Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations

Continuum mechanics with dislocations, with the Cattaneo-type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov-type system of the first-order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the latter formulation as the existence of a companion conservation law. In both formulations the time irreversible part represents gradient dynamics. The Godunov-type formulation brings the mathematical rigor (the local well posedness of the Cauchy initial value problem) and the possibility to discretize while keeping the physical content of the governing equations (the Godunov finite volume discretization).     

Diffusion and Electrical Processes in the Turbulent Boundary Layer and in the Neighborhood of the Stagnation Point

The problem of electric current (engine current) formation in aircraft jet engine ducts as a result of the development of electrical diffusion boundary layers on the surfaces of the duct and internal engine components is investigated. It is assumed that the outer flow containing electrons and positive ions is quasi-neutral and that the electrical quasi-neutrality is violated (and the electric engine current develops) in the wall flow zone as a result of the difference between the electron and ion diffusion coefficients. The problem of the development of an electrical diffusion boundary layer inside the turbulent gasdynamic boundary layer on a plane surface is formulated and solved. The engine current distribution along the duct is found for various values of a turbulent viscosity on the boundary of the gasdynamic boundary layer which affect the laminar-turbulent transition point.The electrical diffusion processes that occurs when an electrically quasi-neutral hydrodynamic stream impinges on a plane surface (simulation of the flow in the neighborhood of a stagnation point) is studied. In this case the Navier-Stokes equations have a self-similar solution. It is shown that the system of electrohydrodynamic equations also has a self-similar solution. The electrical parameter fields are determined and the engine current is found on the basis of this solution.     

Certain characteristics of fluctuations in arc current and voltage and in the brightness of the jet in eddy-type plasmotrons

Some experimental data relating to the character of the pulsations taking place in the current (I_t) and voltage (V_t), and also in the brightness of the jet (B_t) at the output of a plasmotron, are presented. The distribution functions of these parameters obey a normal distribution law. The circuit elements and the external characteristics of the supply source have a marked effect on the fluctuations taking place in these plasmotron parameters.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 168–170, September–October, 1970.     

Centrifugal instability and the rib vortices in the cylinder wake

The physical mechanism for generation of streamwise vortices (or rib vortices) in the cylinder wake is numerically investigated with a finite-difference scheme. Rayleigh's theory of centrifugal instability for inviscid axisymmetric flow is extended to analyze the 2-D primary flows. Accordingly, an analytical dimensionless groupRay=−(r/v _θ)∂v _θ/∂r−1 is derived, wherev _θ represents the velocity of a fluid element relative to the oncoming flow,r is the local curvature radius of the element pathline. Centrifugal instability occurs whenRay>0. Stability analyses are carried out with this discriminant for primary flows at different time levels in a half shedding period of the von Kármán (or vK) vortices. Unstable areas are identified and the locations of rib vortices are coincident well with the unstable areas within the first wavelength of vK vortices behind the cylinder. The numerical results also show that rib vortices experience amplification in this region. It is apparent that centrifugal instability plays an important role in the generation of rib vortices in the cylinder wake. The project spported by the National Natural Science Foundation of China     

Dynamic and stability analysis of the vibratory feeder and parts considering interactions in the hop and the hop-sliding regimes

Nonlinear Dynamics - In this paper, the interactions of a translational vibratory feeder and the parts in the hop and the hop-sliding regimes are studied by means of an improved multi-term...     

Asymptotic expansions and the possibilities to drop the hypotheses in the prandtl problem

The plane problem on the quasistatic compression of a thin perfectly plastic layer between undeformable rough plates (the Prandtl problem) has a well-known analytic solution at all points sufficiently far from the midsection and endpoints of the layer. Both the static and the kinematic component of this solution were obtained on the basis of the Prandtl hypothesis [1] stating that the tangential stress is linear along the layer thickness and is maximal in absolute value on the plate surfaces. (If the plates are perfectly rough, then this maximum value coincides with the shear yield stress.) The Prandtl hypothesis was widely confirmed in experiments carried out after the paper [1] had been published.At the same time, it is natural to ask whether one can construct a classical solution of this problem without imposing any static or kinematic hypotheses on the unknown variables and whether there exist any other mathematical solutions in which these hypotheses do not hold and which themselves are not observed in experiments.In the present paper, we use asymptotic analysis with a natural small geometric parameter and uniquely determine an exact solution (in the sense of finiteness of the number of terms in the asymptotic expansion), which coincides with the Prandtl solution generalized to the case of an arbitrary roughness coefficient of the plates. We rigorously show that such asymptotics cannot hold near the layer midsection, where we construct another, internal asymptotic expansion. In the abovementioned sense, the solution corresponding to the internal expansion is also exact and models the compression of a thin vertical strip in the middle of the layer. We realize two possible versions of matching of the two expansions in the cross-section whose distance from the midsection is equal to the layer thickness.     

