We explore the impact of geometrical corrugations on the near-wall flow properties of a soft material driven in a confined rough microchannel. By means of numerical simulations, we perform a quantitative analysis of the relation between the flow rate ? and the wall stress ?w for a number of setups, by changing both the roughness values as well as the roughness shape. Roughness suppresses the flow, with the existence of a characteristic value of ?w at which flow sets in. Just above the onset of flow, we quantitatively analyze the relation between ? and ?w. While for smooth walls a linear dependence is observed, steeper behaviours are found to set in by increasing wall roughness. The variation of the steepness, in turn, depends on the shape of the wall roughness, wherein gentle steepness changes are promoted by a variable space localization of the roughness.

Drug releasing capsules and droplets are largely used in biomedical applications. Such vehicles consist of a drug-loaded core surrounded by a thin semi-permeable layer. Diffusion is by far the dominant mechanism in drug delivery, beside other physico-chemical factors, such as osmosis, drug dissolution, polymer swelling and degradation. We upgrade existing mechanistic models by extending their applications to the composite structures, and characterize the kinetics of the drug eluted from the vehicle into the external targeted medium. We develop a theoretical and computational study aimed at modelling the drug release from a composite spherical core-shell capsule or a double emulsion having either a protective coating or a surfactant, under the assumption of radial symmetry. The problem of release from such a layer-by-layer composite systems is described by a system of coupled partial differential equations, which we solve analytically in terms of Fourier series or using numerical solutions. In addition to the conventional partitioning and interlayer conditions, we consider a finite mass transfer coefficient, to model the resistance at the surface. Expressions for the concentration and the cumulative mass in all layers are given to show the dependence and sensitivity to parameters, such as diffusivity, permeability and partition coefficients. The release curve characterizes the drug transport mechanism and suggests how to guarantee a controlled release. The proposed model constitutes a simple tool to predict the release from composite materials that, measuring their performance or comparing different configurations, can help in designing novel drug delivery systems.

The migration of endothelial cells (ECs) is critical for various processes including vascular wound healing, tumor angiogenesis, and the development of viable endovascular implants. EC migration is regulated by intracellular ATP and recent observations in our laboratory on ECs cultured on line patterns - surfaces where cellular adhesion is limited to 15 m-wide lines that physically confine the cells - have demonstrated very different migration behavior from cells on control unpatterned surfaces. Specifically, while ECs on unpatterned surfaces exhibit random motion in the absence of flow and persistent directed motion under flow, cells on line patterns both in the presence and absence of flow exhibit three distinct migration phenotypes: a) running- cells are polarized and migrate continuously and persistently on the adhesive lines with possible directional changes, b) undecided- cells are elongated and exhibit periodic changes in the direction of their polarization and minimal net migration, and c) tumbling-like - cells migrate persistently for a certain amount of time but then stop and round up for a few hours before spreading again and resuming migration. We hypothesize that the three migration phenotypes on patterns reflect differences in intracellular ATP profiles. Specifically, we propose that running ECs have sufficiently high ATP concentrations at all time in order to elongate, polarize, and migrate. In contrast, we suggest that undecided ECs have an intermediate level of ATP concentration that is sufficiently high for cell spreading but not for sustained polarization and migration. Finally, tumbling-like cells are thought to have low levels of intracellular ATP during the rounding-up phase but manage to "recharge their batteries" so that ATP levels recover sufficiently for the cells to eventually elongate, polarize, and migrate. To test this hypothesis, we have developed a mathematical model that describes the time evolution of intracellular ATP concentration. The computations provide the time dynamics of both EC length and intracellular ATP concentration. The results demonstrate that depending on the parameter values adopted for the simulations, the different hypothesized intracellular ATP profiles can indeed be obtained. Thus, for certain parameter values, we observe a rapid and sustained increase in ATP concentration, corresponding to the hypothesized behavior for running cells. For other parameter values, the ATP concentration remains within an intermediate range throughout, presumably reflecting undecided cells. Finally, for part of the parameter space, we obtain an initial drop in the concentration followed by recovery, as suggested for tumbling-like cells. The results are consistent with the notion that changes in intracellular ATP modulate the phenotype of EC migration on line patterns.

