Study of the inertial effect and the nonlinearities of?the?CRONE suspension based on the hydropneumatic technology

In this paper, we emphasize two main effects involved in the CRONE car suspension technology (CRONE: French acronym for Commande Robuste d??Ordre Non Entier). In a first time, we present the influence of the inductive or inertial effect of the pipes that links the different cells of the hydropneumatic car suspension. These components are mainly resistive and capacitive devices. Then, we analyze the nonlinear relations that link the hydraulic power variables (the flow and the pressure) of the hydraulic resistors and the hydropneumatic accumulators and we study the effect of the nonlinear terms on the car suspension response. Our study is based on the gamma RC arrangement developed in Altet et al. (In: Analysis and design of hybrid systems??proceedings of ADHS03, pp. 63?C68. Elsevier, Amsterdam, 2003) and Serrier et al. (In: Proceedings of IDETC/CIE 2005: ASME 2005 international design engineering technical conferences and computers and information in engineering conference, Long Beach, CA, USA, 24?C28 September 2005). In a second time, we focus only on the gamma RLC arrangement, introduced in Abi Zeid Daou et al. (Int. J. Electron. 96(12):1207?C1223, 2009). We show whether the parasite effect due to the pipes or the nonlinear RC components affect the system??s response. The simulation results show that neither the inertial effect caused by these parasite pipes of one meter length nor the use of the nonlinear resistors or the accumulators modifies the response of the gamma RC arrangement.     

On the Time Decay of the Solutions of the Navier–Stokes System

We investigate the relationship between the time decay of the solutions u of the Navier–Stokes system on a bounded open subset of and the time decay of the right-hand sides f. In suitable function spaces, we prove that u always inherits at least part of the decay of f, up to exponential, and that the decay properties of u depend only upon the amount and type (e.g., exponential, or power-like) of decay of f. This is done by first making clear what is meant by “type” and “amount” of decay and by next elaborating upon recent abstract results pointing to the fact that, in linear and nonlinear PDEs, the decay of the solutions is often intimately related to the Fredholmness of the differential operator. This work was done while the second author was visiting the Bernoulli Center, EPFL, Switzerland, whose support is gratefully acknowledged.     

On the Characterization of the Navier–Stokes Flows with the Power-Like Energy Decay

We study the energy decay of the turbulent solutions to the Navier–Stokes equations in the whole three-dimensional space. We show as the main result that the solutions with the energy decreasing at the rate \({O(t^{-\alpha}), t \rightarrow \infty, \alpha \in [0, 5/2]}\) , are exactly characterized by their initial conditions belonging into the homogeneous Besov space \({\dot{B}^{-\alpha}_{2, \infty}}\) . Similarly, for a solution u and \({p \in [1, \infty]}\) the integral \({\int_{0}^{\infty} \|t^{\alpha/2} u(t)\|^p \frac{1}{t} dt}\) is finite if and only if the initial condition of u belongs to the homogeneous Besov space \({\dot{B}_{2, p}^{-\alpha}}\) . For the case \({\alpha \in (5/2, 9/2]}\) we present analogical results for some subclasses of turbulent solutions.     

Solutions of the Dirac–Fock Equations and the Energy of the Electron-Positron Field

We consider atoms with closed shells, i.e. the electron number N is 2, 8, 10,..., and weak electron-electron interaction. Then there exists a unique solution γ of the Dirac–Fock equations with the additional property that γ is the orthogonal projector onto the first N positive eigenvalues of the Dirac–Fock operator . Moreover, γ minimizes the energy of the relativistic electron-positron field in Hartree–Fock approximation, if the splitting of into electron and positron subspace is chosen self-consistently, i.e. the projection onto the electron-subspace is given by the positive spectral projection of. For fixed electron-nucleus coupling constant g:=α Z we give quantitative estimates on the maximal value of the fine structure constant α for which the existence can be guaranteed.     

The improvement of the general expression for the stress function Φ of the two-dimensional problem

In this paper, it is pointed that the general expression for the stress function of the plane problem in polar coordinates is incomplete. The problems of the curved bar with an arbitrary distributive load at the boundries can’t he solved by this stress function. For this reason, we suggest two new stress functions and put them into the general expression. Then, the problems of the curved bar applied with an arbitrary distributive load at r=a,b boundaries can be solved. This is a new stress function including geometric boundary constants.     

Superfluous Order and the Proper Solution of the Maxwell Equation

In this paper it is proved that Maxwell equation is equivalent to a fourth order equation.Under a certain condition,its general solution is given by     

On the Strong Solvability of the Navier—Stokes Equations

In this paper we study the strong solvability of the Navier—Stokes equations for rough initial data. We prove that there exists essentially only one maximal strong solution and that various concepts of generalized solutions coincide. We also apply our results to Leray—Hopf weak solutions to get improvements over some known uniqueness and smoothness theorems. We deal with rather general domains including, in particular, those having compact boundaries.     

