A generalized constitutive elasticity law for GLPD micromorphic materials,with application to the problem of a spherical shell subjected to axisymmetric loading conditions

In this work we propose to replace the GLPD hypo-elasticity law by a more rigorous generalized Hooke's law based on classical material symmetry characterization assumptions. This law introduces in addition to the two well-known Lame's moduli, five constitutive constants. An analytical solution is derived for the problem of a spherical shell subjected to axisymmetric loading conditions to illustrate the potential of the proposed generalized Hooke's law.     

On the Stability of Damped Timoshenko Systems: Cattaneo Versus Fourier Law

We consider hyperbolic Timoshenko-type vibrating systems that are coupled to a heat equation modeling an expectedly dissipative effect through heat conduction. While exponential stability under the Fourier law of heat conduction holds, it turns out that the coupling via the Cattaneo law does not yield an exponentially stable system. This seems to be the first example that a removal of the paradox of infinite propagation speed inherent in Fourier’s law by changing to the Cattaneo law causes a loss of the exponential stability property. Actually, for systems with history, the Fourier law keeps the exponential stability known for the pure Timoshenko system without heat conduction, but introducing the Cattaneo coupling even destroys this property. This work was supported by the DFG-project “Hyperbolic Thermoelasticity” (RA 504/3-1).     

Stationary solutions for nonlinear dispersive Schrödinger’s equation

This paper carries out the integration of the nonlinear dispersive Schrödinger’s equation by the aid of Lie group analysis. The stationary solutions are obtained. The two types of nonlinearity that are studied in this paper are power law and dual-power law so that the cases of Kerr law and parabolic law nonlinearity fall out as special cases.     

Temporal analysis of breakup for a power law liquid jet in a swirling gas

The breakup mechanism and instability of a power law liquid jet are investigated in this study. The power law model is used to account for the non-Newtonian behavior of the liquid fluid. A new theoretical model is established to explain the breakup of a power law liquid jet with axisymmetric and asymmetric disturbances, which moves in a swirling gas. The corresponding dispersion relation is derived by a linear approximation, and it is applicable for both shear-thinning and shear-thickening liquid jets. Analysis results are calculated based on the temporal mode. The analysis includes the effects of the generalized Reynolds number, the Weber number, the power law exponent, and the air swirl strength on the breakup of the jet. Results show that the shear-thickening liquid jet is more unstable than its Newtonian and shear-thinning counterparts when the effect of the air swirl is taken into account. The axisymmetric mode can be the dominant mode on the power law jet breakup when the air swirl strength is strong enough, while the non-axisymmetric mode is the domination on the instability of the power liquid jet with a high We and a low Re _n . It is also found that the air swirl is a stabilizing factor on the breakup of the power law liquid jet. Furthermore, the instability characteristics are different for different power law exponents. The amplitude of the power law liquid jet surface on the temporal mode is also discussed under different air swirl strengths.     

Upscaling Forchheimer law

We investigate the high velocity flow in heterogeneous porous media. The model is obtained by upscaling the flow at the heterogeneity scale where the Forchheimer law is assumed to be valid. We use the method of multiple scale expansions, which gives rigorously the macroscopic behaviour without any prerequisite on the form of the macroscopic equations. We show that Forchheimer law does not generally survive upscaling. The macroscopic flow law is strongly non-linear and anisotropic. A 2-point Padé approximation of the flow law in the form of a Forchheimer law is given. However, this approximation is generally poor. These results are illustrated in two particular cases: a layered composite porous media and a composite constituted by a square array of circular porous inclusions embedded in a porous matrix. We show that non-linearities are sources of anisotropy.     

Conservation Law and Application of J-Integral in Multi-Materials

The conservation law of J-integral in two-media with a crack paralleling to the interface of the two media was firstly proved by analytical and numerical finite element method. Then a schedule model was established that an interface crack is inserted in four media. According to the J-integral conservation law on multi-media, the energy release ratio of Ⅰ-type crack was considered to be conservation when the middle medium layers are very thin. And the conservation law was also convinced by numerical method. By means of the dimension analysis on the model, the asymptotic results and formula calculating the energy release ratio and complex stress intensity factor are presented.     

High velocity flow through fractured and porous media: the role of flow non-periodicity

In the present paper we examine the evolution of the macroscopic flow law in a crenellated channel, representing an element of fractured or porous medium and in function of the Reynolds number Re. A numerical analysis based on the Navier–Stokes equations is applied. We focus on the influence of the flow periodicity or non-periodicity upon the macroscopic law. The physical explanation of the non-linear deviation from Darcy's law is still an issue, as the Ergun–Forchheimer law admitted for high Reynolds numbers comes up against some theoretical problems. In the periodic case, three non-linear flow regimes were revealed: a cubic flow with respect to velocity at low Re, an intermediate non-quadratic law, and a self-similar mode independent of Re at very high Re. The Forchheimer law is not confirmed. The case of a non-periodic flow clearly highlights the link between the flow non-periodicity and the quadratic law. The quadratic deviation becomes all the more important as the non-periodicity degree is high.     

