On the instability of steady motion

This paper deals with the instability of steady motions of conservative mechanical systems with cyclic coordinates. The following are applied: Kozlov’s generalization of the first Lyapunov’s method, as well as Rout’s method of ignoration of cyclic coordinates. Having obtained through analysis the Maclaurin’s series for the coefficients of the metric tensor, a theorem on instability is formulated which, together with the theorem formulated in Furta (J. Appl. Math. Mech. 50(6):938–944, 1986), contributes to solving the problem of inversion of the Lagrange-Dirichlet theorem for steady motions. The cases in which truncated equations involve the gyroscopic forces are solved, too. The algebraic equations resulting from Kozlov’s generalizations of the first Lyapunov’s method are formulated in a form including one variable less than was the case in existing literature.     

Local mass/heat transfer from a wall-mounted block in rectangular channel flow

This investigation explores the mass/heat transfer from a wall-mounted block in a rectangular fully developed channel flow. The naphthalene sublimation scheme was used to measure the level of local mass transfer from the block’s surfaces. The heat transfer coefficient can be obtained by analogy between heat and mass transfer. The effects of the Reynolds number on the local mass transfer from the block’s surfaces have been widely discussed. Results showed that, owing to the flow complexity induced by vortices around the block, the block’s surfaces appeared four different spatial Sherwood number distributions, termed “Wave type”, “U type”, “Slant type”, and “Pit type”. A change in the Reynolds number significantly altered the spatial Sherwood number distributions on the block’s surfaces. Besides, four correlations between the Reynolds number and the surface-averaged Sherwood number were presented for the front, top, side, and rear surfaces of the block at a given block’s height, for the purpose of practical applications.     

Calculation of Hugoniot properties for shocked nitromethane based on the improved Tsien’s EOS

We have calculated the Hugoniot properties of shocked nitromethane based on the improved Tsien＇s equa- tion of state （EOS） that optimized by ＂exact＂ numerical molecular dynamic data at high temperatures and pressures. Comparison of the calculated results of the improved Tsien＇s EOS with the existed experimental data and the direct simu- lations show that the behavior of the improved Tsien＇s EOS is very good in many aspects. Because of its simple analytical form, the improved Tsien＇s EOS can be prospectively used to study the condensed explosive detonation coupling with chemical reaction.     

Elastodynamics and Elastostatics by a Unified Method of Potentials for x 3-Convex Domains

A new general solution in terms of two scalar potential functions for classical elastodynamics of x ₃-convex domains is presented. Through the establishment and usage of a set of basic mathematical lemmas, a demonstration of its connection to Kovalevshi–Iacovache–Somigliana elastodynamic solution, and thus its completeness, is realized with the aid of the theory of repeated wave equations and Boggio’s theorem. With the time dependence of the potentials suppressed, the new decomposition can, unlike Lamé’s, degenerate to a complete solution for elastostatic problems.      

The Effects of Fluid Viscosity on the Kinematics and Material Properties of <Emphasis Type="Italic">C. elegans</Emphasis> Swimming at Low Reynolds Number

The effects of fluid viscosity on the kinematics of a small swimmer at low Reynolds numbers are investigated in both experiments and in a simple model. The swimmer is the nematode Caenorhabditis elegans, which is an undulating roundworm approximately 1 mm long. Experiments show that the nematode maintains a highly periodic swimming behavior as the fluid viscosity is varied from 1.0 to 12 mPa s. Surprisingly, the nematode’s swimming speed (~0.35 mm/s) is nearly insensitive to the range of fluid viscosities investigated here. However, the nematode’s beating frequency decreases to an asymptotic value (~1.7 Hz) with increasing fluid viscosity. A simple model is used to estimate the nematode’s Young’s modulus and tissue viscosity. Both material properties increase with increasing fluid viscosity. It is proposed that the increase in Young’s modulus may be associated with muscle contraction in response to larger mechanical loading while the increase in effective tissue viscosity may be associated with the energy necessary to overcome increased fluid drag forces.     

