1,242 research outputs found
Bulk singularities at critical end points: a field-theory analysis
A class of continuum models with a critical end point is considered whose
Hamiltonian involves two densities: a primary
order-parameter field, , and a secondary (noncritical) one, .
Field-theoretic methods (renormalization group results in conjunction with
functional methods) are used to give a systematic derivation of singularities
occurring at critical end points. Specifically, the thermal singularity
of the first-order line on which the disordered or
ordered phase coexists with the noncritical spectator phase, and the
coexistence singularity or of the
secondary density are derived. It is clarified how the renormalization
group (RG) scenario found in position-space RG calculations, in which the
critical end point and the critical line are mapped onto two separate fixed
points and
translates into field theory. The critical RG eigenexponents of and are shown to match.
is demonstrated to have a discontinuity
eigenperturbation (with eigenvalue ), tangent to the unstable trajectory
that emanates from and leads to . The nature and origin of this eigenperturbation as well as the
role redundant operators play are elucidated. The results validate that the
critical behavior at the end point is the same as on the critical line.Comment: Latex file; uses epj stylefiles svepj.clo and svjour.cls. Two eps
files as figures included; uses texdraw to generate some figures Only some
remarks added in last Section of this final versio
Thermodynamic Casimir effects involving interacting field theories with zero modes
Systems with an O(n) symmetrical Hamiltonian are considered in a
-dimensional slab geometry of macroscopic lateral extension and finite
thickness that undergo a continuous bulk phase transition in the limit
. The effective forces induced by thermal fluctuations at and above
the bulk critical temperature (thermodynamic Casimir effect) are
investigated below the upper critical dimension by means of
field-theoretic renormalization group methods for the case of periodic and
special-special boundary conditions, where the latter correspond to the
critical enhancement of the surface interactions on both boundary planes. As
shown previously [\textit{Europhys. Lett.} \textbf{75}, 241 (2006)], the zero
modes that are present in Landau theory at make conventional
RG-improved perturbation theory in dimensions ill-defined. The
revised expansion introduced there is utilized to compute the scaling functions
of the excess free energy and the Casimir force for temperatures
T\geqT_{c,\infty} as functions of , where
is the bulk correlation length. Scaling functions of the
-dependent residual free energy per area are obtained whose
limits are in conformity with previous results for the Casimir amplitudes
to and display a more reasonable
small- behavior inasmuch as they approach the critical value
monotonically as .Comment: 23 pages, 10 figure
Extending fragment-based free energy calculations with library Monte Carlo simulation: Annealing in interaction space
Pre-calculated libraries of molecular fragment configurations have previously
been used as a basis for both equilibrium sampling (via "library-based Monte
Carlo") and for obtaining absolute free energies using a polymer-growth
formalism. Here, we combine the two approaches to extend the size of systems
for which free energies can be calculated. We study a series of all-atom
poly-alanine systems in a simple dielectric "solvent" and find that precise
free energies can be obtained rapidly. For instance, for 12 residues, less than
an hour of single-processor is required. The combined approach is formally
equivalent to the "annealed importance sampling" algorithm; instead of
annealing by decreasing temperature, however, interactions among fragments are
gradually added as the molecule is "grown." We discuss implications for future
binding affinity calculations in which a ligand is grown into a binding site
Renormalization and Computation II: Time Cut-off and the Halting Problem
This is the second installment to the project initiated in [Ma3]. In the
first Part, I argued that both philosophy and technique of the perturbative
renormalization in quantum field theory could be meaningfully transplanted to
the theory of computation, and sketched several contexts supporting this view.
In this second part, I address some of the issues raised in [Ma3] and provide
their development in three contexts: a categorification of the algorithmic
computations; time cut--off and Anytime Algorithms; and finally, a Hopf algebra
renormalization of the Halting Problem.Comment: 28 page
Implications of a positive cosmological constant for general relativity
Most of the literature on general relativity over the last century assumes
that the cosmological constant is zero. However, by now independent
observations have led to a consensus that the dynamics of the universe is best
described by Einstein's equations with a small but positive .
Interestingly, this requires a drastic revision of conceptual frameworks
commonly used in general relativity, \emph{no matter how small is.}
We first explain why, and then summarize the current status of generalizations
of these frameworks to include a positive , focusing on gravitational
waves.Comment: A Key Issues Review, Commissioned by Rep. Prog. Phys. 12 pages, 3
figure
How to implement a modular form
AbstractWe present a model for Fourier expansions of arbitrary modular forms. This model takes precisions and symmetries of such Fourier expansions into account. The value of this approach is illustrated by studying a series of examples. An implementation of these ideas is provided by the author. We discuss the technical background of this implementation, and we explain how to implement arbitrary Fourier expansions and modular forms. The framework allows us to focus on the considerations of a mathematical nature during this procedure. We conclude with a list of currently available implementations and a discussion of possible computational research
Optical Biosensors Based on Semiconductor Nanostructures
The increasing availability of semiconductor-based nanostructures with novel and unique properties has sparked widespread interest in their use in the field of biosensing. The precise control over the size, shape and composition of these nanostructures leads to the accurate control of their physico-chemical properties and overall behavior. Furthermore, modifications can be made to the nanostructures to better suit their integration with biological systems, leading to such interesting properties as enhanced aqueous solubility, biocompatibility or bio-recognition. In the present work, the most significant applications of semiconductor nanostructures in the field of optical biosensing will be reviewed. In particular, the use of quantum dots as fluorescent bioprobes, which is the most widely used application, will be discussed. In addition, the use of some other nanometric structures in the field of biosensing, including porous semiconductors and photonic crystals, will be presented
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