Renormalized field theory and particle density profile in driven diffusive systems with open boundaries

We investigate the density profile in a driven diffusive system caused by a plane particle source perpendicular to the driving force. Focussing on the case of critical bulk density $\bar{c}$ we use a field theoretic renormalization group approach to calculate the density $c(z)$ as a function of the distance from the particle source at first order in $\epsilon=2-d$ ($d$: spatial dimension). For $d=1$ we find reasonable agreement with the exact solution recently obtained for the asymmetric exclusion model. Logarithmic corrections to the mean field profile are computed for $d=2$ with the result $c(z)-\bar{c} \sim z^{-1} (\ln(z))^{2/3}$ for $z \rightarrow \infty$.Comment: 32 pages, RevTex, 4 Postscript figures, to appear in Phys. Rev.

Surface critical behavior of driven diffusive systems with open boundaries

Using field theoretic renormalization group methods we study the critical behavior of a driven diffusive system near a boundary perpendicular to the driving force. The boundary acts as a particle reservoir which is necessary to maintain the critical particle density in the bulk. The scaling behavior of correlation and response functions is governed by a new exponent eta_1 which is related to the anomalous scaling dimension of the chemical potential of the boundary. The new exponent and a universal amplitude ratio for the density profile are calculated at first order in epsilon = 5-d. Some of our results are checked by computer simulations.Comment: 10 pages ReVTeX, 6 figures include

Effects of surfaces on resistor percolation

We study the effects of surfaces on resistor percolation at the instance of a semi-infinite geometry. Particularly we are interested in the average resistance between two connected ports located on the surface. Based on general grounds as symmetries and relevance we introduce a field theoretic Hamiltonian for semi-infinite random resistor networks. We show that the surface contributes to the average resistance only in terms of corrections to scaling. These corrections are governed by surface resistance exponents. We carry out renormalization group improved perturbation calculations for the special and the ordinary transition. We calculate the surface resistance exponents \phi_{\mathcal S \mathnormal} and \phi_{\mathcal S \mathnormal}^\infty for the special and the ordinary transition, respectively, to one-loop order.Comment: 19 pages, 3 figure

Surface critical behavior of random systems at the ordinary transition

We calculate the surface critical exponents of the ordinary transition occuring in semi-infinite, quenched dilute Ising-like systems. This is done by applying the field theoretic approach directly in d=3 dimensions up to the two-loop approximation, as well as in $d=4-\epsilon$ dimensions. At $d=4-\epsilon$ we extend, up to the next-to-leading order, the previous first-order results of the $\sqrt{\epsilon}$ expansion by Ohno and Okabe [Phys.Rev.B 46, 5917 (1992)]. In both cases the numerical estimates for surface exponents are computed using Pade approximants extrapolating the perturbation theory expansions. The obtained results indicate that the critical behavior of semi-infinite systems with quenched bulk disorder is characterized by the new set of surface critical exponents.Comment: 11 pages, 11 figure

Short-time critical dynamics at perfect and non-perfect surface

We report Monte Carlo simulations of critical dynamics far from equilibrium on a perfect and non-perfect surface in the 3d Ising model. For an ordered initial state, the dynamic relaxation of the surface magnetization, the line magnetization of the defect line, and the corresponding susceptibilities and appropriate cumulant is carefully examined at the ordinary, special and surface phase transitions. The universal dynamic scaling behavior including a dynamic crossover scaling form is identified. The exponent $\beta_1$ of the surface magnetization and $\beta_2$ of the line magnetization are extracted. The impact of the defect line on the surface universality classes is investigated.Comment: 11figure

Thermodynamic Casimir effects involving interacting field theories with zero modes

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

Logarithmic corrections in the two-dimensional Ising model in a random surface field

In the two-dimensional Ising model weak random surface field is predicted to be a marginally irrelevant perturbation at the critical point. We study this question by extensive Monte Carlo simulations for various strength of disorder. The calculated effective (temperature or size dependent) critical exponents fit with the field-theoretical results and can be interpreted in terms of the predicted logarithmic corrections to the pure system's critical behaviour.Comment: 10 pages, 4 figures, extended version with one new sectio

Emulsifier and antioxidant properties of by-products obtained by enzymatic degumming of soybean oil

