The Wilson-Polchinski exact renormalization group equation

The critical exponent $\eta$ is not well accounted for in the Polchinski exact formulation of the renormalization group (RG). With a particular emphasis laid on the introduction of the critical exponent $\eta$, I re-establish (after Golner, hep-th/9801124) the explicit relation between the early Wilson exact RG equation, constructed with the incomplete integration as cutoff procedure, and the formulation with an arbitrary cutoff function proposed later on by Polchinski. I (re)-do the analysis of the Wilson-Polchinski equation expanded up to the next to leading order of the derivative expansion. I finally specify a criterion for choosing the ``best'' value of $\eta$ to this order. This paper will help in using more systematically the exact RG equation in various studies.Comment: Some minor changes, a reference added, typos correcte

Porous silica spheres as indoor air pollutant scavengers

Porous silica spheres were investigated for their effectiveness in removing typical indoor air pollutants, such as aromatic and carbonyl-containing volatile organic compounds (VOCs), and compared to the commercially available polymer styrene-divinylbenzene (XAD-4). The silica spheres and the XAD-4 resin were coated on denuder sampling devices and their adsorption efficiencies for volatile organic compounds evaluated using an indoor air simulation chamber. Real indoor sampling was also undertaken to evaluate the affinity of the silica adsorbents for a variety of indoor VOCs. The silica sphere adsorbents were found to have a high affinity for polar carbonyls and found to be more efficient than the XAD-4 resin at adsorbing carbonyls in an indoor environment

Critical behavior of weakly interacting bosons: A functional renormalization group approach

We present a detailed investigation of the momentum-dependent self-energy Sigma(k) at zero frequency of weakly interacting bosons at the critical temperature T_c of Bose-Einstein condensation in dimensions 3<=D<4. Applying the functional renormalization group, we calculate the universal scaling function for the self-energy at zero frequency but at all wave vectors within an approximation which truncates the flow equations of the irreducible vertices at the four-point level. The self-energy interpolates between the critical regime k > k_c, where k_c is the crossover scale. In the critical regime, the self-energy correctly approaches the asymptotic behavior Sigma(k) \propto k^{2 - eta}, and in the short-wavelength regime the behavior is Sigma(k) \propto k^{2(D-3)} in D>3. In D=3, we recover the logarithmic divergence Sigma(k) \propto ln(k/k_c) encountered in perturbation theory. Our approach yields the crossover scale k_c as well as a reasonable estimate for the critical exponent eta in D=3. From our scaling function we find for the interaction-induced shift in T_c in three dimensions, Delta T_c / T_c = 1.23 a n^{1/3}, where a is the s-wave scattering length and n is the density, in excellent agreement with other approaches. We also discuss the flow of marginal parameters in D=3 and extend our truncation scheme of the renormalization group equations by including the six- and eight-point vertex, which yields an improved estimate for the anomalous dimension eta \approx 0.0513. We further calculate the constant lim_{k->0} Sigma(k)/k^{2-eta} and find good agreement with recent Monte-Carlo data.Comment: 23 pages, 7 figure

Critical Phenomena in Continuous Dimension

We present a calculation of critical phenomena directly in continuous dimension d employing an exact renormalization group equation for the effective average action. For an Ising-type scalar field theory we calculate the critical exponents nu(d) and eta(d) both from a lowest--order and a complete first--order derivative expansion of the effective average action. In particular, this can be used to study critical behavior as a function of dimensionality at fixed temperature.Comment: 5 pages, 1 figure, PLB version, references adde

Renormalization of composite operators

The blocked composite operators are defined in the one-component Euclidean scalar field theory, and shown to generate a linear transformation of the operators, the operator mixing. This transformation allows us to introduce the parallel transport of the operators along the RG trajectory. The connection on this one-dimensional manifold governs the scale evolution of the operator mixing. It is shown that the solution of the eigenvalue problem of the connection gives the various scaling regimes and the relevant operators there. The relation to perturbative renormalization is also discussed in the framework of the $\phi^3$ theory in dimension $d=6$.Comment: 24 pages, revtex (accepted by Phys. Rev. D), changes in introduction and summar

Subcutaneous Immunoglobulin Replacement Therapy with Hizentra® is Safe and Effective in Children Less Than 5 Years of Age.