The migration of endothelial cells (ECs) is critical for various processes including vascular wound healing, tumor angiogenesis, and the development of viable endovascular implants. EC migration is regulated by intracellular ATP; thus, elucidating the dynamics of intracellular ATP concentration is important. Recent observations (time-lapse imaging over 12-hr periods) in our laboratory on ECs cultured on line patterns - surfaces where cellular adhesion is limited to 15 ?m-wide lines that physically confine the cells - have demonstrated very different migration behavior from cells on control unpatterned surfaces. Specifically, while ECs on unpatterned surfaces exhibit random motion in the absence of flow and persistent directed motion under flow, cells on line patterns both in the presence and absence of flow exhibit three distinct migration phenotypes (Fig. 1): a) running - cells are polarized and migrate continuously and persistently on the adhesive lines with possible directional changes, b) undecided - cells are elongated and exhibit periodic changes in the direction of their polarization and minimal net migration, and c) tumbling-like - cells migrate persistently for a certain amount of time but then stop and round up for a few hours before spreading again and resuming migration. We hypothesize that the three migration phenotypes on line patterns reflect differences in intracellular ATP profiles. Specifically, we propose that running ECs have sufficiently high ATP concentrations at all time in order to elongate, polarize, and migrate. In contrast, we suggest that undecided ECs have an intermediate level of ATP concentration that is sufficiently high for cell spreading but not for sustained polarization and migration. Finally, tumbling-like cells are thought to have low levels of intracellular ATP during the rounding-up phase but manage to "recharge their batteries" so that ATP levels recover sufficiently for the cells to eventually elongate, polarize, and migrate. To test this hypothesis, we have developed a mathematical model that describes the time evolution of intracellular ATP concentration.

We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as those imposing a finite mass resistance at the external surface of the sphere. While the work is applicable to the generic problem of heat or mass transfer in a multi-layer sphere, the analysis and results are presented in the context of drug kinetics for desorbing and absorbing spherical microcapsules. We derive an analytical solution for the concentration in the sphere and in the surrounding medium that avoids any artificial truncation at a finite distance. The closed-form solution in each concentric layer is expressed in terms of a suitably-defined inverse Laplace transform that can be evaluated numerically. Concentration profiles and drug mass curves in the spherical layers and in the external environment are presented and the dependency of the solution on the mass transfer coefficient at the surface of the sphere analyzed.

In this paper, we consider a multi-layer diffusion model of drug release from a composite spherical microcapsule into an external surrounding medium. Based on this model, we present two approaches for estimating the release time, i.e. the time required for the drug-filled capsule to be depleted. Both approaches make use of temporal moments of the drug concentration at the centre of the capsule, which provide useful insight into the timescale of the process and can be computed exactly without explicit calculation of the full transient solution of the multi-layer diffusion model. The first approach, which uses the zeroth and first temporal moments only, provides a crude approximation of the release time taking the form of a simple algebraic expression involving the various parameters in the model (e.g. layer diffusivities, mass transfer coefficients, partition coefficients) while the second approach yields an asymptotic estimate of the release time that depends on consecutive higher moments. Through several test cases, we show that both approaches provide a computationally- cheap and useful tool to quantify the release time of composite microcapsule configurations.

Nel documento si fornisce una caratterizzazione costruttiva dei Path Graph alternativa a quella già nota e data mediante famiglie di sottografi proibiti.

The Wigner rotations arising from the combination of boosts along two different directions arc rederived from a relative boost point of view and applied to study gyroscope spin precession along timelike geodesics in a Kerr spacetime. First this helps to clarify the geometrical properties of Marck's recipe for reducing the equations of parallel transport along such world lines expressed in terms of the constants of the motion to a single differential equation for the essential planar rotation. Second this shows how to bypass Marck's reduction procedure by direct boosting of orthonormal frames associated with natural observer families. Wigner rotations mediate the relationship between these two descriptions for reaching the same parallel transported frame along a geodesic. The comparison is particularly straightforward in the case of equatorial plane motion of a test gyroscope, where Marck's scalar angular velocity captures the essential cumulative spin precession relative to the spherical frame locked to spatial infinity. These cumulative precession effects are computed explicitly for both bound and unbound equatorial plane geodesic orbits. The latter case is of special interest in view of recent applications to the dynamics of a two-body system with spin. Our results are consistent with the point-particle limit of such two-body results and also pave the way for similar computations in the context of gravitational self-force.