Two Problems of the Semi-Conductor Physics Discussed with the Point of View of the Fluid Dynamics

In this article,we discuss two problems of the semi-conductor physics from the point of view ofthe fluid dynamics.Firstly,we discuss the problem of the p-n junction,and find that the previoustreatment and the previous conclusion of the problem are somewhat erroneous.Secondly,we discussthe coefficient C of the block resistance,and find that the mathematical method of the previoustreatment is erroneous.     

On a Theory of the Infusion Method of Measuring the “Opening Pressure” in the Urethra

At rest the muscles which control the urethra (urine duct) are contracted and its lumen is practically equal to zero over its entire length. To open the urethra, a mechanical effort (due, for example, to a pressure rise in the bladder) must be applied. Reduced contractile activity of the muscles may be one of the reasons for incontinence (enuresis). A widespread method of estimating the blocking capability of the urethra consists in inserting a catheter with lateral perforations near the end. The catheter enters the bladder and is then removed at a constant velocity while a fluid is constantly pumped (infused) into it by a syringe pump at a steady rate and then flows out through the gap between the catheter and the urethral wall. The pumping pressure is considered to be a local measure of the blocking capability, and its dependence on the location of the catheter is regarded as an important diagnostic characteristic.Below, we will consider the simple, longitudinally homogeneous model system formed by an elastic tube pulled over a catheter segment when the initial stresses in the tube are constant over its length. An incompressible viscous fluid flows out of the perforations and percolates in a thin layer along the catheter. In solving the model problem, we will use the lubricating layer approximation under the assumption of small layer curvature. On the basis of an analysis of the results and a comparison of the model with a practical intraurethral measurement procedure, we discuss, firstly, the relationship between the measured quantities and the real characteristics of the urethra and, secondly, the possible formulation of a more realistic model problem.     

On the point spectrum of the Laplace operator with δ-potentials at the vertices of regular polyhedra

We calculate exact criteria for the existence of the point spectrum of the Laplace operator in ³ perturbed by -potentials concentrated at the vertices of regular polyhedra, depending on the distances between the perturbation centers and on the coupling constant.Translated from Neliniini Kolyvannya, Vol. 7, No. 2, pp. 147–154, April–June, 2004.     

On the Theory of the α–β Phase Transition in Quartz

The – phase transition in quartz has features which workers have long found puzzling. My purpose is to explore using a theory for this that is rather different conceptually from those used by other workers. It does suggest different kinds of experiments, likely to shed light on aspects of the transition, and a possible modification of theory which might be helpful in understanding some subtleties.     

On the effect of the nozzle design on the performances of gas–liquid cylindrical cyclone separators

This paper constitutes an experimental study of the separation performances of a gas–liquid cylindrical cyclone (GLCC) separator that interests the oil industry. The global hydrodynamics behavior in the GLCC is characterized by flow visualization under various inflow operating conditions. The effect of the inlet nozzle design on the performances of the separator is studied by using three different nozzles, and it proves to be a key parameter. With an insufficient nozzle restriction, low swirl intensity is imparted to the flow. Due to inadequate centrifugal effects, liquid is prematurely carried over by the gas as flooding occurs in the separator upper part. High amounts of gas are also carried under by the liquid stream. On the other hand, with a too severe nozzle convergence, the important drag applied by the gas leads to liquid “short circuiting” the cyclone toward the gas outlet. In addition to the nozzle design, the separator performances are influenced by phenomena such as liquid bridging or the occurrence of the slug flow regime at the cyclone inlet. This paper leads to a better understanding of the links between the hydrodynamics in the GLCC and its operational limits, which is necessary to enable reliable scaling up tools.     

On the bifurcations of the Lamé solutions in plane-strain elasticity

We consider the in-plane bifurcations experienced by the Lamé solutions corresponding to an elastic annulus subjected to radial tension on the curved boundaries. Numerical investigations of the relevant incremental problem reveal two main bifurcation modes: a long-wave local deformation around the central hole of the domain, or a material wrinkling-type instability along the same boundary. Strictly speaking, the latter scenario is related to the violation of the Shapiro–Lopatinskij condition in an appropriate traction boundary-value problem. It is further shown that the main features of this material instability mode can be found by using a singular-perturbation strategy.     

