In this paper we consider drug binding in the arterialwall following delivery by a drug-eluting stent. Whilst it is now generally accepted that a non-linear saturable reversible binding model is required to properly describe the binding process, the precise form of the binding model varies between authors. Our particular interest in this manuscript is in assessing to what extent modelling specific and non-specific binding in the arterial wall as separate phases is important. We study this issue by extending a recently developed coupled model of drug release and arterial tissue distribution, and comparing simulated profiles of drug concentration and drug mass in each phase within the arterial tissue.

We present a method for applying a class of velocity-dependent forces within a multicomponent lattice Boltzmann equation simulation that is designed to recover continuum regime incompressible hydrodynamics. This method is applied to the problem, in two dimensions, of constraining to uniformity the tangential velocity of a vesicle membrane implemented within a recent multicomponent lattice Boltzmann simulation method, which avoids the use of Lagrangian boundary tracers. The constraint of uniform tangential velocity is carried by an additional contribution to an immersed boundary force, which we derive here from physical arguments. The result of this enhanced immersed boundary force is to apply a physically appropriate boundary condition at the interface between separated lattice fluids, defined as that region over which the phase-field varies most rapidly. Data from this enhanced vesicle boundary method are in agreement with other data obtained using related methods [e.g., T. Kruger, S. Frijters, F. Gunther, B. Kaoui, and J. Harting, Eur. Phys. J. 222, 177 (2013)] and underscore the importance of a correct vesicle membrane condition.

Nowadays, several models of unidimensional fluid jets exploit discrete element methods. In some cases, as for models aiming at describing the electrospinning nanofabrication process of polymer fibers, discrete element methods suffer a non-constant resolution of the jet representation. We develop a dynamic mesh- refinement method for the numerical study of the electro-hydrodynamic behavior of charged jets using discrete element methods. To this purpose, we import ideas and techniques from the string method originally developed in the framework of free-energy landscape simulations. The mesh-refined discrete element method is demonstrated for the case of electrospinning applications.

Classical as well as quantum features of the late-time evolution of cosmological models with fluids obeying a Shan-Chen-like equation of state are studied. The latter is of the type p=weff(?)? and has been used in previous works to describe, e.g., a possible scenario for the growth of the dark-energy content of the present Universe. At the classical level, the fluid dynamics in a spatially flat Friedmann-Robertson-Walker background implies the existence of two possible equilibrium solutions depending on the model parameters associated with (asymptotic) finite pressure and energy density. We show that no future cosmological singularity is developed during the evolution for this specific model. The corresponding quantum effects in the late-time behavior of the system are also investigated within the framework of quantum geometrodynamics, i.e., by solving the (minisuperspace) Wheeler-DeWitt equation in the Born-Oppenheimer approximation, constructing wave packets and analyzing their behavior.

We analytically compute, through the six-and-a-half post-Newtonian order, the second-order-in-eccentricity piece of the Detweiler-Barack-Sago gauge-invariant redshift function for a small mass in eccentric orbit around a Schwarzschild black hole. Using the first law of mechanics for eccentric orbits [A. Le Tiec, First law of mechanics for compact binaries on eccentric orbits, Phys. Rev. D 92, 084021 (2015).] we transcribe our result into a correspondingly accurate knowledge of the second radial potential of the effective-one-body formalism [A. Buonanno and T. Damour, Effective one-body approach to general relativistic two-body dynamics, Phys. Rev. D 59, 084006 (1999).]. We compare our newly acquired analytical information to several different numerical self-force data and find good agreement, within estimated error bars. We also obtain, for the first time, independent analytical checks of the recently derived, comparable-mass fourth-post-Newtonian order dynamics [T. Damour, P. Jaranowski, and G. Schaefer, Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems, Phys. Rev. D 89, 064058 (2014).].

We raise the analytical knowledge of the eccentricity expansion of the Detweiler-Barack-Sago redshift invariant in a Schwarzschild spacetime up to the 9.5th post-Newtonian order (included) for the e(2) and e(4) contributions, and up to the 4th post-Newtonian order for the higher eccentricity contributions through e(20). We convert this information into an analytical knowledge of the effective-one-body radial potentials (d) over bar (u), p(u) and q(u) through the 9.5th post-Newtonian order. We find that our analytical results are compatible with current corresponding numerical self-force data.

Popular models of fast radio bursts (FRBs) involve the gravitational collapse of neutron star progenitors to black holes. It has been proposed that the shedding of the strong neutron star magnetic field (B) during the collapse is the power source for the radio emission. Previously, these models have utilized the simplicity of the Schwarzschild metric which has the restriction that the magnetic flux is magnetic 'hair' that must be shed before final collapse. But neutron stars have angular momentum and charge and a fully relativistic Kerr-Newman solution exists in which B has its source inside of the event horizon. In this Letter, we consider the magnetic flux to be shed as a consequence of the electric discharge of a metastable collapsed state of a Kerr-Newman black hole. It has also been argued that the shedding model will not operate due to pair creation. By considering the pulsar death line, we find that for a neutron star with B = 10(11)-10(13) G and a long rotation period, >1s this is not a concern. We also discuss the observational evidence supporting the plausibility of magnetic flux shedding models of FRBs that are spawned from rapidly rotating progenitors.