Trends in complexity theories and computation in the social sciences

A modified bibliometric study and citation analysis of the use of complexity theories, encompassing chaos and complexity theory, and computational simulation in published literature was conducted. Articles published during 1971-1999 in four disciplines were examined: business, education, psychology and sociology. Overall, there was a marked pattern of increased use in the terms within the social sciences. There was a differentiated use of the terms between disciplines. A qualitative study on a subset from each discipline was generated to create a disciplinary profile of the quantitative and qualitative use of the terms in research activities, called a problem topology. Three research implications that arise from the differential adaptation of the theories and methods into the four social sciences are discussed.     

Flow and coupled heat transfer in the cavity between the rotor and stator

The turbulent flow and coupled heat transfer in the cavity between the rotor and stator is numerically simulated. Reynolds-averaged Navier-Stokes equations closed with equations of the k-ɛ turbulence model are used to calculate the viscous compressible gas flow characteristics and heat transfer; the unsteady heat conduction equation is used to calculate the temperature field in the metal. The influence of the mass flow rate of the coolant on the flow structure and efficiency of cooling of the rotor and stator walls is studied. The calculated results are compared with experimental data.     

Hydraulic modeling of the flow in the delta of the River Neva and in the eastern part of the Gulf of Finland

In connection with the construction of Leningrad's flood defenses the flow in the mouth of River Neva has been investigated on hydraulic models of different scales both unpressurized (see, for example, [1, 2]) and pressurized (see, for example, [3]). Since the results of these investigations are being intensively debated in connection with the discussion of the effect of defensive structures on the ecology of the Leningrad region, it is important to analyze the scientific basis for the hydraulic modeling of such flows.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 57–65, September–October, 1990.     

Generalized logistic growth modeling of the COVID-19 outbreak: comparing the dynamics in the 29 provinces in China and in the rest of the world

Nonlinear Dynamics - Started in Wuhan, China, the COVID-19 has been spreading all over the world. We calibrate the logistic growth model, the generalized logistic growth model, the generalized...     

On the Galerkin vector and the Eshelby solution in linear elasticity

Displacement potentials in linear static elasticity consist of three functions which can be regarded as the three components of a vector, e.g., the Galerkin vector. This research note gives an explanation as to why the biharmonic equations govern these functions in isotropic elasticity as opposed to the sixth-order partial differential equations that govern them in anisotropic elasticity. This note also shows that the Eshelby solution in two-dimensional anisotropic elasticity can be derived from the method of displacement potentials.     

Yang and Yin parameters in the Lorenz system

The history of the Lorenz system is firstly discussed in this paper. In Chinese philosophy, Yin is the negative, historical, or feminine principle in nature, while Yang is the positive, contemporary, or masculine principle in nature. Yin and Yan are two fundamental opposites in Chinese philosophy (therefore, in this paper, these words “Yin parameter,” “Yang parameter,” “historical system,” and “contemporary system” are used to represent the “positive parameter,” “negative parameter,” “time reversed (?t) system,” and “time forward (t) system,” respectively). Simulation results show that chaos of historical Lorenz system can be generated when using “Yin” parameters. To our best knowledge, most characters of contemporary Lorenz system are studied in detail, but there are no articles in making a thorough inquiry about the history of Lorenz system. As a result, the chaos of historical Lorenz system with “Yin parameters” is introduced in this paper and various kinds of phenomena in the historical Lorenz system are investigated by Lyapunov exponents, phase portraits, and bifurcation diagrams.     

On the velocity of ghost particles and the bias errors in Tomographic-PIV

The paper discusses bias errors introduced in Tomographic-PIV velocity measurements by the coherent motion of ghost particles under some circumstances. It occurs when a ghost particle is formed from the same set of actual particles in both reconstructed volumes used in the cross-correlation analysis. The displacement of the resulting ghost particle pair is approximately the average displacement of the set of associated actual particles. The effect is further quantified in a theoretical analysis and in numerical simulations and illustrated in an actual experiment. It is shown that the bias error does not significantly affect the measured flow topology as deduced in an evaluation of the local velocity gradients. Instead, it leads to a systematic underestimation of the measured particle displacement gradient magnitude. This phenomenon is alleviated when the difference between particles displacement along the volume depth is increased beyond a particle image diameter, or when the reconstruction quality is increased or when the accuracy of the tomographic reconstruction is improved. Furthermore, guidelines to detect and avoid such bias errors are proposed.     

