The extra-resistivity due to vacancies in copper, silver and gold

Summary Lattice defects in metals, for instance dislocations, interstitial atoms or vacancies, such as can arise from coldworking or neutron irradiation, cause an extra-resistivity. In this paper the resistivity due to vacancies is calculated for copper, silver and gold. The conduction electrons are supposed to be completely free. The scattering area of a vacancy in Cu is found from the field of this atom, for which we have takena) the negative of the Hartreefield of Cu⁺,b) a suitably chosen rectangular field. The results of these calculations being about the same, the case of Ag and Au is treated, using a rectangular field only. It then turns out that for monovalent metals the extra-resistivity per percent vacancies is proportional to the atomic radius. The results for Cu, Ag and Au are, respectively, 1.3, 1.5 and 1.5 cm/% vacancies; they enable us to calculate the number of vacancies in certain cases. For Cu a vacancy has about the same influence on the resistivity as a dissolved Ni-atom.     

Explicit integration of one problem of motion of the generalized Kowalevski top

In the problem of motion of the Kowalevski top in a double force field the four-dimensional invariant submanifold of the phase space was pointed out by [Kharlamov, M.P., 2002. Mekh. Tverd. Tela 32, 33–38]. We show that the equations of motion on this manifold can be separated by the appropriate change of variables, the new variables s₁, s₂ being elliptic functions of time. The natural phase variables (components of the angular velocity and the direction vectors of the forces with respect to the movable basis) are expressed via s₁, s₂ explicitly in elementary algebraic functions.     

Quantitative planar Raman imaging through a spectrograph: visualisation of a supersonic wedge flow

Planar Raman imaging through a spectrograph is demonstrated as a diagnostic tool for quantitative flow visualisation of internal supersonic wedge flow. A dedicated Bayesian deconvolution filter is used to remove the spectral structure that is introduced by the spectrograph. The 2D density field is determined with ca. 10% precision using average images over 6,000 laser pulses, down to 0.5 mm from the surface of the wedge. Direct interpretations of Raman intensities provide more precise density data than indirect interpretations based on shock geometry in 2D inviscid flow.

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An atomistic-based continuum theory for carbon nanotubes: analysis of fracture nucleation

Carbon nanotubes (CNTs) display unique properties and have many potential applications. Prior theoretical studies on CNTs are based on atomistic models such as empirical potential molecular dynamics (MD), tight-binding methods, or first-principles calculations. Here we develop an atomistic-based continuum theory for CNTs. The interatomic potential is directly incorporated into the continuum analysis through constitutive models. Such an approach involves no additional parameter fitting beyond those introduced in the interatomic potential. The atomistic-based continuum theory is then applied to study fracture nucleation in CNTs by modelling it as a bifurcation problem. The results agree well with the MD simulations.     

Numerical Simulation of Plasma Dynamics in a Nonuniform Magnetic Field

An efficient algorithm is proposed enabling numerical simulations of plasma dynamics in a nonuniform magnetic field. The present numerical data are in good agreement with experimental data obtained in a GOL-3 setup and with previous simulations. The experimentally observed effect of fast transfer of energy to ions is confirmed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 35–45, January–February, 2006.     

PopGen: population-based recruitment of patients and controls for the analysis of complex genotype-phenotype relationships

OBJECTIVE: Patient samples used for mapping complex human disease genes are unlikely to be representative of the phenotype spectrum of the respective population as a whole. On the other hand, most ongoing prospective studies are probably too small for evaluating polygenic disease markers. DESIGN: Precise estimates of population-specific genotypic risks can be obtained efficiently through the complete ascertainment of patients in a geographically confined area. The PopGen project uses the most northern part of Germany as a target region for such a pursuit. RESULTS: PopGen currently pursues recruitment, sampling and processing activities in close collaboration with a multitude of clinical partners, covering cardiovascular, neuropsychiatric and environmental diseases. CONCLUSION: PopGen has successfully established itself as a large-scale genetic epidemiological project of international recognition.     

Global stability analysis of parametrically excited cylindrical shells through the evolution of basin boundaries

In the present study, the large-amplitude vibrations and stability of a perfect circular cylindrical shell subjected to axial harmonic excitation in the neighborhood of the lowest natural frequencies are investigated. Donnell's shallow shell theory is used and the shell spatial discretization is obtained by the Ritz method. An efficient low-dimensional model presented in previous publications is used to discretize the continuous system. The main purpose of this work is to discuss the use of basins of attraction as a measure of the reliability and safety of the structure. First, the nonlinear behavior of the conservative system is discussed and the basin structure and volume is understood from the topologic structure of the total energy and its evolution as a function of the system parameters. Then, the behavior of the forced oscillations of the harmonically excited shell is analyzed. First the stability boundaries in force control space are obtained and the bifurcation events connected with these boundaries are identified. Based on the bifurcation diagrams, the probability of parametric instability and escape are analyzed through the evolution and erosion of basin boundaries within a prescribed control volume defined by the manifolds. Usually, basin boundaries become fractal. This together with the presence of catastrophic subcritical bifurcations makes the shell very sensitive to initial conditions, uncertainties in system parameters, and initial imperfections. Results show that the analysis of the evolution of safe basins and the derivation of appropriate measures of their robustness is an essential step in the derivation of safe design procedures for multiwell systems.     

Buoyancy-driven convection of water near its density maximum with time periodic partially active vertical walls

The effect of density inversion on transient natural convection heat transfer of cold water in a square cavity with partially active vertical walls is studied numerically. The governing equations are solved by control volume method with power law scheme. In the hot location the temperature is varied sinusoidally and in the cold location uniform temperature is maintained. Nine different positions of the active zones are considered. Results are discussed for various values of the amplitude, period and different Grashof numbers and presented graphically in the form of isotherms, streamlines, mid-height velocity profile and average Nusselt number. It is found that density inversion of water affects natural convection flow and heat transfer. Heat transfer rate is enhanced upto 80% when the heating location is in the middle of the hot wall.     

Optimal design of a compound plate weakened by a periodic crack system

We use the minimax criterion to perform atheoretical analysis of determining the optimal interference for fitting elastic inclusions into holes in an isotropic elastic plate weakened by a periodic system of rectilinear cracks. We construct a closed system of algebraic equations that allows us to minimize the fracture parameters depending on the geometric and mechanical characteristics of the inclusions. The obtained fitting interference for the inclusions ensures an increase in the bearing strength of the compound plate under bending.     

A New Class of Weak Solutions of the Navier–Stokes Equations with Nonhomogeneous Data

We investigate a class of weak solutions, the so-called very weak solutions, to stationary and nonstationary Navier–Stokes equations in a bounded domain . This notion was introduced by Amann [3], [4] for the nonstationary case with nonhomogeneous boundary data leading to a very large solution class of low regularity. Here we are mainly interested in the investigation of the “largest possible” class of solutions u for the more general problem with arbitrary divergence k = div u, boundary data g = u|_∂Ω and an external force f, as weak as possible, but maintaining uniqueness. In principle, we will follow Amann’s approach.