The field equations of the recent nonlocal generalization of Einstein's theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of conformally flat spacetimes. Even in this simple case, the field equations are intractable. Therefore, to gain insight into the nature of these equations, we investigate the structure of nonlocal gravity (NLG) in 2D spacetimes. While any smooth 2D spacetime is conformally flat and satisfies Einstein's field equations, only a subset containing either a Killing vector or a homothetic Killing vector can satisfy the field equations of NLG.

We present the first analytic computation of the Detweiler-Barack-Sago gauge-invariant redshift function for a small mass in eccentric equatorial orbit around a spinning black hole. Our results give the redshift contributions that mix eccentricity and spin effects, through second order in eccentricity, second order in spin parameter, and the eight-and-a-half post-Newtonian order.

A 'temporal analogue' of the standard Poynting-Robertson effect is analyzed as induced by a dust of particles (instead of a gas of photons) surrounding a Schwarzschild black hole. Test particles inside this cloud undergo acceleration effects due to the presence of a friction force, so that the fate of their evolution can be completely different from the corresponding geodesic motion. Typical situations are discussed of hyperbolic motion of particles scattered by the black hole in the presence of a dust filling the whole spacetime region outside the horizon as well as particles which free fall radially crossing a corona located at a certain distance from the horizon. The existence of equilibrium orbits may prevent particles from either falling into the hole or escaping to infinity.

We consider Detweiler's redshift variable z for a nonspinning mass m(1) in circular motion (with orbital frequency Omega) around a nonspinning mass m(2). We show how the combination of effective-one-body (EOB) theory with the first law of binary dynamics allows one to derive a simple, exact expression for the functional dependence of z on the (gauge-invariant) EOB gravitational potential u = (m(1) + m(2))/R. We then use the recently obtained high-post-Newtonian(PN)-order knowledge of the main EOB radial potential A(u;v) [where v = m(1)m(2)/(m(1) + m(2))(2)] to decompose the second-self-force-order contribution to the function z(m(2)Omega(,) m(1)/m(2)) into a known part (which goes beyond the 4PN level in including the 5PN logarithmic term and the 5.5PN contribution) and an unknown one [depending on the yet unknown, 5PN, 6PN, ..., contributions to the O(v(2)) contribution to the EOB radial potential A(u;v)]. We apply our results to the second-self-force-order contribution to the frequency shift of the last stable orbit. We indicate the expected singular behaviors, near the lightring, of the second-self-force-order contributions to both the redshift and the EOB A potential. Our results should help both in extracting information of direct dynamical significance from ongoing second-self-force-order computations and in parametrizing their global strong-field behaviors. We also advocate computing second-self-force-order conservative quantities by iterating the time-symmetric Green-function in the background spacetime.

In general relativity, relativistic gravity gradiometry involves the measurement of the relativistic tidal matrix, which is theoretically obtained from the projection of the Riemann curvature tensor onto the orthonormal tetrad frame of an observer. The observer's 4-velocity vector defines its local temporal axis and its local spatial frame is defined by a set of three orthonormal nonrotating gyro directions. The general tidal matrix for the timelike geodesics of Kerr spacetime has been calculated by Marck [Proc. R. Soc. A 385, 431 (1983)]. We are interested in the measured components of the curvature tensor along the inclined "circular" geodesic orbit of a test mass about a slowly rotating astronomical object of mass M and angular momentum J. Therefore, we specialize Marck's results to such a "circular" orbit that is tilted with respect to the equatorial plane of the Kerr source. To linear order in J, we recover the gravitomagnetic beating phenomenon [B. Mashhoon and D.S. Theiss, Phys. Rev. Lett. 49, 1542 (1982)], where the beat frequency is the frequency of geodetic precession. The beat effect shows up as a special long-period gravitomagnetic part of the relativistic tidal matrix; moreover, the effect's short-term manifestations are contained in certain post-Newtonian secular terms. The physical interpretation of this effect is briefly discussed.

The precession of a test gyroscope along stable bound equatorial plane orbits around a Kerr black hole is analyzed, and the precession angular velocity of the gyro's parallel transported spin vector and the increment in the precession angle after one orbital period is evaluated. The parallel transported Marck frame which enters this discussion is shown to have an elegant geometrical explanation in terms of the electric and magnetic parts of the Killing-Yano 2-form and a Wigner rotation effect.

The precession of a test gyroscope along unbound equatorial plane geodesic orbits around a Kerr black hole is analyzed with respect to a static reference frame whose axes point towards the "fixed stars." The accumulated precession angle after a complete scattering process is evaluated and compared with the corresponding change in the orbital angle. Limiting results for the nonrotating Schwarzschild black hole case are also discussed.

