Regulating absence seizures by tri-phase delay stimulation applied to globus pallidus internal

Applied Mathematics and Mechanics - In this paper, a reduced globus pallidus internal (GPI)-corticothalamic (GCT) model is developed, and a tri-phase delay stimulation (TPDS) with sequentially...     

The Γ-Limit of the Two-Dimensional Ohta–Kawasaki Energy. Droplet Arrangement via the Renormalized Energy

This is the second in a series of papers in which we derive a Γ-expansion for the two-dimensional non-local Ginzburg–Landau energy with Coulomb repulsion known as the Ohta–Kawasaki model in connection with diblock copolymer systems. In this model, two phases appear, which interact via a nonlocal Coulomb type energy. Here we focus on the sharp interface version of this energy in the regime where one of the phases has very small volume fraction, thus creating small “droplets” of the minority phase in a “sea” of the majority phase. In our previous paper, we computed the Γ-limit of the leading order energy, which yields the averaged behavior for almost minimizers, namely that the density of droplets should be uniform. Here we go to the next order and derive a next order Γ-limit energy, which is exactly the Coulombian renormalized energy obtained by Sandier and Serfaty as a limiting interaction energy for vortices in the magnetic Ginzburg–Landau model. The derivation is based on the abstract scheme of Sandier-Serfaty that serves to obtain lower bounds for 2-scale energies and express them through some probabilities on patterns via the multiparameter ergodic theorem. Thus, without appealing to the Euler–Lagrange equation, we establish for all configurations which have “almost minimal energy” the asymptotic roundness and radius of the droplets, and the fact that they asymptotically shrink to points whose arrangement minimizes the renormalized energy in some averaged sense. Via a kind of Γ-equivalence, the obtained results also yield an expansion of the minimal energy and a characterization of the zero super-level sets of the minimizers for the original Ohta–Kawasaki energy. This leads to the expectation of seeing triangular lattices of droplets as energy minimizers.     

An experimental study of the effects of pitch-pivot-point location on the propulsion performance of a pitching airfoil

An experimental investigation was conducted to characterize the evolution of the unsteady vortex structures in the wake of a pitching airfoil with the pitch-pivot-point moving from 0.16C to 0.52C (C is the chord length of the airfoil). The experimental study was conducted in a low-speed wind tunnel with a symmetric NACA0012 airfoil model in pitching motion under different pitching kinematics (i.e., reduced frequency k=3.8–13.2). A high-resolution particle image velocimetry (PIV) system was used to conduct detailed flow field measurements to quantify the characteristics of the wake flow and the resultant propulsion performance of the pitching airfoil. Besides conducting “free-run” PIV measurements to determine the ensemble-averaged velocity distributions in the wake flow, “phase-locked” PIV measurements were also performed to elucidate further details about the behavior of the unsteady vortex structures. Both the vorticity–moment theorem and the integral momentum theorem were used to evaluate the effects of the pitch-pivot-point location on the propulsion performance of the pitching airfoil. It was found that the pitch-pivot-point would affect the evolution of the unsteady wake vortices and resultant propulsion performance of the pitching airfoil greatly. Moving the pitch-pivot-point of the pitching airfoil can be considered as adding a plunging motion to the original pitching motion. With the pitch-pivot-point moving forward (or backward), the added plunging motion would make the airfoil trailing edge moving in the same (or opposite) direction as of the original pitching motion, which resulted in the generated wake vortices and resultant thrust enhanced (or weakened) by the added plunging motion.     

Kinetic theory of stellar systems, two-dimensional vortices and HMF model

We discuss the kinetic theories of stellar systems, two-dimensional vortices and Hamiltonian mean field model, stressing their analogies and differences. We describe the evolution of the system as a whole and discuss the timescale of relaxation towards the Boltzmann distribution predicted by statistical mechanics. We also consider the relaxation of a “test” particle in a bath of “field” particles and analyze it with the aid of a Fokker–Planck equation involving a term of diffusion counterbalanced by a friction or a drift.     