SPLITTING OF THE SPECTRAL DOMAIN ELECTRICAL DYADIC GREEN’S FUNCTION IN CHIRAL MEDIA

A new method of formulating dyadic Green‘s functions in lossless , reciprocal and unbounded chiral medium was presented. Based on Helmholtz theorem and the nondivergence and irrotational splitting of dyadic Dirac delta-function was this method, the electrical vector dyadic Green‘s function equation was first decomposed into the nondivergence electrical vector dyadic Green‘s function equation and irrotational electrical vector dyadic Green‘s function equation, and then Fourier‘s transformation was used to derive the expressions of the non-divergence and irrotational component of the spectral domain electrical dyadic Green‘s function in chiral media. It can avoid having to use the wavefield decomposition method and dyadic Green‘s function eigenfunction expansion technique that this method is used to derive the dyadic Green‘s functions in chiral media.     

Anisotropy of elastic properties of materials

Papers dealing with the generalized Hooke’s law for linearly elastic anisotropic media are reviewed. The papers considered are based on Kelvin’s approach disclosing the structure of the generalized Hooke’s law, which is determined by six eigenmoduli of elasticity and six orthogonal eigenstates. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 131–151, November–December, 2008.     

A Three-Dimensional Flow and Transport Modeling of an Aquifer Contaminated by Perchloroethylene Subject to Multi-PRB Remediation

Although subsurface contamination by organic chemicals is a pervasive environmental problem, a permeable reactive barrier (PRB) as a typical in-situ remediation technology is often successful at many sites. Laboratory tests have shown that perchloroethylene (PCE) can be dechlorinated by the combination of zero-valent iron and anaerobic microbial communities (FeMB), and the degradation pathway was: PCE → TCE → 1, 1-DCE → ethylene→  ethane (Ma amd Wu Environ Geol 55(1):47–54, 2008). Based on Ma’s experimental results, we have extended MT3DMS to simulate mother-daughter chain reactions using MODFLOW-2005 V1.7/MT3DMS V5.2. Second, using FeMB as multi-PRB’s reactive media, a 5-component transport model for a three-dimensional aquifer contaminated by PCE subject to multi-PRB remediation was built. Third, the adsorption and degradation parameters of reactive media were estimated by means of genetic algorithm. Finally, the three-dimensional, homogeneous aquifer contaminated by PCE subject to multi-PRB remediation was simulated. Overall, the purpose of this paper was to use FeMB as multi-PRB’s reactive media, and develop a modified MODFLOW/MT3DMS that can simulate a three-dimensional aquifer contaminated by PCE and its daughters. Results demonstrated that FeMB could be a potential reactive media for PCE-contaminated groundwater. Multi-PRB could be a preferred option for secondly pollution caused by application of one-stage PRB. The modified MODFLOW/MT3DMS can effectively simulate multispecies mother–daughter chain kinetic reactions. Sensitivity analysis showed that losses of reactivity and permeability may have a significant effect on remediation’s success.     

A driver’s memory lattice model of traffic flow and its numerical simulation

A new lattice model of traffic flow based on Nagatani’s model is proposed by taking the effect of driver’s memory into account. The linear stability condition of the extended model is obtained by using the linear stability theory. The analytical results show that the stabile area of the new model is larger than that of the original lattice hydrodynamic model by adjusting the driver’s memory intensity parameter p of the past information in the system. The modified KdV equation near the critical point is derived to describe the traffic jam by nonlinear analysis, and the phase space could be divided into three regions: the stability region, the metastable region, and the unstable region, respectively. Numerical simulation also shows that our model can stabilize the traffic flow by considering the information of driver’s memory.     

Micromechanical modeling of linear viscoelastic behavior of heterogeneous materials

Study of effective behavior of heterogeneous materials, starting from the properties of the microstructure, represents a critical step in the design and modeling of new materials. Within this framework, the aim of this work is to introduce a general internal variables approach for scale transition problem in linear viscoelastic case. A new integral formulation is established, based on the complete taking into account of field equations and differential constitutive laws of the heterogeneous problem, in which the effects of elasticity and viscosity interact in a representative volume element. Thanks to Green’s techniques applied to space convolution’s term, a new concentration relation is obtained. The step of homogenization is then carried out according to the self-consistent approximation. The results of the present model are illustrated and compared with those provided by Hashin’s and Rougier’s ones, considered as references, and by internal variables models such as those of Weng and translated fields.     

