of a recently proposed order parameter and identifying the ordered phase over a wide range of copolymer compositions (0.2 <= f <= 0.8). Consistent with experiments, the disordered phase is found to exhibit direct first-order transitions to each of the ordered morphologies. This includes the spontaneous formation of a perforated-lamellar phase, which presumably forms in place of the gyroid morphology due to finite-size and/or nonequilibrium effects. Also included in our study is a detailed examination of disordered cylinder-forming (f=0.3) diblock copolymers, revealing a substantial degree of pretransitional chain stretching and short-range order that set in well before the ODT, as observed previously in analogous studies on lamellar-forming (f=0.5) molecules. (c) 2006 American Institute of Physics.

Monte Carlo phase diagram for diblock copolymer melts

The phase diagram for diblock copolymer melts is evaluated from lattice-based Monte Carlo simulations using parallel tempering, improving upon earlier simulations that used sequential temperature scans. This new approach locates the order-disorder transition (ODT) far more accurately by the occurrence of a sharp spike in the heat capacity. The present study also performs a more thorough investigation of finite-size effects, which reveals that the gyroid (G) morphology spontaneously forms in place of the perforated-lamellar (PL) phase identified in the earlier study. Nevertheless, there still remains a small region where the PL phase appears to be stable. Interestingly, the lamellar (L) phase next to this region exhibits a small population of transient perforations, which may explain previous scattering experiments suggesting a modulated-lamellar (ML) phase.

Highly asymmetric phase diagram of a poly(1,2-octylene oxide)-poly(ethylene oxide) diblock copolymer system comprising a brush-like poly(1,2-octylene oxide) block

The phase diagram of a series of poly(1,2-octylene oxide)-poly(ethylene oxide) (POO-PEO) diblock copolymers is determined by small-angle X-ray scattering. The Flory-Huggins interaction parameter was measured by small-angle neutron scattering. The phase diagram is highly asymmetric due to large conformational asymmetry that results from the hexyl side chains in the POO block. Non-lamellar phases (hexagonal and gyroid) are observed near f(PEO) = 0.5, and the lamellar phase is observed for f(PEO) >= 0.5.

Steady periodic water waves with constant vorticity: regularity and local bifurcation

This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is transformed into a quasilinear pseudodifferential equation for a periodic function of one variable. The new formulation leads to a regularity result and, by use of bifurcation theory, to the existence of waves of small amplitude even in the presence of stagnation points in the flow.

Monte Carlo phase diagram for a polydisperse diblock copolymer melt

The phase diagram for an AB diblock copolymer melt with polydisperse A blocks and monodisperse B blocks is evaluated using lattice-based Monte Carlo simulations. Experiments on this system have shown that the A-block polydispersity shifts the order-order transitions (OOTs) towards higher A-monomer content, while the order-disorder transition (ODT) moves towards higher temperatures when the A blocks form the minority domains and lower temperatures when the A blocks form the matrix. Although self-consistent field theory (SCFT) correctly accounts for the change in the OOTs, it incorrectly predicts the ODT to shift towards higher temperatures at all diblock copolymer compositions. In contrast, our simulations predict the correct shifts for both the OOTs and the ODT. This implies that polydispersity amplifies the fluctuation-induced correction to the mean-field ODT, which we attribute to a reduction in packing frustration. Consistent with this explanation, polydispersity is found to enhance the stability of the perforated-lamellar phase.

Bifurcation Analysis of Eigenstructure Assignment Control in a Simple Nonlinear Aircraft Model

Aircraft systems are highly nonlinear and time varying. High-performance aircraft at high angles of incidence experience undesired coupling of the lateral and longitudinal variables, resulting in departure from normal controlled � ight. The construction of a robust closed-loop control that extends the stable and decoupled � ight envelope as far as possible is pursued. For the study of these systems, nonlinear analysis methods are needed. Previously, bifurcation techniques have been used mainly to analyze open-loop nonlinear aircraft models and to investigate control effects on dynamic behavior. Linear feedback control designs constructed by eigenstructure assignment methods at a � xed � ight condition are investigated for a simple nonlinear aircraft model. Bifurcation analysis, in conjunction with linear control design methods, is shown to aid control law design for the nonlinear system.

Humanitarian law, human rights law and the bifurcation of armed conflict

This article offers a fresh examination of the distinction drawn in international humanitarian law (IHL) between international and non-international armed conflicts. In particular, it considers this issue from the under-explored perspective of the influence of international human rights law (IHRL). It is demonstrated how, over time, the effect of IHRL on this distinction in IHL has changed dramatically. Whereas traditionally IHRL encouraged the partial elimination of the distinction between types of armed conflict, more recently it has been invoked in debates in a manner that would preserve what remains of the distinction. By exploring this important issue, it is hoped that the present article will contribute to the ongoing debates regarding the future development of the law of non-international armed conflict.

The transaction cost economics theory of the family firm: family-based human asset specificity and the bifurcation bias

We develop a transaction cost economics theory of the family firm, building upon the concepts of family-based asset specificity, bounded rationality, and bounded reliability. We argue that the prosperity and survival of family firms depend on the absence of a dysfunctional bifurcation bias. The bifurcation bias is an expression of bounded reliability, reflected in the de facto asymmetric treatment of family vs. nonfamily assets (especially human assets). We propose that absence of bifurcation bias is critical to fostering reliability in family business functioning. Our study ends the unproductive divide between the agency and stewardship perspectives of the family firm, which offer conflicting accounts of this firm type's functioning. We show that the predictions of the agency and stewardship perspectives can be usefully reconciled when focusing on how family firms address the bifurcation bias or fail to do so.