Infinitesimal Stability of the Equilibrium States of?an?Incompressible, Isotropic Elastic Tube Under?Pressure

The infinitesimal stability of the equilibrium states of an arbitrary incompressible, isotropic and homogeneous elastic cylindrical shell in a pure radial expansion under a constant inflation pressure is studied for both thick- and thin-walled shells. The classical criterion of infinitesimal stability yields a general stability theorem relating the frequency and pressure response and reveals that points at which the pressure is stationary define the domain of unstable or neutrally stable states. All results are expressed in terms of a general shear response function, and specific results are provided for the Mooney-Rivlin, Gent and Ogden models, the second having limited extensibility, the last including experimental data. Every static state of a Mooney-Rivlin tube is stable so long as the pressure is less than an asymptotic limit that increases with the thickness. Otherwise, only the Ogden model exhibits static states of instability for all long cylindrical tubes of thickness less than a transitional value above which all static states are infinitesimally stable. A long cylindrical cavity in all three unbounded models is stable for all pressures. All results are illustrated graphically.     

Qualifications of public health geneticists?

Public health genetics is a rapidly emerging field that is not well defined. One way of helping to define the field is to describe the competences of the professionals who participate in it. The information presented here attempts to define the knowledge base, skills, and attitudes needed to be a public health geneticist. It is hoped that this information will be used to create a uniform definition of public health genetics, and also help education programs train individuals who want to participate in the field.     

Oscillations of a?beam with a?time-varying mass

This paper analyzes dynamical behavior of a simply supported Euler?CBernoulli beam with a time-varying mass on its surface. Though the system under consideration is linear, it exhibits dynamics similar to a nonlinear system behavior including internal resonances. The asymptotical solutions for the beam displacement has been found by combining the classical Galerkin method with the averaging method for equations in Banach spaces. The resonance conditions have been derived. It has been proposed a method for finding a number of possible resonances.Effect of the beam parameters on its dynamical behavior is investigated as well.     

Global dynamics and integrity of a two-dof model of?a?parametrically excited cylindrical shell

In this paper the global dynamics and topological integrity of the basins of attraction of a parametrically excited cylindrical shell are investigated through a two-degree-of-freedom reduced order model. This model, as shown in previous authors?? works, is capable of describing qualitatively the complex nonlinear static and dynamic buckling behavior of the shell. The discretized model is obtained by employing Donnell shallow shell theory and the Galerkin method. The shell is subjected to an axial static pre-loading and then to a harmonic axial load. When the static load is between the buckling load and the minimum post-critical load, a three potential well is obtained. Under these circumstances the shell may exhibit pre- and post-buckling solutions confined to each of the potential wells as well as large cross-well motions. The aim of the paper is to analyze in a systematic way the bifurcation sequences arising from each of the three stable static solutions, obtaining in this way the parametric instability and escape boundaries. The global dynamics of the system is analyzed through the evolution of the various basins of attraction in the four-dimensional phase space. The concepts of safe basin and integrity measures quantifying its magnitude are used to obtain the erosion profile of the various solutions. A detailed parametric analysis shows how the basins of the various solutions interfere with each other and how this influences the integrity measures. Special attention is dedicated to the topological integrity of the various solutions confined to the pre-buckling well. This allows one to evaluate the safety and dynamic integrity of the mechanical system. Two characteristic cases, one associated with a sub-critical parametric bifurcation and another with a super-critical parametric bifurcation, are considered in the analysis.     

Transient ?ow of magnetized Maxwell nano?uid: Buongiorno model perspective of Cattaneo-Christov theory

