On the Motion of Substance in a Channel of a Network: Extended Model and New Classes of Probability Distributions

We discuss the motion of substance in a channel containing nodes of a network. Each node of the channel can exchange substance with: (i) neighboring nodes of the channel, (ii) network nodes which do not belong to the channel, and (iii) environment of the network. The new point in this study is that we assume possibility for exchange of substance among flows of substance between nodes of the channel and: (i) nodes that belong to the network but do not belong to the channel and (ii) environment of the network. This leads to an extension of the model of motion of substance and the extended model contains previous models as particular cases. We use a discrete-time model of motion of substance and consider a stationary regime of motion of substance in a channel containing a finite number of nodes. As results of the study, we obtain a class of probability distributions connected to the amount of substance in nodes of the channel. We prove that the obtained class of distributions contains all truncated discrete probability distributions of discrete random variable ω which can take values 0,1,⋯,N. Theory for the case of a channel containing infinite number of nodes is presented in Appendix A. The continuous version of the discussed discrete probability distributions is described in Appendix B. The discussed extended model and obtained results can be used for the study of phenomena that can be modeled by flows in networks: motion of resources, traffic flows, motion of migrants, etc.     

Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.     

Magneto-Galvanic Resonances in Hollow Cathode Discharge Lamps

The galvanic behavior of a hollow cathode discharge versus an external weak magnetic field is investigated. The application of this field leads to disordering of the self-aligned states, which is detected as a resonance in the discharge current, named the magneto-galvanic signal. A correlation magneto-galvanic signal–operating voltage-current point is established and attributed to Penning ionization. The contribution of the metastable Ne I 1 s₅ to the magneto-galvanic resonance is also verified.     

Size effects in monodomain magnetite based ferrofluids

Ferrofluids based on two types of hybrid particles Fe₃O₄/β-cyclodextrin were prepared: Using monodomain (below 60 nm) magnetite nanoparticles with (A) non-superparamagnetic (non-SPM) behaviour and (B) with superparamagnetic (SPM) behaviour. We found a strong dependence of the hybrid particles’ magnetic properties on their size and homogeneity. In both types of ferrofluids we observed hyperthermia upon applying an ac electromagnetic field with frequency 40 kHz and amplitude 30 kA/m. The maximal ΔТ upon irradiation with duration of about 12 min for the non-SPM particles was 12 °C, while for the SPM ones it was 3.5 °C.     

Controlled two-pulse generation in Q-switch mode from a single laser using Q-modulator with frustrated total internal reflection

In this work a cavity design for double-pulse generation in Q-switched mode from a single laser is proposed, based on the construction of a second laser channel using a FTIR (frustrated total internal reflection) Q-modulator. A time interval between the two pulses from 500 ns to 120 μs is obtained in a Nd:YAG laser. A comparison with other methods and cavity designs for double-pulse generation is presented. The case when this technique is applied on a tunable laser with metastable upper laser level (Cr:LiCAF, Cr:LiSAF, Alexandrite, Co:MgF₂ or other) is also considered. Even though the method presented in the paper does not rely only on the cavity configuration proposed, some advantages can be obtained – both polarization and wavelength-independent tuning without polarization and wavelength restrictions in combination with the possibility of different wavelengths and polarizations in each pulse. Moreover, by using an active medium generating wavelengths around and up to 3 μm, the Pockels-cell-Q-switch optical transmission problems can be avoided. Received: 9 May 2001 / Revised version: 2 August 2001 / Published online: 15 October 2001     

Prediction of the frequency spectrum of AT-cut contoured quartz resonators by means of X-ray diffraction topography

This paper presents some important relationships relating to frequencies in contoured AT-cut quartz resonators. It is shown that frequency interval relations are not affected by the piezoelement geometry but are functionally related solely to the indices of the Hermite functions. According to the analysis of trapped-energy resonators, an X-ray technique for predicting the frequency spectrum can be derived. It is based on the use of X-ray patterns of two wave motions and enables one to determine the whole frequency spectrum in the vicinity of any odd harmonic overtone of vibration. Two contoured resonator analyses show that the X-ray topography predictions are in good agreement with experimental data.     

Study of mercury surface diffusion on tantalum with and without an electric field by means of a field emission microscope

The surface diffusion of mercury atoms on tantalum substrate with and without high electric field was studied by means of a field emission microscope (Müller's). The activation energy during surface migration Q_m of mercury atoms with and without an electric field F on tantalum substrate depending on the thickness of the adsorbate was measured. It is shown that the electron density distribution at coverage θ < 0.65 with adsorbate is due to a dipole momentum P. At θ > 0.65 the slope of the curves of Q^F_m = ?(θ) is explained with the appearance of the effect of polarization. The energy of desorption Q_d as a function of the thickness of the adsorbed layer in the temperature range 100–300 K was measured also.     

Thiophenylazobenzene: An Alternative Photoisomerization Controlled by Lone-Pair⋅⋅⋅π Interaction

Azoheteroarene photoswitches have attracted attention due to their unique properties. We present the stationary photochromism and ultrafast photoisomerization mechanism of thiophenylazobenzene (TphAB). It demonstrates impressive fatigue resistance and photoisomerization efficiency, and shows favorably separated (E)- and (Z)-isomer absorption bands, allowing for highly selective photoconversion. The (Z)-isomer of TphAB adopts an unusual orthogonal geometry where the thiophenyl group is perfectly perpendicular to the phenyl group. This geometry is stabilized by a rare lone-pair⋅⋅⋅π interaction between the S atom and the phenyl group. The photoisomerization of TphAB occurs on the sub-ps to ps timescale and is governed by this interaction. Therefore, the adoption and disruption of the orthogonal geometry requires significant movement along the inversion reaction coordinates (CNN and NNC angles). Our results establish TphAB as an excellent photoswitch with versatile properties that expand the application possibilities of AB derivatives.