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71.
Francesco Pappalardi 《Journal of Number Theory》2003,103(1):122-131
We obtain an asymptotic formula for the number of square-free values among p−1, for primes p?x, and we apply it to derive the following asymptotic formula for L(x), the number of square-free values of the Carmichael function λ(n) for 1?n?x,
72.
The classical mathematical treatment governing nonlinear wave propagation in solids relies on finite strain theory. In this scenario, a system of nonlinear partial differential equations can be derived to mathematically describe nonlinear phenomena such as acoustoelasticity (wave speed dependency on quasi-static stress), wave interaction, wave distortion, and higher-harmonic generation. The present work expands the topic of nonlinear wave propagation to the case of a constrained solid subjected to thermal loads. The origin of nonlinear effects in this case is explained on the basis of the anharmonicity of interatomic potentials, and the absorption of the potential energy corresponding to the (prevented) thermal expansion. Such “residual” energy is, at least, cubic as a function of strain, hence leading to a nonlinear wave equation and higher-harmonic generation. Closed-form solutions are given for the longitudinal wave speed and the second-harmonic nonlinear parameter as a function of interatomic potential parameters and temperature increase. The model predicts a decrease in longitudinal wave speed and a corresponding increase in nonlinear parameter with increasing temperature, as a result of the thermal stresses caused by the prevented thermal expansion of the solid. Experimental measurements of the ultrasonic nonlinear parameter on a steel block under constrained thermal expansion confirm this trend. These results suggest the potential of a nonlinear ultrasonic measurement to quantify thermal stresses from prevented thermal expansion. This knowledge can be extremely useful to prevent thermal buckling of various structures, such as continuous-welded rails in hot weather. 相似文献
73.
Thierry Barbot Francesco Bonsante Jean-Marc Schlenker 《Communications in Mathematical Physics》2014,327(3):691-735
We investigate globally hyperbolic 3-dimensional AdS manifolds containing “particles”, i.e., cone singularities of angles less than 2π along a time-like graph Γ. To each such space (equipped with a time-like vector field satisfying some additional properties) we associate a graph and a finite family of pairs of hyperbolic surfaces with cone singularities. We show that this data is sufficient to recover the space locally (i.e., in the neighborhood of a fixed metric). This is a partial extension of a result of Mess for non-singular globally hyperbolic AdS manifolds. 相似文献
74.
The structure of groups in which many subgroups have a certain property X has been investigated for several choices of the property X. Groups whose non-normal subgroups satisfy certain finite rank conditions are studied in this article. In particular, a classification of groups in which every subgroup is either normal or polycyclic is given.(Dedicated to Mario Curzio on the occasion of his 70th birthday)1991 Mathematics Subject Classification: 20F16 相似文献
75.
Egidio Di Gialleonardo Francesco Braghin Stefano Bruni 《Journal of sound and vibration》2012,331(19):4246-4258
This paper investigates the effect of different models for track flexibility on the simulation of railway vehicle running dynamics on tangent and curved track. To this end, a multi-body model of the rail vehicle is defined including track flexibility effects on three levels of detail: a perfectly rigid pair of rails, a sectional track model and a three-dimensional finite element track model. The influence of the track model on the calculation of the nonlinear critical speed is pointed out and it is shown that neglecting the effect of track flexibility results in an overestimation of the critical speed by more than 10%. Vehicle response to stochastic excitation from track irregularity is also investigated, analysing the effect of track flexibility models on the vertical and lateral wheel–rail contact forces. Finally, the effect of the track model on the calculation of dynamic forces produced by wheel out-of-roundness is analysed, showing that peak dynamic loads are very sensitive to the track model used in the simulation. 相似文献
76.
