Stretching an heteropolymer

We study the influence of some quenched disorder in the sequence of monomers on the entropic elasticity of long polymeric chains. Starting from the Kratky-Porod model, we show numerically that some randomness in the favoured angles between successive segments induces a change in the elongation versus force characteristics, and this change can be well described by a simple renormalisation of the elastic constant. The effective coupling constant is computed by an analytic study of the low force regime.Comment: Latex, 7 pages, 3 postscript figur

A new geometric invariant on initial data for Einstein equations

For a given asymptotically flat initial data set for Einstein equations a new geometric invariant is constructed. This invariant measure the departure of the data set from the stationary regime, it vanishes if and only if the data is stationary. In vacuum, it can be interpreted as a measure of the total amount of radiation contained in the data.Comment: 5 pages. Important corrections regarding the generalization to the non-time symmetric cas

Structural, mechanical and thermodynamic properties of a coarse-grained DNA model

We explore in detail the structural, mechanical and thermodynamic properties of a coarse-grained model of DNA similar to that introduced in Thomas E. Ouldridge, Ard A. Louis, Jonathan P.K. Doye, Phys. Rev. Lett. 104 178101 (2010). Effective interactions are used to represent chain connectivity, excluded volume, base stacking and hydrogen bonding, naturally reproducing a range of DNA behaviour. We quantify the relation to experiment of the thermodynamics of single-stranded stacking, duplex hybridization and hairpin formation, as well as structural properties such as the persistence length of single strands and duplexes, and the torsional and stretching stiffness of double helices. We also explore the model's representation of more complex motifs involving dangling ends, bulged bases and internal loops, and the effect of stacking and fraying on the thermodynamics of the duplex formation transition.Comment: 25 pages, 16 figure

Microscopic formulation of the Zimm-Bragg model for the helix-coil transition

A microscopic spin model is proposed for the phenomenological Zimm-Bragg model for the helix-coil transition in biopolymers. This model is shown to provide the same thermophysical properties of the original Zimm-Bragg model and it allows a very convenient framework to compute statistical quantities. Physical origins of this spin model are made transparent by an exact mapping into a one-dimensional Ising model with an external field. However, the dependence on temperature of the reduced external field turns out to differ from the standard one-dimensional Ising model and hence it gives rise to different thermophysical properties, despite the exact mapping connecting them. We discuss how this point has been frequently overlooked in the recent literature.Comment: 11 pages, 2 figure

The Newtonian Limit for Asymptotically Flat Solutions of the Vlasov-Einstein System

It is shown that there exist families of asymptotically flat solutions of the Einstein equations coupled to the Vlasov equation describing a collisionless gas which have a Newtonian limit. These are sufficiently general to confirm that for this matter model as many families of this type exist as would be expected on the basis of physical intuition. A central role in the proof is played by energy estimates in unweighted Sobolev spaces for a wave equation satisfied by the second fundamental form of a maximal foliation.Comment: 24 pages, plain TE

On rationality of the intersection points of a line with a plane quartic

We study the rationality of the intersection points of certain lines and smooth plane quartics C defined over F_q. For q \geq 127, we prove the existence of a line such that the intersection points with C are all rational. Using another approach, we further prove the existence of a tangent line with the same property as soon as the characteristic of F_q is different from 2 and q \geq 66^2+1. Finally, we study the probability of the existence of a rational flex on C and exhibit a curious behavior when the characteristic of F_q is equal to 3.Comment: 17 pages. Theorem 2 now includes the characteristic 2 case; Conjecture 1 from the previous version is proved wron

Absorption spectrum in the wings of the potassium second resonance doublet broadened by helium

We have measured the reduced absorption coefficients occurring in the wings of the potassium 4S-5P doublet lines at 404.414 nm and at 404.720 nm broadened by helium gas at pressures of several hundred Torr. At the experimental temperature of 900 K, we have detected a shoulder-like broadening feature on the blue wing of the doublet which is relatively flat between 401.8 nm and 402.8 nm and which drops off rapidly for shorter wavelengths, corresponding to absorption from the X doublet Sigma+ state to the C doublet Sigma+ state of the K-He quasimolecule. The accurate measurements of the line profiles in the present work will sharply constrain future calculations of potential energy surfaces and transition dipole moments correlating to the asymptotes He-K(5p), He-K(5s), and He-K(3d).Comment: 2 figure

Trapped Surfaces in Vacuum Spacetimes

An earlier construction by the authors of sequences of globally regular, asymptotically flat initial data for the Einstein vacuum equations containing trapped surfaces for large values of the parameter is extended, from the time symmetric case considered previously, to the case of maximal slices. The resulting theorem shows rigorously that there exists a large class of initial configurations for non-time symmetric pure gravitational waves satisfying the assumptions of the Penrose singularity theorem and so must have a singularity to the future.Comment: 14 page

Risk of schizophrenia in relation to parental origin and genome-wide divergence

Background. Second-generation immigrants have an increased risk of schizophrenia, a finding that still lacks a satisfactory explanation. Various operational definitions of second-generation immigrants have been used, including foreign parental country of birth. However, with increasing global migration, it is not clear that parental country of birth necessarily is informative with regard to ethnicity. We compare two independently collected measures of parental foreign ethnicity, parental foreign country of birth versus genetic divergence, based on genome-wide genotypic data, to access which measure most efficiently captures the increased risk of schizophrenia among second-generation immigrants residing in Denmark. Method. A case-control study covering all children born in Denmark since 1981 included 892 cases of schizophrenia and 883 matched controls. Genetic divergence was assessed using principal component analyses of the genotypic data. Independently, parental foreign country of birth was assessed using information recorded prospectively in the Danish Civil Registration System. We compared incidence rate ratios of schizophrenia associated with these two independently collected measures of parental foreign ethnicity. Results. People with foreign-born parents had a significantly increased risk of schizophrenia [relative risk (RR) 1.94 (95% confidence intervals (CI) 1.41-2.65)]. Genetically divergent persons also had a significant increased risk [RR 2.43 ( 95% CI 1.55-3.82)]. Mutual adjustment of parental foreign country of birth and genetic divergence showed no difference between these measures with regard to their potential impact on the results. Conclusions. In terms of RR of schizophrenia, genetic divergence and parental foreign country of birth are interchangeable entities, and both entities have validity with regard to identifying second-generation immigrants

The influence of anesthetics, neurotransmitters and antibiotics on the relaxation processes in lipid membranes

In the proximity of melting transitions of artificial and biological membranes fluctuations in enthalpy, area, volume and concentration are enhanced. This results in domain formation, changes of the elastic constants, changes in permeability and slowing down of relaxation processes. In this study we used pressure perturbation calorimetry to investigate the relaxation time scale after a jump into the melting transition regime of artificial lipid membranes. This time corresponds to the characteristic rate of domain growth. The studies were performed on single-component large unilamellar and multilamellar vesicle systems with and without the addition of small molecules such as general anesthetics, neurotransmitters and antibiotics. These drugs interact with membranes and affect melting points and profiles. In all systems we found that heat capacity and relaxation times are related to each other in a simple manner. The maximum relaxation time depends on the cooperativity of the heat capacity profile and decreases with a broadening of the transition. For this reason the influence of a drug on the time scale of domain formation processes can be understood on the basis of their influence on the heat capacity profile. This allows estimations of the time scale of domain formation processes in biological membranes.Comment: 12 pages, 6 figure