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The helical micro fin tubes (HFT) are commonly used in various double pipe heat exchangers because of the excellent processing and anti-fouling performance. It is of great significance to further improve the overall efficiency of the HFT so as to diminish energy consumption. In this work, the heat transfer and flow characteristics of the HFT are studied by numerical simulation. The results show that the heat transfer enhancement factors of the HFT are the secondary flow generated near the wall and the increase of the heat exchange area. In addition, the effects of the geometrical parameters on thermal–hydraulic performance are studied at Re = 36,636. It is found that the micro fin height (e), the helical angle (φ), and the number of starts (Ns) have a significant impact on the overall performance, and there is a strong mutual coupling between them. According to the parametric analysis, the HFT with a low micro fin height and a large number of starts is considered to be a better geometrical type. Finally, in order to select (or design) the HFT quickly under the specific working conditions, based on the exergy destruction minimization principle, the geometrical parameters are optimized by using the artificial neural network and genetic algorithm. An optimal solution (e = 0.23 mm, φ = 36.1°, and Ns = 66) is selected from the Pareto front by the TOPSIS method. The results indicate that the optimal solution has a sensible balance between the exergy destruction caused by heat transfer and fluid flow. Besides, it has a better thermal–hydraulic performance as well (PEC = 1.73). This work fills the gap of heat transfer and the geometrical optimization study of HFT based on the second law of thermodynamics and provides strong evidence that the exergy destruction minimization principle is still applicable in the case of the periodic model and fully developed turbulence. We hope that it will be contributed to the structural design of the HFT.

This study presents codes and detailed crop-specific descriptions for the growth stages of the lychee tree in southern China. Our codes are based on the extended Biologische Bundesantalt, Bundessortenamt, and Chemische Industrie (BBCH)-scale and describe the growth stages of the lychee plant using a three-digit numerical system. A total of 7 principal growth stages are described for bud, leaf, and shoot development, inflorescence emergence, flowering, fruit development, and fruit maturity. In addition, 41 secondary growth stages are described. The extended BBCH-scale for lychee presented in this study is broadly applicable because it describes all the phenophases pertaining to bud, shoot, leaf, panicle, and fruit development, as well as the growth pattern of the shoots and their seasonal variation. These data should facilitate more effective management of lychee orchards and contribute to the standardization of international testing systems for fruit growing.

A two-degree-of-freedom system with impact is considered. The symmetry of the system and its Poincare map is described. The symmetric period n−2 motion corresponding to the symmetric fixed point of the Poincare map is obtained. If the Jacobian matrix of the Poincare map at the fixed point has a real eigenvalue crossing the unit circle at +1, the symmetric fixed point will bifurcate into two antisymmetric fixed points, which have the same stability via pitchfork bifurcation. The numerical simulation shows that the symmetric fixed points may have pitchfork bifurcations and Hopf bifurcations. While the control parameter changes continuously, the two antisymmetric fixed points will give birth to two synchronous bifurcation sequences.

International audience; An inertial shaker as a vibratory system with impact is considered. By means of differential equations, periodicity and matching conditions, the theoretical solution of periodic n-1 impacting motion can be obtained and the Poincaré map is established. Dynamics of the system are studied with special attention to interaction of Hopf and period doubling bifurcations corresponding to a codimension-2 one when a pair of complex conjugate eigenvalues crosses the unit circle and the other eigenvalue crosses -1 simultaneously for the Jacobi matrix. The four-dimensional map can be reduced to a three-dimensional normal form by the center manifold theorem and the theory of normal forms. The two-parameter unfoldings of local dynamical behavior are put forward and the singularity is investigated. It is proved that there exist curve doubling bifurcation (a torus doubling bifurcation), Hopf bifurcation of 2–2 fixed points as well as period doubling bifurcation and Hopf bifurcation of 1–1 fixed points near the critical point. Numerical results indicate that the vibro-impact system presents complicated and interesting curve doubling bifurcation and Hopf bifurcation as the two controlling parameters vary.

