Subleading critical exponents from the renormalisation group

We study exact renormalisation group equations for the 3d Ising universality class. At the Wilson-Fisher fixed point, symmetric and antisymmetric correction-to-scaling exponents are computed with high accuracy for an optimised cutoff to leading order in the derivative expansion. Further results are derived for other cutoffs including smooth, sharp and background field cutoffs. An estimate for higher order corrections is given as well. We establish that the leading antisymmetric corrections to scaling are strongly subleading compared to the leading symmetric ones.Comment: 10 pages, 5 figure

Asymmetric Fluid Criticality I: Scaling with Pressure Mixing

The thermodynamic behavior of a fluid near a vapor-liquid and, hence, asymmetric critical point is discussed within a general ``complete'' scaling theory incorporating pressure mixing in the nonlinear scaling fields as well as corrections to scaling. This theory allows for a Yang-Yang anomaly in which \mu_{\sigma}^{\prime\prime}(T), the second temperature derivative of the chemical potential along the phase boundary, diverges like the specific heat when T\to T_{\scriptsize c}; it also generates a leading singular term, |t|^{2\beta}, in the coexistence curve diameter, where t\equiv (T-T_{\scriptsize c}) /T_{\scriptsize c}. The behavior of various special loci, such as the critical isochore, the critical isotherm, the k-inflection loci, on which \chi^{(k)}\equiv \chi(\rho,T)/\rho^{k} (with \chi = \rho^{2} k_{\scriptsize B}TK_{T}) and C_{V}^{(k)}\equiv C_{V}(\rho,T)/\rho^{k} are maximal at fixed T, is carefully elucidated. These results are useful for analyzing simulations and experiments, since particular, nonuniversal values of k specify loci that approach the critical density most rapidly and reflect the pressure-mixing coefficient. Concrete illustrations are presented for the hard-core square-well fluid and for the restricted primitive model electrolyte. For comparison, a discussion of the classical (or Landau) theory is presented briefly and various interesting loci are determined explicitly and illustrated quantitatively for a van der Waals fluid.Comment: 21 pages in two-column format including 8 figure

Application of the functional renormalization group method to classical free energy models

A simple functional renormalization group method is presented to correct the behavior of classical free energy models near the critical point. This approach is applied to the Soave-Redlich-Kwong equation of state to illustrate its ability to better reproduce the phase behavior of simple fluids and to understand the influence of its parameters on the shape of the vapor-liquid phase diagram. The method is then extended to account for the correlations induced by intramolecular bonds. It is then applied to a first order thermodynamic perturbation theory for chain fluids to examine fluids composed of linearly bonded Lennard-Jones atoms. Unlike previous approaches for applying renormalization group corrections to chain fluids, this is able to accurately reproduce the critical point without predicting an overly flat liquid-vapor coexistence region

Dynamics of fluctuations in a fluid below the onset of Rayleigh-B\'enard convection

We present experimental data and their theoretical interpretation for the decay rates of temperature fluctuations in a thin layer of a fluid heated from below and confined between parallel horizontal plates. The measurements were made with the mean temperature of the layer corresponding to the critical isochore of sulfur hexafluoride above but near the critical point where fluctuations are exceptionally strong. They cover a wide range of temperature gradients below the onset of Rayleigh-B\'enard convection, and span wave numbers on both sides of the critical value for this onset. The decay rates were determined from experimental shadowgraph images of the fluctuations at several camera exposure times. We present a theoretical expression for an exposure-time-dependent structure factor which is needed for the data analysis. As the onset of convection is approached, the data reveal the critical slowing-down associated with the bifurcation. Theoretical predictions for the decay rates as a function of the wave number and temperature gradient are presented and compared with the experimental data. Quantitative agreement is obtained if allowance is made for some uncertainty in the small spacing between the plates, and when an empirical estimate is employed for the influence of symmetric deviations from the Oberbeck-Boussinesq approximation which are to be expected in a fluid with its density at the mean temperature located on the critical isochore.Comment: 13 pages, 10 figures, 52 reference

Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps

We study crossover phenomena in a model of self-avoiding walks with medium-range jumps, that corresponds to the limit $N\to 0$ of an $N$-vector spin system with medium-range interactions. In particular, we consider the critical crossover limit that interpolates between the Gaussian and the Wilson-Fisher fixed point. The corresponding crossover functions are computed using field-theoretical methods and an appropriate mean-field expansion. The critical crossover limit is accurately studied by numerical Monte Carlo simulations, which are much more efficient for walk models than for spin systems. Monte Carlo data are compared with the field-theoretical predictions concerning the critical crossover functions, finding a good agreement. We also verify the predictions for the scaling behavior of the leading nonuniversal corrections. We determine phenomenological parametrizations that are exact in the critical crossover limit, have the correct scaling behavior for the leading correction, and describe the nonuniversal lscrossover behavior of our data for any finite range.Comment: 43 pages, revte

Trajectories of inflammatory biomarkers over the eighth decade and their associations with immune cell profiles and epigenetic ageing

Background: Epigenetic age acceleration (an older methylation age compared to chronological age) correlates strongly with various age-related morbidities and mortality. Chronic systemic inflammation is thought to be a hallmark of ageing, but the relationship between an increased epigenetic age and this likely key phenotype of ageing has not yet been extensively investigated. Methods: We modelled the trajectories of the inflammatory biomarkers C-reactive protein (CRP; measured using both a high- and low-sensitivity assay) and interleukin-6 (IL-6) over the eighth decade in the Lothian Birth Cohort 1936. Using linear mixed models, we investigated the association between CRP and immune cell profiles imputed from the methylation data and examined the cross-sectional and longitudinal association between the inflammatory biomarkers and two measures of epigenetic age acceleration, derived from the Horvath and Hannum epigenetic clocks. Results: We found that low-sensitivity CRP declined, high-sensitivity CRP did not change, and IL-6 increased over time within the cohort. CRP levels inversely associated with CD8+T cells and CD4+T cells and positively associated with senescent CD8+T cells, plasmablasts and granulocytes. Cross-sectionally, the Hannum, but not the Horvath, measure of age acceleration was positively associated with each of the inflammatory biomarkers, including a restricted measure of CRP (≤ 10 mg/L) likely reflecting levels relevant to chronic inflammation. Conclusions: We found a divergent relationship between inflammation and immune system parameters in older age. We additionally report the Hannum measure of epigenetic age acceleration associated with an elevated inflammatory profile cross-sectionally, but not longitudinally

Training differentially regulates elastin level and proteolysis in skeletal and heart muscles and aorta in healthy rats

Exercise induces changes in muscle fibers and the extracellular matrix that may depend on elastin content and the activity of proteolytic enzymes. We investigated the influence of endurance training on the gene expression and protein content and/or activity of elastin, elastase, cathepsin K, and plasmin in skeletal and heart muscles and in the aorta. Healthy rats were randomly divided into untrained (n=10) and trained (n=10; 6 weeks of endurance training with increasing load) groups. Gene expression was evaluated via qRT-PCR. Elastin content was measured via enzyme-linked immunosorbent assay and enzyme activity was measured fluorometrically. Elastin content was significantly higher in skeletal (P=0.0014) and heart muscle (P=0.000022) from trained rats versus untrained rats, but not in the aorta. Although mRNA levels in skeletal muscle did not differ between groups, the activities of elastase (P=0.0434), cathepsin K (P=0.0343) and plasmin (P=0.000046) were higher in trained rats. The levels of cathepsin K (P=0.0288) and plasminogen (P=0.0005) mRNA were higher in heart muscle from trained rats, but enzyme activity was not. Enzyme activity in the aorta did not differ between groups. Increased elastin content in muscles may result in better adaption to exercise, as may remodeling of the extracellular matrix in skeletal muscle