Use of structural components of specific work of internal forces for estimating the strength of viscoelastic structures in local stress concentration regions

Material fracture experiments on specimens and structures testify that materials can resist greater stresses in local stress concentration regions than in regions with a nearly homogeneous stress state. Taking this fact into account in design stress analysis permits one to reveal additional structure loading and/or service life margins. One approach aimed at taking into account the increased strength in local stress concentration regions is to use averaged limit characteristics parametrically depending on the characteristic size L of the averaging region. One version of this approach is the concept of “elementary block” of a material [1, 2]. The averaged limit characteristics are determined by an experiment-calculation method involving the analysis of the stress-strain state of a material specimen with a stress concentrator at the time when the specimen attains the limit state preceding macrofracture.In [3], the dependence of the averaged limit separation stresses on the size of the averaging region was determined on the basis of numerical analysis of the singular stress state of the specimen used to determine the standard characteristics of the adhesion strength of a filled polymer material. In the present paper, we generalize the above approach to the case of a viscoelastic material. For the limit characteristics of the material in the local stress concentration region we take the volume-averaged components of the specific work of internal forces [4, 5] (the averaged specific absorbed energy and the averaged specific instantaneously reversible energy). The introduction of two limit energies originates from the fact that, to initiate the process of macrofracture, it is necessary to satisfy the following two conditions simultaneously: the material must be “damaged” sufficiently strongly by the preceding loading, and the “damaged” material must be loaded sufficiently strongly. As an example of determining the material averaged limit energy characteristics in a local stress concentration region, we consider the problem about the strain of a viscoelastic specimen used to determine the standard adhesion strength characteristics. The problem is solved numerically under the following assumptions: the specimen material is assumed to be linearly viscoelastic, and the specific absorbed energy in the stress concentration region is assumed to coincide in magnitude with the specific scattered energy. To estimate the accuracy of the numerical method, we use the solution of the model problem about the action of a plane circular die on a half-space consisting of a linearly viscoelastic incompressible material.     

Numerical analysis of effective elastic properties of geomaterials containing voids using 3D random fields and finite elements

The purpose of the study is to investigate the influence of porosity and void size on effective elastic geotechnical engineering properties with a 3D model of random fields and finite element. The random field theory is used to generate models of geomaterials containing spatially random voids with controlled porosity and void size. A “tied freedom” analysis is developed to evaluate the effective Young’s modulus and Poisson’s ratio in an ideal block material of finite elements. To deliver a mean and standard deviation of the elastic parameters, this approach uses Monte-Carlo simulations and finite elements, where each simulation leads to an effective value of the property under investigation. The results are extended to investigate an influence of representative volume element (RVE). A comparison of the effective elastic stiffness of 2D and 3D models is also discussed.     

Experimental and numerical analysis of spray-atomization characteristics of biodiesel fuel in various fuel and ambient temperatures conditions

The purpose of this work is to reveal the effects of fuel temperatures and ambient gas conditions on the spray-atomization behavior of soybean oil methyl ester (SME) fuel. The spray-atomization behavior was analyzed through spray parameters such as the axial distance from the nozzle tip, local and overall Sauter mean diameter (SMD). These parameters were obtained from a spray visualization system and a droplet measuring system. In addition, the experimental results were compared with the numerical results calculated by the KIVA-3V code. It was revealed that the increase of the fuel temperature (from 300 K to 360 K) little affects the spray liquid tip penetration. The increase of the ambient gas temperature (from 300 K to 450 K) caused a increase in the spray liquid tip penetration. Also, biodiesel fuel evaporation actively occurred due to the increase in the fuel temperature and the ambient gas temperature. Of special significance was that the highest vapor fuel mass concentration was observed at the center region of the spray axis. In the results of the microscopic characteristics, the detected local droplet size at the axial direction and overall droplet size at the axial and radial direction in a control volume increased when the fuel temperature increased. This is believed to be due to an increase in the number of small droplets that quickly evaporated. In addition, the increased fuel temperature caused the decrease of the number of droplets and the increase of the vapor fuel mass. The mean axial velocity of droplets decreased with increasing fuel temperature.     

