[en] We obtain a new solution of the paraxial Helmholtz equation that describes a family of three-dimensional and two-dimensional form-invariant half-Pearcey beams (HP-beams). HP-beams generalize Pearcey beams obtained in Ring et al (2012) Opt. Express 20 18955, since these Pearcey beams can be considered as the sum of two first-order HP-beams. Three-dimensional HP-beams have angular spectra of plane waves, which are non-zero at a half parabola. For functions of HP-beam complex amplitudes, the orthogonality properties have been revealed. Using a spatial phase modulator, we generated superposition of HP-beams. For two-dimensional HP-beam acceleration and deceleration of trajectory has been shown for areas before and beyond the focal plane respectively. (paper)

[en] We consider the billiard dynamical system in a domain bounded by confocal parabolas. We describe such domains in which the billiard problem can be correctly stated. In each such domain we prove the integrability for the system, analyse the arising Liouville foliation, and calculate the invariant of Liouville equivalence--the so-called marked molecule. It turns out that billiard systems in certain parabolic domains have the same closures of solutions (integral trajectories) as the systems of Goryachev-Chaplygin-Sretenskii and Joukowski at suitable energy levels. We also describe the billiard motion in noncompact domains bounded by confocal parabolas, namely, we describe the topology of the Liouville foliation in terms of rough molecules. Bibliography: 16 titles

[en] Exact explicit rational solutions of two- and one-dimensional multicomponent Yajima–Oikawa (YO) systems, which contain multi-short-wave components and single long-wave one, are presented by using the bilinear method. For two-dimensional system, the fundamental rational solution first describes the localized lumps, which have three different patterns: bright, intermediate and dark states. Then, rogue waves can be obtained under certain parameter conditions and their behaviors are also classified to above three patterns with different definition. It is shown that the simplest (fundamental) rogue waves are line localized waves which arise from the constant background with a line profile and then disappear into the constant background again. In particular, two-dimensional intermediate and dark counterparts of rogue wave are found with the different parameter requirements. We demonstrate that multirogue waves describe the interaction of several fundamental rogue waves, in which interesting curvy wave patterns appear in the intermediate times. Different curvy wave patterns form in the interaction of different types fundamental rogue waves. Higher-order rogue waves exhibit the dynamic behaviors that the wave structures start from lump and then retreat back to it, and this transient wave possesses the patterns such as parabolas. Furthermore, different states of higher-order rogue wave result in completely distinguishing lumps and parabolas. Moreover, one-dimensional rogue wave solutions with three states are constructed through the further reduction. Specifically, higher-order rogue wave in one-dimensional case is derived under the parameter constraints. - Highlights: • Exact explicit rational solutions of two-and one-dimensional multicomponent Yajima–Oikawa systems. • Two-dimensional rogue wave contains three different patterns: bright, intermediate and dark states. • Multi- and higher-order rogue waves exhibit distinct dynamic behaviors in two-dimensional case. • One-dimensional higher-order rogue wave is derived under the parameter constraints

[en] We study the solvability of linear inverse problems for ultraparabolic equations with an unknown coefficient depending only on the spatial variables. The feature of such problems is special overdetermination conditions. We use the method based on reducing the inverse problem to a nonlocal boundary-value problem for ultraparabolic equations.

[en] Energetic particles spectra at interplanetary shocks often exhibit a power law within a narrow momentum range softening at higher energy. We introduce a transport equation accounting for particle acceleration and escape with diffusion contributed by self-generated turbulence close to the shock and by preexisting turbulence far upstream. The upstream particle intensity steepens within one diffusion length from the shock as compared with diffusive shock acceleration rollover. The momentum spectrum, controlled by macroscopic parameters such as shock compression, speed, far-upstream diffusion coefficient, and escape time at the shock, can be reduced to a log-parabola and also to a broken power law. In the case of upstream uniform diffusion coefficient, the largely used power-law/exponential cutoff solution is retrieved.