On the Stability in Weak Topology of the Set of Global Solutions to the Navier–Stokes Equations

Let X be a suitable function space and let ${\mathcal{G} \subset X}$ be the set of divergence free vector fields generating a global, smooth solution to the incompressible, homogeneous three-dimensional Navier–Stokes equations. We prove that a sequence of divergence free vector fields converging in the sense of distributions to an element of ${\mathcal{G}}$ belongs to ${\mathcal{G}}$ if n is large enough, provided the convergence holds “anisotropically” in frequency space. Typically, this excludes self-similar type convergence. Anisotropy appears as an important qualitative feature in the analysis of the Navier–Stokes equations; it is also shown that initial data which do not belong to ${\mathcal{G}}$ (hence which produce a solution blowing up in finite time) cannot have a strong anisotropy in their frequency support.     

the future of PARTICUOLOGY

I congratulate the Chinese Society of Particuology(and especially my friend Professor Mooson Kwauk,the Society's distinguished President Emeritus) forits initiative in launching a new journal devoted to studiesof particle science and technology.     

Influence of the pressure drop and the air lock on the solid flux in a cross-flow moving bed

The gas-solid flow pattern in a rectangular cross-flow moving bed is simulated by the multiphase particle-in-cell(MP-PIC)model with the Barracuda software.The computed results are verified by the experimental data.In the bed,the actual solid flux generally equals the solid flow rates in the solid feed and discharge tubes.However,these two flow rates are greatly influenced by the air lock and the pressure drop in the solid feed and discharge tubes,namely,the negative and positive pressure gradients,respectively,rather than the traditional opinion that they are merely controlled by the valve openings.The pressure drops in these tubes are calculated by the proposed“common pressure pool with multiple outlets”(CPPMO)and the“common pressure pool”(CPP)methods.It is found that the local gas resistance dominates the pressure drop in the solid discharge tubes,while the gas frictional resistance determines the pressure drop in the solid feed tube.In addition,when the solid flow rate nearly tends to zero in the solid feed tube,the air lock forms.A solid flux equation is then given by considering both the air lock and the pressure drop factors in the cross-flow moving bed.     

Thermal convection initiated by the quasistatic component of the microacceleration field on the “Mir” orbital station

The three-dimensional unsteady thermal convection developing in a cubic cavity on board the “Mir” station under the action of the quasistatic component of the microacceleration caused by the earth’s gravity field strength gradient and the motion of the station about the centre of mass is investigated numerically. The calculations are carried out for two real time intervals of motion of the station about the centre of mass using actual values of the quasistatic component. Moscow, Sankt-Peterburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 39–45, May–June, 2000.     

A Navier–Stokes Approximation of the 3D Euler Equation with the Zero Flux on the Boundary

Under assumptions on smoothness of the initial velocity and the external body force, we prove that there exists T ₀ > 0, ν ₀ > 0 and a unique continuous family of strong solutions u ^ν (0 ≤ ν < ν ₀) of the Euler or Navier–Stokes initial-boundary value problem on the time interval (0, T ₀). In addition to the condition of the zero flux, the solutions of the Navier–Stokes equation satisfy certain natural boundary conditions imposed on curl u ^ν and curl ² u ^ν .      

Hadamard Variational Formula for the Green’s Function of the Boundary Value Problem on the Stokes Equations

For every ${\varepsilon > 0}$ , we consider the Green’s matrix ${G_{\varepsilon}(x, y)}$ of the Stokes equations describing the motion of incompressible fluids in a bounded domain ${\Omega_{\varepsilon} \subset \mathbb{R}^d}$ , which is a family of perturbation of domains from ${\Omega\equiv \Omega_0}$ with the smooth boundary ${\partial\Omega}$ . Assuming the volume preserving property, that is, ${\mbox{vol.}\Omega_{\varepsilon} = \mbox{vol.}\Omega}$ for all ${\varepsilon > 0}$ , we give an explicit representation formula for ${\delta G(x, y) \equiv \lim_{\varepsilon\to +0}\varepsilon^{-1}(G_{\varepsilon}(x, y) - G_0(x, y))}$ in terms of the boundary integral on ${\partial \Omega}$ of ${G_0(x, y)}$ . Our result may be regarded as a classical Hadamard variational formula for the Green’s functions of the elliptic boundary value problems.     

Graphical Illustrations for the Nur-Byerlee-Carroll Proof of the Formula for the Biot Effective Stress Coefficient in?Poroelasticity

This work presents a graphically illustrated version of the Nur-Byerlee-Carroll proof of the formula for the Biot effective stress coefficient in poroelasticity. The original elegant proof was provided by Nur and Byerlee (J. Geophys. Res. 76:6414, 1971) for isotropic materials and extended by Carroll (J. Geophys. Res. 84:7510?C7512, 1979) to anisotropic materials. Although the application of this result is in poroelasticity or in the analysis of composite materials, the proof is an analytical thought experiment in linear elasticity, and should be appreciated as such.