Scalar field self-force effects on a scalar charge orbiting a Reissner-Nordström black hole are investigated. The scalar wave equation is solved analytically in a post-Newtonian framework, and the solution is used to compute the self-field (up to 7.5 post-Newtonian order) as well as the components of the self-force at the particle's location. The energy fluxes radiated to infinity and down the hole are also evaluated. Comparison with previous numerical results in the Schwarzschild case shows a reasonable agreement in both strong field and weak field regimes.

The scattering of massive particles by a Schwarzschild black hole also undergoing a drag force is considered. The latter is modeled as a viscous force acting on the orbital plane, with components proportional to the associated particle 4-velocity components. The energy and angular momentum losses as well as the dependence of the hyperbolic scattering angle on the strength of the drag are investigated in situations where strong field effects cause large deflections.

Objectives Identifying the predictive factors of Sustained Virological Response (SVR) represents an important challenge in new interferon-based DAA therapies. Here, we analyzed the kinetics of antiviral response associated with a triple drug regimen, and the association between negative residual viral load at different time points during treatment. Methods Twenty-three HCV genotype 1 (GT 1a n = 11; GT1b n = 12) infected patients were included in the study. Linear Discriminant Analysis (LDA) was used to establish possible association between HCV RNA values at days 1 and 4 from start of therapy and SVR. Principal compo- nent analysis (PCA) was applied to analyze the correlation between HCV RNA slope and SVR. A ultrasensitive (US) method was established to measure the residual HCV viral load in those samples which resulted "detected <12IU/ml" or undetectable with ABBOTT stan- dard assay, and was retrospectively used on samples collected at different time points to establish its predictive power for SVR. Results According to LDA, there was no association between SVR and viral kinetics neither at time points earlier than 1 week (days 1 and 4) after therapy initiation nor later. The slopes were not relevant for classifying patients as SVR or no-SVR. No significant differences were observed in the median HCV RNA values at T0 among SVR and no-SVR patients. HCV RNA values with US protocol (LOD 1.2 IU/ml) after 1 month of therapy were considered; the area under the ROC curve was 0.70. Overall, PPV and NPV of undetectable HCV RNA with the US method for SVR was 100% and 46.7%, respectively; sensitivity and specificity were 38.4% and 100% respectively. Conclusion HCV RNA "not detected" by the US method after 1 month of treatment is predictive of SVR in first generation Protease inhibitor (PI)-based triple therapy. The US method could have clinical utility for advanced monitoring of virological response in new interferon based DAA combination regimens.

A deep understanding of the dynamics and rheology of suspensions of vesicles, cells, and capsules is relevant for different applications, ranging from soft glasses to blood flow [1]. I will present the study of suspensions of fluid vesicles by a combination of molecular dynamics and mesoscale hydrodynamics simulations (multi-particle collision dynamics) in two dimensions [2], pointing out the big potential of the numerical method to address problems in soft matter. The flow behavior is studied as a function of the shear rate, the volume fraction of vesicles, and the viscosity ratio between inside and outside fluids. Results are obtained for the interactions of two vesicles, the intrinsic viscosity of the suspension, and the cell-free layer near the walls [3-5]. [1] D. Barthes-Biesel, Annu. Rev. Fluid Mech. 48, 25 (2016) [2] R. Finken, A. Lamura, U. Seifert, and G. Gompper, Eur. Phys. J. E 25, 309 (2008) [3] A. Lamura and G. Gompper, EPL 102, 28004 (2013) [4] A. Lamura and G. Gompper, Procedia IUTAM 16, 3 (2015) [5] E. Afik, A. Lamura, and V. Steinberg, EPL 113, 38003 (2016)

We give a general Gaussian bound for the first chaos (or innovation) of point processes with stochastic intensity constructed by embedding in a bivariate Poisson process. We apply the general result to nonlinear Hawkes processes, providing quantitative central limit theorems.

Bootstrap percolation is a well-known activation process in a graph, in which a node becomes active when it has at least r active neighbors. Such process, originally studied on regular structures, has been recently investigated also in the context of random graphs, where it can serve as a simple model for a wide variety of cascades, such as the spreading of ideas, trends, viral contents, etc. over large social networks. In particular, it has been shown that in G(n, p) the final active set can exhibit a phase transition for a sub-linear number of seeds. In this paper, we propose a unique framework to study similar sub-linear phase transitions for a much broader class of graph models and epidemic processes. Specifically, we consider i) a generalized version of bootstrap percolation in G(n, p) with random activation thresholds and random node-tonode influences; ii) different random graph models, including graphs with given degree sequence and graphs with community structure (block model). The common thread of our work is to show the surprising sensitivity of the critical seed set size to extreme values of distributions, which makes some systems dramatically vulnerable to large-scale outbreaks. We validate our results running simulation on both synthetic and real graphs.