1,242 research outputs found

    Bulk singularities at critical end points: a field-theory analysis

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    A class of continuum models with a critical end point is considered whose Hamiltonian H[ϕ,ψ]{\mathcal{H}}[\phi,\psi] involves two densities: a primary order-parameter field, ϕ\phi, and a secondary (noncritical) one, ψ\psi. 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 ∼∣t∣2−α\sim|{t}|^{2-\alpha} of the first-order line on which the disordered or ordered phase coexists with the noncritical spectator phase, and the coexistence singularity ∼∣t∣1−α\sim |{t}|^{1-\alpha} or ∼∣t∣β\sim|{t}|^{\beta} 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 PCEP∗{\mathcal P}_{\mathrm{CEP}}^* and Pλ∗{\mathcal P}_{\lambda}^* translates into field theory. The critical RG eigenexponents of PCEP∗{\mathcal P}_{\mathrm{CEP}}^* and Pλ∗{\mathcal P}_{\lambda}^* are shown to match. PCEP∗{\mathcal P}_{\mathrm{CEP}}^* is demonstrated to have a discontinuity eigenperturbation (with eigenvalue y=dy=d), tangent to the unstable trajectory that emanates from PCEP∗{\mathcal P}_{\mathrm{CEP}}^* and leads to Pλ∗{\mathcal P}_{\lambda}^*. 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

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    Systems with an O(n) symmetrical Hamiltonian are considered in a dd-dimensional slab geometry of macroscopic lateral extension and finite thickness LL that undergo a continuous bulk phase transition in the limit L→∞L\to\infty. The effective forces induced by thermal fluctuations at and above the bulk critical temperature Tc,∞T_{c,\infty} (thermodynamic Casimir effect) are investigated below the upper critical dimension d∗=4d^*=4 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 Tc,∞T_{c,\infty} make conventional RG-improved perturbation theory in 4−ϵ4-\epsilon 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 L≡L/ξ∞\mathsf{L}\equiv L/\xi_\infty, where ξ∞\xi_\infty is the bulk correlation length. Scaling functions of the LL-dependent residual free energy per area are obtained whose L→0\mathsf{L}\to0 limits are in conformity with previous results for the Casimir amplitudes ΔC\Delta_C to O(ϵ3/2)O(\epsilon^{3/2}) and display a more reasonable small-L\mathsf{L} behavior inasmuch as they approach the critical value ΔC\Delta_C monotonically as L→0\mathsf{L}\to 0.Comment: 23 pages, 10 figure

    Extending fragment-based free energy calculations with library Monte Carlo simulation: Annealing in interaction space

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    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

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    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

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    Most of the literature on general relativity over the last century assumes that the cosmological constant Λ\Lambda 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 Λ\Lambda. Interestingly, this requires a drastic revision of conceptual frameworks commonly used in general relativity, \emph{no matter how small Λ\Lambda is.} We first explain why, and then summarize the current status of generalizations of these frameworks to include a positive Λ\Lambda, focusing on gravitational waves.Comment: A Key Issues Review, Commissioned by Rep. Prog. Phys. 12 pages, 3 figure

    How to implement a modular form

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    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

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    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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