Exact Free Energy Functional for a Driven Diffusive Open Stationary Nonequilibrium System

We obtain the exact probability $\exp[-L {\cal F}(\{\rho(x)\})]$ of finding a macroscopic density profile $\rho(x)$ in the stationary nonequilibrium state of an open driven diffusive system, when the size of the system $L \to \infty$. $\cal F$, which plays the role of a nonequilibrium free energy, has a very different structure from that found in the purely diffusive case. As there, $\cal F$ is nonlocal, but the shocks and dynamic phase transitions of the driven system are reflected in non-convexity of $\cal F$, in discontinuities in its second derivatives, and in non-Gaussian fluctuations in the steady state.Comment: LaTeX2e, RevTeX4, PiCTeX. Four pages, one PiCTeX figure included in TeX source fil

TIE1 and TEK signalling, intraocular pressure, and primary open-angle glaucoma: a Mendelian randomization study

Background: In primary open-angle glaucoma (POAG), lowering intraocular pressure (IOP) is the only proven way of slowing vision loss. Schlemm’s canal (SC) is a hybrid vascular and lymphatic vessel that mediates aqueous humour drainage from the anterior ocular chamber. Animal studies support the importance of SC endothelial angiopoietin-TEK signalling, and more recently TIE1 signalling, in maintaining normal IOP. However, human genetic support for a causal role of TIE1 and TEK signalling in lowering IOP is currently lacking. Methods: GWAS summary statistics were obtained for plasma soluble TIE1 (sTIE1) protein levels (N = 35,559), soluble TEK (sTEK) protein levels (N = 35,559), IOP (N = 139,555) and POAG (Ncases = 16,677, Ncontrols = 199,580). Mendelian randomization (MR) was performed to estimate the association of genetically proxied TIE1 and TEK protein levels with IOP and POAG liability. Where significant MR estimates were obtained, genetic colocalization was performed to assess the probability of a shared causal variant (PPshared) versus distinct (PPdistinct) causal variants underlying TIE1/TEK signalling and the outcome. Publicly available single-nucleus RNA-sequencing data were leveraged to investigate differential expression of TIE1 and TEK in the human ocular anterior segment. Results: Increased genetically proxied TIE1 signalling and TEK signalling associated with a reduction in IOP (− 0.21 mmHg per SD increase in sTIE1, 95% CI = − 0.09 to − 0.33 mmHg, P = 6.57 × 10–4, and − 0.14 mmHg per SD decrease in sTEK, 95% CI = − 0.03 to − 0.25 mmHg, P = 0.011), but not with POAG liability. Colocalization analysis found that the probability of a shared causal variant was greater for TIE1 and IOP than for TEK and IOP (PPshared/(PPdistinct + PPshared) = 0.98 for TIE1 and 0.30 for TEK). In the anterior segment, TIE1 and TEK were preferentially expressed in SC, lymphatic, and vascular endothelium. Conclusions: This study provides novel human genetic support for a causal role of both TIE1 and TEK signalling in regulating IOP. Here, combined evidence from cis-MR and colocalization analyses provide stronger support for TIE1 than TEK as a potential IOP-lowering therapeutic target

TIE1 and TEK signalling, intraocular pressure, and primary open-angle glaucoma: a Mendelian randomization study

BACKGROUND: In primary open-angle glaucoma (POAG), lowering intraocular pressure (IOP) is the only proven way of slowing vision loss. Schlemm's canal (SC) is a hybrid vascular and lymphatic vessel that mediates aqueous humour drainage from the anterior ocular chamber. Animal studies support the importance of SC endothelial angiopoietin-TEK signalling, and more recently TIE1 signalling, in maintaining normal IOP. However, human genetic support for a causal role of TIE1 and TEK signalling in lowering IOP is currently lacking. METHODS: GWAS summary statistics were obtained for plasma soluble TIE1 (sTIE1) protein levels (N = 35,559), soluble TEK (sTEK) protein levels (N = 35,559), IOP (N = 139,555) and POAG (Ncases = 16,677, Ncontrols = 199,580). Mendelian randomization (MR) was performed to estimate the association of genetically proxied TIE1 and TEK protein levels with IOP and POAG liability. Where significant MR estimates were obtained, genetic colocalization was performed to assess the probability of a shared causal variant (PPshared) versus distinct (PPdistinct) causal variants underlying TIE1/TEK signalling and the outcome. Publicly available single-nucleus RNA-sequencing data were leveraged to investigate differential expression of TIE1 and TEK in the human ocular anterior segment. RESULTS: Increased genetically proxied TIE1 signalling and TEK signalling associated with a reduction in IOP (- 0.21 mmHg per SD increase in sTIE1, 95% CI = - 0.09 to - 0.33 mmHg, P = 6.57 × 10-4, and - 0.14 mmHg per SD decrease in sTEK, 95% CI = - 0.03 to - 0.25 mmHg, P = 0.011), but not with POAG liability. Colocalization analysis found that the probability of a shared causal variant was greater for TIE1 and IOP than for TEK and IOP (PPshared/(PPdistinct + PPshared) = 0.98 for TIE1 and 0.30 for TEK). In the anterior segment, TIE1 and TEK were preferentially expressed in SC, lymphatic, and vascular endothelium. CONCLUSIONS: This study provides novel human genetic support for a causal role of both TIE1 and TEK signalling in regulating IOP. Here, combined evidence from cis-MR and colocalization analyses provide stronger support for TIE1 than TEK as a potential IOP-lowering therapeutic target

