Experimental Measurement of Local Burning Velocity Within a Rotating Flow

The work presented in this paper details the implementation of a new technique for the measurement of local burning velocity using asynchronous particle image velocimetry. This technique uses the local flow velocity ahead of the flame front to measure the movement of the flame by the surrounding fluid. This information is then used to quantify the local burning velocity by taking into account the translation of the flame via convection. In this paper the developed technique is used to study the interaction between a flame front and a single toroidal vortex for the case of premixed stoichiometric methane and air combustion. This data is then used to assess the impact of vortex structure on flame propagation rates. The burning velocity data demonstrates that there is a significant enhancement to the rate of flame propagation where the flame directly interacts with the rotating vortex. The increases found were significantly higher than expected but are supported by burning velocities (Filatyev et al, Combust Flame 141:1?C21, 2005; Kobayashi et al, Proc Combust Inst 29:1793?C1800, 2002; Shepherd et al. 1998) found in turbulent flames of the same mixture composition. Away from this interaction with the main vortex core, the flame exhibits propagation rates around the value recorded in literature for unperturbed laminar combustion (Tahtouh et al, Combust Flame 159:1735?C1743, 2009; Hassan et al, Combust Flame 115:539?C550, 1998); Halter et al, Proc Combust Inst 30:201?C208, 2005; Coppens et al, Exp Therm Fluid Sci 31:437?C444, 2007).     

Dynamics of Isotropic Homogeneous Turbulence with Linear Forcing Using a Lattice Boltzmann Method

The Lattice Boltzmann Method (LBM) has proved to be a promising approach to solve the Navier–Stokes equations, especially for incompressible and isothermal cases. For turbulent flows, the quality of the predictions has been previously studied considering standard spectral forced (ten Cate et al., Comput Fluids 35:1239–1251, 2006) statistically homogeneous isotropic turbulence. In the present contribution, a recently proposed linear forcing scheme working in physical space (Lundgren 2003; Rosales and Meneveau, Phys Fluids 17(9):095106–1,8, 2005) has been integrated in a three-dimensional fifteen-velocity LBM formulation. Results have been analyzed, with special attention to the dynamics of the flow through the invariants of the velocity tensor. This topic had not been studied yet for the linear forcing, regardless of the nature (spectral or LBM) of the numerical method. Results fully agree with standard pseudo-spectral direct numerical simulations, results proving the validity of the LBM with linear forcing in real space to study this kind of turbulent flows.     

Scale effect on unsteady cloud cavitation

No experiment was conducted, yet, to investigate the scale effects on the dynamics of developed cavitating flow with periodical cloud shedding. The present study was motivated by the unclear results obtained from the experiments in a Venturi-type section that was scaled down 10 times for the purpose of measurements by ultra-fast X-ray imaging (Coutier-Delgosha et al. 2009). Cavitation in the original size scale section (Stutz and Reboud in Exp Fluids 23:191–198, 1997, Exp Fluids 29:545–552 2000) always displays unsteady cloud separation. However, when the geometry was scaled down, the cavitation became quasi steady although some oscillations still existed. To investigate this phenomenon more in detail, experiments were conducted in six geometrically similar Venturi test sections where either width or height or both were scaled. Various types of instabilities are obtained, from simple oscillations of the sheet cavity length to large vapor cloud shedding when the size of the test section is increased. It confirms that small scale has a significant influence on cavitation. Especially the height of the test section plays a major role in the dynamics of the re-entrant jet that drives the periodical shedding observed at large scale. Results suggest that the sheet cavity becomes stabile when the section is scaled down to a certain point because re-entrant jet cannot fully develop.     