The present research article is devoted to studying the characteristics of Cattaneo-Christov heat and mass ?uxes in the Maxwell nano?uid ?ow caused by a stretching sheet with the magnetic ?eld properties. The Maxwell nano?uid is investigated with the impact of the Lorentz force to examine the consequence of a magnetic ?eld on the?ow characteristics and the transport of energy. The heat and mass transport mechanisms in the current physical model are analyzed with the modi?ed versions of Fourier's and Fick's laws, respectively. Additionally, the well-known Buongiorno model for the nano?uids is ?rst introduced together with the Cattaneo-Christov heat and mass ?uxes during the transient motion of the Maxwell ?uid. The governing partial di?erential equations(PDEs) for the ?ow and energy transport phenomena are obtained by using the Maxwell model and the Cattaneo-Christov theory in addition to the laws of conservation.Appropriate transformations are used to convert the PDEs into a system of nonlinear ordinary di?erential equations(ODEs). The homotopic solution methodology is applied to the nonlinear di?erential system for an analytic solution. The results for the time relaxation parameter in the ?ow, thermal energy, and mass transport equations are discussed graphically. It is noted that higher values of the thermal and solutal relaxation time parameters in the Cattaneo-Christov heat and mass ?uxes decline the thermal and concentration ?elds of the nano?uid. Further, larger values of the thermophoretic force enhance the heat and mass transport in the nanoliquid. Moreover, the Brownian motion of the nanoparticles declines the concentration ?eld and increases the temperature ?eld.The validation of the results is assured with the help of numerical tabular data for the surface velocity gradient.     

Multiscale Dynamics of Heterogeneous Media in?the?Peridynamic Formulation

A methodology is presented for investigating the dynamics of heterogeneous media using the nonlocal continuum model given by the peridynamic formulation. The approach presented here provides the ability to model the macroscopic dynamics while at the same time resolving the dynamics at the length scales of the microstructure. Central to the methodology is a novel two-scale evolution equation. The rescaled solution of this equation is shown to provide a strong approximation to the actual deformation inside the peridynamic material. The two scale evolution can be split into a microscopic component tracking the dynamics at the length scale of the heterogeneities and a macroscopic component tracking the volume averaged (homogenized) dynamics. The interplay between the microscopic and macroscopic dynamics is given by a coupled system of evolution equations. The equations show that the forces generated by the homogenized deformation inside the medium are related to the homogenized deformation through a history dependent constitutive relation.     

Adaptive bidirectionally coupled synchronization of?chaotic?systems with unknown parameters

This paper investigates the chaos synchronization of two bidirectionally coupled chaotic systems. In comparison with previous methods (identical bidirectionally coupled synchronization), the present control scheme is different bidirectionally coupled synchronization, which includes different complete bidirectionally coupled synchronization and different partial bidirectionally coupled synchronization. Based on the Lasalle invariance principle, adaptive schemes are designed to make two different bidirectionally coupled chaotic systems asymptotically synchronized, and unknown parameters are identified simultaneously in the process of synchronization. Theoretical analysis and numerical simulations are shown to verify the results.     

Controlling Hopf�CHopf interaction bifurcations of?a?two-degree-of-freedom self-excited system with?dry?friction

The feedback control problem of designing Hopf?CHopf interaction bifurcations into a dry friction system at a pre-specified parameter point is addressed. A new bifurcation criterion without using eigenvalues is established to preferably determine the control gains. Numerical simulation shows that the torus solution of Hopf?CHopf interaction bifurcation can be created in the friction system at a desired parameter location.     

Boundary layer ?ow of Maxwell ?uid due to torsional motion of cylinder: modeling and simulation

This paper investigates the boundary layer ?ow of the Maxwell ?uid around a stretchable horizontal rotating cylinder under the in?uence of a transverse magnetic?eld. The constitutive ?ow equations for the current physical problem are modeled and analyzed for the ?rst time in the literature. The torsional motion of the cylinder is considered with the constant azimuthal velocity E. The partial di?erential equations(PDEs)governing the torsional motion of the Maxwell ?uid together with energy transport are simpli?ed with the boundary layer concept. The current analysis is valid only for a certain range of the positive Reynolds numbers. However, for very large Reynolds numbers, the ?ow becomes turbulent. Thus, the governing similarity equations are simpli?ed through suitable transformations for the analysis of the large Reynolds numbers. The numerical simulations for the ?ow, heat, and mass transport phenomena are carried out in view of the bvp4 c scheme in MATLAB. The outcomes reveal that the velocity decays exponentially faster and reduces for higher values of the Reynolds numbers and the ?ow penetrates shallower into the free stream ?uid. It is also noted that the phenomenon of stress relaxation, described by the Deborah number, causes to decline the ?ow ?elds and enhance the thermal and solutal energy transport during the ?uid motion. The penetration depth decreases for the transport of heat and mass in the ?uid with the higher Reynolds numbers. An excellent validation of the numerical results is assured through tabular data with the existing literature.     