A two-degree-of-freedom system having symmetrically placed rigid stops and subjected to periodic excitation is considered. Such models play an important role in the studies of mechanical systems with clearances or gaps. The period-one double-impact symmetrical motion and its Poincare map are derived analytically. Stability and local bifurcations of the period-one double-impact symmetrical motion are analyzed by the equation of Poincare map. The routes from period-one double-impact symmetrical motion to chaos, via pitchfork bifurcations and period-doubling bifurcation, are studied by numerical simulation. Some non-typical routes to chaos, caused by grazing the stops and Hopf bifurcation of period two four-impact motion, are analyzed. Hopf bifurcations of period-one double-impact symmetrical and antisymmetrical motions are shown to exist in the two-degree-of-freedom vibratory system with two-sided stops. Interesting feature like the period-one four-impact symmetrical motion is also found, and its route to chaos is analyzed. It is of special interest to acquire an overall picture of the system dynamics for some extreme values of parameters, especially those which relate to the degenerated case of a single-degree-of-freedom system, and these analyses are presented here.

A two-degree-of-freedom (d.o.f.) impact system with proportional damping is considered. The maximum displacement of one of the masses is limited to a threshold value by a rigid wall, which gives rise to a non-linearity in the system. A limiting case of a dynamical problem arising in the mechanical systems with amplitude constraints is investigated. For the perfectly plastic vibro-impact case, dynamics of a two-degree-of-freedom vibratory system contacting a single stop is represented by a three-dimensional map. Existence and stability of period n single-impact motions are analyzed by analytical and numerical methods. It is shown that the vibro-impact system may exhibit two different types of periodic motions due to the piecewise property of the map. Transitions of two types of period n single-impact motions are demonstrated. The singularities of the Poincare map, caused by grazing boundary motion of the impact oscillator, are considered. Due to the piecewise discontinuities and singularities of the map, the vibro-impact system is shown to undergo period-doubling bifurcations followed by complex sequence of transitions, in which the period-doubling cascades do not occur and extremely long-periodic and chaotic motions are generated directly with the motions with grazing boundary occurring. Finally, the influence of system parameters on periodic impacts and global bifurcations is discussed.

The group G = SU(2, 1) possesses nonempty holomorphic, antiholomorphic, and nonholomorphic discrete series. The restriction of these discrete series to the spherical subgroup G1 = S(U(1) × U(1, 1)) is studied in this paper. We prove that direct integral decomposition of any restricted discrete series of G is multiplicity free. In (J. Funct. Anal.103 (1992), 352-371), J. Vargas claimed that there was no discrete part in the direct integral of any restricted nonholomorphic discrete series. Unfortunately, his proof was wrong. Our argument in Section 5 shows that there are infinitely many discrete series of G1 occurring in the discrete part for any restricted nonholomorphic discrete series of G, and both the discrete and the continuous parts are not empty. The decomposition in Section 5 confirms a conjecture of B. Gross (B. H. Gross and D. Prasad, Canad. J. Math.44, No. 5 (1992), 974-1002) for these groups. Our main interest is of course in the restriction of nonholomorphic discrete series, but for completeness, we consider all discrete series of G.

International audience; The bifurcation problem of a two-degree-of-freedom system vibrating against a rigid surface is studied in this paper. It is shown that there exist Hopf bifurcations in the vibro-impact systems with two or more degrees of freedom under suitable system parameters. In the paper, a centre manifold theorem technique is applied to reduce the Poincaré map of the vibro-impact system to a two-dimensional one, and then the theory of Hopf bifurcation of maps inR2is applied to conclude the existence of Hopf bifurcation of the vibro-impact system. The theoretical solutions are verified by numerical computations. The quasi-periodic response of the system, represented by invariant circles in the projected Poincaré sections, is obtained by numerical simulations, and routes of quasi-periodic impacts to chaos are stated briefly.