Generalised potential for computing classical turning points of molecular oscillators

Expressions for classical turning points of the molecular oscillator are derived using a generalised first-order potential. Equivalence of the potential is established with results derived from the Morse, Dunham, and RKR potentials wwhen the energy is a quadratic function of the vibrational quantum number.     

Simplified mobility expressions for infinite in-vacuo pipes

In this paper, closed-form expressions for the mobility of the circumferential modes in an infinite in-vacuo thin-walled pipe are derived in terms of the axial wave receptances for each mode. These expressions are valid below the ring frequency. By using simplified expressions for the wavenumbers, low-frequency approximations for the point and transfer mobilities are also derived. These new mobility expressions are validated experimentally, and are used to examine the dynamic behaviour of an in-vacuo pipe.     

Simplified closed form expressions for irreducible tensor operators

A general closed form expression is derived which enables one to write a spherical tensor of rank L and projection k, T_uk^L, in terms of the familiar angular momentum operators, S_z and S². The simplicity of this expression results from an intriguing relationship between these spherical tensor operators (diagonal operator equivalents) and successive derivatives of Tchebichef orthogonal polynomials.     

Simplified expressions of the T-matrix integrals for electromagnetic scattering

The extended boundary condition method, also called the null-field method, provides a semianalytic solution to the problem of electromagnetic scattering by a particle by constructing a transition matrix (T-matrix) that links the scattered field to the incident field. This approach requires the computation of specific integrals over the particle surface, which are typically evaluated numerically. We introduce here a new set of simplified expressions for these integrals in the commonly studied case of axisymmetric particles. Simplifications are obtained using the differentiation properties of the radial functions (spherical Bessel) and angular functions (associated Legendre functions) and integrations by parts. The resulting simplified expressions not only lead to faster computations, but also reduce the risks of loss of precision and provide a simpler framework for further analytical work.     

A classical iteration procedure valid for certain strongly nonlinear oscillators

A classical iteration procedure is applied to nonlinear oscillations of conservative single-degree-of-freedom systems with odd nonlinearity. With the procedure, the analytical approximate frequency and the corresponding periodic solution, valid for small as well as large amplitudes of oscillation, can be obtained. Two examples are given to illustrate the accuracy and effectiveness of the method. Another advantage of this classical iteration approach is that it also works if the linear part of restoring force is zero.     

Electromagnetically induced transparency in ensembles of classical oscillators

We develop a classical model of the parametric effect of electromagnetically induced transparency (EIT) within the line of resonance absorption of an electromagnetic wave in the medium--an effect initially discovered for a quantum three-level system. On the basis of this model, the EIT effect for electromagnetic waves at frequencies of the electron-cyclotron resonance in a cold plasma is considered. Similar to the analogous quantum scheme, the EIT window in the classical model is characterized by group deceleration of the reference electron-cyclotron wave.     

Mutual synchronization of molecular oscillators

Radiophysics and Quantum Electronics -     

Neutron excess in analytical expressions for fusion barrier parameters

The neutron excess dependence of heavy-ion fusion barriers is investigated, guided by predictions of different ion-ion potentials. We develop phenomenological expressions for the fusion barrier radii and heights, involving both the entrance channel mass asymmetry and neutron excess of the projectile and target. Compared to commonly used formulas, the developed expressions reproduce theoretical barrier parameters with a higher accuracy. Furthermore, they provide a means to assess the importance of the neutron excess degree of freedom implied by each potential.Received: 1 April 2003, Revised: 31 January 2004, Published online: 10 August 2004PACS: 24.10.-i Nuclear reaction models and methods - 25.70.-z Low and intermediate energy heavy-ion reactions - 25.70.Jj Fusion and fusion-fission reactions - 25.60.Pj Fusion reactions     

Geometrical optics of dispersive media with turning points

The modification of the geometrical optics approximation developed in our earlier paper has been extended to problems in which the classical conditions for its validity are violated, e.g. problems in which turning points are present, and tunnelling and over-barrier reflection are studied. The application of the method to difference equations has been demonstrated by the example of the propagation of electric waves through a one-dimensional array of charged nonlinear oscillators with nearest-neighbour interactions.     

On the stationary distribution of self-sustained oscillators around bifurcation points

A double expansion in powers of the damping coefficient and noise intensity is shown to be a powerful method for obtaining the stationary distribution of systems that after rescaling become weakly damped conservative ones. Systems undergoing Hopf bifurcations belong to this class. As an illustrative example, the generalized van der Pol oscillator is considered around its bifurcation point. A calculation is carried out up to third order in both the noise intensity and the bifurcation parameter (damping coefficient).     

