Simple procedure for solving few-body equations

In this work we propose a procedure for iterative improvement of the adiabatic solution of the hyperspherical-harmonics technique. The usefulness of the method is demonstrated by calculating the binding energies of the ground and first excited state of the⁴He nucleus using several nucleon-nucleon interactions. The procedure is found to be simple and very stable. We compare the elastic charge form factor of the⁴He nucleus obtained by the usual adiabatic solutions and the improved version of this work. This comparison gives valuable physical insight into the nature of the adiabatic approximations.     

Kernel approximation for solving few-body integral equations

This paper investigates an approximate method for solving integral equations that arise in few-body problems. The method is to replace the kernel by a degenerate kernel defined on a finite dimensional subspace of piecewise Lagrange polynomials. Numerical accuracy of the method is tested by solving the two-body Lippmann-Schwinger equation with non-separable potentials, and the three-body Amado-Lovelace equation with separable two-body potentials.     

Gravitational waves without gravitons

The radiation connection induced on an isotropic hypersurface of a Lorentz manifold is described. Consequences for the energy tensor in Einstein field equation are analyzed. A cosmological interpretation is proposed.     

Modified extended exp-function method for a system of nonlinear partial differential equations defined by seismic sea waves

A steady-state model has been considered to explain the observed properties of the LSSS RXJ0925.7-4748 / MR Vel. The steady-state models consist of a C–O core surrounded by a hydrogen-rich envelope of the solar abundances. At the bottom of the envelope, hydrogen is burned at the same rate as the star accreted it. Using the most recent proton capturing reaction rates and \(\beta \)-decay rates, the cyclic reactions have been studied. In the present work, effort has been made to explain the observed characteristics of the source RXJ0925.7-4758 / MR Vel considering the above mentioned model. The calculated values of luminosity (\(8.56 \times 10^{37} \, \hbox {erg}\,\hbox {s}^{-1}\)) and effective temperature (94.19 eV) tally well with the observed one. Photoionisation code CLOUDY has been used to explain the observed absorption edges in the spectrum of RXJ0925.7-4758 / MR Vel.     

Formulation of a Relativistic Theory without Constraints

A relativistic, i.e., Lorentz co-variant theory without constraints is formulated. This is possible if we allow the dynamical variables to depend on an invariant parameter . Thus we obtain a dynamical theory in spacetime, called relativistic dynamics. First the case of a point particle, and then of extended objects such as membranes of arbitrary dimensions are considered.     

Neutron-deuteron scattering in high partial waves

The simple formula is derived for calculating the n + d phase shifts for states with high relative orbital angular momentum. The only parameters appearing in the formula are the deuteron binding energy and the triplet effective range. The formula is tested by comparing it with the results of an exactly solvable model, and it is found to be quite accurate at low energies for L ? 3.     

Amplitude equations for non-linear Rayleigh waves

We investigate asymptotic equations describing small amplitude surface elastic waves in the half-plane (Rayleigh waves). For hyperelastic materials such model equations are Hamiltonian systems, and are seen to lead to the formation of singularities in the surface elastic displacement. At the time of singularity formation the Fourier spectra of the solutions exhibit power law decay, and the observed exponents suggest the existence of both differentiable and non-differentiable singular profiles.     

Summation of partial waves for large-angle scattering

For large-angle elastic scattering different methods of summing partial wave amplitudes are investigated for their accuracy and simplicity of computation. It is found that among the approximations considered, the method of expanding the T-matrix in terms of the weighted orthogonal polynomials proposed by Brysk is the most accurate way of calculating the scattering amplitude in the backward direction. If the two-particle interaction is assumed to be a Yukawa potential, then the lth partial sum of the T-matrix with the weighted polynomials can be expressed as the lth partial sum with the Legendre polynomials and a correction term which depends on the phase shift for the lth partial wave.     

Properties of pseudopotentials for higher partial waves

Contact psuedopotentials for relative angular momentum greater than zero are of interest for the study of cold atomic gases. For bosons, it is known that when the s-wave scattering length becomes infinite, an infinite number of three-body bound states, called Efimov states, are predicted by such potentials. Realistic potentials also exhibit the such states, thus a study of the Efimov effect for contact psuedopotentials for higher partial waves and fermions is important for the study of cold atoms. In this Letter we analyze three-body states of three particles interacting via psuedopotentials for higher partial waves and show that there is an Efimov effect for three fermions interacting via p-wave psuedopotentials.     

Wave equations for matter force waves

Regarding phase space—time as a physical space for quantum matter particles, the wave equations are considered in the cases of scalar, vector, and spinor fields. Electrodynamics in pulsed space—time does not contain singularities in the force fields. Expressions are found for the particle propagators in momentum subspace. Order-of-magnitude estimates of force-wave emission and absorption for atomic and nuclear structures show that force waves cannot be neglected in nuclear processes. Force waves are not emitted by particles in a constant force field; the rate of emission is proportional to the square of the rate of force variation over time.NIIVTs Research Center, M. V. Lomosov Moscow State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 32–39, July, 1994.     

Stable standing waves of nonlinear Klein-Gordon equations

In this paper we give sufficient conditions for the stability of the standing waves of least energy for nonlinear Klein-Gordon equations.     

An attractive analytical technique for coupled system of fractional partial differential equations in shallow water waves with conformable derivative

Mathematical simulation of nonlinear physical and abstract systems is a very vital process for predicting the solution behavior of fractional partial differential equations(FPDEs)corresponding to different applications in science and engineering. In this paper, an attractive reliable analytical technique, the conformable residual power series, is implemented for constructing approximate series solutions for a class of nonlinear coupled FPDEs arising in fluid mechanics and fluid flow, which are often designed to demonstrate the behavior of weakly nonlinear and long waves and describe the interaction of shallow water waves. In the proposed technique the n-truncated representation is substituted into the original system and it is assumed the(n-1) conformable derivative of the residuum is zero. This allows us to estimate coefficients of truncation and successively add the subordinate terms in the multiple fractional power series with a rapidly convergent form. The influence, capacity, and feasibility of the presented approach are verified by testing some real-world applications. Finally, highlights and some closing comments are attached.     

Experimental evidence for partial waves in the optical investigation of Lamb waves

An optical probing technique has been used to determine the propagation parameters and the acoustic field distribution of the longitudinal and shear partial waves coupled in Lamb modes. The partial wave momenta were determined from measurements of the light diffraction spectrum and partial acoustic fields analysed by combining spatial light filtering and polarization discrimination techniques. A method for the identification of the Lamb mode is presented.     

Improved estimates of few-body ground-state energies

A method for the estimation of ground-state energies of few-body systems is proposed, which is a combination of an inequality due to Post and the 1/d-expansion. The effectiveness of the method is illustrated for power-law potentials.     

Critical nonlinearities in partial differential equations

The paper is devoted to the role of critical nonlinearities in the framework of the theory of global solvability of nonlinear partial differential equations. In particular, a new approach to blow-up problems for solutions of nonlinear partial differential equations is suggested.     

The peripheral partial waves in kaon-nucleon scattering

A detailed and critical calculation is presented of the partial-wave amplitudes with large angular momentum in kaon-proton scattering up to a lab momentum of 3.2 GeV/c.     

Generalized symmetries of nonlinear partial differential equations

We propose a rigorous definition of the generalized infinitesimal symmetries using the notion of k-vector fields, and we derive an algorithm for their determination. We show that Bäcklund transformations between evolution equations are differential operators having prescribed symmetries.