热湍流研究的新十年:从聚焦传统到延伸拓展

热湍流(浮力驱动湍流)作为一种典型的湍流现象,广泛存在于自然界和工程应用中. Rayleigh-Bénard (RB)湍流是从众多自然现象中抽象出来研究热湍流的经典模型, RB湍流的典型特征是系统中存在大尺度环流和羽流等不同尺度的湍流结构,这些结构通过作用于边界层,影响RB湍流的输运效率.因此,明确不同尺度湍流结构的生成、演化和作用机理,对理解RB湍流的输运特性至关重要,也是通过控制湍流结构调控输运效率的科学基础.本文重点从湍流结构的时空演化规律、输运特性、湍流调控和热湍流在其他领域的拓展四个方面评述近十年来RB湍流研究所取得的新进展,并对今后的研究方向做出展望.     

Three-dimensional mathematical model and its application in the neighborhood of the Three Gorges Reservoir dam in the Yangtze River

The calculation of flow and sediment transport is one of the most important tasks in river engineering. The task is particularly difficult because a number of complex physical phenomena should be accounted for more realistically in a model with a predictive power. Three-dimensional calculations of river flow and suspended sediment transport are performed in this paper with application in the Three Gorges Reservoir in the Yangtze River. A period of 76 years after the dam is built is simulated and the results are compared with laboratory measurements obtained by Tsinghua University whereby the model is verified and calibrated. Generally speaking, the calculated results agree well with the experiments, demonstrating that the present model can be used for flow and sediment transport prediction in rivers. The project supported by the National Natural Science Foundation of China (50009004)     

Characteristic waves and dissipation in the 13-moment-case

Extended thermodynamics derives dissipative, hyperbolic field equations for monatomic gases. One example is the system of the 13-field-case, which is a dissipative extension of the Euler equations. In this paper the system is investigated by solving a Riemann problem. Additionally some model equations are introduced so as to discuss the main properties in a transparent manner. There arises an interesting interplay of the characteristic waves and the dissipation in the system. For the 13-field-case it turns out that not every Riemann problem has a solution, because of the loss of hyperbolicity of the system. Received April 13, 2000     

On the impedance of the pipe in laminar and turbulent pulsating flows

The response of a facility, consisting of a valveless reciprocating pump, a large settling chamber and a long straight smooth pipe, to a periodic change in the volume was analysed. The impedance of the pipe was estimated in both laminar and turbulent flow regimes under otherwise identical flow conditions. A good agreement with theory was obtained for the laminar flow. The estimate of the pipe impedance from the experimental data in turbulent flow was based on the momentum equation as well as on the measured resonant frequency of the system. These independent methods show that the inertance of the pipe has a qualitatively different behavior in laminar and turbulent flow regimes.     

ON THE UNIFICATION OF THE HAMILTON PRINCIPLES IN NONHOLONOMIC SYSTEM AND IN HOLONOMIC SYSTEM

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Fluctuations and the ionization potential in dense plasmas

A semi-analytic model is developed to estimate continuum lowering in dense plasmas including fluctuations. The model is applied to aluminum and compared with recent experiments at the Linac Coherent Light Source [O. Ciricosta et al., Phys. Rev. Lett. 109 (2012) 065002] that reported the ionization potential depression of K-shell electrons in solid density aluminum at temperatures up to 180 eV. The analysis suggests fluctuations, which are neglected in most continuum lowering models but are essential to describe energy absorption by a system, are sufficiently large to impact the interpretation of the experimental results.     

Progress in the Use of Non-Linear Two-Equation Models in the Computation of Convective Heat-Transfer in Impinging and Separated Flows

The paper considers the application of the Craft et al. [6]non-linear eddy-viscosity model to separating and impinging flows. The original formulation was found to lead to numerical instabilities when applied to flow separating from a sharp corner. An alternative formulation for the variation of the turbulent viscosity parameterc _μ with strain rate is proposed which, together with a proposed improvement in the implementation of the non-linear model, removes this weakness. It does, however, lead to worse predictions in an impinging jet, and a further modification in the expression for c _μ is proposed, which both retains the stability enhancements and improves the prediction of the stagnating flow. The Yap [24] algebraic length-scale correction term, included in the original model, is replaced with a differential form, developed from that proposed by Iacovides and Raisee [10]. This removes the need to prescribe the wall-distance, and is shown to lead to superior heat-transfer predictions in both an abrupt pipe flow and the axisymmetric impinging jet. One predictive weakness still, however, remains. The proposed model, in common with other near-wall models tested for the abrupt pipe expansion, returns a stronger dependence of Nusselt number on the Reynolds number than that indicated by the experimental data. This revised version was published online in July 2006 with corrections to the Cover Date.