Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O(2) sigma model

In the presence of a chemical potential, the physics of level crossings leads to singularities at zero temperature, even when the spatial volume is finite. These singularities are smoothed out at a finite temperature but leave behind nontrivial finite size effects which must be understood in order to extract thermodynamic quantities using Monte Carlo methods, particularly close to critical points. We illustrate some of these issues using the classical nonlinear O(2) sigma model with a coupling β and chemical potential μ on a 2+1-dimensional Euclidean lattice. In the conventional formulation this model suffers from a sign problem at nonzero chemical potential and hence cannot be studied with the Wolff cluster algorithm. However, when formulated in terms of the worldline of particles, the sign problem is absent, and the model can be studied efficiently with the "worm algorithm." Using this method we study the finite size effects that arise due to the chemical potential and develop an effective quantum mechanical approach to capture the effects. As a side result we obtain energy levels of up to four particles as a function of the box size and uncover a part of the phase diagram in the (β,μ) plane. © 2010 The American Physical Society.

[N]pT ensemble and finite-size-scaling study of the critical isostructural transition in the generalized exponential model of index 4.

First-order transitions of system where both lattice site occupancy and lattice spacing fluctuate, such as cluster crystals, cannot be efficiently studied by traditional simulation methods, which necessarily fix one of these two degrees of freedom. The difficulty, however, can be surmounted by the generalized [N]pT ensemble [J. Chem. Phys. 136, 214106 (2012)]. Here we show that histogram reweighting and the [N]pT ensemble can be used to study an isostructural transition between cluster crystals of different occupancy in the generalized exponential model of index 4 (GEM-4). Extending this scheme to finite-size scaling studies also allows us to accurately determine the critical point parameters and to verify that it belongs to the Ising universality class.

Leveraging nanoscale plasmonic modes to achieve reproducible enhancement of light.

The strongly enhanced and localized optical fields that occur within the gaps between metallic nanostructures can be leveraged for a wide range of functionality in nanophotonic and optical metamaterial applications. Here, we introduce a means of precise control over these nanoscale gaps through the application of a molecular spacer layer that is self-assembled onto a gold film, upon which gold nanoparticles (NPs) are deposited electrostatically. Simulations using a three-dimensional finite element model and measurements from single NPs confirm that the gaps formed by this process, between the NP and the gold film, are highly reproducible transducers of surface-enhanced resonant Raman scattering. With a spacer layer of roughly 1.6 nm, all NPs exhibit a strong Raman signal that decays rapidly as the spacer layer is increased.

Explanatory Model for the Use of Traditional Medicines in Kilimanjaro, Tanzania

Introduction: Traditional medicines are one of the most important means of achieving total health care coverage globally, and their importance in Tanzania extends beyond the impoverished rural areas. Their use remains high even in urban settings among the educated middle and upper classes. They are a critical component healthcare in Tanzania, but they also can have harmful side effects. Therefore we sought to understand the decision-making and reasoning processes by building an explanatory model for the use of traditional medicines in Tanzania.

Methods: We conducted a mixed-methods study between December 2013 and June 2014 in the Kilimanjaro Region of Tanzania. Using purposive sampling methods, we conducted focus group discussions (FGDs) and in-depth interviews of key informants, and the qualitative data were analyzed using an inductive Framework Method. A structured survey was created, piloted, and then administered it to a random sample of adults. We reported upon the reliability and validity of the structured survey, and we used triangulation from multiple sources to synthesize the qualitative and quantitative data.

Results: A total of five FGDs composed of 59 participants and 27 in-depth interviews were conducted in total. 16 of the in-depth interviews were with self-described traditional practitioners or herbal vendors. We identified five major thematic categories that relate to the decision to use traditional medicines in Kilimanjaro: healthcare delivery, disease understanding, credibility of the traditional practices, health status, and strong cultural beliefs.

A total of 473 participants (24.1% male) completed the structured survey. The most common reasons for taking traditional medicines were that they are more affordable (14%, 12.0-16.0), failure of hospital medicines (13%, 11.1-15.0), they work better (12%, 10.7-14.4), they are easier

to obtain (11%, 9.48-13.1), they are found naturally or free (8%, 6.56-9.68), hospital medicines have too many chemical (8%, 6.33-9.40), and they have fewer side effects (8%, 6.25-9.30). The most common uses of traditional medicines were for symptomatic conditions (42%), chronic diseases (14%), reproductive problems (11%), and malaria and febrile illnesses (10%). Participants currently taking hospital medicines for chronic conditions were nearly twice as likely to report traditional medicines usage in the past year (RR 1.97, p=0.05).

Conclusions: We built broad explanatory model for the use of traditional medicines in Kilimanjaro. The use of traditional medicines is not limited to rural or low socioeconomic populations and concurrent use of traditional medicines and biomedicine is high with frequent ethnomedical doctor shopping. Our model provides a working framework for understanding the complex interactions between biomedicine and traditional medicine. Future disease management and treatment programs will benefit from this understanding, and it can lead to synergistic policies with more effective implementation.

A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs

We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. It is shown that if Hörmander's bracket condition holds at every point of this Hilbert space, then a lower bound on the Malliavin covariance operatorμt can be obtained. Informally, this bound can be read as "Fix any finite-dimensional projection on a subspace of sufficiently regular functions. Then the eigenfunctions of μt with small eigenvalues have only a very small component in the image of Π." We also show how to use a priori bounds on the solutions to the equation to obtain good control on the dependency of the bounds on the Malliavin matrix on the initial condition. These bounds are sufficient in many cases to obtain the asymptotic strong Feller property introduced in [HM06]. One of the main novel technical tools is an almost sure bound from below on the size of "Wiener polynomials," where the coefficients are possibly non-adapted stochastic processes satisfying a Lips chitz condition. By exploiting the polynomial structure of the equations, this result can be used to replace Norris' lemma, which is unavailable in the present context. We conclude by showing that the two-dimensional stochastic Navier-Stokes equations and a large class of reaction-diffusion equations fit the framework of our theory.