BACKGROUND:Hizentra® (IGSC 20%) is a 20% liquid IgG product approved for subcutaneous administration in adults and children 2 years of age and older who have primary immunodeficiency disease (PIDD). There is limited information about the use of IGSC 20 % in very young children including those less than 5 years of age. METHODS:A retrospective chart review involved 88 PIDD infants and children less than 5 years of age who received Hizentra®. RESULTS:The mean age at the start of Hizentra® was 34 months (range 2 to 59 months). IGSC 20 % was administered weekly to 86 infants (two additional infants received twice weekly and three times weekly infusions, respectively) and included an average of 63 infusions (range 6-182) for an observation period up to 45.5 months. Infusion by manual delivery occurred in 15 patients. The mean dose was 674 mg/kg/4 weeks. The mean IgG level was 942 mg/dL while on IGSC 20 %, compared to a mean trough IgG level of 794 mg/dL (p &lt; 0.0001) during intravenous or subcutaneous IgG administration prior to IGSC 20 %. Average infusion time was 47 (range 5-120) minutes, and the median number of infusion sites was 2 (range 1-4). Local reactions were mostly mild and observed in 36/88 (41%) children. No serious adverse events were reported. A significant increase in weight percentile (7 % ± 19.2, p = 0.0012) among subjects was observed during IGSC 20% administration. The rate of serious bacterial infections was 0.067 per patient-year while receiving IGSC 20%, similar to previously reported efficacy studies. CONCLUSIONS:Hizentra® is effective in preventing infections, and is well tolerated in children less than age 5 years

Wegner-Houghton equation and derivative expansion

We study the derivative expansion for the effective action in the framework of the Exact Renormalization Group for a single component scalar theory. By truncating the expansion to the first two terms, the potential $U_k$ and the kinetic coefficient $Z_k$, our analysis suggests that a set of coupled differential equations for these two functions can be established under certain smoothness conditions for the background field and that sharp and smooth cut-off give the same result. In addition we find that, differently from the case of the potential, a further expansion is needed to obtain the differential equation for $Z_k$, according to the relative weight between the kinetic and the potential terms. As a result, two different approximations to the $Z_k$ equation are obtained. Finally a numerical analysis of the coupled equations for $U_k$ and $Z_k$ is performed at the non-gaussian fixed point in $D<4$ dimensions to determine the anomalous dimension of the field.Comment: 15 pages, 3 figure

Photocatalytic air-purification: A low-cost, real-time gas detection method

This research demonstrates the use of a gas detector as a feasible alternative to the standardized analytical methods typically found in photocatalytic air-purification ISO standard tests and academic literature. A methyl mercaptan detector is calibrated and validated (for linearity) using a standard gas generator. The detector can be directly connected to the photoreactor exit allowing real-time span gas measurement with data-logging at one minute intervals. The detector successfully differentiated samples with different photocatalytic performance. The use of such detectors offers an easy-to-use, low-cost alternative to gas measurement with applications in academic research, proof-of-concept photocatalytic tests and also as an educational tool

Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation

The relation between the Wilson-Polchinski and the Litim optimized ERGEs in the local potential approximation is studied with high accuracy using two different analytical approaches based on a field expansion: a recently proposed genuine analytical approximation scheme to two-point boundary value problems of ordinary differential equations, and a new one based on approximating the solution by generalized hypergeometric functions. A comparison with the numerical results obtained with the shooting method is made. A similar accuracy is reached in each case. Both two methods appear to be more efficient than the usual field expansions frequently used in the current studies of ERGEs (in particular for the Wilson-Polchinski case in the study of which they fail).Comment: Final version to appear in Nucl. Phys. B. Some references added correctl