Bipotential versus return mapping algorithms: Implementation of non associated flow rules

Numerical implementation of constitutive laws involves specific incremental methods. The “return mapping” (Simo and Hughes, 1998) and the “bipotential” (de Saxcé, 1992) are one of those, associated respectively to two different classes of materials: the General Standard Materials (GSM) for the return mapping and the Implicit Standard Materials (ISM) for the bipotential.The objective of this paper is then to compare the implementation of those both methods in the case of non associated flow rules in plasticity.In the first section, the properties of the different previous material classes will be recalled and the methods of “return mapping” and “bipotential” will be detailed. The comparison of both methods is realised on the non linear kinematic hardening rule of Armstrong–Frederick (Armstrong and Frederick, 1966) in a second section and the details are given in a third part. The numerical implementation is realised in Abaqus/Standard 6.11 by the means of a UMat subroutine and the practical simple case of tension–compression is analysed in a last section.     

Numerical modeling of a two-dimensional vertical turbulent two-phase jet

The results of numerically modeling two-dimensional two-phase flow of the “gas-solid particles” type in a vertical turbulent jet are presented for three cases of its configuration, namely, descending, ascending, and without account of gravity. Both flow phases are modeled on the basis of the Navier-Stokes equations averaged within the framework of the Reynolds approximation and closed by an extended k-? turbulence model. The averaged two-phase flow parameters (particle and gas velocities, particle concentration, turbulent kinetic energy, and its dissipation) are described using the model of mutually-penetrating continua. The model developed allows for both the direct effect of turbulence on the motion of disperse-phase particles and the inverse effect of the particles on turbulence leading to either an increase or a decrease in the turbulent kinetic energy of the gas. The model takes account for gravity, viscous drag, and the Saffman lift. The system of equations is solved using a difference method. The calculated results are in good agreement with the corresponding experimental data which confirms the effect of solid particles on the mean and turbulent characteristics of gas jets.     

Turbulence in a three‐dimensional wall‐bounded shear flow

A new turbulent flow with distinct three‐dimensional characteristics has been designed in order to study the impact of mean‐flow skewing on the turbulent coherent vortices and Reynolds‐averaged statistics. The skewing of a unidirectional plane Couette flow was achieved by means of a spanwise pressure gradient. Direct numerical simulations of the statistically steady Couette–Poiseuille flow enabled in‐depth explorations of the turbulence field in the skewed flow. The imposition of a modest spanwise gradient turned the mean flow about 8° away from the original Couette flow direction and this turning angle remained nearly the same over the entire cross section. Nevertheless, a substantial non‐alignment between the turbulent shear stress angle and the mean velocity gradient angle was observed. The structure parameter turned out to slightly exceed that in the pure Couette flow, contrary to the observations made in some other three‐dimensional shear flows. Coherent flow structures, which are known to be associated with the Reynolds shear stress in near‐wall regions, were identified by the λ₂‐criterion. Instantaneous and ensemble‐averaged vortices resembled those found in the unidirectional Couette flow. In the skewed flow, however, the vortex structures were turned to align with the local mean‐flow direction. The conventional symmetry between Case 1 and Case 2 vortices was broken due to the mean‐flow three‐dimensionality. The turning of the coherent vortices and the accompanying symmetry‐breaking gave rise to secondary and tertiary turbulent shear stress components. By averaging the already ensemble‐averaged shear stresses associated with Case 1 and Case 2 vortices in the homogeneous directions, a direct link between the educed near‐wall structures and the Reynolds‐averaged turbulent stresses was established. These observations provide evidence in support of the hypothesis that the structural model proposed for two‐dimensional turbulent boundary layers remains valid also in flows with moderate mean three‐dimensionality. Copyright © 2009 John Wiley & Sons, Ltd.     

Dipolic Flows Relevant to Aquifer Storage and Recovery: Strack’s Sink Solution Revisited

Steady, 2-,3-D Darcian flows generated by a dipole (a pair of horizontal or vertical injection–abstraction wells closely placed one above another), with circulation of fresh water inside an interface confined lens or “bubble” underneath an impermeable caprock, surrounded by a static saline groundwater, are analytically studied. For 2-D dipole, the complex potential domain is a plane with a horizontal cut. This domain is conformally mapped onto a reference half-plane where the Keldysh–Sedov formula is used to obtain the complex physical coordinates. Explicit closed-form expressions for the vase-shaped interface, flow net, isohypses, magnitudes of the Darcian velocity and Riesenkampf’s resultant force are obtained, depending on the dipole moment, its position with respect to the caprock, and the ratio of densities of the two fluids. It is shown that for sufficiently small injection-pumping rates the fresh water “vase” separates from the caprock and becomes a circle, inside which streamlines are Newtons’ loops of monodiametral degenerate hyperbolae (cubics). Two numerical codes, MT3DMS and SEAWAT, are also used for delineation of isoconcentric lines, which qualitatively corroborate the analytical solutions in delineation of the “bubble” in the part where the sharp interface model predicts stable free boundaries and evidencing “dimples” on the boundary of the “bubble” where the saline water overlies the fresh one. For 3-D dipole not bounded by the caprock, the analytical fresh water “bubble” is a sphere and solution follows, mutatis mutandis, from the textbook formulae for flow of an ideal fluid past an impermeable sphere. The Stokes streamlines inside the sphere are sixtics; isotachs are plotted in an axial section. Stability of the soil matrix near the wells is also discussed.     