Bio-Marangoni convection ?ow of Casson nanoliquid througha porous medium in the presence of chemicallyreactive activation energy?

正J. K. MADHUKESH1, G. K. RAMESH2, B. C. PRASANNAKUMARA1,S. A. SHEHZAD3,, F. M. ABBASI4     

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.     

Dynamics of three coupled limit cycle oscillators with?vastly?different frequencies

A system of three coupled limit cycle oscillators with vastly different frequencies is studied. The three oscillators, when uncoupled, have the frequencies ?? ₁=O(1), ?? ₂=O(1/??) and ?? ₃=O(1/?? ²), respectively, where ???1. The method of direct partition of motion (DPM) is extended to study the leading order dynamics of the considered autonomous system. It is shown that the limit cycles of oscillators 1 and 2, to leading order, take the form of a Jacobi elliptic function whose amplitude and frequency are modulated as the strength of coupling is varied. The dynamics of the fastest oscillator, to leading order, is unaffected by the coupling to the slower oscillator. It is also found that when the coupling strength between two of the oscillators is larger than a critical bifurcation value, the limit cycle of the slower oscillator disappears. The obtained analytical results are formal and are checked by comparison to solutions from numerical integration of the system.     

A Representation Theorem for Material Tensors of?Weakly-Textured Polycrystals and?Its Applications in?Elasticity

Material tensors pertaining to polycrystalline aggregates should manifest also the influence of crystallographic texture on the material properties in question. In this paper we make use of tensors which form bases of irreducible representations of the rotation group and prove a representation theorem by which a given material tensor of a weakly-textured polycrystal is expressed as a linear combination of an orthonormal set of irreducible basis tensors, with the components given explicitly in terms of texture coefficients and a set of undetermined material parameters. Once the irreducible basis tensors that appear in the formula are determined, the representation formula, which is valid for all texture and crystal symmetries, will delineate quantitatively the effect of crystallographic texture on the material tensor in question. We present an integral formula and an orthonormalization process which serve as the basis for a procedure to determine explicitly the irreducible basis tensors required in the representation formula. For applications we determine a set of irreducible basis tensors for the elasticity tensor and a set for fourth-order tensors that define constitutive equations in incompressible elasticity and Hill’s quadratic yield functions in plasticity. We show that orientation averaging of a tensor can be done easily if we have in hand a set of irreducible basis tensors for the decomposition of the tensor in question. As illustration we derive a formula, which is valid for all texture and crystal symmetries, for the elasticity tensor under the Voigt model.     

Hard-material Adhesion: Which Scales of Roughness Matter?

Background

Surface topography strongly modifies adhesion of hard-material contacts, yet roughness of real surfaces typically exists over many length scales, and it is not clear which of these scales has the strongest effect. Objective: This investigation aims to determine which scales of topography have the strongest effect on macroscopic adhesion.

Methods

Adhesion measurements were performed on technology-relevant diamond coatings of varying roughness using spherical ruby probes that are large enough (0.5-mm-diameter) to sample all length scales of topography. For each material, more than 2000 measurements of pull-off force were performed in order to investigate the magnitude and statistical distribution of adhesion. Using sphere-contact models, the roughness-dependent effective values of work of adhesion were measured, ranging from 0.08 to 7.15 mJ/m² across the four surfaces. The data was more accurately fit using numerical analysis, where an interaction potential was integrated over the AFM-measured topography of all contacting surfaces.

Results

These calculations revealed that consideration of nanometer-scale plasticity in the materials was crucial for a good quantitative fit of the measurements, and the presence of such plasticity was confirmed with AFM measurements of the probe after testing. This analysis enabled the extraction of geometry-independent material parameters; the intrinsic work of adhesion between ruby and diamond was determined to be 46.3 mJ/m². The range of adhesion was 5.6 nm, which is longer than is typically assumed for atomic interactions, but is in agreement with other recent investigations. Finally, the numerical analysis was repeated for the same surfaces but this time with different length-scales of roughness included or filtered out.