Exact analytical expressions for the dispersion relation of one-dimensional chiral photonic crystals

We consider one-dimensional photonic crystals made of alternating layers of two kinds of isotropic chiral media. The two layers are characterized by the dielectric permittivities ε₁ and ε₂, the magnetic permeabilities μ₁ and μ₂, the chirality parameters γ₁ and γ₂ and the thicknesses d₁ and d₂. By diagonalizing an 8 × 8 matrix derived from the two coupled wave equations satisfied by our system, we obtain exact analytical expressions for the dispersion relation for plane electromagnetic waves propagating at an arbitrary angle with respect to the layers. We present a detailed analysis of our dispersion relation and explore the evolution of the photonic band structure as the frequency, the chirality parameter and the incident angle vary, with a special emphasis on the generation of the cross- and co-polarization bandgaps.     

Frequency-lock system for microwave local oscillators using molecular absorption lines

We describe the frequency-lock (FL) system for local oscillators in receivers in the 130 to 360 GHz range, using the resonance lines of molecules with a known absorption spectrum. The functions of a frequency discriminator, a diplexer, and a noise rejector are performed by a Mach-Zehnder interferometer with a gas cell. Deceased Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 11, pp. 1399–1404, November, 1998.     

Superradiation in ensembles of classical electron oscillators under conditions of group synchronism

We consider the cyclotron superradiation of a moving electron bunch under conditions of group synchronism when the forward velocity of the bunch is equal to the group velocity of the electromagnetic wave. It is shown that this mode of operation makes it possible to increase the increment of superradiant instability and raise the peak radiated power.Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, Nos. 3–4, pp. 292–297, March–April, 1995.     

Cooperative behaviors of coupled nonidentical oscillators with the same equilibrium points

The cooperative behaviors resulted from the interaction of coupled identical oscillators have been investigated intensively. However, the coupled oscillators in practice are nonidentical, and there exist mismatched parameters. It has been proved that under certain conditions, complete synchronization can take place in coupled nonidentical oscillators with the same equilibrium points, yet other cooperative behaviors are not addressed. In this paper, we further consider two coupled nonidentical oscillators with the same equilibrium points, where one oscillator is convergent while the other is chaotic,and explore their cooperative behaviors. We find that the coupling mode and the coupling strength can bring the coupled oscillators to different cooperation behaviors in unidirectional or undirected couplings. In the case of directed coupling,death islands appear in two-parameter spaces. The mechanism inducing these transitions is presented.     

Excited classical oscillators under conditions of differing lifetime in the interaction space

The article considers the mechanism of interaction between oscillators and a high-frequency field, associated with differing lifetime of particles in the interaction space as a result of the fact that the drift velocity of the oscillators depends on their energy. Examples are given of interaction in which amplification results from the differing-lifetime mechanism.Translated from Izvestiya Vysshikh Uchebnyk Zavedenii, Radiofizika, Vol. 21, No. 12, pp. 1761–1765, December, 1978.     

General analytical expressions for the bit error rate of atmospheric optical communication systems

General analytical expressions are derived for the average bit error rate of an intensity modulation and direct detection link using unbounded optical wavefront with on-off keying signalling technique propagating under all possible irradiance fluctuation conditions. These expressions include in a single equation the link performance of most of the proposed statistical models derived until now.     

Intermediate asymptotic expressions for high-order spin correlation functions in a two-dimensional classical ferromagnet

Different-point spin correlation functions are calculated for a two-dimensional classical ferromagnet in a pacerturbative range of distances r: a<r?m ^?1, where a is the lattice parameter and m ^?1 is the correlation length. The expressions for the four-and higher-order correlation functions are presented.     

Optical tomography of the distribution function of an ensemble of classical harmonic oscillators

We discuss the optical tomography of the statistical system of noninteracting identical one-dimensional classical harmonic oscillators, using the examples of mechanical oscillators and electrical oscillatory LC circuits.     

Exact analytical expressions for diatomic rotational and centrifugal distortion constants for a Kratzer-Fues oscillator

The exact closed-form expression for the vibrational-rotational eigenvalues of the Kratzer-Fues oscillator served as the starting point for a derivation of exact analytical expressions for the rotational constant B_υ, and the set D_υ to S_υ of centrifugal distortion constants up to 11th-order. The derivations employed the MAPLE symbolic algebra coprocessor. The expressions for B_υ to S_υ were then employed in the calculation of a set of constants for a Kratzer-Fues potential with specified dissociation energy and equilibrium internuclear separation for a hypothetical diatomic molecule with a reduced mass of unity. The tabulated constants serve as a benchmark against which the reliability of various existing or future numerical methods for the determination of rotational and centrifugal distortion constants may be assessed. The near-dissociation behaviour of the calculated constants was also examined and is useful in predicting the behaviour of such constants for real electronic states having pure ionic long-range form.     

“Inversionless” stimulated emission of radiation by nonequilibrium ensembles of classical oscillators

We find classical analogs of quantum systems capable of stimulated emission of radiation in the absence of inversion. We show that cyclotron parametric instability in low-frequency modulation of the distribution function of resonant particles can amplify a bichromatic high-frequency field when amplification of each spectral component separately is impossible. We point to similar modes for a Cherenkov resonance and a model system with lumped parameters. Finally, we suggest using this effect for converting microwave radiation to a higher frequency. Zh. éksp. Teor. Fiz. 112, 1176–1196 (October 1997)