Reynolds number dependence of Reynolds and dispersive stresses in turbulent channel flow past irregular near-Gaussian roughness

Direct numerical simulations of fully-developed turbulent channel flow with irregular rough walls have been performed at four friction Reynolds numbers, namely, 180, 240, 360 and 540, yielding data in both the transitionally- and fully-rough regime. The same roughness topography, which was synthesised with an irregular, isotropic and near-Gaussian height distribution, is used in each simulation. Particular attention is directed towards the wall-normal variation of flow statistics in the near-roughness region and the fluid-occupied region beneath the crests, i.e. within the roughness canopy itself. The goal of this study is twofold. (i) Provide a detailed account of first- and second-order double-averaged velocity statistics (including profiles of mean velocity, dispersive stresses, Reynolds stresses, shear stress gradients and an analysis of the mean force balance) with the overall aim of understanding the relative importance of “form-induced” and “turbulence-induced” quantities as a function of the friction Reynolds number. (ii) Investigate the possibility of predicting the levels of streamwise dispersive stress using a phenomenological closure model. Such an approach has been applied successfully in the context of idealised vegetation canopies (Moltchanov & Shavit, 2013, Water Resour. Res., vol. 49, pp. 8222-8233) and is extended here, for the first time, to an irregular rough surface. Overall, the results reveal that strong levels of dispersive stress occur beneath the roughness crests and, for the highest friction Reynolds number considered in this study, show that the magnitude (and gradient) of these “form-induced” stresses exceed their Reynolds stress counterparts. In addition, this study emphasises that the dominant source of spatial heterogeneity within the irregular roughness canopy are “wake-occupied” regions and that a suitable parameterisation of the wake-occupied area is required to obtain an accurate prediction of streamwise dispersive stress.     

Statistical description of a cloud of compressible bubbles

We use the methods of statistical mechanics to describe the interaction of N compressible gas bubbles in an incompressible, inviscid and irrotational liquid. The governing equations for bubble positions, radii and corresponding momenta form a Hamiltonian system depending on the virtual mass matrix. An explicit expression of the virtual mass matrix is presented, which is calculated with accuracy (b/d)³, where b and d are respectively the mean bubble radius and the mean inter-bubble distance. We study two limit cases: the limit of moving rigid spheres and the limit of immobile oscillating bubbles. In each case, we construct a canonical ensemble partition function. In the limit of rigid spheres, we improve results by Yurkovetsky and Brady (phys Fluids 8(4): 881–895, 1996). In particular, we derive an analytic expression for the “attractive” potential which may be responsible for the clustering effect, and show why the accuracy (b/d)³ is not sufficient to characterize the “repulsive potential” . In the limit of immobile oscillating bubbles, we prove the existence of a long range repulsive potential.     

Energetics of axisymmetric fluid-filled pipes up to high frequencies

The energetics of motions of axisymmetric fluid-filled pipes are presented in this paper, in view of high-frequency modelling. This study deals in particular with derivations of local energy equations well suited for the prediction of averaged response of coupled fluid–structure systems. The derivation of the latter requires special manipulation of the kinematic dynamics based here on the notion of propagation modes. Thus, the focus is on the Donnell–Mushtari cylindrical shell with an internal acoustic fluid, a typical example of waveguides with multiple transmission mechanisms. “Exact” and statistical approaches are developed for this system. A state-space representation is first proposed; it allows the characterization of propagating modes in a general manner. This propagating content then leads to the formulation of the local energy approach for this canonical problem.     

