The Millimeter Wave Radiation of a Traveling Wave Sinusoidal Wire Antenna

In this paper, investigation of radiation properties of the traveling-wave sinusoidal wire antennas is extended to the millimeter-wave frequencies (Ka-band) for the antennas whose geometrical dimensions vary in a wide range. Far-field patterns and S-parameters of composed three antenna sets were measured. A mathematical model was constructed for the structure and a MATLAB code based on this theoretical approach was written to calculate patterns, phase and attenuation constants of all investigated antennas. Frequency characteristics and the relation of antenna dimensions with wave parameters were investigated. Measured and calculated patterns were also compared with the constructed far-field patterns obtained by MoM (method of moments) and the MoM current distributions were used to explain the loss mechanisms of antennas. A directive, undistorted and smooth radiation can be achieved only choosing small undulated antennas whose peak-to-peak amplitude to period ratio κ is smaller than 0.4 (κ < 0.4). It is shown that wavelength of broadside radiation is not equal to antenna period for all antennas, except for very small undulated antennas (κ < 0.2). This antenna type can be used as a frequency-scan antenna for millimeter wave radars.

Quasi-Stationary Regime of a Branching Random Walk in Presence of an Absorbing Wall

A branching random walk in presence of an absorbing wall moving at a constant velocity v undergoes a phase transition as the velocity v of the wall varies. Below the critical velocity v _c , the population has a non-zero survival probability and when the population survives its size grows exponentially. We investigate the histories of the population conditioned on having a single survivor at some final time T. We study the quasi-stationary regime for v<v _c when T is large. To do so, one can construct a modified stochastic process which is equivalent to the original process conditioned on having a single survivor at final time T. We then use this construction to show that the properties of the quasi-stationary regime are universal when v→v _c . We also solve exactly a simple version of the problem, the exponential model, for which the study of the quasi-stationary regime can be reduced to the analysis of a single one-dimensional map.     

A numerical investigation of blow-up in reaction-diffusion problems with traveling heat sources

This paper studies the numerical solution of a reaction-diffusion differential equation with traveling heat sources. According to the fact that the locations of heat sources are known, we add auxiliary mesh points exactly at heat sources and present a novel moving mesh algorithm for solving the problem. Several examples are provided to demonstrate the efficiency of the new moving mesh method, especially in the case of two or three traveling heat sources. Moreover, numerical results illustrate that the speed of the movement of the heat source is critical for blow-up when there is only one traveling heat source. For the case of two traveling heat sources, blow-up depends not only on the speed but also on the distance between the two traveling heat sources.     

Modified Tunneladder Slow-Wave Structures for High-Power Millimeter-Wave TWTs

In this paper, five modified Tunneladder slow-wave structures (SWS), the ridge-loaded stub-supported meander line with circular electron tunnel (CET-RSML), ring-plane frame line (RPFL), the ridge-loaded thick ladder line (RLTLL), the ridge-loaded pole-piece folded-waveguide circuit (RLPFWL), and the double-period Tunneladder line (DPTL) were discussed. The dispersion characteristics and the interaction impedances of the five modified Tunneladder SWS were calculated by simulation and the corresponding analytic models. The calculation results explain that the CET-RSML and the RLTLL hold wider bandwidth in comparison with the Tunneladder, when the volume dimensional lengths are same. When the bandwidth is definite, the interaction impedance of RLTLL can be higher than Tunneladder, but that of CET-RSML can’t. The dispersion curves of the RLPFWL and the DPTL are more linear in comparison with Tunneladder, but the interaction impedances are very low. Supported by the National Natural Science Foundation of China, under Grant No. 60532010.     

Cuspons and Smooth Solitons of the Degasperis–Procesi Equation Under Inhomogeneous Boundary Condition

This paper is contributed to explore all possible single peakon solutions for the Degasperis–Procesi (DP) equation m _t  + m _x u + 3mu _x  = 0, m = u − u _xx . Our procedure shows that the DP equation either has cusp soliton and smooth soliton solutions only under the inhomogeneous boundary condition lim_|x|→ ∞ u =A ≠0, or possesses the regular peakon solutions ce ^{− |x − ct|} ∈ H ¹ (c is the wave speed) only when lim_|x|→ ∞ u = 0 (see Theorem 4.1). In particular, we first time obtain the stationary cuspon solution of the DP equation. Moreover we present new cusp solitons (in the space of ) and smooth soliton solutions in an explicit form. Asymptotic analysis and numerical simulations are provided for smooth solitons and cusp solitons of the DP equation.      

Elimination of Anti-spiral Waves by Local Inhomogeneity in Oscillatory Systems

Anti-spiral waves are controlled in an oscillatory system by using a local inhomogeneity. The inhomogeneity acts as a wave source, and gives rise to the propagating plane waves. It is found that there is a critical pacemaking domain size below which no wave will be created at all. Two types of ordered waves (target waves and traveling waves) are created depending on the geometry of the local inhomogeneity. The competition between the anti-spiral waves and the ordered waves is discussed. Two different competition mechanisms were observed, which are related to the ordered waves obtained from different local inhomogeneities. It is found that traveling waves with either lower frequency or higher frequency can both eliminate the anti-spiral waves, while only the target waves with lower absolute value of frequency can eliminate the anti-spiral waves.This method also applies to outwardly rotating spiral waves. The control mechanism is intuitively explained and the control method is easily operative.     

Traveling waves,impulses and diffusion chaos in excitable media

In the present work it is shown, that the FitzHugh–Nagumo type system of partial differential equations with fixed parameters can have an infinite number of different stable wave solutions, traveling along the space axis with arbitrary speeds, and also traveling impulses and an infinite number of different states of spatiotemporal (diffusion) chaos. Those solutions are generated by cascades of bifurcations of cycles and singular attractors according to the FSM theory (Feigenbaum–Sharkovskii–Magnitskii) in the three-dimensional system of ordinary differential equations (ODEs), to which the FitzHugh–Nagumo type system of equations with self-similar change of variables can be reduced.     

The exact solutions to （2＋1）-dimensional nonlinear Schroedinger equation

By using the extended F-expansion method,the exact solutions,including periodic wave solutions expressed by Jaeobi elliptic functions,for (2 1)-dimensional nonlinear Schroedinger equation are derived.In the limit cases,the solitary wave solutions and the other type of traveling wave solutions for the system are obtained.     

When the greedy algorithm fails

We provide a characterization of the cases when the greedy algorithm may produce the unique worst possible solution for the problem of finding a minimum weight base in an independence system when the weights are taken from a finite range. We apply this theorem to TSP and the minimum bisection problem. The practical message of this paper is that the greedy algorithm should be used with great care, since for many optimization problems its usage seems impractical even for generating a starting solution (that will be improved by a local search or another heuristic).     

A reaction-diffusion equation and its traveling wave solutions

In the present paper, we study a non-linear reaction-diffusion equation, which can be considered as a generalized Fisher equation. An exact solution and traveling wave solutions to the generalized Fisher equation are obtained by means of the Cole-Hopf transformation and the Lie symmetry method.