Extreme sensitivity to detuning for globally coupled phase oscillators

We discuss the sensitivity of a population of coupled oscillators to differences in their natural frequencies, i.e., to detuning. We argue that for three or more oscillators, one can get great sensitivity even if the coupling is strong. For N globally coupled phase oscillators we find there can be bifurcation to extreme sensitivity, where frequency locking can be destroyed by arbitrarily small detuning. This extreme sensitivity is absent for N = 2, appears at isolated parameter values for N = 3 and N = 4, and can appear robustly for open sets of parameter values for N > or = 5 oscillators.     

Neural networks convergence using physicochemical data

An investigation of the neural network convergence and prediction based on three optimization algorithms, namely, Levenberg-Marquardt, conjugate gradient, and delta rule, is described. Several simulated neural networks built using the above three algorithms indicated that the Levenberg-Marquardt optimizer implemented as a back-propagation neural network converged faster than the other two algorithms and provides in most of the cases better prediction. These conclusions are based on eight physicochemical data sets, each with a significant number of compounds comparable to that usually used in the QSAR/QSPR modeling. The superiority of the Levenberg-Marquardt algorithm is revealed in terms of functional dependence of the change of the neural network weights with respect to the gradient of the error propagation as well as distribution of the weight values. The prediction of the models is assessed by the error of the validation sets not used in the training process.     

On the “function” and “lattice” definitions of a narrow operator

We prove that the function and lattice definitions of a narrow operator defined on a Köthe Banach space E on a finite atomless measure space \((\Omega , \Sigma , \mu )\) are equivalent if and only if the set of all simple functions is dense in E. This answers Problem 10.3 from Popov and Randrianantoanina (Narrow operators on function spaces and vector lattices, De Gruyter studies in mathematics 45, De Gruyter, Berlin, 2013).     

Ergodicity of non-equilibrium Glauber dynamics in continuum

We study asymptotic properties of the continuous Glauber dynamics with unbounded death and constant birth rates. In particular, an information about the location of the spectrum for the symbol of the Markov generator is obtained. The latter fact is used for the proof of the ergodicity of this process. We show that the speed of convergence to the equilibrium is exponential.     

Oscillation of solutions of second-order linear differential equations and corresponding difference equations

In this paper, we present conditions ensuring that solutions of linear second-order differential equations oscillate, provided solutions of corresponding difference equations oscillate. We also establish the converse result, namely, when oscillation of solutions of difference equations implies oscillation of solutions of corresponding differential equations.     

Measurements of the nanovibration amplitude by a frequency-modulated laser autodyne

A method to measure the reflector nanovibration amplitudes from the low-frequency spectrum of a signal from a frequency-modulated laser autodyne is suggested. The frequency-modulated autodyne signal at the harmonic vibrations of the reflector is theoretically described, and relationships for the autodyne signal spectral components are derived using expansions into Fourier and Bessel series. The respective experimental setup is considered, and measuring data for the nanovibration amplitudes of the reflector and the autodyne spectra are considered.     

Suppression of electron spin relaxation in Mn-doped GaAs

We report a surprisingly long spin relaxation time of electrons in Mn-doped p-GaAs. The spin relaxation time scales with the optical pumping and increases from 12 ns in the dark to 160 ns upon saturation. This behavior is associated with the difference in spin relaxation rates of electrons precessing in the fluctuating fields of ionized or neutral Mn acceptors, respectively. For the latter, the antiferromagnetic exchange interaction between a Mn ion and a bound hole results in a partial compensation of these fluctuating fields, leading to the enhanced spin memory.     

Effect of Mechanical Stress on the Splitting of Spin Sublevels in 4H-SiC

JETP Letters - The effect of static mechanical strain on the splitting of spin sublevels of color centers based on spin 3/2 silicon vacancies in silicon carbide at room temperature has been shown....     

Transverse conductivity in Pr_yY_{1-y}Ba_2Cu_3O_{7-\delta } single crystals in a wide range of praseodymium concentrations

A single-sized dielectric cylinder-based metamaterial is fabricated from TiO₂ nanoparticles, using a bottom-up approach. The sub-elements constituting the metalayer are embedded in a nonmagnetic transparent host matrix in the microwave regime and arranged in a square lattice. We demonstrate numerically and experimentally a broadband magnetic activity. The key feature to achieve this performance remains in the high aspect ratio of the metamaterial building blocks. This is a very promising step towards complex electromagnetic functions, involving low-cost metamaterials with simple fabrication.