The energy content of cylindrical gravitational wave spacetimes is analyzed by considering two local descriptions of energy associated with the gravitational field, namely those based on the C-energy and the Bel-Robinson super-energy tensor. A Poynting-Robertson-like effect on the motion of massive test particles, beyond the geodesic approximation, is discussed, allowing them to interact with the background field through an external force which accounts for the exchange of energy and momentum between particles and waves. In addition, the relative strains exerted on a bunch of particles displaced orthogonally to the direction of propagation of the wave are examined, providing invariant information on spacetime curvature effects caused by the passage of the wave. The explicit examples of monochromatic waves with either a single or two polarization states as well as pulses of gravitational radiation are discussed.

Spinning neutron stars acquire a quadrupole moment due to their own rotation. This quadratic-in-spin, self-spin effect depends on the equation of state (EOS) and affects the orbital motion and rate of inspiral of neutron star binaries. Building upon circularized post-Newtonian results, we incorporate the EOS-dependent self-spin (or monopole-quadrupole) terms in the spin-aligned effective-one-body (EOB) waveform model TEOBResumS at next-to-next-to-leading (NNLO) order, together with other (bilinear, cubic and quartic) nonlinear-in-spin effects (at leading order, LO). We point out that the structure of the Hamiltonian of TEOBResumS is such that it already incorporates, in the binary black hole case, the recently computed [Levi and Steinhoff, arXiv: 1607.04252] quartic-in-spin LO term. Using the gauge-invariant characterization of the phasing provided by the function Q(omega) = omega(2)/omega of omega = 2 pi f, where f is the gravitational wave frequency, we study the EOS dependence of the self-spin effects and show that: (i) the next-to-leading order (NLO) and NNLO monopole-quadrupole corrections yield increasingly phase-accelerating effects compared to the corresponding LO contribution; (ii) the standard TaylorF2 post-Newtonian (PN) treatment of NLO (3PN) EOS-dependent self-spin effects makes their action stronger than the corresponding EOB description; (iii) the addition to the standard 3PN TaylorF2 post-Newtonian phasing description of self-spin tail effects at LO allows one to reconcile the self-spin part of the TaylorF2 PN phasing with the corresponding TEOBResumS one up to dimensionless frequencies M omega similar or equal to 0.04-0.06. Such a tail-augmented TaylorF2 approximant then yields an analytically simplified, EOB-faithful, representation of the EOS-dependent self-spin phasing that can be useful to improve current PN-based (or phenomenological) waveform models for inspiralling neutron star binaries. Finally, by generating the inspiral dynamics using the post-adiabatic approximation, incorporated in a new implementation of TEOBResumS, one finds that the computational time needed to obtain a typical waveform (including all multipoles up to l = 8) from 10 Hz is of the order of 0.4 sec.

Using standard cylindrical-like coordinates naturally adapted to the cylindrical symmetry of the Godel spacetime, we study elliptic like geodesic motion on hyperplanes orthogonal to the symmetry axis through an eccentricity-semi-latus rectum parametrization which is familiar from the Newtonian description of a two-body system. We compute several quantities which summarize the main features of the motion, namely the coordinate time and proper time periods of the radial motion, the frequency of the azimuthal motion, the full variation of the azimuthal angle over a period, and so on. Exact as well as approximate (i.e., Taylor-expanded in the limit of small eccentricity) analytic expressions of all these quantities are obtained. Finally, we consider their application to the gyroscope precession frequency along these orbits, generalizing the existing results for the circular case.

We investigate the motion of uncharged particles scattered by a binary system consisting of extremely charged black holes in equilibrium as described by the Majumdar-Papapetrou solution. We focus on unbound orbits confined to the plane containing both black holes. We consider the two complementary situations of particles approaching the system along a direction parallel to the axis where the black holes are displaced and orthogonal to it. We numerically compute the scattering angle as a function of the particle's conserved energy parameter, which provides a gauge-invariant information of the scattering process. We also study the precession of a test gyroscope along such orbits and evaluate the accumulated precession angle after a full scattering, which is another gauge-invariant quantity.

The Detweiler-Barack-Sago redshift function for particles moving along slightly eccentric equatorial orbits around a Kerr black hole is currently known up to the second order in eccentricity, second order in spin parameter, and the 8.5 post-Newtonian order. We improve the analytical computation of such a gaugeinvariant quantity by including terms up to the fourth order in eccentricity at the same post-Newtonian approximation level. We also check that our results agrees with the corresponding post-Newtonian expectation of the same quantity, calculated by using the currently known Hamiltonian for spinning binaries.