Numerical simulation of blood flow and interstitial fluid pressure in solid tumor microcirculation based on tumor-induced angiogenesis

A coupled intravascular–transvascular–interstitial fluid flow model is developed to study the distributions of blood flow and interstitial fluid pressure in solid tumor microcirculation based on a tumor-induced microvascular network. This is generated from a 2D nine-point discrete mathematical model of tumor angiogenesis and contains two parent vessels. Blood flow through the microvascular network and interstitial fluid flow in tumor tissues are performed by the extended Poiseuille’s law and Darcy’s law, respectively, transvascular flow is described by Starling’s law; effects of the vascular permeability and the interstitial hydraulic conductivity are also considered. The simulation results predict the heterogeneous blood supply, interstitial hypertension and low convection on the inside of the tumor, which are consistent with physiological observed facts. These results may provide beneficial information for anti-angiogenesis treatment of tumor and further clinical research. The project supported by the National Natural Science Foundation of China (10372026).     

On the viscoelastic characterization of the Jeffreys–Lomnitz law of creep

In 1958, Jeffreys (Geophys J?R Astron Soc 1:92–95) proposed a power law of creep, generalizing the logarithmic law earlier introduced by Lomnitz, to broaden the geophysical applications to fluid-like materials including igneous rocks. This generalized law, however, can be applied also to solid-like viscoelastic materials. We revisit the Jeffreys–Lomnitz law of creep by allowing its power law exponent α, usually limited to the range 0?≤?α?≤?1 to all negative values. This is consistent with the linear theory of viscoelasticity because the creep function still remains a Bernstein function, that is positive with a completely monotone derivative, with a related spectrum of retardation times. The complete range α?≤?1 yields a continuous transition from a Hooke elastic solid with no creep $\left(\alpha \,\to\, -\infty\right)$ to a Maxwell fluid with linear creep $\left(\alpha \,=\,1\right)$ passing through the Lomnitz viscoelastic body with logarithmic creep $\left(\alpha\, =0\right)$ , which separates solid-like from fluid-like behaviors. Furthermore, we numerically compute the relaxation modulus and provide the analytical expression of the spectrum of retardation times corresponding to the Jeffreys–Lomnitz creep law extended to all α?≤?1.     

The vector refraction law for shock waves

The law is formulated in vector form and is shown to be a powerful principle for studying the refraction of shock waves. A variety of criteria for the onset of irregular refraction are discussed. The refraction index matrix is defined and it is shown that it arises naturally from the law. A projection matrix is also defined and it is found to be useful for operating on the vector wave impedance. It is expected that the methods described here will be useful for the numerical solution of problems in the refraction of shocks by materials with continuous changes in properties. The refraction law is violated in fast-slow refraction by the reflected wave over-running the incident shock to produce an irregular refraction which is either the anomalous type or the Mach-reflection-refraction type. For slow-fast refraction the law is violated by the transmitted wave becoming a precursor and also over-running the incident shock. The precursor may either be a shock or an evanescent compression wave band.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Reconsideration on the role of the specific heat ratio in Arrhenius law applications

Arrhenius law implicates that only those molecules which possess the internal energy greater than the activation energy Ea can react. However, the internal energy will not be proportional to the gas temperature if the specific heat ratio y and the gas constant R vary during chemical reaction processes. The varying y may affect significantly the chemical reaction rate calculated with the Arrhenius law under the constant γ assumption, which has been widely accepted in detonation and combustion simulations for many years. In this paper, the roles of variable γ and R in Arrhenius law applications are reconsidered, and their effects on the chemical reaction rate are demonstrated by simulating one- dimensional C-J and two-dimensional cellular detonations. A new overall one-step detonation model with variable γ and R is proposed to improve the Arrhenius law. Numerical experiments demonstrate that this improved Arrhenius law works well in predicting detonation phenomena with the numerical results being in good agreement with experimental data.     

On the history of the dry friction law

We discuss the role played by Amontons, Coulomb, Leonardo daVinci,Morin, and Euler in the discovery of the dry friction law. In particular, reference is given to Euler’s 1748 paper,where an exhaustive statement of the dry friction law was given 37 years before Coulomb’s main publications. Painlevé’s criticism of the Coulomb law is assessed, and the main points of the theory of polycomponent dry friction are given.     

Cross-Properties Relations in 3D Percolation Networks: II. Network Permeability

An efficient method to estimate the absolute permeability of three-dimensional percolation networks was proposed. It uses a Kozeny–Carman relationship in the form of a scaling law to relate the network permeability to its hydraulic characteristic length. This characteristic length was determined at the network percolation threshold using a three-dimensional extension of the Hoshen–Kopelman algorithm. For developing the scaling laws, the network permeability was calculated by solving the Kirchoff’s law for all sample spanning clusters that had been identified by the three-dimensional version of the Hoshen–Kopelman algorithm. The method was tested with simple cubic site-bond network models with and without spatial correlations. The universality of the exponents in the scaling laws were also investigated. It was shown that, once the scaling law has been derived, the permeability value can be estimated 3–9 times faster using the present method.     