Pier?Paolo?ProsiniEmail author Maria?Carewska Gabriele?Tarquini Fabio?Maroni Agnese?Birrozzi Francesco?Nobili 《Ionics》2016,22(4):515-528
This paper describes the preparation and characterization of a high-voltage lithium-ion battery based on Sn-decorated reduced graphene oxide and LiNi0.5Mn1.5O4 as the anode and cathode active materials, respectively. The Sn-decorated reduced graphene oxide is prepared using a microwave-assisted hydrothermal synthesis method followed by reduction at high temperature of a mixture of (C6H5)2SnCl2 and graphene oxide. The so-obtained anode material is characterized by thermogravimetric analysis, X-ray diffraction, scanning electron microscopy, and electron diffraction spectroscopy. The LiNi0.5Mn1.5O4 is a commercially available product. The two materials are used to prepare composite electrodes, and their electrochemical properties are investigated by galvanostatic charge/discharge cycles at various current densities in lithium cells. The electrodes are then used to assemble a high-voltage lithium-ion cell, and the cell is tested to evaluate its performance as a function of discharge rate and cycle number. 相似文献
77.
We investigate the effects of a weak gravitational wave, modelled as a gaussian wavepacket, on the polarization state of an
electromagnetic field enclosed in a cavity. Our approach is semiclassical, in that the electromagnetic field is described as a quantum field, while the gravitational perturbation is treated classically,
as a slightly curved background spacetime. Assuming that before the interaction the electromagnetic field has been prepared
in a given polarization state, we show that – due to the gravitational scattering with the wave – some photons having different
polarization states are found in the cavity at late times. Such polarization scattering has some resemblance with Thomson
scattering, well-known in Quantum Electrodynamics: hence the motivation for the title. We give a numerical estimate of the
resulting photon polarization spreading in the case of a typical gravitational burst from a final supernova rebound. We also
briefly comment about the possible influence of such gravitational scattering on the Cosmic Microwave Background (CMB) polarization. 相似文献
78.
Young S. Lee Francesco Nucera Alexander F. Vakakis D. Michael McFarland Lawrence A. Bergman 《Physica D: Nonlinear Phenomena》2009,238(18):1868-1896
We study complex damped and undamped dynamics and targeted energy transfers (TETs) in systems of coupled oscillators, consisting of single-degree-of-freedom primary linear oscillators (LOs) with vibro-impact attachments, acting, in essence, as vibro-impact nonlinear energy sinks (VI NESs). First, the complicated dynamics of such VI systems is demonstrated by computing the VI periodic orbits of underlying Hamiltonian systems and depicting them in appropriate frequency–energy plots (FEPs). Then, VI damped transitions and distinct ways of passive TETs from the linear oscillators to the VI attachments for various parameter ranges and initial conditions are investigated. As in the case of smooth stiffness nonlinearity [Y. Lee, G. Kerschen, A. Vakakis, P. Panagopoulos, L. Bergman, D.M. McFarland, Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment, Physica D 204 (1–2) (2005) 41–69], both fundamental and subharmonic TET can be realized in the VI systems under consideration. It is found that the most efficient mechanism for VI TET is through the excitation of highly energetic VI impulsive orbits (IOs), i.e., of periodic or quasiperiodic orbits corresponding to zero initial conditions except for the initial velocities of the linear oscillators. In contrast to NESs with smooth essential nonlinearities considered in previous works, VI NESs are capable of passively absorbing and locally dissipating significant portions of the energies of the primary systems to which they are attached, at fast time scale. This renders such devices suitable for applications, like seismic mitigation, where dissipation of vibration energy in the early, highly energetic regime of the motion is a critical requirement. 相似文献
79.
Domiziano Mostacci Vincenzo Molinari Francesco Pizzio 《Central European Journal of Physics》2010,8(5):709-716
Bohm’s interpretation of Quantum Mechanics leads to the derivation of a Quantum Kinetic Equation (QKE): in the present work,
propagation of waves in charged quantum gases is investigated starting from this QKE. Dispersion relations are derived for
fully and weakly degenerate fermions and bosons (for the latter above critical temperature) and the differences discussed.
Use of a kinetic equation permits investigation of “Landau-type” damping: it is found that the presence of damping in fermion
gases is dependent upon the degree of degeneracy, whereas it is always present in boson gases. In fully degenerate fermions
a phenomenon appears that is akin to the “zero sound” propagation. 相似文献
80.