Conclusions

The results demonstrate a critical band of length-scales—between 43 nm and 1.8 µm in lateral size—that has the strongest effect on the total adhesive force for these hard, rough contacts.

     

What is the Correct Definition of Average Pressure?

Use of a correct definition of average pressure is important in numerical modeling of oil reservoirs and aquifers, where the simulated domain can be very large. Also, the average pressure needs to be defined in the application of pore-network modeling of (two-phase) flow in porous media, as well as in the (theoretical) upscaling of flow equations. Almost always the so-called intrinsic phase-volume average operator, which weighs point pressure values with point saturation values, is employed. Here, we introduce and investigate four other potentially plausible averaging operators. Among them is the centroid-corrected phase-average pressure, which corrects the intrinsic phase-volume average pressure for the distance between the centroid of the averaging volume and the phase. We consider static equilibrium of two immiscible fluids in a homogeneous, one-dimensional, vertical porous medium domain under a series of (static) drainage conditions. An important feature of static equilibrium is that the total potential (i.e., the sum of pressure and gravity potentials) is constant for each phase over the whole domain. Therefore, its average will be equal to the same constant. It is argued that the correct average pressure must preserve the fact that fluid potentials are constant. We have found that the intrinsic phase-volume average pressure results in a gradient in the total phase potential, i.e., the above criterion is violated. In fact, only the centroid-corrected operator satisfies this criterion. However, at high saturations, use of the centroid-corrected average can give rise to negative values of the difference between the average nonwetting and wetting phase pressures. For main drainage, differences among various averaging operators are significantly less because both phases are present initially, such that the difference between the centroids of phases, and the middle of the domain are relatively small.     

Topological chaos of universal elementary cellular automata?rule

The dynamical behaviors of elementary cellular automata rule 110 are analyzed from the viewpoint of symbolic dynamics in the space of bi-infinite symbolic sequences. This paper conducts a rigorous analysis of the relationship between rules 110, 170 and 240 by applying blocking transformation and releasing transformation. Based on this result, the topological chaos of T ₁₁₀ induced by rule 110 is evaluated; that is, $T_{110}^{9}$ and $T_{110}^{16}$ are topologically mixing and possess the positive topological entropies on their respective subsystems. Therefore, it is natural to argue that the intrinsic complexity of rule 110 is high according to the usual measure of complexity organized around the symbolic dynamics of stationary symbol sequences. Finally, it is worth mentioning that the method presented in this paper is also applicable to other blocking transformation equivalences therein.     

Can one measure the temperature of a curve?

The entropy of a plane curve is defined in terms of the number of intersection points with a random line. The Gibbs distribution which maximizes the entropy enables one to define the temperature of the curve. At 0 temperature, the curve reduces to a straight segment. At high temperature, the curve is somewhat chaotic and behaves like a perfect gas. We attempt to show that thermodynamic formalism can be used for the study of plane curves. The curves we discuss have finite length, unlike Mandelbrot's fractal curves [1], yet we feel our approach to the mathematics is not far from his.     

Finite-time synchronization of switched stochastic R?ssler systems

This paper presents the finite-time synchronization between switched stochastic R?ssler systems accompanied by a time-driven switching law. Based on the Ito formula and Lyapunov stability theory, the finite-time synchronization of switched stochastic master-slave R?ssler systems and the finite-time stability for the mean of error states are developed with the proposed feedback controller. Numerical simulations demonstrate the effectiveness of the proposed methods.     

Higher Regularity of H?lder Continuous Solutions of Parabolic Equations with Singular Drift Velocities

Motivated by an equation arising in magnetohydrodynamics, we prove that H?lder continuous weak solutions of a nonlinear parabolic equation with singular drift velocity are classical solutions. The result is proved using the space?Ctime Besov spaces introduced by Chemin and Lerner (J Differ Equ 121(2):314?C328, 1995), combined with energy estimates, without any minimality assumption on the H?lder exponent of the weak solutions.