Local Controllability to Trajectories of the Magnetohydrodynamic Equations

In this paper we prove the local controllability to trajectories of the three dimensional magnetohydrodynamic equations by means of two internal controls, one in the velocity equations and the other in the magnetic field equations and both localized in an arbitrary small subset with not empty interior of the domain. This paper improves the previous results (Barbu et al. in Comm Pure Appl Math 56:732–783, 2003; Barbu et al. in Adv Differ Equ 10:481–504, 2005; Havârneanu et al. in Adv Differ Equ 11:893–929, 2006; Havârneanu, in SIAM J Control Optim 46:1802–1830, 2007) where the second control is not localized and it allows to deduce the local controllability to trajectories with boundary controls. The proof relies on the Carleman inequality for the Stokes system of Imanuvilov et al. (Carleman estimates for second order nonhomogeneous parabolic equations, preprint) to deal with the velocity equations and on a new Carleman inequality for a Dynamo-type equation to deal with the magnetic field equations.     

A phenomenological model for microstructure-dependent inelasticity in shape-memory alloys

Degradation in shape-memory alloy response is a crucial concern for a variety of innovative applications. Under cyclic loadings, these materials generally experience permanent inelastic deformations. The onset of plasticization is known to be very sensitive to the microstructure of the polycrystalline specimen. Moving from recent experimental findings (Malard et al. in Funct Mater Lett 2:45–54, 2009; Acta Mater 59:1542–1556, 2011), we present a phenomenological model for permanent inelastic effects in shape-memory alloys taking into account the polycrystalline microstructure. In particular, the mechanical response under cyclic loadings is investigated in connection with the mean crystal grain size. Formulated within the variational frame of generalized standard materials, the model consists in an extension of the model in Auricchio et al. (Int J Plast 23:207–226, 2007) to the case of microstructure-dependent parameters. The mathematical setting is discussed and numerical simulations showing the capability of the model to reproduce experiments are presented.     

Mean Flow Structures Inside the Human Upper Airway

The lattice Boltzmann method (LBM) was used to conduct a direct numerical simulation study of the airflow inside an idealised human upper airway. Results from both a modest resolution (18 million control volumes, 320 Gb data set) and an extreme resolution (148 million control volumes, 800 Gb data set) LBM simulation were compared to those from experimental results (Johnstone, A.: Hot wire measurements in an oropharyngeal pathway. M.Sc. Thesis, Queen’s University, Kingston, ON, Canada, 2002; Johnstone et al., Expt Fluids 37(5): 673–689, 2004). A coarse resolution simulation (2.4 million control volumes, 105 Gb data set) was used to record the entire time-varying flow field; the nature of the mean structures in the three-dimensional flow field was studied using this data set. For the mean statistics, the LBM calculations yield better results than do the Reynolds averaged Navier–Stokes methods (Ball et al., Comput Fluids, 2007); the LBM reproduces significant detail of experimentally observed flow features. The flow is three-dimensional, obviously, and the interrogation of the mean flow structure is found to be unsteady so that sagittal plane and time-integrated measurements alone are insufficient to verify the accuracy of computational predictions of this flow.     

Dynamics and Control at Feedback Vertex Sets. I: Informative and Determining Nodes in Regulatory Networks

We consider systems of differential equations which model complex regulatory networks by a graph structure of dependencies. We show that the concepts of informative nodes (Mochizuki and Saito, J Theor Biol 266:323–335, 2010) and determining nodes (Foias and Temam, Math Comput 43:117–133, 1984) coincide with the notion of feedback vertex sets from graph theory. As a result we can determine the long-time dynamics of the entire network from observations on only a feedback vertex set. We also indicate how open loop control at a feedback vertex set, only, forces the remaining network to stably follow prescribed stable or unstable trajectories. We present three examples of biological networks which motivated this work: a specific gene regulatory network of ascidian cell differentiation (Imai et al., Science 312:1183–1187, 2006), a signal transduction network involving the epidermal growth factor in mammalian cells (Oda et al., Mol Syst Biol 1:1–17, 2005), and a mammalian gene regulatory network of circadian rhythms (Mirsky et al., Proc Natl Acad Sci USA 106:11107–11112, 2009). In each example the required observation set is much smaller than the entire network. For further details on biological aspects see the companion paper (Mochizuki et al., J Theor Biol, 2013, in press). The mathematical scope of our approach is not limited to biology. Therefore we also include many further examples to illustrate and discuss the broader mathematical aspects.     

