The orbit of a classical particle in a central field, due to the angular momentum conservation, must lie in a plane perpendicular to the angular momentum. However, the orbit is, in general, not closed. In classical mechanics there is a famous Bertrand’s theorem [1,2], which says that the only central forces that result in closed orbits for all bound particles are the inverse square law and Hook...

Background: A study was undertaken to test the hypothesis that patients respond better to lung volume reduction surgery (LVRS) if their emphysema is confluent and predominantly located in the upper lobes. Methods: A density mask analysis was used to identify voxels inflated beyond 10.2 ml gas/g tissue (–910 HU) on preoperative and postoperative CT scans from patients receiving LVRS. These hyper...

This paper studies the ability of salt diapirs to lift large inclusions of dense rocks (rafts). Dense inclusions will be lifted if salt in the diapir rises faster than the inclusions sink. The power-law rheologies of six different salts, and viscosities estimated for Newtonian salt are used to calculate the settling velocity of these inclusions as a function of their radii and density as well a...

BACKGROUND A study was undertaken to test the hypothesis that patients respond better to lung volume reduction surgery (LVRS) if their emphysema is confluent and predominantly located in the upper lobes. METHODS A density mask analysis was used to identify voxels inflated beyond 10.2 ml gas/g tissue (-910 HU) on preoperative and postoperative CT scans from patients receiving LVRS. These hyper...

Without incorporation of weak-shock theory, the lossless Burgers equation predicts a multivalued waveform for nonlinear propagation beyond a certain distance. Inclusion of thermoviscous attenuation, which increases quadratically with frequency, prevents the occurrence of multivalued waveforms. The same is true for any attenuation law that is proportional to frequency raised to an exponent great...

A mesh-free method based on moving least squares approximation (MLS)  and weak form of governing equations including two dimensional equations of motion and Maxwell’s equation is used to analyze the free vibration of functionally graded piezoelectric material (FGPM) beams. Material properties in beam are determined using a power law distribution. Essential boundary conditions are imposed by the...

This paper obtains the soliton solutions to the Boussinesq equation with the effect of surface tension being taken into account. The power law nonlinearity is considered. Three integration tools are adopted in order to extract the soliton solutions. They are the traveling wave hypothesis, ansatz method and the semi-inverse variational principle. Finally, the Lie symmetry approach is adopted to ...

Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations with the averaging with respect to fast variable is used. The main assumption is that the correlator of probability densities of particles to make a step has a power-law dependence. As a result,...

In this paper, the unsteady flow of non-Newtonian fluid through a porous medium when an external magnetic field is applied is investigated. The non linear equation of motion is transformed to a similarity differential equation which is solved using the method of successive approximations. The rheological effects are shown and discussed on the velocity profile in terms of rheological parameter o...

In the case of tight transverse confinement (cigar-shaped trap) the threedimensional (3D) nonlinear Schrödinger equation, describing superfluid Fermi atoms at unitarity (infinite scattering length |a| → ∞), is reduced to an effective one-dimensional form by averaging over the transverse coordinates. The resultant effective equation is a 1D nonpolynomial Schrodinger equation, which produces resu...