Diffraction of normal shock for monoatomic gases

In the present investigation, vorticity distribution of a particle over the normal diffracted shock has been obtained for monoatomic gases, CO₂ and SF₆. Further some results using Lighthill’s theory (Lighthill in Proc R Soc A 198:454–470, 1949) and Whitham’s theory (Whitham in J Fluid Mech 2:145–171, 1957) have been obtained.     

Growth of a new phase in a substance in a metastable state

A model of kinetics of phase transitions in a substance in a metastable state is proposed, where the probability of extensive nucleation owing to homogeneous mechanisms is rather large; the model is an alternative to Kolmogorov’s model. The use of this model is demonstrated to offer analytical solutions that describe both the crystallization processes with similar densities of the liquid and solid phases and, for instance, the kinetics of nucleation and growth of bubbles in surface boiling. Solutions obtained by Kolmogorov’s model and by the present model coincide at the initial stage of the process where the volume fraction of the new phase is small. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 75–80, March–April, 2007.     

Transversal forced vibrations of an axially moving sandwich belt system

Based on the author’s previously published results for transversal free vibrations of axially moving sandwich belts described by coupled partial differential equations, which are derived and analytically solved, this paper contains new analytical results, for forced vibrations of the same system excited by transversal external excitation. The transversal forced vibrations of the axially moving sandwich belts are described by the coupled partial nonhomogeneous differential equations. The partial differential equations are analytically solved. Bernoulli’s method of particular integrals and Lagrange’s method of the variations of the constants are used.     

Acceleration of metal plates by a tangential detonation wave

The studies of the two-dimensional acceleration of metal plates that began in the 1960s at the Siberian Division of the Russian Academy of Sciences under the supervision of Academician M. A. Lavrent’ev in connection with explosion-welding works are reviewed briefly. Some new results concerning the use of industrial high-explosives (HE) that operate under conditions of nonideal detonation are given. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 68–74, September–October, 2000.     

Integration of the journal Prikladnaya Mekhanika (International Applied Mechanics) into the world’s scientific community

Two new tendencies in the integration of the journal Prikladnaya Mekhanika (International Applied Mechanics) into the world’s scientific community are discussed. One tendency is that representatives of the world’s scientific community publish their articles in the journal. The other tendency is positioning of this journal in the world’s scientific information environment. The number of full-text article requests as per the document Springer—the Language of Science: International Applied Mechanics, Publisher’s Report, July 1 (2011) is discussed.Anew publication evaluation criterion based on this metric is offered     

A Two-Scale Model for Coupled Electro-Chemo-Mechanical Phenomena and Onsager’s Reciprocity Relations in Expansive Clays: II Computational Validation

In Part I Moyne and Murad [Transport in Porous Media 62, (2006), 333–380] a two-scale model of coupled electro-chemo-mechanical phenomena in swelling porous media was derived by a formal asymptotic homogenization analysis. The microscopic portrait of the model consists of a two-phase system composed of an electrolyte solution and colloidal clay particles. The movement of the liquid at the microscale is ruled by the modified Stokes problem; the advection, diffusion and electro-migration of monovalent ions Na⁺ and Cl⁻ are governed by the Nernst–Planck equations and the local electric potential distribution is dictated by the Poisson problem. The microscopic governing equations in the fluid domain are coupled with the elasticity problem for the clay particles through boundary conditions on the solid–fluid interface. The up-scaling procedure led to a macroscopic model based on Onsager’s reciprocity relations coupled with a modified form of Terzaghi’s effective stress principle including an additional swelling stress component. A notable consequence of the two-scale framework are the new closure problems derived for the macroscopic electro-chemo-mechanical parameters. Such local representation bridge the gap between the macroscopic Thermodynamics of Irreversible Processes and microscopic Electro-Hydrodynamics by establishing a direct correlation between the magnitude of the effective properties and the electrical double layer potential, whose local distribution is governed by a microscale Poisson–Boltzmann equation. The purpose of this paper is to validate computationally the two-scale model and to introduce new concepts inherent to the problem considering a particular form of microstructure wherein the clay fabric is composed of parallel particles of face-to-face contact. By discretizing the local Poisson–Boltzmann equation and solving numerically the closure problems, the constitutive behavior of the diffusion coefficients of cations and anions, chemico-osmotic and electro-osmotic conductivities in Darcy’s law, Onsager’s parameters, swelling pressure, electro-chemical compressibility, surface tension, primary/secondary electroviscous effects and the reflection coefficient are computed for a range particle distances and sat concentrations.     