Analytical Validation of a Continuum Model for Epitaxial Growth with Elasticity on Vicinal Surfaces

Within the context of heteroepitaxial growth of a film onto a substrate, terraces and steps self-organize according to misfit elasticity forces. Discrete models of this behavior were developed by Duport et al. (J Phys I 5:1317–1350, 1995) and Tersoff et al. (Phys Rev Lett 75:2730–2733, 1995). A continuum limit of these was in turn derived by Xiang (SIAM J Appl Math 63:241–258, 2002) (see also the work of Xiang and Weinan Phys Rev B 69:035409-1–035409-16, 2004; Xu and Xiang SIAM J Appl Math 69:1393–1414, 2009). In this paper we formulate a notion of weak solution to Xiang’s continuum model in terms of a variational inequality that is satisfied by strong solutions. Then we prove the existence of a weak solution.     

On the Formulation of Continuum Thermodynamic Models for Solids as General Equations for Non-equilibrium Reversible-Irreversible Coupling

The purpose of this work is the comparison of some aspects of the formulation of material models in the context of continuum thermodynamics (e.g., ?ilhavý in The mechanics and thermodynamics of continuous media, Springer, Berlin, 1997) with their formulation in the form of a General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC: e.g., Grmela and Öttinger in Phys. Rev. E 56: 6620–6632, 1997; Öttinger and Grmela in Phys. Rev. E 56: 6633–6655, 1997; Öttinger in Beyond equilibrium thermodynamics, Wiley, New York, 2005; Grmela in J. Non-Newton. Fluid Mech. 165: 980–998, 2010). A GENERIC represents a generalization of the Ginzburg-Landau model for the approach of non-equilibrium systems to thermodynamic equilibrium. Originally developed to formulate non-equilibrium thermodynamic models for complex fluids, it has recently been applied to anisotropic inelastic solids in a Eulerian setting (Hütter and Tervoort in J. Non-Newton. Fluid Mech. 152: 45–52, 2008; 53–65, 2008; Adv. Appl. Mech. 42: 254–317, 2009) as well as to damage mechanics (Hütter and Tervoort in Acta Mech. 201: 297–312, 2008). In the current work, attention is focused for simplicity on the case of thermoelastic solids with heat conduction and viscosity in a Lagrangian setting (e.g., ?ilhavý in The mechanics and thermodynamics of continuous media, Springer, Berlin, 1997, Chaps. 9–12). In the process, the relation of the two formulations to each other is investigated in detail. A particular point in this regard is the concept of dissipation and its model representation in both contexts.     

The Two-Dimensional Euler Equations on Singular Domains

We establish the existence of global weak solutions of the two-dimensional incompressible Euler equations for a large class of non-smooth open sets. Loosely, these open sets are the complements (in a simply connected domain) of a finite number of obstacles with positive Sobolev capacity. Existence of weak solutions with L ^p vorticity is deduced from a property of domain continuity for the Euler equations that relates to the so-called γ-convergence of open sets. Our results complete those obtained for convex domains in Taylor (Progress in Nonlinear Differential Equations and their Applications, Vol. 42, 2000), or for domains with asymptotically small holes (Iftimie et al. in Commun Partial Differ Equ 28(1–2), 349–379, 2003; Lopes Filho in SIAM J Math Anal 39(2), 422–436, 2007).     

