Recent developments of the lattice Boltzmann method for large-scale haemodynamic applications are presented, with special focus on multiscale aspects, including the self-consistent dynamics of suspended biological bodies and their coupling to surface structures, such as the glycocalyx, in the proximity of endothelium using unstructured grids. The description of such multiscale phenomena, each one treated with a suitable variation of the lattice Boltzmann method, opens up new perspectives for a fundamental understanding of the physical mechanisms underlying cardiovascular pathologies, such as plaque growth and the subsequent development of atherosclerotic diseases.

Fluid flow through porous media is of great importance for many natural systems, such as transport of groundwater flow, pollution transport and mineral processing. In this paper, we propose and validate a novel finite volume formulation of the lattice Boltzmann method for porous flows, based on the Brinkman-Forchheimer equation. The porous media effect is incorporated as a force term in the lattice Boltzmann equation, which is numerically solved through a cell-centered finite volume scheme. Correction factors are introduced to improve the numerical stability. The method is tested against fully porous Poiseuille, Couette and lid-driven cavity flows. Upon comparing the results with well-documented data available in literature, a satisfactory agreement is observed. The method is then applied to simulate the flow in partially porous channels, in order to verify its potential application to fractured porous conduits, and assess the influence of the main porous media parameters, such as Darcy number, porosity and porous media thickness. © 2013 Springer Science+Business Media New York.

We present a polar coordinate lattice Boltzmann kinetic model for compressible flows. A method to recover the continuum distribution function from the discrete distribution function is indicated. Within the model, a hybrid scheme being similar to, but different from, the operator splitting is proposed. The temporal evolution is calculated analytically, and the convection term is solved via a modified Warming-Beam (MWB) scheme. Within the MWB scheme a suitable switch function is introduced. The current model works not only for subsonic flows but also for supersonic flows. It is validated and verified via the following well-known benchmark tests: (i) the rotational flow, (ii) the stable shock tube problem, (iii) the Richtmyer-Meshkov (RM) instability, and (iv) the Kelvin-Helmholtz instability. As an original application, we studied the nonequilibrium characteristics of the system around three kinds of interfaces, the shock wave, the rarefaction wave, and the material interface, for two specific cases. In one of the two cases, the material interface is initially perturbed, and consequently the RM instability occurs. It is found that the macroscopic effects due to deviating from thermodynamic equilibrium around the material interface differ significantly from those around the mechanical interfaces. The initial perturbation at the material interface enhances the coupling of molecular motions in different degrees of freedom. The amplitude of deviation from thermodynamic equilibrium around the shock wave is much higher than those around the rarefaction wave and material interface. By comparing each component of the high-order moments and its value in equilibrium, we can draw qualitatively the main behavior of the actual distribution function. These results deepen our understanding of the mechanical and material interfaces from a more fundamental level, which is indicative for constructing macroscopic models and other kinds of kinetic models.

We review the general ideas behind coarse-grained representations of fluid dynamics, with special focus on two mesoscopic techniques which have proven particularly successful over the last two decades for the simulation of complex fluid flows, namely Dissipative Particle Dynamics and the Lattice Boltzmann method.

The main purpose of this paper is to develop a novel thermal lattice Boltzmann method (LBM) based on finite volume (FV) formulation. Validation of the suggested formulation is performed by simulating plane Poiseuille, backward-facing step and flow over circular cylinder. For this purpose, a cell-centered scheme is used to discretize the convection operator and the double distribution function model is applied to describe the temperature field. To enhance stability, weighting factors are defined as flux correctors on a D2Q9 lattice. The introduction of pressure-temperature-dependent flux-control coefficients in the streaming operator, in conjunction with suitable boundary conditions, is shown to result in enhanced numerical stability of the scheme. In all cases, excellent agreement with the existing literature is found and shows that the presented method is a promising scheme in simulating thermo-hydrodynamic phenomena.

This contribution aims at introducing the topics of this book. We start with a brief historical excursion on the developments from the law of large numbers to the central limit theorem and large deviations theory. The same topics are then presented using the language of probability theory. Finally, some applications of large deviations theory in physics are briefly discussed through examples taken from statistical mechanics, dynamical and disordered systems.

In this paper we investigate the ability of some recently introduced discrete kinetic models of vehicular traffic to catch, in their large time behavior, typical features of theoretical fundamental diagrams. Specifically, we address the so-called "spatially homogeneous problem" and, in the representative case of an exploratory model, we study the qualitative properties of its solutions for a generic number of discrete microscopic states. This includes, in particular, asymptotic trends and equilibria, whence fundamental diagrams originate.

