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The phase space of a Hamiltonian system is symplectic. However, the post-Newtonian Hamiltonian formulation of spinning compact binaries in existing publications does not have this property, when position, momentum and spin variables [X, P , S1, S2] compose its phase space. This may give a convenient application of perturbation theory to the derivation of the post-Newtonian formulation, but also makes classic theories of a symplectic Hamiltonian system be a serious obstacle in application, especially in diagnosing integrability and nonintegrability from a dynamical system theory perspective. To completely understand the dynamical characteristic of the integrability or nonintegrability for the binary system, we construct a set of conjugate spin variables and reexpress the spin Hamiltonian part so as to make the complete Hamiltonian formulation symplectic. As a result, it is directly shown with the least number of independent isolating integrals that a conservative Hamiltonian compact binary system with both one spin and the pure orbital part to any post-Newtonian order is typically integrable and not chaotic. And a conservative binary system consisting of two spins restricted to the leading order spin-orbit interaction and the pure orbital part at all post-Newtonian orders is also integrable, independently on the mass ratio. For all other various spinning cases, the onset of chaos is possible. PACS numbers: 45.20.Jj, 05.45.-a, 04.25.Nx, 95.10.Ce

Within the framework of the scalar-tensor theory (STT), its second post-Newtonian (2PN) approximation is obtained with Chandrasekhar's approach. By focusing on an N -point-masses system as the first step, we reduce the metric to its 2PN form for light propagation. Unlike previous works, at 2PN order, we abandon the hierarchized hypothesis and do not assume two parametrized post-Newtonian (PPN) parameters γ and β to be unity. We find that although there exist γ and β in the 2PN metric, only γ appears in the 2PN equations of light. As a simple example for applications, a gauge-invariant angle between the directions of two incoming photons for a differential measurement is investigated after the light trajectory is solved in a static and spherically symmetric spacetime. It shows the deviation from the general relativity (GR) δθ STT does not depend on β even at 2PN level in this circumstance, which is consistent with previous results. A more complicated application is light deflection in a 2-point-masses system. We consider a case that the light propagation time is much less than the time scale of its orbital motion and thus treat it as a static system. The 2-body effect at 2PN level originating from relaxing the hierarchized hypothesis is calculated. Our analysis shows the 2PN 2-body effect in the Solar System is one order of magnitude less than future ∼ 1 nas experiments, while this effect could be comparable with 1PN component of δθ STT in a binary system with two Sun-like stars and separation by ∼ 0.1 AU if an experiment would be able to measure γ − 1 down to ∼ 10 −6 .

As an extension of a previous work in which perihelion advances are considered only and as an attempt to find more stringent constraints on its parameters, we investigate effects on astronomical observation and experiments conducted in the Solar System due to the f (T ) gravity which contains a quadratic correction of αT 2 (α is a model parameter) and the cosmological constant Λ. Using a spherical solution describing the Sun's gravitational field, the resulting secular evolution of planetary orbital motions, light deflection, gravitational time delay and frequency shift are calculated up to the leading contribution. Among them, we find qualitatively that the light deflection holds a unique bound on α, without dependence on Λ, and the time delay experiments during inferior conjunction impose a clean constraint on Λ, regardless of α. Based on observation and experiments, especially the supplementary advances in the perihelia provided by the INPOP10a ephemeris, we obtain the upper-bounds quantitatively: |α| 1.2 × 10 2 m 2 and |Λ| 1.8 × 10 −43 m −2 , at least 10 times tighter than the previous result.

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This paper is mainly devoted to applying the invariant, fast, Lyapunov indicator to clarify some doubt regarding the apparently conflicting results of chaos in spinning compact binaries at the second-order post-Newtonian approximation of general relativity from previous literatures. It is shown with a number of examples that no single physical parameter or initial condition can be described as responsible for causing chaos, but a complicated combination of all parameters and initial conditions is responsible. In other words, a universal rule for the dependence of chaos on each parameter or initial condition cannot be found in general. Chaos does not depend only on the mass ratio, and the maximal spins do not necessarily bring the strongest effect of chaos. Additionally, chaos does not always become drastic when the initial spin vectors are nearly perpendicular to the orbital plane, and the alignment of spins cannot trigger chaos by itself.Comment: 16 pages, 7 figure

Harvesting low-density ambient microwave power as an alternative power source for small ubiquitous wireless nodes has been proposed in recent papers discussing emerging technologies like the Internet of Things and Smart Cities. However, a literature review of the state-of-the-art Schottky diode based microwave rectifiers shows that a maximum efficiency has been reached for such devices operating in the low-power regime, as is the case for ambient microwave power-harvesters. This work examines the underlying physical mechanisms responsible for this RF-to-dc power conversion efficiency limitation, and explores a high I-V curvature backward tunnel diode to overcome this efficiency limitation. Measurements of the 2.4 GHz RF-to-dc power conversion efficiency at 40 dBm input power demonstrates that the backward tunnel diode outperforms the HSMS-285B Schottky diode by a factor of 10.5 and the Skyworks SMS7630 by a factor of 5.5 in a lossless matching network scenario. A prototype built using a new GSG probe embedded with a matching circuit showed a total power conversion efficiency of 3.8% for 40 dBm input power and 18.2% for 30 dBm input power at 2.35 GHz.Index Terms-Backward tunnel diode, microwave power harvesting, microwave power rectification, rectenna, Schottky diode. I. INTRODUCTIONT HE way the internet is perceived by its users is going through a significant transformation. Today, nearly two billion people have access to the internet [1], using it to browse websites, play games, work, send and receive e-mails and messages, among many other on-line applications. Most of these applications, however, share a common characteristic: an end-user terminal. Nonetheless an important revolution is in progress, in which ubiquitous objects will be more and more connected to the internet or other local networks, leading to the Internet of Things (IoT) [1], [2]. Some emerging applications of this new Manuscript

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