Estimation of the largest Lyapunov exponent-like (LLEL) stability measure parameter from the perturbation vector and its derivative dot product (part 2) experiment simulation

Controlling system dynamics with use of the Largest Lyapunov Exponent (LLE) is employed in many different areas of the scientific research. Thus, there is still need to elaborate fast and simple methods of LLE calculation. This article is the second part of the one presented in Dabrowski (Nonlinear Dyn 67:283–291, 2012). It develops method LLEDP of the LLE estimation and shows that from the time series of two identical systems, one can simply extract value of the stability parameter which value can be treated as largest LLE. Unlike the method presented in part, one developed method (LLEDPT) can be applied to the dynamical systems of any type, continuous, with discontinuities, with time delay and others. The theoretical improvement shows simplicity of the method and its obvious physical background. The proofs for the method effectiveness are based on results of the simulations of the experiments for Duffing and Van der Pole oscillators. These results were compared with ones obtained with use of the Stefanski method (Stefanski in Chaos Soliton Fract 11(15):2443–2451, 2000; Chaos Soliton Fract 15:233–244, 2003; Chaos Soliton Fract 23:1651–1659, 2005; J Theor Appl Mech 46(3):665–678, 2008) and LLEDP method. LLEDPT can be used also as the criterion of stability of the control system, where desired behavior of controlled system is explicitly known (Balcerzak et al. in Mech Mech Eng 17(4):325–339, 2013). The next step of development of the method can be considered in direction that allows estimation of LLE from the real time series, systems with discontinuities, with time delay and others.     

Comparison of dynamical cores for NWP models: comparison of COSMO and Dune

We present a range of numerical tests comparing the dynamical cores of the operationally used numerical weather prediction (NWP) model COSMO and the university code Dune, focusing on their efficiency and accuracy for solving benchmark test cases for NWP. The dynamical core of COSMO is based on a finite difference method whereas the Dune core is based on a Discontinuous Galerkin method. Both dynamical cores are briefly introduced stating possible advantages and pitfalls of the different approaches. Their efficiency and effectiveness is investigated, based on three numerical test cases, which require solving the compressible viscous and non-viscous Euler equations. The test cases include the density current (Straka et al. in Int J Numer Methods Fluids 17:1–22, 1993), the inertia gravity (Skamarock and Klemp in Mon Weather Rev 122:2623–2630, 1994), and the linear hydrostatic mountain waves of (Bonaventura in J Comput Phys 158:186–213, 2000).     

Zero singularity of codimension two or three in a four-neuron BAM neural network model with multiple delays

In this paper, a four-neuron BAM neural network model with multiple delays is considered. The existence conditions under which that the origin of the system is Bogdanov–Takens (B–T) or triple zero singularity are given. By choosing the connected weights as bifurcation parameters and using the center manifold reduction and the normal form theory and the formula developed by Xu and Huang (J Differ Equ 244:582–598 2008) and Qiao et al. (Chinese Ann Math Ser A 31:59–70 2010), the versal unfoldings and the normal forms for this singularity were given to analyze the behaviors of the system. This paper is a further study of paper Cao and Xiao (IEEE Trans Neural Netw 18:416–430 2007).     

Kirchhoff plates with viscous boundary dissipation

In this paper, we confine our attention to Kirchhoff thin plates in presence of boundary viscoelastic dissipative mechanisms, in order to investigate the well-posedness and the asymptotic behavior within the minimal state approach, following the guidelines proposed in Deseri et al. (Arch Rational Mech Anal 181:43–96, 2006) [see also Fabrizio et al. (Arch Rational Mech Anal 198:189–232, 2010)].     

The reinforcement of ancient timber-joints with carbon nano-composites

The paper describes an experimental research activity on the application of a polymeric resin reinforced with carbon nanotubes on an ancient timber structures belonging to cultural heritage (Bertolini Cestari et al. in Proc. of SAHC2008. VI International Conference, pp. 941–947, 2008; Marzi in Ph.D. Thesis, 2010; Bertolini Cestari et al. in Proc. of ICRACM-2010—3rd International Conference on Recent Advances in Composite Materials, 2011). The proposed approach aims at the conservation of a specific wooden joint belonging to traditional constructions. Therefore the research was addressed to the definition and assessment of a methodology of preparation and application of the nano-composite with the aim of verifying an increased mechanical resistance in comparison with traditional reinforcement methods. Different wood species have been considered and the experimentation has been carried out in view of a possible in-situ application of the technique. Laboratory tests were carried out at first on small wooden samples, and afterwards on wooden elements having real dimension. These last ones were taken from ancient and decayed wooden floors belonging to an important historical building that were dismantled during restoration works. A numerical analysis of the structural behavior of the joint is provided, in order to assess the different possible collapse mechanisms. The results obtained from the tests are promising for future developments of the application of these nano-composite materials.     

