Statistical Field Theory and Effective Action Method for scalar Active Matter

We employ Statistical Field Theory techniques for coarse-graining the steady-state properties of Active Ornstein-Uhlenbeck particles. The computation is carried on in the framework of the Unified Colored Noise approximation that allows an effective equilibrium picture. We thus develop a mean-field theory that allows to describe in a unified framework the phenomenology of scalar Active Matter. In particular, we are able to describe through spontaneous symmetry breaking mechanism two peculiar features of Active Systems that are (i) The accumulation of active particles at the boundaries of a confining container, and (ii) Motility-Induced Phase Separation (MIPS). \textcolor{black}{We develop a mean-field theory for steric interacting active particles undergoing to MIPS and for Active Lennard-Jones (ALJ) fluids.} \textcolor{black}{Within this framework}, we discuss the universality class of MIPS and ALJ \textcolor{black}{showing that it falls into Ising universality class.} We \textcolor{black}{thus} compute analytically the critical line $T_c(\tau)$ for both models. In the case of MIPS, $T_c(\tau)$ gives rise to a reentrant phase diagram compatible with an inverse transition from liquid to gas as the strength of the noise decreases. \textcolor{black}{However, in the case of particles interacting through anisotropic potentials, } the field theory acquires a $\varphi^3$ term that, \textcolor{black}{in general, cannot be canceled performing the expansion around the critical point.} In this case, the \textcolor{black}{Ising} critical point might \textcolor{black}{be replaced} by a first-order phase transition \textcolor{black}{region}

Effective equilibrium picture in xy−xy-model with exponentially correlated noise

We study the effect of exponentially correlated noise on $xy-$model in the limit of small correlation time discussing the order-disorder transition in mean-field and the topological transition in two dimensions. We map the steady states of the non-equilibrium dynamics into an effective equilibrium theory. In mean-field, the critical temperature increases with the noise correlation time $\tau$ indicating that memory effects promote ordering. This finding is confirmed by numerical simulations. The topological transition temperature in two dimensions remains untouched. However, finite size effects induce a crossover in the vortices proliferation that is confirmed by numerical simulations

Effective potential method for active particles

We investigate the steady state properties of an active fluid modeled as an assembly of soft repulsive spheres subjected to Gaussian colored noise. Such a noise captures one of the salient aspects of active particles, namely the persistence of their motion and determines a variety of novel features with respect to familiar passive fluids. We show that within the so-called multidimensional unified colored noise approximation, recently introduced in the field of active matter, the model can be treated by methods similar to those employed in the study of standard molecular fluids. The system shows a tendency of the particles to aggregate even in the presence of purely repulsive forces because the combined action of colored noise and interactions enhances the the effective friction between nearby particles. We also discuss whether an effective two-body potential approach, which would allow to employ methods similar to those of density functional theory, is appropriate. The limits of such an approximation are discussed.Comment: 14 pages, 6 figures in Molecular Physics, 11 march 2016. arXiv admin note: text overlap with arXiv:cond-mat/0605094 by other author

Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature

We prove that the boundary of a (not necessarily connected) bounded smooth set with constant nonlocal mean curvature is a sphere. More generally, and in contrast with what happens in the classical case, we show that the Lipschitz constant of the nonlocal mean curvature of such a boundary controls its $C^2$-distance from a single sphere. The corresponding stability inequality is obtained with a sharp decay rate.Comment: 17 page

Generalized energy equipartition in harmonic oscillators driven by active baths

We study experimentally and numerically the dynamics of colloidal beads confined by a harmonic potential in a bath of swimming E. coli bacteria. The resulting dynamics is well approximated by a Langevin equation for an overdamped oscillator driven by the combination of a white thermal noise and an exponentially correlated active noise. This scenario leads to a simple generalization of the equipartition theorem resulting in the coexistence of two different effective temperatures that govern dynamics along the flat and the curved directions in the potential landscape.Comment: 4 pages, 3 figure

Pressure in an exactly solvable model of active fluid

We consider the pressure in the steady-state regime of three stochastic models characterized by self-propulsion and persistent motion and widely employed to describe the behavior of active particles, namely the Active Brownian particle (ABP) model, the Gaussian colored noise (GCN) model and the unified colored noise model (UCNA). Whereas in the limit of short but finite persistence time the pressure in the UCNA model can be obtained by different methods which have an analog in equilibrium systems, in the remaining two models only the virial route is, in general, possible. According to this method, notwithstanding each model obeys its own specific microscopic law of evolution, the pressure displays a certain universal behavior. For generic interparticle and confining potentials, we derive a formula which establishes a correspondence between the GCN and the UCNA pressures. In order to provide explicit formulas and examples, we specialize the discussion to the case of an assembly of elastic dumbbells confined to a parabolic well. By employing the UCNA we find that, for this model, the pressure determined by the thermodynamic method coincides with the pressures obtained by the virial and mechanical methods. The three methods when applied to the GCN give a pressure identical to that obtained via the UCNA. Finally, we find that the ABP virial pressure exactly agrees with the UCNA and GCN result.Comment: 12 pages, 1 figure Submitted for publication 23rd of January 2017 The introduction has been modifie

Ambient Synthesis of Tricyclic Naphthalenes via Stepwise Styryl-yne Dearomative Diels{ extendash}Alder Cyclization

A cascade of styrylynols promoted by MnO2 allows the synthesis of fused tricycles with a naphthalene core. The reaction occurs under ambient conditions, offering a practical synthetic tool because of the inexpensive and abundant manganese species. The method affords products through the sequential oxidation of a propargyl alcohol, stepwise Diels-Alder cyclization, and finally rearomatization. According to density functional theory, the usually unfavorable stepwise Diels-Alder mechanism is instead a general tool for eliciting otherwise challenging dearomative annulation

Body mass index and age correlate with antioxidant supplementation effects on sperm quality: Post hoc analyses from a double-blind placebo-controlled trial

Spermatozoa are vulnerable to lack of energy and oxidative stress as a result of elevated levels of reactive oxygen species. Therefore, it is essential that appropriate nutrients are available during maturation. This randomised, double-blind, placebo-controlled trial investigated the effect of 6-month supplementation with carnitines and other micronutrients on sperm quality in 104 subjects with oligo- and/or astheno- and/or teratozoospermia with or without varicocele. Semen analyses were done at the beginning and end of the treatment. In addition to main analyses, post hoc analyses for age and body mass index (BMI) were carried out. Results were interpreted by dividing the population into two age and BMI classes. In 94 patients who completed the study, all sperm parameters increased in supplemented patients compared to the placebo group. A significant (p = .0272) difference in supplementation efficacy was observed for total motility on patients with varicocele and BMI < 25. In the same group, also the progressive motility was significantly superior (p = .0159). For Responder analysis, total motility results were confirmed in both the cited group (p = .0066) and in the varicocele group with BMI < 25 and age < 35 (p = .0078). This study suggests that supplementation is more effective in subjects with varicocele younger than 35 years with BMI < 25