Spin dynamics for the Lebwohl-Lasher model

A spin dynamics algorithm, combining checkerboard updating and a rotation algorithm based on the local second-rank ordering field, is developed for the Lebwohl-Lasher model of liquid crystals. The method is shown to conserve energy well and to generate simulation averages that are consistent with those obtained by Monte Carlo simulation. However, care must be taken to avoid the undesirable effects of director rotation, and a method for doing this is proposed

The interplay between financial regulations, resilience, and growth

Interconnectedness has been an important source of market failures, leading to the recent financial crisis. Large financial institutions tend to have similar exposures and thus exert externalities on each other through various mechanisms. Regulators have responded by putting in place more regulations with many layers of regulatory complexity, leading to ambiguity and market manipulation. Mispricing risk in complex models and the arbitrage opportunities through the regulatory loopholes have provided incentives for certain activities to be more concentrated in the regulated entities and for other activities to leave the banking into new shadow banking areas. How can we design an effective regulatory framework that would perfectly rule out bank runs and TBTF and to do so without introducing incentives for financial firms to take excessive risk? It is important for financial regulations to be coordinated across regulatory entities and jurisdictions and for financial regulations to be forward looking, rather than aiming to address problems of the past

NVU dynamics. III. Simulating molecules at constant potential energy

This is the final paper in a series that introduces geodesic molecular dynamics at constant potential energy. This dynamics is entitled NVU dynamics in analogy to standard energy-conserving Newtonian NVE dynamics. In the first two papers [Ingebrigtsen et al., J. Chem. Phys. 135, 104101 (2011); ibid, 104102 (2011)], a numerical algorithm for simulating geodesic motion of atomic systems was developed and tested against standard algorithms. The conclusion was that the NVU algorithm has the same desirable properties as the Verlet algorithm for Newtonian NVE dynamics, i.e., it is time-reversible and symplectic. Additionally, it was concluded that NVU dynamics becomes equivalent to NVE dynamics in the thermodynamic limit. In this paper, the NVU algorithm for atomic systems is extended to be able to simulate geodesic motion of molecules at constant potential energy. We derive an algorithm for simulating rigid bonds and test this algorithm on three different systems: an asymmetric dumbbell model, Lewis-Wahnstrom OTP, and rigid SPC/E water. The rigid bonds introduce additional constraints beyond that of constant potential energy for atomic systems. The rigid-bond NVU algorithm conserves potential energy, bond lengths, and step length for indefinitely long runs. The quantities probed in simulations give results identical to those of Nose-Hoover NVT dynamics. Since Nose-Hoover NVT dynamics is known to give results equivalent to those of NVE dynamics, the latter results show that NVU dynamics becomes equivalent to NVE dynamics in the thermodynamic limit also for molecular systems.Comment: 14 pages, 12 figure

Information acquisition and financial contagion.

This paper incorporates costly voluntary acquisition of information à la Nikitin and Smith (2007) [Nikitin, M., Smith, R.T., 2007. Information acquisition, coordination, and fundamentals in a financial crisis. Journal of Banking and Finance, in press, doi:10.1016/j.jbankfin.2007.04.031], in a framework similar to Allen and Gale (2000) [Allen, F., Gale, D., 2000. Financial contagion. Journal of Political Economy 108, 1–33], without relying on any unexpected shock to model contagion. In this framework, contagion and financial crises are the result of information gathering by depositors, weak fundamentals and an incomplete market structure of banks. It also shows how financial systems entering a recession can affect others with apparently stronger economic conditions (contagion). Finally, this is the first paper to investigate the effectiveness of the Contingent Credit Line procedures, introduced by the IMF at the end of the nineties, as a mechanism to prevent the propagation of crises.Central Bank; Contingent credit line; Financial contagion; Fundamentals; Verification equilibrium;

Government guarantees and financial stability

Banks are intrinsically fragile because of their role as liquidity providers. This results in under-provision of liquidity. We analyze the effect of government guarantees on the interconnection between banks' liquidity creation and likelihood of runs in a global-game model, where banks' and depositors' behavior are endogenous and affected by the amount and form of guarantee. The main insight of our analysis is that guarantees are welfare improving because they induce banks to improve liquidity provision, although that sometimes increases the likelihood of runs or creates distortions in banks' behavior

Abelian Gauge Theory in de Sitter Space

Quantization of spinor and vector free fields in 4-dimensional de Sitter space-time, in the ambient space notation, has been studied in the previous works. Various two-points functions for the above fields are presented in this paper. The interaction between the spinor field and the vector field is then studied by the abelian gauge theory. The U(1) gauge invariant spinor field equation is obtained in a coordinate independent way notation and their corresponding conserved currents are computed. The solution of the field equation is obtained by use of the perturbation method in terms of the Green's function. The null curvature limit is discussed in the final stage.Comment: 10 pages, typos corrected, reference adde

Evaluating the provision of school performance information for school choice

We develop and implement a framework for determining the optimal performance metrics to help parents choose a school. This approach combines the three major critiques of the usefulness of performance tables into a natural metric. We implement this for 500,000 students in England for a range of performance measures. Using performance tables is strongly better than choosing at random: a child who attends the highest ex ante performing school within their choice set will ex post do better than the average outcome in their choice set twice as often as they will do worse

Effective mass overshoot in single degree of freedom mechanical systems with a particle damper

We study the response of a single degree of freedom mechanical system composed of a primary mass, M, a linear spring, a viscous damper and a particle damper. The particle damper consists in a prismatic enclosure of variable height that contains spherical grains (total mass m_p). Contrary to what it has been discussed in previous experimental and simulation studies, we show that, for small containers, the system does not approach the fully detuned mass limit in a monotonous way. Rather, the system increases its effective mass up and above M+m_p before reaching this expected limiting value (which is associated with the immobilization of the particles due to a very restrictive container). Moreover, we show that a similar effect appears in the tall container limit where the system reaches effective masses below the expected asymptotic value M. We present a discussion on the origin of these overshoot responses and the consequences for industrial applications.Comment: 16 pages, 6 figure

The Allen-Cahn equation with dynamic boundary conditions and mass constraints

The Allen-Cahn equation, coupled with dynamic boundary conditions, has recently received a good deal of attention. The new issue of this paper is the setting of a rather general mass constraint which may involve either the solution inside the domain or its trace on the boundary. The system of nonlinear partial differential equations can be formulated as variational inequality. The presence of the constraint in the evolution process leads to additional terms in the equation and the boundary condition containing a suitable Lagrange multiplier. A well-posedness result is proved for the related initial value problem.Comment: Key words: Allen-Cahn equation, dynamic boundary condition, mass constraint, variational inequality, Lagrange multiplie