Second-order theory for the two-body problem with varying mass including periastron effect

The model of varying mass function, including periastron effect, in terms of Delaunay variables will be expanded. The Hamiltonian of the problem is developed in the extended phase space by introducing a new canonical pair of variable (\(q_4, Q_4\)). The first “\(q_4 \)” is defined as explicit function of time and the initial mass of the system. The conjugate momenta “\(Q_4\)” is assigned as the momenta raises from the varying mass. The short-period analytical solution through a second-order canonical transformation using “Hori’s” method developed by “Kamel” is obtained. The variation equations for the orbital elements are obtained too. The results of the effect of the varying mass and the periastron effect in the case \(n = 2\) are analyzed.     

A door to model reduction in high-dimensional parameter space

Model reduction techniques such as Proper Generalized Decomposition (PGD) are decision-making tools that are about to revolutionize many domains. Unfortunately, their computation is still problematic for problems involving many parameters, for which one has to face the “curse of dimensionality”. An answer to this challenge is given in solid mechanics by the so-called “parameter-multiscale PGD”, which is based on Saint-Venant's principle. In this article, a model problem composed of up to a thousand parameters is presented, showing that the method is able to overcome the “curse of dimensionality”.     

The damping in MEMS inertial sensors both at high and low pressure levels

Except for MEMS working in a ultra high vacuum, the main cause of damping is the air surrounding the system. When the working pressure is equal to the atmospheric one (from now on called “high pressure,” i.e., 10⁵ Pa), the mean free path of an air molecule is much smaller than typical MEMS dimensions. Thus, air can be considered as a viscous fluid and two phenomena occur: flow damping and squeeze film damping. These two phenomena can be evaluated through a simplified Navier–Stokes equation. In a medium vacuum (from now on called “low pressure”), i.e., the “packaging” pressure, the air cannot be considered as a viscous fluid any more since the mean free path of an air molecule is of the same order of magnitude of typical MEMS dimensions. Thus, the molecular fluid theory must be used to estimate the damping. To predict the damping of a MEMS device both at high and low pressure levels, a multiphysics code was used. The proposed approach was validated through comparison with experimental data.     

THE FLUID–STRUCTURE INTERACTION IN SUPPORTING A THIN FLEXIBLE CYLINDRICAL WEB WITH AN AIR CUSHION

The mechanics of the fluid–structure interaction between a thin flexible web, wrapped around a cylindrical drum (reverser), and the air cushion formed by external pressurization through the holes of this drum is analyzed. Derivation of a “new” theory for the moderately large deflections of a thin cylindrical shell to model the web is presented. This theory allows for large web deflections, while using a self-adjusting strain-free reference state for the web in order to keep the circumferential web tension around a constant level. The theory also incorporates the redistribution of the in-plane stress resultants in the axial and shear directions using the Airy stress function. The air-flow is averaged over the height direction of the web-reverser clearance. The surface area of the pressure holes is averaged locally over the total reverser surface. The resulting equations are a modified form of the Navier–Stokes and mass balance equations with nonlinear source terms. The coupled fluid–structure system is solved numerically. The mechanics of the interaction between the web deflections and the air cushion generated by the reverser is explained. The effects of the problem parameters on the overall equilibrium are presented. Parameter distributions which cause the web to contact the reverser are identified, and suggestions are made to avoid this state.     

Contributions of Computational Aeroacoustics to Jet Noise Research and Prediction

A brief review of recent progress in the field of computational aeroacoustics (CAA) is proposed. This paper is complementary to the previous reviews of Tam [(1995a) “Computational aeroacoustics: issues and methods”, AIAA J. 33(10), 1788–1796], Lele [(1997) “Computational Aeroacoustics: a review”, AIAA Paper 97–0018, 35th Aerospace Sciences Meeting and Exhibit, Reno, Nevada] and Glegg [(1999) “Recent advances aeroacoustics: the influence of computational fluid dynamics”, 6th International Congress on Sound and Vibration, Copenhagen, Danemark, 5–8 July, 43–58] on advances in CAA. After a short introduction concerning the current motivations of jet noise studies, connections between computational fluid dynamics (CFD) and CAA using hybrid approaches are discussed in the first part. The most spectacular advances are probably provided by the direct computation of jet noise, and some recent results are shown in the second part.