Simultaneous planar measurement of droplet velocity and size with gas phase velocities in a spray by combined ILIDS and PIV techniques

A new approach for simultaneous planar measurement of droplet velocity and size with gas phase velocities is reported, which combines the out-of-focus imaging technique ‘Interferometric Laser Imaging Droplet Sizing’ (ILIDS) for planar simultaneous droplet size and velocity measurements with the in-focus technique ‘Particle Image Velocimetry’ (PIV) for gas velocity measurements in the vicinity of individual droplets. Discrimination between the gas phase seeding and the droplets is achieved in the PIV images by removing the glare points of focused droplet images, using the droplet position obtained through ILIDS processing. Combination of the two optical arrangements can result in a discrepancy in the location of the centre of a droplet, when imaging through ILIDS and PIV techniques, of up to about 1 mm, which may lead to erroneous identification of the glare points from droplets on the PIV images. The magnitude of the discrepancy is a function of position of the droplet’s image on the CCD array and the degree of defocus, but almost independent of droplet size. Specifically, it varies approximately linearly across the image along the direction corresponding to the direction of propagation of the laser sheet for a given defocus setting in ILIDS. The experimental finding is supported by a theoretical analysis, which was based on geometrical optics for a simple optical configuration that replicates the essential features of the optical system. The discrepancy in the location was measured using a monodisperse droplet generator, and this was subtracted from the droplet centres identified in the ILIDS images of a polydisperse spray without ‘seeding’ particles. This reduced the discrepancy between PIV and ILIDS droplet centres from about 1 mm to about 0.1 mm and hence increased the probability of finding the corresponding fringe patterns on the ILIDS image and glare points on the PIV image. In conclusion, it is shown that the proposed combined method can discriminate between droplets and ‘seeding’ particles and is capable of two-phase measurements in polydisperse sprays.     

Effects of Body Cross-sectional Shape on Flying Snake Aerodynamics

Despite their lack of appendages, flying snakes (genus Chrysopelea) exhibit aerodynamic performance that compares favorably to other animal gliders. We wished to determine which aspects of Chrysopelea’s unique shape contributed to its aerodynamic performance by testing physical models of Chrysopelea in a wind tunnel. We varied the relative body volume, edge sharpness, and backbone protrusion of the models. Chrysopelea’s gliding performance was surprisingly robust to most shape changes; the presence of a trailing-edge lip was the most significant factor in producing high lift forces. Lift to drag ratios of 2.7–2.9 were seen at angles of attack (α) from 10–30°. Stall did not occur until α > 30° and was gradual, with lift falling off slowly as drag increased. Chrysopelea actively undulates in an S-shape when gliding, such that posterior portions of the snake’s body lie in the wake of the more anterior portions. When two Chrysopelea body segment models were tested in tandem to produce a two dimensional approximation to this situation, the downstream model exhibited an increased lift-to-drag ratio (as much as 50% increase over a solitary model) at all horizontal gaps tested (3–7 chords) when located slightly below the upstream model and at all vertical staggers tested (±2 chords) at a gap of 7 chords.     

Dynamic rheology of the immiscible blends of liquid crystalline polymers and flexible chain polymers

Immiscible blends containing liquid crystalline polymers (LCP) as dispersed phases show different dynamic rheological properties than those composed of flexible polymers. The widely used Palierne’s model was shown by many authors to be insufficient to describe the frequency dependence of dynamic modulus of such blends. A new model was presented to describe the dynamic rheology of the immiscible blend containing LCP as a dispersed phase. The flexible chain polymer matrix was assumed to be a linear viscoelastic material under small amplitude oscillatory shear flow, and the LCP was assumed to be an Ericksen’s transversely isotropic fluid. The Rapini-Papoular equation of anisotropic interfacial energy was used to account for the effect of nematic orientation on the interfacial tension. It was found that the orientation of the director and the anchoring energy greatly influenced the storage modulus at the “shoulder” regime. The overall dynamic modulus of the blend can be well described by the model with suitable choice of the orientation of the director and anchoring energy of LCP.