This book presents mathematical models and numerical simulations of crowd dynamics. The core topic is the development of a new multiscale paradigm, which bridges the microscopic and macroscopic scales taking the most from each of them for capturing the relevant clues of complexity of crowds. The background idea is indeed that most of the complex trends exhibited by crowds are due to an intrinsic interplay between individual and collective behaviors. The modeling approach promoted in this book pursues actively this intuition and profits from it for designing general mathematical structures susceptible of application also in fields different from the inspiring original one. The book considers also the two most traditional points of view: the microscopic one, in which pedestrians are tracked individually, and the macroscopic one, in which pedestrians are assimilated to a continuum. Selected existing models are critically analyzed. The work is addressed to researchers and graduate students.

In this paper we present mathematical tools inspired by the kinetic theory, which can be used to model the social behaviors of large communities of individuals. The focus is especially on human societies, such as the population of a certain country, and on the interplays between concurrent social dynamics, for instance economic issues linked to the formation of political opinions, which sometimes can even degenerate into dramatic extreme events with massive impact (Black Swans). Starting from Boltzmann-type models, we present an evolution of the classical approach of statistical mechanics, whose hallmark is the use of stochastic game theory for the description of social interactions. By this we mean that the latter are modeled as games whose payoffs, however, are known only in probability. This is consistent with the basic unpredictability of human reactions, which ultimately cannot be compared to deterministic mechanical-like "collisions".

In this paper we study a model for traffic flow on networks based on a hyperbolic system of conservation laws with discontinuous flux. Each equation describes the density evolution of vehicles having a common path along the network. In this formulation the junctions disappear since each path is considered as a single uninterrupted road. We consider a Godunov-based approximation scheme for the system which is very easy to implement. Besides basic properties like the conservation of cars and positive bounded solutions, the scheme exhibits other nice properties, being able to select automatically a solution at network's nodes without requiring external procedures (e.g., maximization of the flux via a linear programming method). Moreover, the scheme can be interpreted as a discretization of the traffic models with buffer, although no buffer is introduced here. Finally, we show how the scheme can be recast in the framework of the classical theory of traffic flow on networks, where a conservation law has to be solved on each arc of the network. This is achieved by solving the Riemann problem for a modified equation, and showing that its solution corresponds to the one computed by the numerical scheme.

The problem of diurnal variation in surface emissivity over the Sahara Desert during non-raining days is studied and assessed with observations from the Infrared Atmospheric Sounding Interferometer (IASI). The analysis has been performed over a Sahara Desert dune target area during July 2010. Spinning Enhanced Visible and Infrared Imager observations from the European geostationary platform Meteosat-9 (Meteorological Satellite 9) have been also used to characterize the target area. Although the amplitude of this daily cycle has been shown to be very small, we argue that suitable nighttime meteorological conditions and the strong contrast of the reststrahlen absorption bands of quartz (8-14 ?m) can amplify its effect over the surface spectral emissivity. The retrieval of atmospheric parameters show that, at nighttime, an atmospheric temperature inversion occurs close to the surface yielding a thin boundary layer which acts like a lid, keeping normal convective overturning of the atmosphere from penetrating through the inversion. This mechanism traps water vapor close to the land and drives the direct adsorption of water vapor at the surface during the night. The diurnal variation in emissivity at 8.7 ?m has been found to be as large as 0.03 with high values at night and low values during the day. At 10.8 ?m and 12 ?m, the variation has the same sign as that at 8.7 ?m, but with a smaller amplitude, 0.019 and 0.014, respectively. The impact of these diurnal variations on the retrieval of surface temperature and atmospheric parameters has been analyzed. Key Points Diurnal variation in desert emissivity during the dry season assessed with IASI Assessment of the meteorological conditions which favors the phenomenon Impact of emissivity variation on atmospheric parameters retrieval ©2013. American Geophysical Union. All Rights Reserved.

Results: We carried out a simulation study to assess the performance of 5 widely used tools, such as: CEM, Cufflinks, iReckon, RSEM, and SLIDE. All of them have been used with default parameters. In particular, we considered the effect of the following three different scenarios: the availability of complete annotation, incomplete annotation, and no annotation at all. Moreover, comparisons were carried out using the methods in three different modes of action. In the first mode, the methods were forced to only deal with those isoforms that are present in the annotation; in the second mode, they were allowed to detect novel isoforms using the annotation as guide; in the third mode, they were operating in fully data driven way (although with the support of the alignment on the reference genome). In the latter modality, precision and recall are quite poor. On the contrary, results are better with the support of the annotation, even though it is not complete. Finally, abundance estimation error often shows a very skewed distribution. The performance strongly depends on the true real abundance of the isoforms. Lowly (and sometimes also moderately) expressed isoforms are poorly detected and estimated. In particular, lowly expressed isoforms are identified mainly if they are provided in the original annotation as potential isoforms. Background: The main goal of the whole transcriptome analysis is to correctly identify all expressed transcripts within a specific cell/tissue- at a particular stage and condition - to determine their structures and to measure their abundances. RNA-seq data promise to allow identification and quantification of transcriptome at unprecedented level of resolution, accuracy and low cost. Several computational methods have been proposed to achieve such purposes. However, it is still not clear which promises are already met and which challenges are still open and require further methodological developments.