Hydrodynamic Coupling of Two Brownian Spheres to a Planar Surface

We describe direct imaging measurements of the collective and relative diffusion of two colloidal spheres near a flat plate. The bounding surface modifies the spheres' dynamics, even at separations of tens of radii. This behavior is captured by a stokeslet analysis of fluid flow driven by the spheres' and wall's no-slip boundary conditions. In particular, this analysis reveals surprising asymmetry in the normal modes for pair diffusion near a flat surface.Comment: 4 pages, 4 figure

Screened and Unscreened Phases in Sedimenting Suspensions

A coarse-grained stochastic hydrodynamical description of velocity and concentration fluctuations in steadily sedimenting suspensions is constructed, and analyzed using self-consistent and renormalization group methods. We find that there exists a dynamical, non-equilibrium phase transition from an "unscreened" phase in which we recover the Caflisch-Luke (R.E. Caflisch and J.H.C. Luke, Phys. Fluids 28, 759 (1985)) divergence of the velocity variance to a "screened" phase where the velocity fluctuations have a finite correlation length growing as $\phi^{-1/3}$ where $\phi$ is the particle volume fraction, in agreement with Segr\`e et. al. (Phys. Rev. Lett. 79, 2574 (1997)) and the velocity variance is independent of system size. Detailed predictions are made for the correlation function in both phases and at the transition.Comment: 4 pages, revtex 1 figur

Hydrodynamic interactions in colloidal ferrofluids: A lattice Boltzmann study

We use lattice Boltzmann simulations, in conjunction with Ewald summation methods, to investigate the role of hydrodynamic interactions in colloidal suspensions of dipolar particles, such as ferrofluids. Our work addresses volume fractions $\phi$ of up to 0.20 and dimensionless dipolar interaction parameters $\lambda$ of up to 8. We compare quantitatively with Brownian dynamics simulations, in which many-body hydrodynamic interactions are absent. Monte Carlo data are also used to check the accuracy of static properties measured with the lattice Boltzmann technique. At equilibrium, hydrodynamic interactions slow down both the long-time and the short-time decays of the intermediate scattering function $S(q,t)$, for wavevectors close to the peak of the static structure factor $S(q)$, by a factor of roughly two. The long-time slowing is diminished at high interaction strengths whereas the short-time slowing (quantified via the hydrodynamic factor $H(q)$) is less affected by the dipolar interactions, despite their strong effect on the pair distribution function arising from cluster formation. Cluster formation is also studied in transient data following a quench from $\lambda = 0$; hydrodynamic interactions slow the formation rate, again by a factor of roughly two

Re-Examination of Generation of Baryon and Lepton Number Asymmetries by Heavy Particle Decay

It is shown that wave function renormalization can introduce an important contribution to the generation of baryon and lepton number asymmetries by heavy particle decay. These terms, omitted in previous analyses, are of the same order of magnitude as the standard terms. A complete cancellation of leading terms can result in some interesting cases.Comment: 12 pages, 2 Feynman graphs (not included), UPR-055

Long-range correlations in non-equilibrium systems: Lattice gas automaton approach

In systems removed from equilibrium, intrinsic microscopic fluctuations become correlated over distances comparable to the characteristic macroscopic length over which the external constraint is exerted. In order to investigate this phenomenon, we construct a microscopic model with simple stochastic dynamics using lattice gas automaton rules that satisfy local detailed balance. Because of the simplicity of the automaton dynamics, analytical theory can be developed to describe the space and time evolution of the density fluctuations. The exact equations for the pair correlations are solved explicitly in the hydrodynamic limit. In this limit, we rigorously derive the results obtained phenomenologically by fluctuating hydrodynamics. In particular, the spatial algebraic decay of the equal-time fluctuation correlations predicted by this theory is found to be in excellent agreement with the results of our lattice gas automaton simulations for two different types of boundary conditions. Long-range correlations of the type described here appear generically in dynamical systems that exhibit large scale anisotropy and lack detailed balance.Comment: 23 pages, RevTeX; to appear in Phys. Rev.

Comparative simulation study of colloidal gels and glasses

Using computer simulations, we identify the mechanisms causing aggregation and structural arrest of colloidal suspensions interacting with a short-ranged attraction at moderate and high densities. Two different non-ergodicity transitions are observed. As the density is increased, a glass transition takes place, driven by excluded volume effects. In contrast, at moderate densities, gelation is approached as the strength of the attraction increases. At high density and interaction strength, both transitions merge, and a logarithmic decay in the correlation function is observed. All of these features are correctly predicted by mode coupling theory