The enzymes used in degumming, called phospholipases, specifically act on phospholipids without degrading the oil itself. Degumming using a phospholipase C enzyme allows to meet all market specifications while it increases the oil yield. The aim of this study was to evaluate antioxidant and emulsifier properties of the recovered gum (RG) obtained by enzymatic oil degumming process of crude soybean oil subjected to modifications as deoiling (RG deoiled) or ethanol fractionation (RG soluble and insoluble). RG soluble allowed obtaining more stable O/W emulsions (30:70 w/w) in comparison with those by-products assayed at different concentrations (0.1?1.0%). Also, deoiled soybean lecithin (DSL) andRG deoiled had a similar behavior in relation to the kinetic destabilization (%BS profiles), despite the different degumming processes used to obtain these samples. The study on induction times (Metrohm Rancimat) showed a significant antioxidant effect (p<0.05) against a refined sunflower oil associated with all the by-products analyzed. However, RG soluble and DSL showed a strong effect on the oil stability at high concentrations (1000?2000 ppm). These results showed that the deoiled recovered gum and its derivates obtained by ethanol fractionation are a potential alternative for industrial application as additive.Centro de Investigación y Desarrollo en Criotecnología de AlimentosConsejo Nacional de Investigaciones Científicas y Técnica

Emulsifier and antioxidant properties of by-products obtained by enzymatic degumming of soybean oil

The enzymes used in degumming, called phospholipases, specifically act on phospholipids without degrading the oil itself. Degumming using a phospholipase C enzyme allows to meet all market specifications while it increases the oil yield. The aim of this study was to evaluate antioxidant and emulsifier properties of the recovered gum (RG) obtained by enzymatic oil degumming process of crude soybean oil subjected to modifications as deoiling (RG deoiled) or ethanol fractionation (RG soluble and insoluble). RG soluble allowed obtaining more stable O/W emulsions (30:70 w/w) in comparison with those by-products assayed at different concentrations (0.1?1.0%). Also, deoiled soybean lecithin (DSL) andRG deoiled had a similar behavior in relation to the kinetic destabilization (%BS profiles), despite the different degumming processes used to obtain these samples. The study on induction times (Metrohm Rancimat) showed a significant antioxidant effect (p<0.05) against a refined sunflower oil associated with all the by-products analyzed. However, RG soluble and DSL showed a strong effect on the oil stability at high concentrations (1000?2000 ppm). These results showed that the deoiled recovered gum and its derivates obtained by ethanol fractionation are a potential alternative for industrial application as additive.Centro de Investigación y Desarrollo en Criotecnología de AlimentosConsejo Nacional de Investigaciones Científicas y Técnica

Critical Casimir effect in films for generic non-symmetry-breaking boundary conditions

Systems described by an O(n) symmetrical $\phi^4$ Hamiltonian are considered in a $d$-dimensional film geometry at their bulk critical points. A detailed renormalization-group (RG) study of the critical Casimir forces induced between the film's boundary planes by thermal fluctuations is presented for the case where the O(n) symmetry remains unbroken by the surfaces. The boundary planes are assumed to cause short-ranged disturbances of the interactions that can be modelled by standard surface contributions $\propto \bm{\phi}^2$ corresponding to subcritical or critical enhancement of the surface interactions. This translates into mesoscopic boundary conditions of the generic symmetry-preserving Robin type $\partial_n\bm{\phi}=\mathring{c}_j\bm{\phi}$. RG-improved perturbation theory and Abel-Plana techniques are used to compute the $L$-dependent part $f_{\mathrm{res}}$ of the reduced excess free energy per film area $A\to\infty$ to two-loop order. When $d<4$, it takes the scaling form $f_{\mathrm{res}}\approx D(c_1L^{\Phi/\nu},c_2L^{\Phi/\nu})/L^{d-1}$ as $L\to\infty$, where $c_i$ are scaling fields associated with the surface-enhancement variables $\mathring{c}_i$, while $\Phi$ is a standard surface crossover exponent. The scaling function $D(\mathsf{c}_1,\mathsf{c}_2)$ and its analogue $\mathcal{D}(\mathsf{c}_1,\mathsf{c}_2)$ for the Casimir force are determined via expansion in $\epsilon=4-d$ and extrapolated to $d=3$ dimensions. In the special case $\mathsf{c}_1=\mathsf{c}_2=0$, the expansion becomes fractional. Consistency with the known fractional expansions of D(0,0) and $\mathcal{D}(0,0)$ to order $\epsilon^{3/2}$ is achieved by appropriate reorganisation of RG-improved perturbation theory. For appropriate choices of $c_1$ and $c_2$, the Casimir forces can have either sign. Furthermore, crossovers from attraction to repulsion and vice versa may occur as $L$ increases.Comment: Latex source file, 40 pages, 9 figure