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The study of a planing flat plate may be considered as a topic of wide interest for academic and industrial applications. From experimental and numerical studies, flow separation occurs near the stagnation point and a thin jet sprays forward along the plate, while a clear wave pattern develops downstream. In the present study, the effect on the jet-root position caused by a cushion pressure applied on the downstream free surface is considered and the consequent variation in lift and drag coefficients is studied. This canonical problem is important in the design of Surface Effects Ships (SES), the bow seal of which may be assumed as a planing deformable surface with a cushion pressure behind it. This study focuses on the hydrodynamic interaction between the plate and the cushion pressure; as such, the plate geometry is prescribed. A two-dimensional numerical study of this problem has been performed in the present work using a finite-volume Chimera-overlapping-grids approach to numerically solve the Navier-Stokes equations; the free surface is handled by means of two-phase level-set method. Validity of the results is assessed by the comparison with theoretical and numerical results available in the literature.

The analysis of a propeller operating in off-design conditions is one of the most attractive and challenging topics in naval hydrodynamics, because of its close connections with different aspects of ship design and performances. For these reasons, wake dynamics and propeller loads are analyzed in the present paper by means of a numerical code based on the solution of the Reynolds averaged Navier-Stokes equations, whose capability to capture propeller hydrodynamics in these extreme conditions are also investigated. The test case considered is the CNR-INSEAN E779A propeller model, for which a detailed experimental database exists for axial flow conditions; propeller geometry and computational domain are discretized by means of an overlapping grid approach.A wide range of incidence angles (10-50°) at two different loading conditions are considered, in order to analyze the propeller performance during severe off-design conditions, similar to those experienced during very complicated maneuvering scenarios. Details of average and instantaneous loads are reported, for both the complete propeller and for a single blade.The present paper is an extension of the analysis of propeller performance in oblique flow, recently proposed in [1]; here, the focus is on propeller performance at very high angle of incidence. The k - {small element of} and a DES turbulence models have been exploited also, in order to provide a reliable verification of the numerical results in the absence of experimental data in these extreme operating conditions. © 2013 Elsevier Ltd.

A Boundary Element Method (BEM) hydrodynamics combined with a flow-alignment technique to evaluate blades shed vorticity is presented and applied to a marine propeller in open water. Potentialities and drawbacks of this approach in capturing propeller performance, slipstream velocities, blade pressure distribution and pressure disturbance in the flow-field are highlighted by comparisons with available experiments and RANSE results. In particular, correlations between the shape of the convected vortex- sheet and the accuracy of BEM results are discussed throughout the paper. To this aim, the analysis of propeller thrust and torque is the starting point towards a detailed discussion on the capability of a 3-D free-wake BEM hydrodynamic approach to describe the local features of the flow-field behind the propeller disk, in view of applications to propulsive configurations where the shed wake plays a dominant role.

This chapter deals with models of living complex systems, chiefly human crowds, by methods of conservation laws and measure theory. We introduce a modeling framework which enables one to address both discrete and continuous dynamical systems in a unified manner using common phenomenological ideas and mathematical tools as well as to couple these two descriptions in a multiscale perspective. Furthermore, we present a basic theory of well-posedness and numerical approximation of initial-value problems and we discuss its implications on mathematical modeling.

The onset and the nature of dynamic instabilities experienced by the wake of a marine propeller set in oblique flow are investigated by means of detached eddy simulations. In particular, the destabilization process is inspected by a systematic comparison of the wake morphology of a propeller operating in pure axisymmetric flow and in drift with angle of 20 degrees, under different loading conditions. The wake behaviour in oblique flow shows a markedly different character with respect to the axisymmetric condition: in the latter, the destabilization is triggered by an increasing interaction of the main vorticity confined in the tip vortex; whereas, in the former, the role of the secondary vorticity (oriented in the streamwise direction) as well as the hub vortex seems to be crucial. The features of the wake have been investigated by the lambda(2) criterion (Jeong & Hussain, J. Fluid Mech., vol. 285, 1995, pp. 69-94) and typical flow variables (pressure, velocity and vorticity), for both the averaged and instantaneous flow fields. Moreover, in order to further inspect the evolution of the vortical structures, as well as their interaction and destabilization, the spectra of the kinetic energy have been considered. This investigation aims to broaden the knowledge from previous works on the subject of rotor wake instabilities, focusing on the differences between an ideal (axisymmetric) and actual operating conditions occurring in typical engineering applications.