A proof of Culter’s theorem on the existence of periodic orbits in polygonal outer billiards

We prove a recent theorem by C. Culter every polygonal outer billiard in the affine plane has a periodic trajectory.      

Thermal Effects of Microwave Energy in Agricultural Soil Radiation

The thermal treatment by millimeter waves for the soil disinfection can be one possible alternative to chemical treatments. This physical method is based on incrementing the soil temperature and its pathogens irradiating with high frequency electromagnetic waves. So the previous knowledge of the temperature distribution in the irradiated soil is essential for achieving an effective bad microorganism and weed seeds elimination. This report analyse the heating kinetic and spatial distribution of the maximum temperatures reached by the soil. It is presented a mathematic model about how are distributed the reached temperatures in the depth of the irradiated soil. This model concludes that when an orchard soil is irradiated superficially by microwaves, the microwaves have a big attenuation due to the soil dielectric properties and the water located in the pores of the most superficial layer. This fact causes a shield effect blocking the waves penetration in few centimetres. The heating by radiation is reduced to the superficial layer. The heating propagation in the depth is occurred by conduction following the Fourier equations.     

Periodic solutions for p-Laplacian neutral functional differential equation with multiple deviating arguments

By using the theory of coincidence degree, we study a kind of periodic solutions to p-Laplacian neutral functional differential equation with multiple deviating arguments, a new result on the existence of periodic solutions is obtained.     

Thermal effects on parallel resonance energy of whistler mode wave

In this short communication, we have evaluated the effect of thermal velocity of the plasma particles on the energy of resonantly interacting energetic electrons with the propagating whistler mode waves as a function of wave frequency and L-value for the normal and disturbed magnetospheric conditions. During the disturbed conditions when the magnetosphere is depleted in electron density, the resonance energy of the electron enhances by an order of magnitude at higher latitudes, whereas the effect is small at low latitudes. An attempt is made to explain the enhanced wave activity observed during magnetic storm periods.     

Numerical Soliton and Oscillating Wave Solutions for Flierl-Petviashvili Equation in Plasmas

Numerical axisymmetric soliton and oscillating wave solutions for the Flierl-Petviashvili equation in plasmas are presented. Solution branch paradigm and examples are given. Some implications of results to ion drift wave as well as force-free field of magnetic equilibrium are briefly discussed.     

Upward and downward heat and mass transfer with miniature periodically operating loop thermosyphons

Upward and downward two-phase heat and mass transfer has been considered in the present paper. The heat and mass transfer with the condenser located below the evaporator has been obtained by inserting an accumulator tank in the liquid line of a loop thermosyphon and enforcing a pressure pulsation. In previous papers these heat transfer devices have been called pulsated two phase thermosyphons (PTPT). A mini PTPT has been experimentally investigated. It has shown a stable periodic heat transfer regime weakly influenced by the position of the condenser with respect to the evaporator. In contrast a classical loop mini thermosyphon (diameter of connecting pipes 4 mm) did not achieve a stable functioning for the investigated level differences between evaporator and condenser lower than 0.37 m. The present study shows that the functioning of a PTPT device does not directly depend on the level difference or the presence of noncondensable gas. In order to obtain a natural circulation in mini or micro loops, a periodically operating heat transfer regime should therefore be considered.     

The twist coefficient of periodic solutions of a time-dependent Newton's equation

This paper gives sufficient conditions for the existence of periodic solutions of twist type of a time-dependent differential equation of the second order. The concept of periodic solution of twist type is defined in terms of the corresponding Birkhoff normal form and, in particular, implies that the solution is Lyapunov stable. Some applications to nonlocal problems are given.     

Averaged topological equations for dispersed two-phase flows

A general relationship between the volume fraction and the specific interfacial area for averaged dispersed two-phase flows is proposed. This relationship, expressed as a basic set of two scalar evolution equations and two vectorial non-uniformity state equations, is an analytical result obtained by a systematic approach using the derivatives of some generalized functions and a local volume-averaging technique. The proposed set of equations was expressed for measurable macroscopic parameters of the system and has the same generality as the averaged transport equations of two-phase flows. By combination of the basic set of equations, called the averaged topological equations (ATEs), second-order ATEs for the volume fraction were found. The second-order ATEs were expressed both by a Lagrangian formulation and by a Eulerian formulation. The importance and physical meaning of the ATEs developed in this study were clarified within the framework of the theory of kinematic waves.     

Periodic solutions of a second order forced sublinear differential equation with delay

In this paper, existence criteria are established for the existence of periodic solutions of a second order sublinear differential equation with delay and forcing function. Our method is based on careful a priori estimation and continuation theorems, and our sublinear condition is an improvement of the boundedness condition in some recent results.     

Letter: Some Remarks on Standing Gravitational Waves

An intuitive definition of standing gravitational waves is proposed. Some main classes of exact vacuum solutions are searched for standing gravitational waves, in most cases with a negative result. Only some Einstein–Rosen waves meet the conditions.