[en] In a sound wave measurement engineer, a combination focusing device of right angle cone and parabola was designed to increase the emission sound pressure, and by exploring and simulating the relationship between the position and size of the spherical focus area and the height of the right-angled cone, the position of the apex of the right-angled cone, the focal length of the parabolic and other parameters. The analytical relationship between each parameter and the sound pressure level of the spherical area focused at a certain position from the vertex of the right-angled cone is obtained. (paper)

[en] Highlights: • Five parts of heat loads are discussed in the TBM room. • Field tests of the air temperature in the TBM room are carried out. • An unsteady model is developed to predict the air temperature in the TBM room. • A linearly increase of air temperature with RT and TBM efficiency is obtained. • Ventilation cannot ensure the air temperature lower than 28 °Cfor RT higher than 45 °C. -- Abstract: In this work, field tests on the air temperature in the TBM (tunnel boring machine) room are initially carried out for TBM on and off, respectively. A simulation model is subsequently developed and reproduced the tests. The comparison shows an acceptable agreement, thus this model is adopted to study effects of RT (rock temperature), TBM utilization factor and construction ventilation on the air temperature in the TBM room. The results show the air temperature reaches a steady state after 20 min. The steady air temperature increases linearly with the increase of RT and TBM utilization factor. The air temperature is higher than 28 °C when RT is greater than 17.7 °C or when TBM utilization factor is greater than 38.0%. Effects of construction ventilation are discussed as well. The air temperature is observed to decreases in a form of parabola with the increase of fresh air volume, whereas it increases linearly with the increase of fresh air temperature. As a result, it can be found that ventilation is a very useful method to reduce the air temperature in the TBM room. But it is not enough to provide a workable and comfortable thermal environment when RT is higher than 45 °C.

[en] Highlights: • A Gross-Pitaevskii (GP) equation with a parabola external potential is considered. • We study the non-autonomous wave solutions of GP equation with a parabola external potential. • These obtained bright-dark soliton solutions can give some potential applications in Bose-Einstein condensates. -- Abstract: A Gross-Pitaevskii (GP) equation with a parabola external potential is considered, and is transformed into a standard nonlinear Schrödinger (NLS) equation. By using the homogeneous balance principle and F-expansion method, we study non-autonomous wave solutions of the GP equation with a parabola external potential. In particular, based on the similarity transformation, several families of non-autonomous wave solutions of the GP equation are presented with snaking behaviors and different amplitude surfaces. These obtained bright-dark soliton solutions can give some potential applications in Bose-Einstein condensates.

[en] A new, versatile Thomson parabola ion energy (TPIE) analyzer has been designed and constructed for use at the OMEGA-EP facility. Multi-MeV ions from EP targets are transmitted through a W pinhole into a (5- or 8-kG) magnetic field and subsequently through a parallel electric field of up to 30 kV/cm. The ion drift region may have a user-selected length of 10, 50, or 80 cm. With the highest fields, 500-Me V C⁶⁺ and C⁵⁺ may be resolved. TPIE is TIM-mounted at OMEGA-EP and is qualified in all existing TIMs. The instrument runs on pressure-interlocked 15-VDC power available in EP TIM carts. It may be inserted to within several inches of the target to attain sufficient flux for a measurement. For additional flux control, the user may select a square-aperture W pinhole of 0.004-inch or 0.010-inch. The detector consists of CR-39 backed by an image plate. The fully relativistic design code and design features are discussed. Ion spectral results from first use at OMEGA-EP are expected.

[en] The mass-number (A) dependence Z_β(A) for nuclei lying on the beta-stability line (BSL) is calculated for A and Z values in the ranges of A = 2–258 and Z = 1–100, respectively. The calculated values are compared with experimental data. The deviations ΔZ = Z_expt − Z_β are analyzed. This analysis of ΔZ reveals that there are three regions of A values in which the A dependence of ΔZ is parabolic. The possible forms of the A dependence of ΔZ are analyzed, and it is shown that the majority of nuclei belong to several parabolas simultaneously.