We analytically compute the gravitational self-force correction to the gyroscope precession along slightly eccentric equatorial orbits in the Kerr spacetime, generalizing previous results for the Schwarzs-child spacetime. Our results are accurate through the 9.5 post-Newtonian order and to second order in both eccentricity and rotation parameter. We also provide a post-Newtonian check of our results based on the currently known Hamiltonian for spinning binaries.

We propose an approach to the numerical simulation of thin-film flows based on the lattice Boltzmann method. We outline the basic features of the method, show in which limits the expected thin-film equations are recovered, and perform validation tests. The numerical scheme is applied to the viscous Rayleigh-Taylor instability of a thin film and to the spreading of a sessile drop toward its equilibrium contact angle configuration. We show that the Cox-Voinov law is satisfied and that the effect of a tunable slip length on the substrate is correctly captured. We address, then, the problem of a droplet sliding on an inclined plane, finding that the Capillary number scales linearly with the Bond number, in agreement with experimental results. At last, we demonstrate the ability of the method to handle heterogenous and complex systems by showcasing the controlled dewetting of a thin film on a chemically structured substrate.

Single-cell RNA-seq (scRNAseq) is a powerful tool to study heterogeneity of cells. Recently, several clustering based methods have been proposed to identify distinct cell populations. These methods are based on different statistical models and usually require to perform several additional steps, such as preprocessing or dimension reduction, before applying the clustering algorithm. Individual steps are often controlled by method-specific parameters, permitting the method to be used in different modes on the same datasets, depending on the user choices. The large number of possibilities that these methods provide can intimidate non-expert users, since the available choices are not always clearly documented. In addition, to date, no large studies have invistigated the role and the impact that these choices can have in different experimental contexts. This work aims to provide new insights into the advantages and drawbacks of scRNAseq clustering methods and describe the ranges of possibilities that are offered to users. In particular, we provide an extensive evaluation of several methods with respect to different modes of usage and parameter settings by applying them to real and simulated datasets that vary in terms of dimensionality, number of cell populations or levels of noise. Remarkably, the results presented here show that great variability in the performance of the models is strongly attributed to the choice of the user-specific parameter settings. We describe several tendencies in the performance attributed to their modes of usage and different types of datasets, and identify which methods are strongly affected by data dimensionality in terms of computational time. Finally, we highlight some open challenges in scRNAseq data clustering, such as those related to the identification of the number of clusters.

Background A subset of individuals affected by imprinting disorders displays multi-locus imprinting disturbances (MLID). MLID has been associated with maternal-effect variants that alter the maintenance of methylation at germline-derived differentially methylated regions (gDMRs) in early embryogenesis. Pedigrees of individuals with MLID also include siblings with healthy phenotype. However, it is unknown if these healthy individuals have MLID themselves or if their methylation patterns differ from those associated with imprinting disorders, and in general, if MLID affects the clinical phenotype. Methods We have investigated gDMR methylation by locus-specific and whole-genome analyses in a family with multiple pregnancy losses, a child with Beckwith-Wiedemann syndrome (BWS) and a further child with no clinical diagnosis of imprinting disorder or other pathologies. Results We detected MLID with different methylation profiles in the BWS-affected and healthy siblings. Whole-exome sequencing demonstrated the presence of novel loss-of-function variants of NLRP5 in compound heterozygosity in the mother. The methylation profiles of the two siblings were compared with those of other cases with MLID and control groups by principal component analysis and unsupervised hierarchical clustering, but while their patterns were clearly separated from those of controls, we were unable to cluster those associated with specific clinical phenotypes among the MLID cases. Conclusion The identification of two novel maternal-effect variants of NLRP5 associated with poly-abortivity and MLID adds further evidence to the role of this gene in the maintenance of genomic imprinting in early embryos. Furthermore, our results demonstrate that within these pedigrees, MLID can also be present in the progeny with healthy phenotype, indicating that some sort of compensation occurs between altered imprinted loci in these individuals. The analysis of larger cohorts of patients with MLID is needed to formulate more accurate epigenotype-phenotype correlations.