Narrow Results

Recently, synchronization in the Burridge–Knopoff model has been found to depend on the initial conditions. Here we report the existence of three modes of oscillations of the system of three blocks. In one of the modes, two lateral blocks are synchronized. In the second mode, the central block moves with almost constant velocity, i.e., it does not stick. Two lateral blocks do stick and they move in opposite phases. In the third mode, the blocks oscillate with aperiodic amplitude. The lateral blocks move in opposite phases and their frequency is lower than the one for the central block. The mode selected by the system depends on the initial conditions. Numerical results indicate that there is no modes in the phase space.

In an earlier paper the authors described the isomorphic lattices of quasivarieties of commutative quasigroup modes and of cancellative commutative binary modes. This paper extends the earlier result, and provides a description of the lattice of some irregular quasivarieties of commutative binary modes, i.e. quasivarieties that do not contain semilattices.

Instabilities in nanosized, externally pressurized spherical shells are important for their applications in nano and biotechnology. Mechanics at such length scale is described by nonlocal and Strain Gradient (SG) field theories. However, analysis of shell buckling is involved and becomes even more complicated in presence of nonlocal and SG interactions. This paper demonstrates that such analysis can be largely simplified by a shallow segment representation of the shell by assuming short wave lengths for the incipient buckling modes. The governing equations are derived and linearized equations are solved to obtain a closed form solution for the critical external pressure causing buckling for a pressurized nonlocal shell. Nonlocal interactions are shown to reduce, whereas the SG interaction increases the critical pressure. The relative reduction/increase becomes more prominent for higher modes of buckling and for increasingly thinner shell. A constricting relationship between the two set of wave numbers expressing the buckling modes is also shown to be modified by the nonlocal and SG scale parameters. Consequent wave numbers increase/decrease, accompanied by decreasing/increasing number of wavelengths, thereby further justifying the shallow segment representation employed herein.

Field transmission coefficients for microwave radiation between arrays of points on the incident and output surfaces of random samples are analyzed to yield the underlying quasi-normal modes and transmission eigenchannels of each realization of the sample. The linewidths, central frequencies, and transmitted speckle patterns associated with each of the modes of the medium are found. Modal speckle patterns are found to be strongly correlated leading to destructive interference between modes. This explains distinctive features of transmission spectra and pulsed transmission. An alternate description of wave transport is obtained from the eigenchannels and eigenvalues of the transmission matrix. The maximum transmission eigenvalue, τ₁ is near unity for diffusive waves even in turbid samples. For localized waves, τ₁ is nearly equal to the dimensionless conductance, which is the sum of all transmission eigenvalues, g = Στ_n. The spacings between the ensemble averages of successive values of lnτ_n are constant and equal to the inverse of the bare conductance in accord with predictions by Dorokhov. The effective number of transmission eigenvalues N_eff determines the contrast between the peak and background of radiation focused for maximum peak intensity. The connection between the mode and channel approaches is discussed.

The seismic method on ice provides rich information and a feasible technical way for acoustic study in ice-covered water. This paper presents a method to determine the modes in ice–water bi-layer waveguides. We achieve the purpose by deducing the scaled boundary formulation for solid and fluid layers then coupling them with the coupling matrix. The wave numbers and mode shapes are compared with the results of the finite element method. It shows that the configuration for ice–water bi-layer waveguide is of high precision. In underwater acoustic applications, the depth of water is comparatively large relative to ice thickness, which addresses the additional difficulty of accuracy in high frequency. The study on convergence is carried out, and approximate formulas are addressed based on the calculated results, giving a quick insight into piratical application.

Field transmission coefficients for microwave radiation between arrays of points on the incident and output surfaces of random samples are analyzed to yield the underlying quasi-normal modes and transmission eigenchannels of each realization of the sample. The linewidths, central frequencies, and transmitted speckle patterns associated with each of the modes of the medium are found. Modal speckle patterns are found to be strongly correlated leading to destructive interference between modes. This explains distinctive features of transmission spectra and pulsed transmission. An alternate description of wave transport is obtained from the eigenchannels and eigenvalues of the transmission matrix. The maximum transmission eigenvalue, τ₁ is near unity for diffusive waves even in turbid samples. For localized waves, τ₁ is nearly equal to the dimensionless conductance, which is the sum of all transmission eigenvalues, g = Στ_n. The spacings between the ensemble averages of successive values of lnτ_n are constant and equal to the inverse of the bare conductance in accord with predictions by Dorokhov. The effective number of transmission eigenvalues N_eff determines the contrast between the peak and background of radiation focused for maximum peak intensity. The connection between the mode and channel approaches is discussed.