Well-Posedness for the Motion of Physical Vacuum of the Three-dimensional Compressible Euler Equations with or without Self-Gravitation

This paper concerns the well-posedness theory of the motion of a physical vacuum for the compressible Euler equations with or without self-gravitation. First, a general uniqueness theorem of classical solutions is proved for the three dimensional general motion. Second, for the spherically symmetric motions, without imposing the compatibility condition of the first derivative being zero at the center of symmetry, a new local-in-time existence theory is established in a functional space involving less derivatives than those constructed for three-dimensional motions in (Coutand et al., Commun Math Phys 296:559–587, 2010; Coutand and Shkoller, Arch Ration Mech Anal 206:515–616, 2012; Jang and Masmoudi, Well-posedness of compressible Euler equations in a physical vacuum, 2008) by constructing suitable weights and cutoff functions featuring the behavior of solutions near both the center of the symmetry and the moving vacuum boundary.     

Measurements of an unsteady liquid metal flow during spin-up driven by a rotating magnetic field

A cylindrical cavity with an aspect ratio of unity is filled with liquid metal and suddenly exposed to an azimuthal body force generated by a rotating magnetic field (RMF). This experimental study is concerned with the secondary meridional flow during the time, if the fluid spins up from rest. Vertical profiles of the axial velocity have been measured by means of the ultrasound Doppler velocimetry. The flow measurements confirm the spin-up concept by Ungarish (J Fluid Mech 347:105–118, 1997) and the continuative study by Nikrityuk et al. (Phys Fluids 17:067101, 2005) who suggested the existence of two stages during the RMF-driven spin-up, in particular the so-called initial adjustment phase followed by an inertial phase which is dominated by inertial oscillations of the secondary flow. Evolving instabilities of the double-vortex structure of the secondary flow have been detected at a Taylor number of 1.24 × 10⁵ verifying the predictions of Grants and Gerbeth (J Fluid Mech 463:229–240, 2002). Perturbations in form of Taylor–Görtler vortices have been observed just above the instability threshold.     

Simultaneous assessment of peak-locking and CCD readout errors through a multiple Δt strategy

The multiple ??t strategy is an inexpensive procedure that can be implemented with any usual particle image velocimetry (PIV) set up. The only requirement is acquiring different series of PIV image pairs, setting a different time between laser pulses for each series. With this additional information, robust procedures for error assessment are possible. Within this strategy, this paper offers new discoveries that correct and complement previous works by the authors. Nogueira et al. (Meas Sci Technol 20?C7:074001, 2009) addressed the tasks of assessing CCD readout and peak-locking bias errors separately. In this paper, a new approach, of general application to PIV, is proposed for assessing both errors simultaneously. Additionally, it unveils the effect of the flow variability on the local amplitude of the peak-locking bias. In a different work, Nogueira et al. (Exp Fluids. doi: 10.1007/s00348-011-1094-2, 2011) have focused on assessing peak-locking rms error. That paper achieved only order of magnitude estimations of the rms error because one of its components was overlooked. Here, the new term is included and the assessment obtained is good enough to correct rms systematic errors, improving the measurement of the turbulent kinetic energy or similar flow magnitudes. After describing the strategies, the application to selected synthetic and real cases is presented, validating the modeling of the errors behavior when dealing with turbulent flows. The results indicate the possibility to assess bias errors in the range from 0.01 to 0.2 pixels for both sources (peak locking and CCD readout) simultaneously. Furthermore, the previous works simply assessed the magnitude of the errors, but the results of the new procedures proposed here, in some cases, are good enough to correct the measurement itself. In addition, the determination of zones where these errors are not the dominant ones is presented.