Adaptive–adaptive robust boundary control for uncertain mechanical systems with inequality constraints

In this paper, adaptive–adaptive robust boundary control is proposed for uncertain mechanical systems with inequality constraints. First, inequality constraints are taken into consideration, which are derived from the system or environment constraints on state bounds and control input bounds. Moreover, the original system with inequality constraints is transformed into a novel system with merely equality constraints by constraint reorganization techniques. Second, an adaptive robust control with a two-layer adaptive law is initiated. Here, the lower-layer adaptive law is used to overcome the (possibly rapidly time-varying) system uncertainty, which is bounded but unknown. Additionally, the adaptive law design parameters are chosen online by the upper-layer adaptive law, rather than according to the empirically set fixed values. Finally, the performance of the controller with uniform boundedness and uniform ultimate boundedness is theoretically and experimentally verified. The control strategy allows the electric cylinder-driven pitch system to achieve highly accurate and error-controllable motion within the motor drive capability.

     

On the general form of the law of dynamics

The dynamics of Lagrangian systems is formulated with a differential geometric approach and according to a new paradigm of the calculus of variations. Discontinuities in the trajectory, non-potential force systems and linear constraints are taken into account with a coordinate-free treatment. The law of dynamics, characterizing the trajectory in a general non-linear configuration manifold, is expressed in terms of a variational principle and of differential and jump conditions. By endowing the configuration manifold with a connection, the general law is shown to be tensorial in the velocity of virtual flows and to depend on the torsion of the connection. This result provides a general expression of the EULER-LAGRANGE operator. POINCARÉ and LAGRANGE forms of the law are recovered as special cases corresponding, respectively, to the connection induced by natural and mobile reference frames. For free motions, the geodesic property of the trajectory is directly inferred by adopting the LEVI-CIVITA connection induced by the kinetic energy.     

落体法测刚体转动惯量的测量方法比较

用JIJG—I刚体转动惯量实验仪的同组数据,分别用测角加速度法和测时间法计算待测圆盘的转动惯量,结果表明,测角加速度法比测时间法的测量精度可提高1到2个数量级,具有明显优点;同时分析了测时间法产生误差的主要原因,也指出了使用测角加速度法的注意事项．     

Examples of non-uniqueness and non-existence of solutions to quasistatic contact problems with friction

Summary This work considers a contact problem with friction involving one contact point and two degrees-of-freedom. The contacting structure is linear elastic. Two different models of contact interaction are considered, the classical Signorini unilateral contact law and a normal compliance law. Coulomb's law of friction is used. All possible so-called rate problems are solved, from which one concludes that the quasistatic problem may possess non-uniqueness and non-existence of solutions. In the case of the normal compliance law this can be explained by a softening structural response. For Signorini's law softening explains only some of the possible situations where non-uniqueness can occur.

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Beispiele der Nichteindeutigkeit und Nichtexistenz der Lösung quasistatischer Kontaktprobleme mit Reibung

Übersicht In dieser Arbeit wird ein Kontaktproblem mit Reibung behandelt, das einen Kontaktpunkt und zwei Freiheitsgrade einschließt. Die kontaktgebende Struktur ist linearelastisch. Zwei verschiedene Modelle der Kontaktwirkung sind berücksichtigt: Erstens das klassische einseitige Signorini-Kontaktgesetz und zweitens ein Gesetz für die Nachgiebigkeit in Normalenrichtung. Das Coulombsche Reibungsgesetz wird verwendet. Alle möglichen sogenannten Geschwindigkeitsprobleme werden gelöst, woraus geschlossen wird, daß das quasistatische Problem Nichteindeutigkeit und Nichtexistenz der Lösung besitzen kann. Im Fall des Nachgiebigkeitsgesetzes kann dieses als abfallende Struktursteifigkeit erklärt werden. Im Fall eines Signorini-Gesetzes erklärt dieses nur einige der möglichen Situationen, wo Nichteindeutigkeit auftreten kann.

     

The Effect of Double Dispersion on Natural Convection Heat and Mass Transfer in a Non-Newtonian Fluid Saturated Non-Darcy Porous Medium

The effect of power law index parameter of the non-Newtonian fluid on free convection heat and mass transfer from a vertical wall is analyzed by considering double dispersion in a non-Darcy porous medium with constant wall temperature and concentration conditions. The Ostwald–de Waele power law model is used to characterize the non-Newtonian fluid behavior. In this case a similarity solution is possible. The variation of heat and mass transfer coefficients with the governing parameters such as power law index, thermal and solutal dispersion parameters, inertia parameter, buoyancy ratio, and the Lewis number is discussed for a wide range of values of these parameters.